Democracy Defended (Contemporary Political Theory)

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Democracy Defended

Is there a public good? A prevalent view in political science is that democracy is unavoidably chaotic, arbitrary, meaningless, and impossible. Such skepticism began with Condorcet in the eighteenth century, and continued most notably with Arrow and Riker in the twentieth century. In this powerful book, Gerry Mackie confronts and subdues these long-standing doubts about democratic governance. Problems of cycling, agenda control, strategic voting, and dimensional manipulation are not sufﬁciently harmful, frequent, or irremediable, he argues, to be of normative concern. Mackie also examines every serious empirical illustration of cycling and instability, including Riker’s famous argument that the US Civil War was due to arbitrary dimensional manipulation. Almost every empirical claim is erroneous, and none is normatively troubling, Mackie says. This spirited defence of democratic institutions should prove both provocative and inﬂuential.   is Assistant Professor of Political Science at the University of Notre Dame. He has been Research Fellow, Social and Political Theory Program, Research School of Social Sciences, Australian National University; and Junior Research Fellow in Politics, St. John’s College, University of Oxford.

Contemporary Political Theory Series Editor Ian Shapiro Editorial Board Russell Hardin Stephen Holmes Jeffrey Isaac John Keane Elizabeth Kiss Susan Okin Phillipe Van Parijs Philip Pettit As the twenty-ﬁrst century begins, major new political challenges have arisen at the same time as some of the most enduring dilemmas of political association remain unresolved. The collapse of communism and the end of the Cold War reﬂect a victory for democratic and liberal values, yet in many of the Western countries that nurtured those values there are severe problems of urban decay, class and racial conﬂict, and failing political legitimacy. Enduring global injustice and inequality seem compounded by environmental problems, disease, the oppression of women, racial, ethnic and religious minorities, and the relentless growth of the world’s population. In such circumstances, the need for creative thinking about the fundamentals of human political association is manifest. This new series in contemporary political theory is needed to foster such systematic normative reﬂection. The series proceeds in the belief that the time is ripe for a reassertion of the importance of problem-driven political theory. It is concerned, that is, with works that are motivated by the impulse to understand, think critically about, and address the problems in the world, rather than issues that are thrown up primarily in academic debate. Books in the series may be interdisciplinary in character, ranging over issues conventionally dealt with in philosophy, law, history, and the human sciences. The range of materials and the methods of proceeding should be dictated by the problem at hand, not the conventional debates or disciplinary divisions of academia. Other books in the series Ian Shapiro and Casiano Hacker-Cordon ´ (eds.) Democracy’s Value Ian Shapiro and Casiano Hacker-Cordon ´ (eds.) Democracy’s Edges Brooke A. Ackerly Political Theory and Feminist Social Criticism Clarissa Rile Hayward De-Facing Power John Kane The Politics of Moral Capital Ayelet Shachar Multicultural Jurisdictions: Cultural Differences and Women’s Rights John Keane Global Civil Society? Rogers M. Smith Stories of Peoplehood: The Politics and Morals of Political Membership

Democracy Defended Gerry Mackie

   Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge  , United Kingdom Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521827089 © Gerry Mackie 2003 This book is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2003 - isbn-13 978-0-511-07110-2 eBook (EBL) - isbn-10 0-511-07110-8 eBook (EBL) - isbn-13 978-0-521-82708-9 hardback - isbn-10 0-521-82708-6 hardback - isbn-13 978-0-521-53431-4 paperback -  paperback isbn-10 0-521-53431-3 Cambridge University Press has no responsibility for the persistence or accuracy of s for external or third-party internet websites referred to in this book, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.

To Agnes and Ren´ee

—— What sphinx of cement and aluminum bashed open their skulls and ate up their brains and imagination? (Ginsberg 1956, 17)

Contents

List of ﬁgures List of tables Acknowledgments 1 A long, dark shadow over democratic politics

page xi xii xiv 1

2 The doctrine of democratic irrationalism

23

3 Is democratic voting inaccurate?

44

4 The Arrow general possibility theorem

72

5 Is democracy meaningless? Arrow’s condition of unrestricted domain

95

6 Is democracy meaningless? Arrow’s condition of the independence of irrelevant alternatives

123

7 Strategic voting and agenda control

158

8 Multidimensional chaos

173

9 Assuming irrational actors: the Powell amendment

197

10 Assuming irrational actors: the Depew amendment

217

11 Unmanipulating the manipulation: the Wilmot Proviso

241

12 Unmanipulating the manipulation: the election of Lincoln

258

13 Antebellum politics concluded

281

14 More of Riker’s cycles debunked

310

15 Other cycles debunked

335

16 New dimensions

378 ix

x

Contents

17 Plebiscitarianism against democracy

409

18 Democracy resplendent

432

Endnotes References Index

444 450 468

Figures

8.1 8.2 8.3 12.1 12.2

Single-peaked Non-single-peaked Win-sets of median point Single-peakedness, 1860 Riker’s cycle, 1860

page 174 174 177 271 272

xi

Tables

1.1 Preference proﬁle of three factions over three alternatives 1.2 Pairwise-comparison matrix for proﬁle in Table 1.1 1.3 Another voter proﬁle 1.4 Strong preference rankings over three alternatives 1.5 Condorcet paradox of voting 1.6 Summary of empirical ﬁndings 3.1 Five alternatives, ﬁve procedures, ﬁve winners 3.2 Five winners: pairwise comparison matrix and Borda count 3.3 Convergence of voting rules, Danish leaders 3.4 Some axiomatic properties of some voting rules 3.5 Pairwise comparison matrix to illustrate Young–Kemeny rule 3.6 Borda reversal 5.1 Probability of Condorcet winner, impartial culture, strong preference order 5.2 Probability of Condorcet winner, increasing homogeneity, three alternatives 5.3 Egomaniacal redistributional instability 5.4 Impartiality displaces partiality 5.5 An unbalanced cycle 5.6 An almost balanced cycle 5.7 Another unbalanced cycle 6.1 Violation of IIA(A) 6.2 Violation of IIA(RM) 6.3 Substantively rational to violate IIA(A) 6.4 The relevance of irrelevant alternatives 6.5 Borda manipulation, initial situation 6.6 Borda manipulation, ﬁrst step 6.7 Borda manipulation, second step 7.1 Contrived outcomes xii

page 6 7 7 8 8 18 45 45 53 57 58 62 96 98 99 101 118 120 121 128 129 134 139 151 152 152 159

List of tables

7.2 9.1 9.2 9.3 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 11.1 12.1 12.2 12.3 12.4 14.1 14.2 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 15.10 15.11 15.12 15.13

Unfair agenda setter Distribution of votes, 1956 Riker’s estimates of factions and preference rankings, 1956 Pairwise comparison matrix: Riker (1982), Riker (1986) Bristow and Rayner amendments compared Votes on 17th Amendment compared Replacement senators, from 61st to 62nd Senate Riker’s inference of 61st Senate vote on 17th Amendment Mackie’s estimates of distribution of preferences in 61st Congress Mackie’s inference of 61st Senate vote on 17th Amendment Mackie’s estimates of distribution of preferences in 62nd Congress Mackie’s inference of 62nd Senate vote on 17th Amendment Datum and warrant, Wilmot proviso State-level aggregation of ﬁrst-place winners, Upper North State-level aggregation of ﬁrst-place winners, Middle America State-level aggregation of ﬁrst-place winners, Lower South Pairwise comparison matrix, 1860 election Riker’s estimates, Agricultural Appropriations, 1958 Pairwise comparison matrix, Agricultural Appropriations, 1958 Blydenburgh’s analysis, Revenue Act, 1932 Pairwise comparison matrix, Revenue Act, 1932 Neufeld et al.’s account of Muscle Shoals preferences Pairwise comparison matrix, Neufeld et al.’s count Mackie’s inferred rankings, Muscle Shoals Summary of Mackie’s rankings, Muscle Shoals Pairwise comparison matrix, before vote switch Pairwise comparison matrix, after vote switch Distribution of hypothetical PR voters Aggregation of preferences by individual not cyclical Aggregation of preferences by parties cyclical Iowa Senate preferences, anticorporate farming Cycle, Danish prime minister

xiii

168 199 203 203 227 232 234 235 235 236 237 237 244 273 274 275 278 331 332 338 342 355 356 358 360 360 361 364 364 364 369 371

Acknowledgments

Thanks for help and encouragement, direct or indirect, to: Tjitske Akkerman, the late Michael Bacharach, Samuel Bowles, Geoffrey Brennan, Alaine Chanter, Thomas Christiano, the late James Coleman, Gary Cox, Dhammika Dharmapala, Keith Dowding, John Dryzek, David Estlund, James Fearon, Nancy Folbre, Diego Gambetta, Elise Giuliano, Robert Goodin, Wendy Gordon, Donald Green, Mark Hansen, Russell Hardin, Gretchen Helmke, Roberta Hoelzle, Stephen Holmes, Ken Hoover, Eric Humphreys, Jeffery Jenkins, James Johnson, Desmond King, Peter Kuurild-Klitgaard, Jack Knight, Michael Kochin, David Laitin, Eerik Lagerspetz, Christian List, Leonard McEwen, Iain McLean, Janet McLean, David Marsh, Ian Marsh, David Mayhew, Molly Melching, Brad Moody, Peter Morriss, Tim Mulgan, Michael Munger, Jack Nagel, Michael Neblo, Avner Offer, Damian O’Leary, John Orbell, Shepley Orr, John Padgett, Philip Pettit, Samuel Popkin, Michel Regenwetter, Benjamin Reilly, Stuart Romm, Susan Rose-Ackerman, Donald Saari, Ian Shapiro, Cindy Skach, Priscilla Southwell, Alfred Stepan, Alex Tabarrok, John Uhr, Robert van der Veen, Federico Varese, Bruno Verbeek, Stewart Wood, Peyton Young, and Jakub Zielinski. Special thanks to my dissertation committee, Jon Elster, chair, Bernard Manin, and Adam Przeworski, for their inspiration, and especially for their patience, and to my several ﬁne teachers at the University of Chicago. None of them is to blame for what I say. The list should be longer, and I apologize for omissions, which are inadvertent. I learned more about democracy from my fellow forestry workers in the Hoedads cooperative than from anybody in academia, and I thank every person who made that happen. I also thank various colloquia where some of this material was presented: American Political Science Association in convention; Social and Political Theory Program, Brown Bag Seminar, RSSS, Australian National University; American Politics Workshop, University of Chicago; Workshop on Deliberative Democracy, University of Chicago; xiv

Acknowledgments

xv

Department of Political Science, Duke University; Department of Political Science, University of Oregon; Political Economy Seminar, Nufﬁeld College, University of Oxford (twice); Political Theory Workshop, Nufﬁeld College, University of Oxford; Philosophy, Politics, and Economics Society, St John’s College, University of Oxford; Public Choice Society in convention; Department of Political Science, Stanford University; and Department of Political Science, Yale University. Warm appreciation to these institutions for material and intellectual support: University Fellowship, Searle Fellowship, and Mellon Fellowship at the University of Chicago; the University of Chicago; the Junior Research Fellowship in Politics, provided by the Fellows of St. John’s College, University of Oxford; the people of Australia, whose taxes paid for my Research Fellowship in the Social and Political Theory Program, Research School of Social Sciences, Institute for Advanced Studies, Australian National University. Of the many sources for this book, I have made particular use of the work of William H. Riker and Kenneth J. Arrow, and also: Bo Bjurulf and Richard G. Niemi; John C. Blydenburgh; James Burnham; Melissa P. Collie; Robert Cooter and Peter Rappoport; Robert Dahl; Bernard DeVoto; Dwight L. Dumond; Robin Farquharson; David M. Farrell; Dan S. Felsenthal and coauthors, Kurt Taylor Gaubatz, William V. Gehrlein, Leo Goodman and Harry Markowitz; Donald Green and Ian Shapiro; Bernard Grofman and coauthors, Donald Gross, Melvin J. Hinich and Michael T. Munger; Herbert Hovenkamp; Keith Krehbiel and Douglas Rivers; Peter Kurrild-Klitgaard; Eerik Lagerspetz; Samuel Merrill III; Chaplain W. Morrison; John L. Neufeld and coauthors, Hannu Nurmi, Keith T. Poole and Howard Rosenthal; Eric Redman; Donald Saari; Charles Sellers; Amartya Sen; Kenneth Shepsle and Mark S. Bonchek; Gerald S. Strom; Barry Weingast, and others (omissions are inadvertent), adapting data presented in their contributions and working with their ideas. Where my engagement is critical, I hope it is also constructive. I am indebted to the foundation they have provided. Precise sources are referenced in notes where these debts occur, and in the book’s bibliography. Before graduate school I operated in a competitive political environment where argument was harsh but friendly. As a result, earlier drafts of this material were in part too polemical for the academic setting, and I regret that. My thanks to several people, and especially to one eloquent reviewer, who convinced me to reform permanently my rhetorical habits. Further, I want it understood that my criticisms of arguments imply no personal disrespect for the thinkers who authored them. I agree with

xvi

Acknowledgments

Jevons (1871, 275–276), that: If, instead of welcoming inquiry and criticism, the admirers of a great author accept his writings as authoritative, both in their excellences and in their defects, the most serious injury is done to truth. In matters of philosophy and science, authority has ever been the great opponent of truth. A despotic calm is usually the triumph of error. In the republic of the sciences, sedition and even anarchy are beneﬁcial in the long run to the greatest happiness of the greatest number.

I have tried to avoid errors, but I discover more of my own every time I revise the manuscript. All scholars err, despite their best efforts. My purpose in this volume is not the allegation of error for its own sake, but rather to show that a pattern of errors lies behind the irrationalist view of democracy. Portions of Chapter 2 appeared in abbreviated form in Gerry Mackie, “All Men are Liars,” in Jon Elster, ed., Deliberative Democracy, Cambridge: Cambridge University Press. Bits and pieces of this material are included in a brief essay, “Saving Democracy from Political Science,” in Robert Dahl, Ian Shapiro, and Jose Cheibub, eds., The Democracy Sourcebook, Cambridge, MA: MIT Press, 2003. This volume is a revision and expansion of my Ph.D thesis, “Is Democracy Impossible? A Preface to Deliberative Democracy,” University of Chicago, 2000. Otherwise the material is unpublished elsewhere. When I was a small child living in the country outside the small lumber town of Coquille, Oregon, USA, my mother, Agnes I.H. Mackie, drove me to the library every week, and otherwise always encouraged my aberrant intellectual inclinations. I remember exactly and vividly how delighted she was when I read out my ﬁrst words. I dedicate the volume to her memory, and to my mother-in-law, Ren´ee Heiman, who has consistently supported my son Brendan and I through life’s difﬁculties.

The publisher has used its best endeavours to ensure that the URLs for external websites referred to in this book are correct and active at the time of going to press. However, the publisher has no responsibility for the websites and can make no guarantee that a site will remain live or that the content is or will remain appropriate.

1

A long, dark shadow over democratic politics

Democracy and the intellectuals Democracy is on the march in the world today. By democracy I mean something like free and equal people associating and communicating in public spheres, informed by liberal presuppositions, and governed politically by representative institutions based on wide suffrage and contested elections. I do not say that democracy is victorious in the world today, because its reign is fragile in the developing world, is ﬂawed in the developed world (especially in the United States), and is barely emergent on the international scene. Evaluation should be a comparative enterprise, however, and most people aware of the alternatives believe that they are better off under democracy, and democracy is more widely spread now than it has ever been before. There were a handful of developing democracies a hundred years ago (Dahl 1989, 240). Democratic aspirations ﬂared in continental Europe and areas under its inﬂuence as World War I came to an end, but Communism and then Fascism smothered the democratic ﬂame. Fascism was discredited as World War II came to an end, and also political imperialism went into decline, only to be replaced by the realpolitik of the Cold War. The Communists were glad to extend their tyranny to broad new territories, and the democracies found it expedient to justify tyrannies among their subordinate allies. Meanwhile, Fascism was dismantled in Mediterranean Europe in the late 1970s, and the democratization of Spain and Portugal strengthened democratic forces in Latin America in the 1980s. The fall of the Communist regimes in Eastern Europe in 1989, and then in the Soviet Union, conﬁrmed a trend to democratization on a global scale. Most civil wars in Latin America came to an end. Apartheid was dismantled in South Africa. Authoritarian Marcos fell in the Philippines, Suharto in Indonesia. The theocracy in Iran came under democratic pressure. There are no dramatic democratic breakthroughs in the Arab world, however, or with respect to the Israeli–Palestinian conﬂict. In middle Africa one-party and military regimes are less common, 1

2

Democracy Defended

but corruption, poverty, massacre, and war are as grievous as ever. The democratic student movement in China was crushed by the Tiananmen Square massacre in 1989. I do not know why, but from the beginning academics have tended to be more disdainful of democracy than are, say, the demos (the people). Plato’s hatred for democracy is no secret. In our times, “Almost as soon as representative democracy on a large scale appeared in Europe . . . there were misgivings about it, especially among intellectuals on both the Left and the Right” (Plamenatz 1973, ix). Victorian England pioneered mass democracy in Europe, and pioneered in its denunciation: where Plato opposed democracy on the ground that it produced spiritual anarchy in individuals, Carlyle, Ruskin, Arnold, Stephen, Maine, and Lecky opposed democracy on the ground that it led to social anarchy, according to Lippincott (1938, 5). The followers of Marx and Lenin damned democracy as a bourgeois sham, and predicted scientiﬁc administration and the withering away of politics in the communist future (see Schwartz 1995). Plamenatz refers to the “academic attack on democracy” by liberals Mosca, Michels, and Pareto, whose debunking of democracy provided intellectual suckling to fascism. The US had more of a democratic tradition, personiﬁed by Dewey. Dewey’s most inﬂuential rival was Lippmann, who argued that the citizenry is ignorant and that experts must rule in spite of the “democratic fallacy” (Wiebe 1995). In Europe during the interwar period Lindsay (1935) and Barker (1951) were virtually alone as academic defenders of democracy. In the period after World War II, an exhausted conformism in American culture was accompanied by an empirical democratic theory that apotheosized the “beneﬁcial apathy” of the citizenry, and by positivistic animosity to normative theory; Dahl (e.g., 1956) was nevertheless a milestone in democratic theory. In this period, although little good was said about democracy, not much bad was said about it either. The revival of liberal political theory following Rawls (1971) was kinder to democracy, but was much more liberal than democratic: for Rawls (1993, 231–240), the Supreme Court is the exemplar of public reason, not the parliament, not the people. After Habermas (1984; 1987), an emphasis on the transformation rather than the mere aggregation of preferences stimulated wider academic interest in democracy (Elster 1986b; 1998). A robust normative democratic theory, primarily but not exclusively on the theme of deliberation, is beginning to appear. Although democratization is the main trend in the world today, the main intellectual trend in American political science is the view that democracy is chaotic, arbitrary, meaningless, and impossible. This trend

A long, dark shadow over democratic politics

3

originated with economist Kenneth Arrow’s impossibility theorem, which was applied to politics by the late William Riker, political scientist at the University of Rochester. The earlier academic attack on democracy by Mosca, Michels, and Pareto was revived with fashionable new methods. Riker had great organizational resources, and used them to promulgate a particular interpretation of Arrow’s theorem, to further elaborate a doctrine he called “positive political theory” (“scientiﬁc,” rather than “ethical”), and to recruit and place his students far and wide. Riker calls populist any democratic theory which depends on a systematic connection between the opinion or will of the citizens and public policy, and liberalist any democratic theory which requires only that voting result in the random removal of elected ofﬁcials. Riker rejects populist democracy as infeasible, and offers his liberalist democracy in its place. What almost everyone means by democracy is what Riker calls populist democracy; and, I shall argue, Riker’s liberalist alternative fails, descriptively and normatively. Thus, I am tempted to label his doctrine antidemocratic. I believe that it is antidemocratic in consequence, whether or not it is antidemocratic in spirit. But to use such a label throughout this volume would be tendentious. To call his doctrine antipopulist, though, is to beg the question in his favor: the word populism has many negative connotations, and I do not mean to defend such things as Peronism, short-sighted policy, or mob rule. Since Riker’s claim is that in the political sphere the rational individual opinions or desires of citizens cannot be amalgamated accurately and fairly, it is apt to describe his doctrine as one of democratic irrationalism. Riker’s irrationalist doctrine emphasizes principled failings of democracy and recommends a constitutionalist libertarianism and the substitution of economic markets for much of political democracy (Riker and Weingast 1988). Displaced by the forces of economic globalization, I came to graduate school in midlife from a background as a founder and an elected leader of a large forestry workers’ cooperative movement, as a lobbyist for forestry workers with state and federal administrative and legislative agencies, as a litigant for forestry workers, as an organizer of issue and candidate electoral campaigns, as policy aide to an elected ofﬁcial at the apex of a large county government, and as a political journalist. I was quite ﬂabbergasted by the irrationalist dogma I encountered in the political science literature. The elegant models of impossibility and disequilibrium I was taught bore no relation to my democratic experiences. I am not one of those who holds that every human life is best fulﬁlled in politics, but I know that my life was best fulﬁlled in that activity. Although in democratic politics I had seen plenty of crazy things, some inexplicable, and had been

4

Democracy Defended

a hard operator, I had seen nothing that supported the irrationalist models and interpretations of Riker and his followers; and I had seen more crazy things happen in the economy than in politics. At that point I did not know why the models were mistaken, but I did know that if the models do not ﬁt the facts, then it is the models that must go; my political experiences had made me suspicious of those who belittle empiricism. I had already struggled against antidemocratic leftist doctrines in my own mind and in my political environment, and rightist doctrines of the same consequence aroused my suspicions. I am afraid that younger students, without the experience and conﬁdence that I had, tend to accept the irrationalist models, which are transmitted with professorial authority and sometimes by means of hasty and mystifying formalisms. One day in graduate school I was talking with someone who knew a great deal about China. I asked him what he thought about the student movement for democracy there. He replied that Arrow and Riker had shown that democracy is arbitrary and meaningless, and that what China needed was paternalistic dictatorship by the Communist Party. I was dumbfounded. “The models are wrong!” I said. “How are they wrong?” he asked. I could not answer him then, but I had learned something important: not only is positive political theory empirically erroneous, it can have dangerous consequences. The proposition that democratic voting is arbitrary and meaningless can be used not only to justify a constitutional libertarianism such as Riker’s, it can also be used to justify a dictatorship that appeals to the values of stability and order. The irrationalist doctrine is taught in America’s leading political science departments, law schools, and economics departments. Students absorb these teachings, and then move on to join the political and economic elites of the world. I shudder to think of the policies demanded in the international consultancies and ﬁnancial agencies and the national treasury departments of the world by people who were taught the ﬁndings of Arrow as interpreted and expanded by Riker’s school of thought. I worry that authoritarian movements might ﬁnd comfort in Riker’s (1982) irrationalist credo, Liberalism against Populism. One purpose of my work here is to show that Riker’s irrationalist doctrine is mistaken, and thereby to restore democracy as an intellectually respectable method of human organization. I have sketched the progress of democracy in the world, an ongoing academic disdain for democracy, and my motivations for countering the current version of the academic attack on democracy. Next, I introduce the problems of voting that inform the irrationalist view. After that, I provide a sample of quotations from the literature in order to establish that there is a trend to democratic irrationalism in academic opinion.

A long, dark shadow over democratic politics

5

Problems of voting: the basics This section is an introduction to the problems of voting. We start with majority rule. Majority rule doesn’t always report a winner with more than two alternatives, so we might turn to plurality rule. Plurality rule might pick a winner that a majority of the voters is against, so we look for other methods. The Borda method counts the number of times an alternative beats all other alternatives, but it violates a condition called the independence of irrelevant alternatives. The Condorcet method says to pick the alternative that beats all others in pairwise comparison. The Condorcet method might lead to the paradox of voting, however: no alternative wins, called cycling. The Arrow theorem is a generalization of the paradox of voting. If there is cycling, unfair manipulation of the outcome by agenda control and by strategic voting is also possible. Different methods of voting can yield different social outcomes from the same individual preferences. Ordinary majority rule seems to be the most natural, or commonsensical, way of voting. A majority is made up of more than half the voters. Often a majority-rule vote is taken over two alternatives; for example, in a committee a proposal is made to alter the status quo, or often there are only two candidates in an election. When there are two alternatives, majority rule will deliver a winner, except when there is a tie. A tie can be decided by some convention, such as a bias to the status quo, recounting of the votes, or ﬂipping a coin. Everyone is familiar with ordinary majority rule. When there are three or more alternatives there can be problems with majority rule. If there are three candidates, and none receives a majority, then there is no winner, and the method is incomplete. Perhaps without too much thought we might turn to plurality rule as a simple extension of majority rule: whoever gets the most votes, even if short of a majority, is the winner. We might not notice the defects of plurality rule because, as it happens, plurality rule tends to strategically deter more than two serious candidates from the ﬁeld. If there are ﬁve candidates, two of those will be seen as most likely to win the election, and many voters will cast their votes so as to decide between the top two rather than waste their vote on expressing a preference for one of the likely losers. Candidates interested in winning the election, knowing this tendency among voters, tend not to enter the race unless they are likely to be contenders. These are tendencies, not certainties, and I only mention them to explain why we don’t see too many plurality elections with more than a few serious candidates, and that this may blur the distinction between majority rule and plurality rule in our minds.

6

Democracy Defended

Table 1.1. Preference proﬁle of three factions over three alternatives

1st 2nd 3rd

1–40

2–35

3–25

A B C

C B A

B C A

There can be a problem with simple plurality rule, however. Suppose that there are three candidates A, B, and C in an election, and 100 voters. For simplicity, everyone has strong preferences (denoted by >, meaning that voters are not indifferent over any alternatives). Faction 1 is made up of 40 people, and ranks the candidates A > B > C. Faction 2 is made up of 35 people and ranks the candidates C > B > A. Faction 3 makes up 25 people and ranks the candidates B > C > A. It will help to display the preference rankings. With plurality rule, everyone casts a vote for their ﬁrst-ranked alternative. With the proﬁle of voters’ preferences in Table 1.1, A would win by plurality rule, even though 60 percent of the voters are against A. If election were by plurality rule, Factions 2 and 3 might anticipate this outcome and unite their forces on candidate C, who then would win, showing again the tendency to two candidates under plurality rule. The tendency is imperfect, or the election might be among alternatives that don’t respond strategically, and in such circumstances it seems undesirable that A would win the election, as Margaret Thatcher did in these circumstances. Borda wrote on the theory of elections in 1784 (see Black 1958; McLean and Urken 1995). Borda noticed this defect with plurality rule, and proposed his method of marks, which we shall call the Borda count, to remedy the defect. Borda thought we should count whether alternatives are ranked ﬁrst, second, third, and so forth. He proposed that if there were, say, three alternatives, then we would assign two points to each voter’s ﬁrst-ranked preference, one point to her second-ranked preference, and zero points to her third-ranked preference. For the proﬁle in Table 1.1, Alternative A gets 2 × 40 + 0 × 35 + 0 × 25 = 80 points. Alternative B gets 1 × 40 + 1 × 35 + 2 × 25 = 125 points, and is the Borda winner. Alternative C gets 0 × 40 + 2 × 35 + 1 × 25 = 95 points. The full Borda ranking is B > C > A (125 for B > 95 for C > 80 for A). In a pairwise-comparison matrix, as in Table 1.2, we display the alternatives by row and by column, and the cell entry is the number of votes the row entry gets against the column entry. Alternatives don’t get votes against themselves, so those cells are empty. Borda’s method counts the number

A long, dark shadow over democratic politics

7

Table 1.2. Pairwise-comparison matrix for proﬁle in Table 1.1 A A B C

60 60

B

C

40

40 65

Borda = = =

35

80 125 95

Table 1.3. Another voter proﬁle

1st 2nd 3rd

1–51

2–35

3–14

A B C

C B A

B C A

of times that an alternative beats all other alternatives, and the Borda score is also the row sum of the entries in the matrix. Condorcet, another French thinker, wrote on the theory of elections in 1785 (see also McLean and Hewitt 1994; McLean 1995). Condorcet proposed as a criterion that the alternative that beats all other alternatives in pairwise comparison should be the winner. In our example, examining the italicized cells in the matrix, B > A, B > C, and C > A, or B > C > A. In this example (and in most practical circumstances) the Condorcet winner and the Borda winner coincide. They need not, however. Condorcet objected to the Borda method on the ground that it is possible for it to violate a condition that later came to be called the independence of irrelevant alternatives. Assume the proﬁle in Table 1.3. By the Condorcet method, the social ranking is A > B > C, the same as the ranking of the faction with the slender majority of 51. Observe, however, that A is the last choice of 49 voters. The Borda method takes that into account and reports a social ranking of B > A > C. The dispute is this: Condorcet insists that in pairwise comparison A beats every other alternative, Borda insists that B gets more votes over every other alternative than does any other alternative. The Borda method violates the independence condition because in deciding the social ranking between two alternatives X and Y it takes into account individual rankings of alternatives other than X and Y, such as between X and Z and between Y and Z. To comply with the independence condition, for example for faction 2, we can count that an individual ranks C > B, that she ranks B > A, that she ranks C > A, but not that she ranks C > B > A.

8

Democracy Defended

Table 1.4. Strong preference rankings over three alternatives 1. A > B > C 2. A > C > B 3. C > A > B

4. C > B > A 5. B > C > A 6. B > A > C

Table 1.5. Condorcet paradox of voting

1st 2nd 3rd

Huebert

Deuteronomy

Louis

A B C

B C A

C A B

There is also a problem with the Condorcet method, however, known as Condorcet’s paradox of voting. Suppose there are three (or more) alternatives and two (or more) voters. Given three alternatives, there are six possible strong preference rankings, shown in Table 1.4. Given three voters, one each with cyclical rankings 1, 3, and 5 (or with 2, 4, and 6), the result of voting by the Condorcet method over three alternatives is inconsistent, that is, A beats B, B beats C, and C beats A. Suppose that the Duckburg Troop of the Junior Woodchucks have misplaced their Guidebook (which has a section on democratic decision making), and are deciding on how to spend their treasury over three alternatives, as in Table 1.5. Huebert and Louis favor A over B, Huebert and Deuteronomy favor B over C, and Deuteronomy and Louis favor C over A. The collective choice cycles over A > B > C > A. Arrow’s possibility theorem can be understood as a generalization of Condorcet’s paradox, applying not just to simple voting but to any social welfare function that aggregates individual orderings over alternative social states. The Arrow theorem requires that the social ranking be transitive, not intransitive as is the cycle. The Borda method would count the cyclical proﬁle in this paradox example as a tie, A ∼ B ∼ C (∼ denotes indifference), and thus would not report an intransitive social ranking, but the Arrow theorem also requires that a voting rule not violate the independence of irrelevant alternatives condition, thus disqualifying rules such as the Borda count. Historically, Arrow’s theorem is the consequence of noncomparabilist dogma in the discipline of economics, that it is meaningless to compare one person’s welfare to another’s, that interpersonal utility comparisons are impossible.

A long, dark shadow over democratic politics

9

Cycling is one problem with Condorcet voting. A second, and related problem, could be labeled path dependence. What if there were ﬁrst a vote between A and B, which A wins, and second a vote between A and C, which C wins? It seems that we have voted over all three alternatives and that we have a winner, C. We neglected, however, to vote between C and B, which B would win, and which would have disclosed the cycle to us. Unless we take pairwise votes over all alternatives we might not notice the cycle, and normally we don’t take all pairwise votes. To make things worse, what if Louis controlled the agenda, and arranged for that order of voting, A against B, and then the winner against C? Then Louis would have manipulatively brought it about that his ﬁrst-ranked alternative, C, won, arbitrarily, and voters Huebert and Deuteronomy might even not have noticed. A third problem is strategic voting. Suppose again that we have a cycle as above, and an agenda as above, A against B and then the winner against C. Then Huebert would have an incentive to vote strategically in the ﬁrst round: rather than sincerely voting for A over B, Huebert strategically votes for B over A. B wins the contest in the ﬁrst round, and beats C in the second round. By voting strategically, Huebert has avoided the victory of his third-ranked alternative C and brought about the victory of his second-ranked alternative B. Inaccuracy is a fourth problem. I showed already that the Borda and Condorcet procedures can select different social outcomes from the same proﬁle of individuals’ preferences. If apparently fair voting rules each select a different public good from the same voter proﬁle, then arguably the public good is arbitrary. Inaccuracy, agenda control, and strategic voting also raise the possibility that a social outcome might tell us nothing about the sincere individual preferences underlying the outcome. Based on these and further considerations, Riker’s hypothesis is that democratic politics is in pervasive political disequilibrium. These are the basics. For those new to these topics, be assured that they will be presented more slowly and in greater detail as we proceed. A sampling of the literature Those unfamiliar with the particular intellectual subcultures may doubt my claim that there is a trend to democratic irrationalism in academic opinion. To establish my claim, I offer what I shall refer to in the remainder of the volume as a hall of quotations, an unconventional but I hope useful method of exposition. The people we shall hear from are in economics, sociology, history, legal theory, political science, and philosophy; they are anarchists, socialists, liberals, or libertarians; some are my teachers,

10

Democracy Defended

colleagues, or friends. We begin with an essay introducing a recent survey of the state of the political science discipline: r The fall of the Weimar Republic and, more broadly, the collapse of many other constitutional democracies with the rise of fascism and bolshevism in the interwar period alerted the [political science] discipline to the terrible consequences of unstable democracies. Later, Arrow’s impossibility theorem, a key instance of incisive analytical work on the core problems of liberal regimes, set forth the theoretical challenge in stark terms. Instability is an immanent feature of liberal democracy. Under broad conditions, majority rule leads to the cycling of coalitions and policy; only nondemocratic practices can alleviate this deep tendency, convoking a tradeoff between stability and democracy. (Katznelson and Milner 2002, 17–18) r At its most extreme, Arrovian public choice predicts that literally anything can happen when votes are taken. At its most cynical, it reveals that, through agenda manipulation and strategic voting, majoritarian processes can be transformed into the equivalent of a dictatorship. In a more agnostic mode, it merely suggests that the outcomes of collective decisions are probably meaningless because it is impossible to be certain that they are not simply an artifact of the decision process that has been used. (Mashaw 1989, 126–127) r interpersonal comparison of utility has no meaning . . . If we exclude the possibility of interpersonal comparisons of utility, then the only methods of passing from individual tastes to social preferences which will be satisfactory and which will be deﬁned for a wide range of sets of individual orderings are either imposed or dictatorial. (Arrow 1963/1951, 8, 59) r This clearly negative result casts doubt on all assertions that there is a “general will,” a “social contract,” a “social good,” a “will of the people,” a “people’s government,” a “people’s voice,” a “social beneﬁt,” and so on and so forth. (Feldman 1980, 191) r Aristotle must be turning over in his grave. The theory of democracy can never be the same . . . what Kenneth Arrow proved once and for all is that there cannot possibly be found . . . an ideal voting scheme. The search of the great minds of recorded history for the perfect democracy, it turns out, is the search for a chimera, for a logical self-contradiction. (Samuelson 1977, 935, 938)

A long, dark shadow over democratic politics

11

r How can we deﬁne and give expression to the collective wishes of a community? Arrow’s argument shows that our intuitive criteria for democratic decision cannot in fact be satisﬁed . . . Put crudely, what Arrow has done is to show that strict democracy is impossible. (Runciman 1963, 133.) r Almost anything we say and/or anyone has ever said about what society wants or should get is threatened with internal inconsistency. It is as though people have been talking for years about a thing that cannot, in principle, exist . . . The central result is broad, sweeping, and negative. Paul Samuelson rates it as one of the signiﬁcant intellectual achievements of this century . . . It certainly weighed heavily in the decision to award K.J. Arrow the Nobel prize in economics . . . the cycle is the case and not the exception . . . the phenomenon is pervasive . . . If the concepts, which help us speak about how we feel whole societies, polities, and even worlds should behave, do not work at all for the simple case of a society with a handful of people with just a few alternatives, then perhaps we apply them at the global level only because we really do not understand them . . . the concept of social preference itself must go. (Plott 1976, 512, 514, 517, 525) r It is not stating the case too strongly to say that Arrow’s theorem and the research that it inspired wholly undermine the general applicability or meaning of concepts such as the “public interest” and “community goals.” (Ordeshook 1986, 65) r what Arrow showed, with as much rigour as any human scientist could conceivably demand, was that the programme of an educated citizenry deciding social values . . . did not make sense. (Tuck 1993, 79) r there is no universally workable way for aggregating individual interests, preferences, or values into collective decisions. A positive implication of this ﬁnding is that no government of a complex society is likely to be coherently democratic . . . A normative implication of this lesson is that political theory cannot be grounded exclusively in democratic procedural values . . . This is not to say that the democratic, majoritarian urge is wrong . . . But it is nevertheless conceptually incoherent. (Hardin 1993, 169–170) r In fact it turns out that majority rule is fatally ﬂawed by an internal inconsistency which ought to disqualify it from consideration in any political community whatsoever . . . the inconsistency of the voter’s paradox infects virtually every method of

12

Democracy Defended

r

r

r

r

r r

social choice which can lay a reasonable claim to being “democratic.” . . . There would appear to be no alternative but to embrace the doctrine of anarchism and categorically deny any claim to legitimate authority by one man over another. (Wolff 1970, 59, 63, 72) Arrow’s contribution provides incontrovertible support for market process and encouragement for those who seek to constrain the range of collective choice to the limited functions of the minimal state. (Rowley 1993, xiii) One general approach to [the puzzle of why the majority will should be constitutionally constrained] is to deny that it is at all puzzling . . . by denying that there exists any meaningful sense in which any process could even hope to “reﬂect” any such thing as the will of the majority, given the well-known theorem for which Kenneth Arrow received his Nobel Prize in Economics . . . At the least . . . the analysis puts the burden of persuasion on those who assert that legislatures (or executives) deserve judicial deference as good aggregators of individual preference. (Tribe 1988, 12) Judicial review is often defended as the only way to escape the potential tyranny of the majority, but it simultaneously creates the potential for the tyranny of the judges. The general function of constitutional theory has been to specify how judicial review can exist without becoming judicial tyranny. The Arrow theorem metaphor suggests that constitutional theory must fail in that task. (Tushnet 1988, 16–17) The idea that there is a “social decision” that can satisfy everyone has been annihilated by Kenneth Arrow, who in his “impossibility theorem” has demonstrated that no social decision can amalgamate the diverse preferences of a group in the way a single individual can amalgamate his own. Thus, theoretical economics, in its denial of a communal welfare function . . . undermines the application of rationality to public decisions . . . William H. Riker has . . . shown that . . . amendments might be adopted which are not favored by a majority – without this fact ever being known! (Bell 1974, 365, 307–308) William Riker is one of the most inﬂuential political scientists at present writing on the theory and practice of democracy. (Weale 1984, 369) Riker’s later theory of democracy can be viewed as a systematic attempt to work out the implications for the theory of

A long, dark shadow over democratic politics

r

r

r

r

13

democracy of Arrow’s general impossibility theorem within the theory of social choice. (Weale 1995, 377) accurate preference aggregation through politics is unlikely to be accomplished in the light of the conundrums in developing a social welfare function (Riker 1982; Arrow 1963/1951). Public choice theory has shown that cycling problems, strategic and manipulative behavior, sheer chance and other factors make majoritarianism highly unlikely to provide an accurate aggregation of preferences. (Sunstein 1988, 335) In the light of social choice theory, as argued particularly by Riker (1982), the democratic process would not converge to a unique welfare maximum even if one existed. The reasons are those offered by Arrow (1993/1951): There is no procedure for aggregating preferences that would guarantee a unique outcome. Hence, one cannot read voting results as identifying any unique social preference. (Przeworski 1991, 17) Particularly great attention has been paid to equilibria in the subﬁeld of rational or public choice. One depressing conclusion has arisen from this work: In politics, unlike in economics or the natural sciences, virtually no naturally occurring equilibria exist. This has distressed a number of workers in the ﬁeld, including its great guru, the late William Riker. For this ﬁnding means by implication that, in politics, almost anything (theoretically) can happen at almost any time, as equilibria are disrupted with virtually no advance warning. Two examples of this process, of fundamental importance to the course of world history in the twentieth century, can be cited here: the post1928 Nazi surge among major parts of the German electorate – an essential condition for the elite decisions that brought Hitler to power in 1933 – and the abrupt and wholly unpredicted collapse of the Soviet Union in 1991 and 1992. (Burnham 1999, 2250) The most inﬂuential social choice theorist after Arrow is William Riker, who is also founder of the Rochester School of rational choice theory, which now dominates the pages of the American political science discipline’s leading journals. Riker radicalized social choice theory to attack any notion of authentic democracy, particularly what he called “populism.” . . . Not all social choice theory has this radically anti-democratic political cast, but within the discipline of political science the most inﬂuential strand is indeed that associated with Riker and his followers. (Dryzek 2000, 35–36)

14

Democracy Defended

r the rhetorical convention of discussing “the majority” makes no sense. When there exists a modest diversity of preference, which is, after all, the bare necessity for political controversy, then cycles are ubiquitous – there are “too many majorities.” The actual social state chosen by the legislature is determined, not by some process that yields an alternative presumably better than all the rest, but by the order in which the alternatives arise for a vote. The absence of an equilibrium implies that the person in control of the agenda (e.g., a committee leader) can bias legislative choice in favor of his or her most preferred alternative. Thus, there is a fundamental arbitrariness to social choice under majority rule . . . Similarly, strategic voting, typically secret, is always possible . . . Although strategic voting occurs often, it is hard to discover . . . All of this shows that the notion of a “will of the people” has no meaning . . . In modern political science . . . electoral majorities are seen as evanescent, and the legislator himself as a placeholder opportunistically building up an ad hoc majority for the next election . . . Knowing as we do that decisions are often, even typically manipulated, but being unsure just when manipulation occurs, we are forced to suspect that every outcome is manipulated . . . Our examples show that this problem actually arises in practice. (Riker and Weingast 1988, 393–396, 399) r Much of the discussion of public policy has assumed that political solutions can improve on market failures. The model we offer shows that this assumption is not justiﬁed . . . political institutions . . . often lack equilibrium outcomes . . . political choices typically entail preference cycles. For our purposes, the lack of equilibrium implies that there is no basis for unambiguously claiming that a political solution will improve or fail to improve upon the market failure it sought to correct. (Shepsle and Weingast 1984, 417, 421) r There is, in social life, a tradeoff between social rationality and the concentration of power. Social organizations that concentrate power provide for the prospect of social coherence – the dictator knows her own mind and can act rationally in pursuit of whatever it is she prefers . . . Though [social organizations in which power is dispersed] may appear fairer and more democratic to the person in the street, they may also be more likely to be tongue-tied or inconsistent in ordering the alternatives under consideration . . . Short of actually eliminating one of the fairness conditions – for example, by permitting dictators – the

A long, dark shadow over democratic politics

15

Arrow result does not evaporate . . . It is nearly impossible to arrange for the making of fair and coherent group choices. (Shepsle and Bonchek 1997, 67–69,166) r The various paradoxes of collective decision making seriously challenge the presumption that legislative changes generally represent welfare improvements, even in the de gustibus sense of reﬂecting changes in public taste. Enactments that instead reﬂect mere cycling, or changes in the agenda setter or in political tactics, may better be viewed as random and purposeless from the social welfare perspective. (Shaviro 2000, 68) r Arrow’s theorem casts a very long, dark shadow over democratic politics . . . All voting systems have some normative blemish and all voting systems can be manipulated. Social choices in democracy depend on the particular type of majoritarian voting procedure used by a group, on whether voting is sincere or strategic and on the order in which alternatives are considered . . . Voting cycles, according to social choice theory, are endemic to democracy. Social choice theory tells us that for most policy issues, there is some coalition of actors who jointly prefer some other outcome. Whenever they have the power to get this outcome, the social choice may simply reﬂect their power. Stability in politics may well be an arbitrary feature of an institutional arrangement, with losers attempting to dislodge winners of their temporary authority . . . Social choice research shows that policy agreements in a democracy may simply be the product of agenda manipulation . . . It seems that we cannot validly infer anything about the preferences of the society based on the laws produced by a legislature. Nor can we say anything about the preferences of the society when a policy is not produced. This has certainly raised fears among many about the legitimacy of laws in a democracy. (Cain 2001, 111–112) Weale and Dryzek are each commenting on the irrationalist trend rather than endorsing it. Riker and Weingast are brisk and conclusive about the supposed incoherence of democracy, Hardin is mournful and nuanced. Notice that people seize on the disequilibrium results in order to promote their more favored and demote their less favored institutions. Tribe uses the results to elevate the judicial over the other branches of government; Tushnet observes that the judiciary is just as tainted. Rowley, and Shepsle and Weingast, upgrade the market by downgrading the government; Wolff would abolish government altogether. Arrow

16

Democracy Defended

(1997) has recently gone on record that his theorem does not show that democracy is impossible, since it applies to all aggregations of individuals’ preferences, whether by one branch of government or another, and, I would make clear, whether by government or market. The irrationalist doctrines I criticize are not Arrow’s, they are based on interpretations by others of Arrow’s theorem. Many inﬂuential people suggest that democracy is impossible. The main purpose of this book is to argue against that view. Plan of the volume I hope that I have established both that there is an irrationalist trend, and that there is a long dark shadow cast over democratic politics. The proper interpretation of Arrow’s theorem and related social-choice results is a serious endeavor that deserves lengthy and detailed scrutiny. It will take a good deal of spit to displace that ocean of theory. I will argue that the irrationalist interpretations of social choice theory are based on unrealistic assumptions, or illustrate logical possibilities rather than empirical probabilities, or emphasize remediable problems, or are outright mistaken. This volume proceeds in three stages. First, the theory of democratic irrationalism is presented and criticized. Second, the empirical examples used by irrationalists to illustrate and popularize the theory are presented and criticized one after another. Third, brieﬂy, the theory is located in the larger intellectual and political context. Chapter 1 surveys the practical advance of democracy, introduces the problems, and establishes that there is a trend to democratic irrationalism in the academy. Chapter 2 argues that the irrationalist trend has wide inﬂuence in political science, introduces Riker’s distinction between liberalism and populism, and attacks as self-contradictory (among other problems) what I call Riker’s basic argument pattern. Riker repeatedly deploys the basic argument pattern in order to show that preferences are unknowable and hence that democracy is arbitrary and meaningless. Chapter 3 presents Riker’s argument that democracy is arbitrary because it is logically possible for different decision rules to yield different outcomes. I counter that this is logically possible but empirically improbable. Riker also objects that the axiomatic approach does not justify any one unique voting rule. I respond that the axiomatic approach considerably narrows the range of reasonable voting rules, and that choice from among the reasonable voting rules is not arbitrary. Chapters 4 through 6 closely interrogate and denaturalize key assumptions of Arrow’s theorem. Chapter 4 introduces Arrow’s theorem, the

A long, dark shadow over democratic politics

17

basis of the claim that democracy is meaningless. The theorem arises as the consequence of the appearance of the doctrine of noncomparable utility in economics. I show that the cycles that are alleged to make democracy meaningless are rare. Again the question is not one of logical possibility but rather one of empirical probability. In Chapter 5, I examine Arrow’s condition of universal domain (U). Individual preference orders resemble one another, enough so as to avoid cycling and related problems most of the time, which is why we observe so few cycles in the real world. Models of constant-sum redistribution predict total cycling, but such models neglect behavioral constraints that produce approximately fair outcomes but for pathological exceptions. The few cycles that do occur should be trivial, and any which are not trivial can be eliminated by accurate and fair voting rules. In Chapter 6, I criticize the formal and practical arguments offered in justiﬁcation of Arrow’s condition of the independence of irrelevant alternatives (IIA). Surprisingly, many people who support the skeptical interpretation of Arrow’s theorem do so on the basis of a misunderstanding of the content of its independence condition. I show that violating the independence condition can be substantively rational, and argue that the theorem’s conditions are methodological assumptions rather than claims with descriptive or normative force. I scrutinize several justiﬁcations of the condition, and conclude that none is sufﬁcient to justify the repugnant conclusion of Arrow’s theorem: that social choice is impossible except by dictatorship. In Chapter 7, I examine the contention that strategic voting, logrolling, and agenda control permit the undetected manipulation of outcomes. These models of manipulation assume, however, the knowability of preferences, demonstrating again the self-contradictory nature of Riker’s basic argument pattern. Further, we see that the possibility of countermanipulation frequently deters attempts at manipulation; and hence that such manipulation is not frequent, harmful, or irremediable. In Chapter 8, I take up the McKelvey and Schoﬁeld “chaos” theorems, interpreted by Riker to mean that there is complete disequilibrium in multidimensional issue spaces. The predictions of the chaos model fail in human subject experiments, are perhaps impossible to test in natural settings, and utterly lack realism. Realistic amendments to the model result in outcomes in the normatively attractive center of preferences. Moreover, the widespread parliamentary rule permitting a division of the question upon the motion of any one member practically disposes of any problem. These two chapters mostly summarize existing developments in the literature. It is Riker’s dramatic empirical illustrations of political disequilibrium, more than his theoretical arguments, that are responsible for the wide

18

Democracy Defended

Table 1.6. Summary of empirical ﬁndings #, Cite

Subject

Mackie Finding

1 APSR 1958

3 LAP APM

Agricultural Appropriations Agenda Experiment, Flying Club Powell amendment

4 LAP

17th Amendment

5 LAP

Wilmot Proviso

6 LAP

Lincoln election

7 LAP

Antebellum period

8 APSR 1984 APM 9 APM

Morris at the Constitutional Convention Lincoln at Freeport

10 APM 11 APM

The Masters Pliny

No cycle in sincere preferences (Riker recognizes strategic votes); best alternative won. Asymmetric institutions (in this case agenda control and information control) yield asymmetric outcomes. Riker and others allege cycle in 1956 vote; assume irrational voters. Votes, debates, and inferences in 1956 and 1957 show that school aid would have failed with or without Powell’s desegregation amendment. No cycle; best alternative won. Adds to Krehbiel and Rivers 1990. Eleven errors of fact; assumes irrational voters. No cycles, not in 1902, not in 1911. 17th Amendment would have failed with or without a voting-rights rider. Passed in late 1911 due to changed composition of the Senate. Conﬁrms conjecture of Green and Shapiro 1994. Cycle alleged among Mexican war appropriations, antislavery amendment and status quo. Based on egregious misreading of Congressional Globe. No cycle, best alternative won. No cycle. Free soil was primary issue in 1860, and the further north the more antislavery: latitude was attitude. Riker 1982, 230, line 2 mistaken: many Lincoln voters ranked Douglas ahead of Bell. Complemented by Tabarrok and Lee (1999). (Douglas was best alternative, not selected due to antimajoritarian design of electoral college.) Eruptions of slavery issue not due to arbitrary manipulation of multidimensional issue space. Dimensions highly constrained (Poole and Rosenthal 1997). Eruptions related to disruption of political balance following territorial acquisitions (Weingast 1998). Alleged cycle arises from treating similar alternatives as identical. If alternatives properly individuated, then no cycle. Mistaken details; “magic bullet” interpretation of Freeport debate now rejected by American historians. Douglas did face a dilemma, but it was one forced upon him by the changing preferences of the Northern and Southern populations, not by Lincoln’s discourse. Not examined. Based on ﬁction. Shows that agenda control was defeated by strategic voting: best alternative won.

2 LAP APM

A long, dark shadow over democratic politics

19

Table 1.6. (cont.) #, Cite

Subject

12 APM 13 APM 14 APM 15 APM

Vote trading Abstention Gerrymander Magnuson

Mackie Finding

Not on point. Trade fairly represented opinion? Idiosyncratic. Undocumentable. Many details mistaken, does not fully understand the parliamentary situation. Magnuson’s bill supported by vast majority; an explicit deal was made to pass Gravel’s more radical amendment in the Senate, and to withdraw it in Conference, in order to gain Nixon’s attention, and exactly that happened. 16 APM Reed, Cannon Not on point. Majorities enabled? 17 Blyden Internal revenue Flawed logic; inconsistently applied inferences of burgh 1932 preference orders. No cycle, best alternative won. 18 Bjurulf Scandinavian Half of voters absent; evidence of strategic voting; and Niemi parliaments: if only 2 out of 37 voters were strategic then hospital equilibrium in sincere preferences, and best alternative won. 19 Bjurulf Scandinavian Claim that strategic voting led to rejection of best and Niemi parliaments: alternative. Based, however, on unwarranted telephone and assumption that some voters were irrational. telegraph 20 Bjurulf Scandinavian Agenda control countered by creative response and Niemi parliaments: such that best alternative prevailed in long run. riﬂe club 21 Neufeld, et al. Muscle Shoals Cycle only apparent and due to bungled strategic voting that authors recognize; sincere preferences in equilibrium; best alternative won. 22 Lagerspetz Finnish electoral Cycle, and won by non-Borda winner, but perhaps 1997 college, 1931 for extraparliamentary reasons. Institution poorly designed to deliver popular outcome. 23 Lagerspetz Finnish electoral Cycle among same four candidates as 1931, but 1997 college, 1937 won by Borda winner. Poorly designed institution. 24 Lagerspetz Finnish electoral Non-Borda, non-Condorcet winner selected by 1993 college, 1956 electoral college. Poorly designed institution. 25 Gross Iowa Corporate Great evidence, but given that alternatives are on Farming one dimension, cycle unlikely in sincere preferences. 26 KurrildDanish prime Cycle among three evenly tied prime ministerial Klitgaard minister candidates in ﬂeeting poll data. Borda-winner succeeds in actual election. Sources: APM = The Art of Political Manipulation (Riker 1986), APSR (1958) = Riker (1958), APSR (1984) = Riker (1984), Bjurulf and Niemi (1978), Blydenburgh (1971), Gross (1979), Kurrild-Klitgaard (2001a), Lagerspetz (1993, 1997), LAP = Liberalism against Populism (Riker 1982), Neufeld, et al. (1994).

20

Democracy Defended

popularity of his irrationalist views. That the US Civil War came about because of a cycle, for example, is an unforgettable lesson. If the illustrations fail, then so does the doctrine of democratic irrationalism. Chapters 9 through 15 tackle the stories of political disequilibrium. Sometimes the going is tough, but my exposition and commentary is never more difﬁcult than the original material, and is often easier. My examinations are thorough, which serves several purposes. First, I show that almost all published and developed cycle claims are mistaken, and my claim would lack credibility in the absence of thorough argument; remember that I am challenging the most cherished scriptures of a dominant congregation of scholars. Second, by example, I show how it is possible to marry an understanding of historical background creatively to methods of roll-call analysis so as to generate new insights in political history. Third, several of the interpretations I develop of historical events are novel and interesting in their own right, for example, why Douglas lost to Lincoln in 1860. Chapter 9 is about the Powell amendment, a desegregation rider to a school construction aid bill in 1956. Riker believes that a cycle was contrived based on his inference that some voters voted strategically. A manipulation would not have been possible if all voters had voted strategically, so Riker’s ﬁnding of a cycle depends on the assumption that some actors were irrational. Riker’s inference of preference rankings is mistaken, however. It is quite clear that the events Riker strives to explain are a consequence of incomplete knowledge of preference rankings among the actors. Chapter 10 is about Senate deliberations on the 17th Amendment to the US Constitution, which provided for direct election of US senators. Again Riker alleges a cycle, and again he unwittingly assumes irrational actors. Riker’s interpretation of the 17th Amendment collapses due to gross errors of fact. Chapter 11 begins the account of Riker’s major case study on the US Civil War. The Wilmot Proviso in 1846 sought to prohibit slavery in the vast western territories about to be acquired by the United States. Riker’s assertion of a cycle here depends on an incontrovertibly erroneous reading of the Congressional record. Chapter 12 concerns Riker’s allegation that the election of Lincoln in 1860 and the momentous events that followed were the consequence of cyclical preferences among the voters. Riker’s apparently complex argument actually depends entirely on a single claim that Bell, the candidate of the Upper South, and not Douglas, the candidate of the Lower North, was second-ranked by Lincoln voters. Riker does not warrant the claim, and the claim is contrary to the consensus of historians. Douglas was the candidate favored by the median voter in the 1860 election, and in Chapter 13 I offer a hypothesis as to

A long, dark shadow over democratic politics

21

why the ﬂawed presidential election system failed to select Douglas. I go on to criticize Riker’s account of the slavery issue from 1800 to 1860, which he intends to illustrate the possibility of contrived disequilibrium by means of introduction of new issues and dimensions. Riker contends that changes at the collective level on the slavery issue were due to arbitrary manipulation of multidimensional issue space by superior political actors. I defend the conventional hypothesis that collective changes were a consequence of changes in individuals’ views on the issue. Riker’s remaining cycling claims are debunked in Chapter 14. He claims that there was a cycle in the US constitutional convention on the question of the selection of the executive: arbitrary instability formed the US Constitution. I argue that another interpretation of the record is more plausible, and with that interpretation of preference rankings there is no cycle. In 1958 Riker claimed to ﬁnd a cycle in US House consideration of an agricultural appropriations measure. Riker’s inference of a cycle incorrectly aggregates both sincere preferences and sophisticated votes. The ﬁnding of a cycle is based on a conceptual error, because with the aggregation of sincere preferences only there is no cycle. The remaining published and developed claims of cycles from the political science literature are presented in Chapter 15. Blydenburgh claimed to ﬁnd a cycle in deliberations over the Revenue Act of 1932. His analysis fails because it is confused about which alternatives are pitted against which; after the confusions are sorted out, there is no cycle. Bjurulf and Niemi investigated instability and manipulation in Scandinavian parliaments, but I show that their several inferences are defective. Neufeld et al. uncover an apparent cycle in US Senate deliberations over Muscle Shoals in the 1920s, but, as they recognize, sincere preferences were in equilibrium and the alternative favored by the majority prevailed. Lagerspetz produces the best evidence and argument on behalf of a cycle claim, but his cases arise in a poorly designed institution that encourages instability and unpopular choice. A few minor cycle claims are examined. In sum, theoretical considerations show that cycles, disequilibrium, and harmful manipulation are of little practical importance, and almost every published and developed example of cycling and manipulation is called into question. Chapter 16 returns to the possibility of manipulation by the introduction of new issues and dimensions. Why don’t we see the introduction of thousands of issues and dimensions as a manipulative political tactic? The answer is that such introduction is constrained by the consent of the audience to the claim of relevance by the speaker. Furthermore, deliberation in multidimensional issue space can identify a central outcome such as the intersection of the medians from each dimension. It is not

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Democracy Defended

discussion, only voting, and only voting under the unrealistic assumptions of the McKelvey model, that leads to chaos. Disequilibrium is not a problem of much practical importance, but I note ways in which deliberation could further tame disequilibrium should it be a problem. Then I present two anecdotes from Riker’s The Art of Political Manipulation (1986) that he intends to illustrate the theme of destabilizing introduction of new dimensions. One is the debate between Lincoln and Douglas at Freeport. The other is a controversy over the shipment of nerve gas involving Senator Warren Magnuson. I show that Riker commits errors of fact that undermine his cases, and argue that it is not arbitrary manipulations of multidimensional issue space but simply the distribution of preferences in the respective populations that explains these cases. In the end, Riker rejects “populism” (democracy) and accepts “liberalism” – deﬁned as the mere possibility of rejecting ofﬁcials in an election, the theme of Chapter 17. One problem, I argue, is that the objections Riker lodges against populism, if valid, would apply to his liberalism as well. Further, Riker’s liberalism is not the unique alternative to “populism” (democracy). If democracy were arbitrary and meaningless then it could be argued that superior individuals should impose the objective good upon the population. I trace Riker’s ideas on democracy to Pareto, who afﬁrmed such a policy of liberal autocracy. The doctrine of democratic irrationalism can have dangerous consequences. Chapter 18 argues that theoretical instabilities equally afﬂict private organizations and the market. The Arrow theorem applies to the market, there are market analogues to the chaos theorems, and to the Gibbard– Satterthwaite manipulation ﬁndings. Thus, there is no basis to the argument that democracy should be minimized and the market maximized because of the ﬁndings of positive political theory. The chapter also answers the claims made in the hall of quotations.

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The doctrine of democratic irrationalism

Introduction In this chapter, I claim that the Rikerian legacy is the most inﬂuential force in the discipline of political science, but that its reign is controversial. I distinguish the doctrine of democratic irrationalism from rational choice theory in general, and express qualiﬁed support for rational choice theory. In this volume, I do not defend the entirety of democratic principles, only the one narrow but essential principle of the possibility of the accurate and fair social amalgamation of individual opinions and wants. In his Liberalism against Populism, an interpretation of the results of social choice theory, Riker (1982) makes an apparently powerful case against the very intelligibility of majoritarian democracy. I introduce his contrast between liberalism and populism. What everyone else calls democracy, Riker labels populism, a term with pejorative connotations. Such populism is shown by social choice theory to be impossible, he claims. In its stead, he offers liberalism, which he deﬁnes to be the random removal of public ofﬁcials. This liberalism is the only democracy we can expect after social choice theory, he says. Finally, it is not widely appreciated that Riker’s central argument against populist democracy is that the preferences of citizens are unknowable. I begin the volume’s analysis by showing that the most central argument in the irrationalist scheme is self-contradictory and otherwise mistaken.

Commander Riker and Starship Rochester I have taken pains to illustrate the general reception of Arrow’s theorem, and have provided some indications of Riker’s inﬂuence. Now I want to establish further the inﬂuence of Riker and his Rochester school.1 At one point, Riker had published more refereed articles in the American Political Science Review, the premier journal of the political science profession, than any other ﬁgure (Miller, Tien, and Peebler 1996). Indeed an editor of that journal wrote to Riker that, “there is some danger of 23

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turning this journal into the William H. Riker review” (Amadae and Bueno de Mesquita 1999, 281). A New Handbook of Political Science (Goodin and Klingemann 1996) cites Riker, his student Shepsle, and coauthor Weingast as three of the eleven most frequently referenced authors discipline-wide (31), and counts Shepsle and Weingast as two of the ten ﬁrst-ranked integrators in the ﬁeld of political science, and Riker and his former student and coauthor Ordeshook as two of the seven secondranked integrators in the ﬁeld (40–41). A review of the ﬁelds of social choice theory, game theory, and positive political theory by sometime Rochester faculty members Austen-Smith and Banks (1998, 271) follows Riker in ﬁnding that, “from a normative perspective . . . any hope of ﬁnding substantive content in the idea of a ‘collective will’ with respect to policy choice is slender indeed.” Amadae and Bueno de Mesquita (1999, 269, 271) provide a brief history of the conquest of the political science discipline by Riker and his followers: “The Rochester school of political science, led by William H. Riker, pioneered the new method of positive political theory . . . [which] must be acknowledged as a dominant force in political science.” Positive political theory is scientiﬁc, and it assumes that humans are both rational and self-interested actors, according to Amadae and Bueno de Mesquita (270). The movement was born when in the 1960s the Xerox Corporation, headquartered in Rochester, New York, richly endowed the University of Rochester to upgrade its social science departments; Riker was hired to do that job in political science, and over time brought the department from nowhere to one of the most successful in the country (279). Among its other contributions, Riker and the Rochester school “used Arrow’s result to question the efﬁcacy of democratic government in producing outcomes that are somehow publicly beneﬁcial,” they say (286). According to the Rochester Department webpages: For four decades, since William H. Riker arrived at Rochester in the early 1960s, the department has helped transform the discipline of political science . . . The “Rochester School” of political science has entered the vocabulary of an entire scholarly discipline . . . The department strives not only for leadership in advancing rational choice theory but, more broadly, for leadership in advancing the scientiﬁc study of politics . . . We distinguish our programmatic goals from those of other departments by our strong emphasis on positive theory and generalization, and by our historical commitment to (and success in) speaking to the discipline of political science.2 Controlling for size, a 2001 study in PS: Political Science & Politics concluded that Rochester ranked ﬁrst in the country in productivity of its PhD alumni, as measured by publications in leading journals. Rochester is the birthplace of a distinctive approach to studying politics that emphasizes the development of

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formal theory and the analysis of quantitative evidence. A cursory examination of the discipline’s leading journals . . . demonstrates how the ﬁeld was revolutionized by this development.3

Although the Rochester school is not the majority force in the political science discipline, it is the modal force in it. A cover story in The New Republic, “Revenge of the Nerds,” was devoted to Riker and his followers (Cohn 1999). I relate, but do not endorse, some of its contents. The article is an attack on rational choice theory in general, which Cohn identiﬁes with Riker and his Rochester school; but that is not quite correct, there is also the Virginia school, the Bloomington school, the left-liberals formerly centered at the University of Chicago, and individuals not otherwise classiﬁed. Cohn reports that some scholars outside the Rochester school believe that its members want to diminish the role of nonmembers in the discipline of political science, and that Rochester has made considerable progress in realizing its alleged goal. Rational choice scholarship readily yields publications: “all you had to do was come up with a complication that confounded some existing rational theory and then derive a new, more complex equation to answer it,” and as a result Rochester school research exploded into the literature and advanced the careers of its practitioners. James Q. Wilson complained, “They don’t read Supreme Court decisions or history. They just sit around and make models.” The insiders are said to maintain a uniﬁed front, to cite and to referee one another’s papers, to preach that their approach is the only legitimate method in political science, and to establish litmus tests for faculty hiring, according to Cohn’s disgruntled and anonymous informants. “‘Because they are not as broad-minded, they had the advantage,’ says one senior scholar at Harvard. ‘They’d support any candidate who did rational choice, oppose any non-rational-choice scholars,’” Cohn relates.4 Critics call them “imperialists,” “colonizers,” and “Leninists” (in the organizational sense), and hyperbolically describe them as a cult. Cohn says that cultists speak with reverence when they discuss their founders, and continues: It would only be a slight stretch to compare this reverence with the way rational choicers talk about their movement’s founder, the late William Riker, and the intellectual compound he built at the University of Rochester. “Rochester is the mother ship,” Shepsle says. “Its founder . . . was William Riker. ‘Commander Riker,’ as we like to call him. And ‘Starship Rochester.’”

The crew of Starship Rochester respond that these views are unfair caricatures. Shepsle remarks that although “we were all true believers,” there

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was no “grand imperialistic design.” Bueno de Mesquita says that “We’re a handful of people,” and that, “the reason it appears to be this dominant thrust is because the clarity of the work attracts attention.” I will show that a defect of irrationalist scholarship is that its formality obscures as much as it clariﬁes. In June 2000, economics students in Paris rebelled against their rigidly formalist curriculum. Among the reasons they gave were: 1. We wish to escape from imaginary worlds! 2. We oppose the uncontrolled use of mathematics! 3. We are for a pluralism of approaches in economics!

The students opposed the use of mathematics as an end in itself, deplored the domination of economics by highly ideological neoclassical theory, and they rejected what they called its repressive dogmatism. They favored intellectual engagement with concrete empirical realities, a pluralism of approaches, and science rather than an obscurantist scientism. The rebellion, which came to be known as the Post-Autistic Economics Movement (www.paecon.net) spread through France, the Continent, the United Kingdom, and the United States. Parallel declarations emerged at Cambridge University and at a Kansas City conference. The French minister of culture appointed a commission to investigate student concerns, which eventually recommended reforms endorsed by the students. In the same spirit, in November 2000 a new “perestroika-glasnost” movement erupted in the American political science profession, critical of the hegemony of narrow rational choice theory in its professional association and its main journal (Eakin 2000; Jacobsen 2001; Kasza 2001; Miller 2001; all linked at www.paecon.net). Kasza wrote that the problem is hegemony, not rational choice; that the postmodernist hegemony in some literature and history departments may be just as suffocating as rational-choice orthodoxy is in political science. Kasza continued that: William Riker was fond of saying that political science was a sinking ship, and rational choice theory was the only tugboat that might bring it to port. It is truer to say that Riker’s disciples have acted as pirates out to hijack political science to a rather barren island. Their piracy is doomed to failure.

Changes in the association and its journal are coming about. Its 2002, 2003, and 2004 presidents are sympathetic to the movement’s complaints, the perestroika movement is lively and organized, and there is pressure for contested elections in the association to replace its previous system of co-optation.

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Democracy defended The theory of democratic irrationalism is a species of the genus rational choice theory, but I criticize the species and not the genus. The theory is one justiﬁcation for laissez-faire, or perhaps for total anarchism; if successful, my criticism eliminates that irrationalist justiﬁcation for laissez-faire or anarchism, but not other justiﬁcations. The theory attacks democracy in principle, and I defend it in principle; except incidentally, our discussion here is not about how to improve democracy in practice. My defense does not pertain to the entirety of questions involved in the justiﬁcation of democracy, but only to one essential question about the systematic connection of citizens’ opinions and desires to public outcomes. Green and Shapiro (1994) wrote a sustained critical evaluation of rational-choice explanations in political science that received wide attention. Their Chapter Six on “Legislative Behavior and the Paradox of Voting” (98–146) is most relevant to the themes I discuss here. I agree with nearly all of its observations, which I will not duplicate here. As for the book as a whole, I agree with Green and Shapiro’s descriptions of rational choice scholarship, as far as those descriptions go, but not so much with their evaluations. I often prefer the work of scholars who are informed, but not enslaved, by rational choice theory; but I appreciate any work that shows high creative intelligence. I see the study of politics as an interpretive enterprise. A plurality of methods contributes to that enterprise, and the methods of rational choice theory are especially but not exclusively useful for describing and explaining some collective actions, strategically interdependent actions, and the character and consequences of voting rules. Although the terms are used informally and interchangeably, social choice theory is simply the formal description of economic and political aggregation, and is indispensable even if some of it is sterile and scholastic. I cannot imagine doing without noncooperative game theory, which in the right hands yields rich insights into social life, along with testable, and supported, predictions (for example, see Mackie 1996); although some formal work is irrelevant and some applied work is unimaginative. “Many public choice scholars advocate a rather ‘libertarian’ approach, leaving most decision making to the private market while proposing a signiﬁcantly reduced role for government” (Block 1998, 983, emphasis added).5 Although many rational choice practitioners believe that their method requires the assumption of egoism, it need not, and I wholeheartedly reject the assumption that humans are exclusively motivated by egoistic concerns. I agree with Elster’s Davidsonian account of rational choice theory in the narrow sense, as an initial assumption, in

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interpreting individual human action, of the consistency of beliefs and of desires; and I agree with his claim that there is no alternative to it as a set of normative prescriptions (Elster 1986a). Otherwise, “rational choice” in the broad sense is a catch-all term for the use of a grab-bag of methods whose only unity is that they are formal models borrowed from the discipline of economics. I do not see that there can be an objection against formal models as such, used by scholars who understand their assumptions and their scope, although I fear that Walt (1999, 8) more likely than not is correct when he concludes “that the growing technical complexity of recent formal work has not been matched by a corresponding increase in insight.” Schumpeter, Arrow, Buchanan, and their followers subsumed democracy to the market model and likened the voter to the consumer. If that subsumption is supposed to be the basis of rational choice political theory, then rational choice is already dead, because ﬁfty years of scholarship have shown that the analogy of the voter to the consumer is gravely misleading. In idealized market exchange self-interest has benign social consequences, but in the idealized democratic forum self-interest has malign social consequences. The connection between individual choice and individual outcome is direct and obvious for consumers, but comparatively indirect and obscure for voters. Practically, people tend to self-interest in the market, and to impartiality in the forum. The Condorcet paradox of voting predicts radical instability among self-seeking voters, but this is not observed, and the paradox of participation predicts that almost no one will vote, because one individual’s vote almost never makes a difference, but this is not observed either.6 If, as I argue, there is not much intellectual unity to rational choice political science, there is a sociological unity to it, captured by Amadae and Bueno de Mesquita (1999) and Cohn (1999). The scientistic aspirations of the Rochester school are dashed by Green and Shapiro’s demonstration of methodological pathologies such as post hoc theory development, vague or slippery predictions, and selective use of evidence. These pathologies are not necessary implications of the use of formal models in political science, however.7 Finally, we should consider the opportunity costs of rational-choice scholarship. Rational choice was attractive to me as an alternative to what I considered exhausted doctrines, such as Parsonsianism, Freudianism, or Marxism. But if the effect of rational choice on the study of politics is to keep too many scholars and students away from historical knowledge, contextual understandings, exposure to multiple cultures, broadminded appreciation of human motivations, the formulation and testing of competing hypotheses, or the facts and feelings of politics, then its costs would exceed its beneﬁts.

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Hauptmann (1996) afﬁrms the wide inﬂuence of rational choice in political science, and that there are many voices in rational choice theory. She, too, criticizes the analogy from economics to politics (74). Like many unbelievers she seems to be fascinated and appalled by the brutally antidemocratic strain in rational choice theory: On the one hand, rational choice theorists identify democracy with honoring individual choice, a norm they believe has been overshadowed by pursuing what to their minds are the dubious goals of securing the common good or increasing popular participation. On the other hand, they also conclude that the choices citizens are given are not worth making because they are either too insignificant individually to make any difference or are offered and counted in ways that end up distorting the very things that were supposed to be honored . . . these theorists . . . assign such dismal expectations to contemporary democratic systems that they ﬁnd themselves unable to say what is valuable about them. (4–5)

Hauptmann criticizes the concept of choice in rational choice theory, by reference to Aristotle’s usage of prohairesis and an ordinary-language analysis of choice. She points to election of ofﬁcials by lottery in Athens as a democracy not based on choice as a value. Hauptmann adequately identiﬁes shortcomings of rational choice theory, but her external critique is not persuasive, in my opinion. I offer an internal critique of the irrationalist doctrine. My target in this volume is not rational choice theory, but an irrationalist doctrine contingently associated with rational choice theory. True, Riker is “the godfather of rational choice analysis in political science, and the University of Rochester, where he taught for more than a quarter of a century, continues as its intellectual center” (Shepsle and Bonchek 1997, viii). The doctrines I identify and the pathologies of scholarship that Green and Shapiro identify do center on the godfather and perhaps some of his capos, and they do make up much of the content of rational choice theory as it is taught to students. But, to infer guilt by association would be both descriptively and normatively wrong. There are plenty of rational choice theorists who are indifferent to Riker’s irrationalist doctrine, and others who have patiently developed theory and evidence that cumulatively undermine the Rikerian monolith. There are rational choice investigators who do marvelous empirical research, and who dutifully revise theory so as to reﬂect the data. There are many who engage in constructive social choice theory – seeking to contribute solutions to human problems rather than hothousing bugaboo paradoxes.8 Although there are socialists and left-liberals who do not contest Riker’s irrationalist theory, its primary appeal is to the economic right. Public choice theory, in the narrow sense of the term, is the assertion by the Virginia school that government should be limited in order to

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avoid damaging policies enacted by self-seeking interest groups, politicians, and bureaucrats, and the assertion by the Rochester school that government should be limited because democratic outcomes are arbitrary and meaningless. Shapiro (1996, 43) remarks that “the implicit counterfactual in this tradition is that private action is essentially benign,” rather than anarchic chaos. For the public choice tradition, says Shapiro, collective action is only necessary in instances of market failure, but there is no rational way of organizing collective action. Remarkably though, as I shall later show in detail, the Arrow theorem applies to the market, there are strong analogues to the political chaos theorems in economic theory, and the market, too, is subject to strategic misrepresentation of preferences. Rather than declaring the market to be inaccurate and meaningless because of these logical possibilities, and concluding that it should be severely circumscribed, economists instead note undramatically that the model’s prediction does not match observations, and ask what might be wrong with the model’s assumptions. In this volume, I argue against the democratic-irrationalist justiﬁcation of economic libertarianism, but not against other possible justiﬁcations of the minimal state. It might seem curious that irrationalist theory cavils at hypothetical and unproven deviations from the democratic ideal of equal inﬂuence in politics, but neglects actual and proven distortions such as the campaign ﬁnance problem in the United States (Drew 2000). Kuttner (1996, 347) claims that “Public Choice theory is almost entirely silent on the disproportionate purchase of inﬂuence by big money.” The irrationalists do not criticize democracy in practice, I surmise, because practical defects are remediable. The remedy may be difﬁcult to accomplish or involve an unacceptable tradeoff with other values, but remedies are conceivable. Riker’s point is not that democracy is imperfectly approximated in practice. Riker wants to establish that democracy has defects that are irremediable in principle (also see Weale 1999, 140). Therefore, my response defends democracy in principle. I know that in practice democracy is a messy and imperfect business, but the practical shortcomings of democracy are not the topic of this study. Also, if Waldron (1999, 2) is correct, that we have an idealized picture of judging but a disreputable picture of legislating, and that we should “develop a rosy picture of legislatures that matche[s], in its normativity, perhaps in its naivete, the picture of the courts,” then a defense of democracy in principle will be welcomed by some readers. Finally, my defense does not pertain to the whole of democracy and liberalism. Rather my attention is conﬁned to a single question of major importance: the possibility of the accurate and fair amalgamation of opinions

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and wants. It is not just crudely populistic democracy, where the majority could impulsively vote to massacre a minority, that requires a knowable and systematic connection between citizens’ opinions and wants on the one hand and public policy outcomes on the other. A political theory might construct a liberalism from ﬁrst principles, and then suggest that democratic institutions, in an auxiliary fashion, comparatively would best approximate recommended liberal outcomes. But even that thinly democratic scheme requires a systematic connection, rather than one that is haphazard or accidental. According to Riker, the democratic connection is random; if so, then any liberal autocracy better than random would be better than liberal democracy; also, if preferences really are unknowable, then the liberal theorist could not know such things as that most people do not want to die and that a few people want arbitrarily to kill, and thus would lack motivation to formulate liberal principles. Further, it is not just desire-satisfaction accounts of democratic legitimacy that require a systematic connection. Any deliberative approach which concedes (as it must in my view) that reasonable discussion among reasonable people can terminate in disagreement has to propose a method of practical decision. When reason is exhausted, if it is not possible accurately and fairly to amalgamate differing judgments as to the content of the public good, then any deliberation short of unanimity has no practical result. Nor in requiring a systematic connection are we committing a fallacy of composition, improperly ascribing collective desires, beliefs, and preferences to a collective entity, if indeed that is improper. In wanting to know what most experts think about smoking, or in wanting to afﬁliate with a group that settles conﬂicts, not arbitrarily, but according to a voting rule which systematically connects group outcomes to its members’ preferences, I have committed no such fallacy. Liberalism against Populism Riker’s (1982) volume opens with a discussion of the normative features of democracy (adapted, with radical changes, from his 1953 book on democracy in the US). Riker tells us that the democratic ideal is one of individual self-realization and individual self-respect. The democratic method is the free and equal participation of each citizen in the political life of the community. Hitherto democratic theory has assumed that democratic ends (or ideals) can be attained by democratic means (or methods), but Riker says that this assumption may or may not be true. Social choice theory will help us decide whether or not the assumption is true, whether or not democracy is attainable. The Platonic and Marxist conceptions of justice were not attainable, he says, because in each case the means could

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not reach the end. The same question should be asked of democracy as of those conceptions of justice: do its means attain its ends? For Riker, voting is the central act of democracy. The elements of democracy are participation, liberty, and equality, he says. Participation is centered on voting, but voting alone is not sufﬁcient for democracy; only voting surrounded by attendant institutions such as free speech and political parties that facilitate popular choice is democratic. Participation has two purposes. The ﬁrst purpose is instrumental and negative: participation restrains oppressive rule by subjecting ofﬁcials to popular judgment. The second purpose is intrinsic and positive: participation furthers the individual’s self-control – both internal discipline and cooperative management of the physical and social environment. Self-control supports the democratic ideal of self-realization and self-respect. Liberty is instrumentally required to organize participation in government, and has gone on to become an end in itself. Civil liberties, religious liberties, and economic liberties are intrinsic ends and also facilitate self-control. Equality, like liberty and participation, originated as an instrument of voting, according to Riker, and it too promotes self-control and self-respect. “In a society characterized by democratic justice, people are free (by reason of democratic liberty) and have the chance (by reason of democratic equality) to seek self-respect and self-control (through some kind of democratic participation)” (8). The democratic method of voting and its attendant institutions are meant to attain those ideals. The avoidance of the public good in Riker’s normative portrayal of democracy is no accident. There are two interpretations of voting, the liberal and the populist, which Riker implicitly treats as exhaustive and exclusive. Warning: Riker’s usage of the two terms is idiosyncratic, polysemic, and inconsistent at crucial points in his argument. The liberal view is Madisonian, Riker maintains at this point in his narrative, and the populist view is Rousseauvian. Riker eventually concedes that his liberalism would not be endorsed by Madison, and I will shortly show that his populism would not be endorsed by Rousseau. The liberal view, says Riker, is that the purpose of voting is to control ofﬁcials, and nothing more. Madison, he writes, held it necessary that republican government derive all of its powers directly or indirectly from the great body of the people, and sufﬁcient that it be administered by ofﬁcials who hold ofﬁce for limited periods (Federalist No. 39, in Hamilton, Jay, and Madison n.d. (1937)/1787). He adds that Madison said nothing about the quality of popular decision, whether such decision be good or bad (but Riker is wrong, as we shall discuss in Chapter 17: for Madison, the ultimate aim of popular government is “the public good”; see his Federalist No. 10, (1937)/1787). All democrats

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accept the necessary condition, but only Riker’s “liberal” democrats accept the sufﬁcient condition, he claims. Popularness, Madison’s necessary condition, ensures participation and equality; and limited tenure, Madison’s sufﬁcient condition, ensures liberty. That ofﬁcials can be replaced guards against tyranny and protects liberty, Riker says. Another danger to liberty is that ofﬁcials may be inefﬁcient agents of the people, he continues. This is where liberalism and populism part company. Populism assumes popular competence, that the electorate is right. Liberalism assumes that the electorate can change ofﬁcials only if many people are dissatisﬁed or hope for a better performance. All liberalism requires is that ofﬁcials can be rejected by election; however, in order to avoid rejection, ofﬁcials do act so as to avoid giving offense to future majorities; the union of those many possible future majorities is often most of the electorate, hence liberal ofﬁcials are approximately agents of the people, and thus liberalism satisﬁes the democratic ideal of self-control, Riker concludes. For the populist, according to Riker, liberty and hence self-control are obtained by embodying the will of the people in the action of ofﬁcials. Rousseau is the exemplar, or perhaps the demon, of populism. Rousseau posited a general will that is the objectively correct common interest of the incorporated citizens, which is computed by consulting the citizens, Riker claims. “What the sovereign people, when speaking for the public interest, want is justiﬁed because the sovereign people want it and because it is their liberty” (12). Participation in democratic decision is necessary to liberty, according to Riker’s populism, and the rules thus made must be respected as right and proper because they embody that liberty. The hurried reader might reject populism as portrayed by Riker because it is so painfully obvious that democratic decisions can be factually and morally mistaken. Who could be so silly as to believe that actual democratic decisions by deﬁnition precisely carry out some “general will” and thus that they are always true or right? The hurried reader would be attracted to Riker’s liberalism which, at this point, requires only that the decisions of democratic ofﬁcials approximately satisfy the opinions and desires of the people. The hurried reader would be mistaken. As is well known, Rousseau distinguished the general will from the will of all. Chapter 3 of his Social Contract is titled, “Whether the general will can err”: the general will is always rightful and always tends to the public good; but it does not follow that the deliberations of the people are always equally right. We always want what is advantageous to us but we do not always discern it . . . There is often a difference between the will of all and the general will; the general will studies only the common interest while the will of all studies private interest, and is indeed no more than the sum of individual desires. (Rousseau 1968/1762, 72)

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The general will, true or right, is independent from the will of all, which can err in attaining the general will. The will of all, actual democratic decision, might err because it is mistaken about some fact of the matter, or might err because it aggregates partial interests rather than judgments about the general interest. The younger Riker (1953, 156) knows this: The will of the majority is the best guide democrats have to the distinction between political right and wrong. In the end it is their only guide. But that does not mean that majorities are infallible or that time will not prove them wrong.

Thus, for Rousseau, and for the younger Riker, actual democratic decisions variably approximate rather than deﬁne the general will or public good. The democratic public good is deﬁned independently from the output of actual democratic procedures, these days perhaps as the output of an ideal procedure, or by subjective utilitarianism, or by objective measures of welfare such as of health, nutrition, longevity, or by appeal to ethical intuitions, or by secular extension of religious revelation; people debate and vote among such competing conceptions of the public good. No one, no democratic theorist and no democratic participant, equates the entirety of actual democratic output with the democratic public good, else disagreements about what to do would have no content, nor would we ever be able to say (holding conditions constant) that a past decision deserves revision. Riker’s populism is an absurd doctrine, one not even endorsed by its supposed champion Rousseau. Why is Riker tempted into this error about Rousseau? In his ﬁrst chapter he maintains that his liberalism approximates the public good, and if it were sufﬁcient for populism only to approximate the public good, then his distinction between liberalism and populism would collapse. If there were no distinction between the two, then Riker’s argument against the populism he wants to attack would apply as well to the liberalism he wants to defend; and then the ﬁnal conclusion, according to Riker himself, would be that democracy is wholly indefensible (241). Add a third source of error in identifying the general will: the basic problems of aggregating opinions and desires introduced in the previous chapter. Because different voting systems may yield different outcomes from the same proﬁle of individual voters’ preferences, he argues, democracy is inaccurate. Different methods of aggregating individuals’ ﬁxed choices may yield different group choices. Furthermore, although one or more voting rules may be better than other voting rules in a particular setting, there is no one uniquely justiﬁed voting rule across all settings. Finally, from the outcome of any vote it is not possible to infer enough about citizens’ preferences to determine whether that outcome is

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a true and fair aggregation of those preferences. Next, Riker continues, given a ﬁxed voting system, then democracy is meaningless: the outcome of voting is manipulable, and it is not possible to distinguish manipulated from unmanipulated outcomes because of the unknowability of private intentions underlying public actions. The spirit of the argument is best conveyed by Condorcet’s paradox of voting. The Condorcet paradox of voting is a special case of the Arrow possibility theorem; the Arrow theorem shows more generally that, assuming all logically possible individual orderings over alternative social states, no method of aggregating individuals’ transitive preference orderings guarantees a collective preference ordering that is transitive. Therefore, even the same method of aggregating individuals’ ﬁxed choices may yield different group choices, as the choice arbitrarily or manipulatively cycles from one alternative to the next. Associated with the possibility of cycling are the possibilities of unfairly manipulating the outcome by means of strategic voting, agenda control, and introduction of new alternatives or dimensions to the issue space. The liberal interpretation of voting, says Riker, accepts that democratic voting and discussion are inaccurate and meaningless. The only democracy that withstands the scrutiny of “modern political science” (Riker and Weingast 1988, 396) is the liberal institution of regular elections that permits both the rejection of tyrannical rulers and the “circulation of leadership” (Riker 1982, 253), preferably supplemented by the liberal constraints of divided government. The kind of democracy that thus survives is not, however, popular rule, but rather an intermittent, sometimes random, even perverse, popular veto. Social choice theory forces us to recognize that the people cannot rule as a corporate body in the way that populists suppose. Instead, ofﬁcials rule, and they do not represent some indeﬁnable popular will. (Riker 1982, 244)

One problem with Riker’s “liberal” justiﬁcation of voting is that his proposed constraint is no constraint at all and thus ofﬁcials would do as they please (see Cohen 1986, 30). True, if there is a random chance of getting a ticket for driving faster than the speed limit, then my speeding is constrained. But if there is a random chance of getting a ticket whether or not I am driving faster than the speed limit, then I will do as I please. In the ﬁrst chapter of the volume, Riker’s liberalism approximates the public good (11); but in frank contradiction by the last chapter of the volume there is no such thing as a knowable public good, the connection between the democratic electorate and its ofﬁcials is random, and Riker has to admit that Madison would not endorse his conception (242–243).

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Democracy Defended

Riker’s liberal interpretation of voting fails as a democratic method to attain democratic ideals, to use his terms, despite his weak assertions to the contrary. The younger Riker (1953, 106) supplies the reasons: responsible government means that public ofﬁcers submit themselves in elections to the judgement of the people . . . in addition it requires that voters have a clear sense of their power of selection or at least of their power of choice. How else can they hold ofﬁcers responsible unless they are aware that voting does some good, that it is clearly related to their own personal circumstances? On the other hand, in the ofﬁcials themselves this general responsibility requires a continuing consciousness of the popular, electoral sanction.

The instrumental and negative purpose of participation, to restrain oppressive rule, is thwarted under the liberal interpretation of voting, because the removal of ofﬁcials is not only imperfect, but wholly random, and ofﬁcials are thus unrestrained. The intrinsic and positive purpose of participation, to further the individual’s self-control, is thwarted, because there is no knowable relationship between the individual’s vote and the collective outcome. Liberty is unguarded, because there is no effective restraint on ofﬁcials. Equality is mocked, because any one decision can be unfairly manipulated, and hence all decisions could be unfairly manipulated, if the older Riker’s argument is correct. What if Riker’s argument were incorrect? What if the preferences of citizens were approximately knowable, what if democracy were approximately accurate, what if democracy were approximately unmanipulated? Remember that Riker’s populism requires that democratic decisions deﬁne, not merely approximate, the public good. If any problems of aggregation were to result in the slightest indeterminacy or error, then populist democracy fails entirely, Riker insists (291). We need not be cornered by Riker’s deﬁnition of “populism,” however. We are free to adopt a more standard view, that it is sufﬁcient for the outcomes of actual democratic procedure to approximate a democratic ideal of the public good. In this volume I will endeavor to show that, in principle, democratic procedures adequately approximate the public good. If the reader is a bit vague about the distinction between populism and liberalism, some concrete examples may help. A present-day manifestation of populism, according to Riker in 1982, is Marcus Raskin of the American New Left, and a present-day manifestation of liberalism is William Rusher of the American New Right. Populism is typiﬁed by American progressivism and Franklin Roosevelt’s New Deal (Riker 1982, 63), and Riker’s liberalism would roll back progressive-era and New Deal reforms and reestablish the minimal state of the Gilded Age (Riker and Weingast 1988). Riker continues his discussion of liberalism

The doctrine of democratic irrationalism

37

and populism in his last chapter, and I continue my commentary in the next to the last chapter of this volume. Riker’s basic argument pattern Riker knows that he cannot rest his argument only on divergent outcomes from the same proﬁle and on the mere possibility of cycling, strategic voting, and agenda control. The problem, despite much repetition to the contrary in subsequent literature of the Rochester school, is that these harmful possibilities are not shown to be empirical actualities of normative consequence. The endpoint of Riker’s argument is the skeptical assertion that populist democracy is impossible because individual preferences are unknowable. Everything else is a step on the way to this destination. As to accuracy, his ﬁnal conclusion is: Outcomes of voting cannot, in general, be regarded as accurate amalgamations of voter’s values. Sometimes they may be accurate, sometimes not; but since we seldom know which situation exists, we cannot, in general, expect accuracy. Hence we cannot expect fairness either. (Riker 1982, 236)

And, as to meaninglessness, his ﬁnal conclusion is: Outcomes of any particular method of voting lack meaning because often they are manipulated amalgamations rather than fair and true amalgamations of voters’ judgments and because we can never know for certain whether an amalgamation has been manipulated. (Riker 1982, 238)

Most of Riker’s commentators miss this aspect of his argument. They are more interested in his discussions of inaccuracy and manipulation. If I succeed in disposing of the issue of the unknowability of other individuals’ preferences early on, that will simplify the rest of the discussion on inaccuracy and manipulation in the remaining chapters. Riker’s several lines of attack against the populist interpretation of voting all ultimately depend on the following pattern of argument: (1) Because of cycling, strategic voting, agenda control, and multidimensional issue spaces, it is possible that the outcome of any one vote can be manipulated. (a) If underlying preferences must be indirectly inferred, then it is possible in any one instance of voting for there to be undetected manipulation; (b) Revealed tastes, actual choices such as votes, are directly observed, but true tastes, the underlying preferences, must be indirectly inferred; (c) Undetected manipulation is possible in any one instance of voting.

38

Democracy Defended

(2) (a) If undetected manipulation is possible in any one instance of voting then it is possible in all instances taken together; (b) Undetected manipulation is possible in any one instance of voting (1c); (c) Therefore, in all instances taken together, underlying preferences cannot be inferred from votes. (3) (a) If underlying preferences of individuals cannot be known, then it is impossible to aggregate such preferences; (b) Underlying preferences cannot be known (2c); (c) Therefore, it is impossible to aggregate underlying preferences; any such claim is meaningless. Notice that by substituting “communication” for references to voting in (2), the amended argument would prove the “meaninglessness” of all communication, including political discussion. Riker claims not only that undetected manipulation is possible (1c) but also that it is frequent, but the frequency claim is not essential to his argument. Moreover, the frequency claim verges on self-contradiction: if true preferences cannot be known (2c), then it would not be possible for any observer to estimate the frequency of manipulation. Also, the claim that actual choices are directly observed but that underlying preferences must be inferred (1b) is heuristic in some investigations but it is not fundamental. When someone buys a Cadillac, what choice has been revealed: a means of transportation, a status symbol, a dating ploy, a nostalgic memory of the buyer’s father, a tax dodge, a mistake? When the only information we have is that someone refrains from buying a feasibly available Cadillac, what choice has been revealed? As for voting, raising one’s hand might be a sincere vote, might be a strategic vote, might be a mistake, might be a yawn and a stretch, might be the sign of a follower of St. John the Baptist, might be a joke, might be an involuntary reﬂex. How do we know whether or not something is a choice? The more fundamental distinction, it seems to me, is between movement and action (Fay 1996, 92–95). Movements are directly observed, but actions (including forbearances) must be interpreted. To infer an agent’s action from a collection of movements requires initial attributions of intention and of agent rationality. In other words, if there really were an insurmountable problem of interpretation, then not only would the inference of preference from revealed choice such as voting fail as Riker would have it, so would the inference of voting from mere movements: we would never know, given Riker’s requirement of certainty, whether particular motions are an act of voting or something else altogether and thus even the “liberal” defense

The doctrine of democratic irrationalism

39

of voting would collapse since humans would be completely opaque to one another. Nevertheless, we may for the sake of argument grant Riker his claim that preferences are inferred from choice (1b). His fatal error is the move from the claim that undetected manipulation is possible in any one instance to the claim that in all instances taken together it is therefore impossible to infer preferences from choices (2a). I will argue that (2a) is defective and thus that (2c) does not follow; it is false that in all instances taken together, underlying preferences cannot be inferred from votes. What does my conclusion do to the claim that it is impossible to aggregate preferences? Riker’s third argument is that if underlying preferences are unknowable, then it is impossible to aggregate such preferences (3a), or if p then q. I say that underlying preferences are knowable, not-p. In the present context, then, I do not show generally that it is possible to aggregate preferences. I only show here that if it were impossible to aggregate preferences then the unknowability of preferences would not be the reason for such an impossibility. It may be impossible to aggregate preferences for some other reason, for example the claims arising from some interpretations of the Arrow theorem, a contention disposed of separately in upcoming chapters. Knowledge of other minds Now for the challenge to (2a). If all we know are public votes over alternatives, without discussion, in a single, static instance, then what do we know about the underlying preferences behind the actual choices? Strictly speaking, we do not even know what kind of entities emit the vote; all we know are some bare rankings, an aggregation rule, and an outcome. With so little information we could not say that choices might strategically misrepresent preferences. The best we could say is either that choices are preferences, or that “underlying preference” is a meaningless concept. We could not discover that choices may strategically misrepresent preferences unless we have information from beyond the single instance. It is obvious to us that choices may misrepresent preferences because we do not live in the single instance. In the richer information environment, we know that choices sometimes misrepresent preferences only because we know that choices sometimes do represent preferences. Much of one’s knowledge, and almost all of one’s discursive knowledge, political or not, depends on the testimony of others (Shapin 1994; Coady 1992). Could that testimony be “generally” wrong? The skeptic denies the possibility of knowing an outside world, or denies the possibility of knowing other minds, on the argument that since each of our beliefs

40

Democracy Defended

(about an outside world or about other minds) taken alone may be false, they might all be false. The philosopher Donald Davidson replies that it does not follow from the fact that any one of the bills in my pocket may have the highest serial number, that all the bills in my pocket have the highest serial number; nor that since anyone may be elected President, that everyone may be elected President. Nor could it happen that all our beliefs might be false (Davidson 1991a, 193). “[E]nough in the framework and the fabric of our beliefs must be true to give content to the rest” (Davidson 1991b, 160). There is no assigning beliefs to a person one by one on the basis of his verbal behavior, his choices, or other local signs no matter how plain and evident, for we make sense of particular beliefs only as they cohere with other beliefs, with preferences, with intentions, hopes, fears, expectations, and the rest . . . Crediting people with a large degree of consistency cannot be counted mere charity: it is unavoidable if we are to be in a position to accuse them meaningfully of error and some degree of irrationality. Global confusion, like universal mistake, is unthinkable, not because imagination boggles, but because too much confusion leaves nothing to be confused about and massive error erodes the background of true belief against which alone failure can be construed. (Davidson 1980, 222)

In interpreting the beliefs of another as intelligible, I must assume that the objects of his beliefs correspond well enough to the objects of my own to permit contrast on points where we plainly disagree. Much the same is true in interpreting another’s desires. In interpreting beliefs of another, we must, to make sense of exceptions, assume a pressure in the direction of logical consistency and a pressure in the direction of truth. In interpreting desires, to make sense of exceptions, we must assume a pressure in the direction of transitive consistency, and, although less so than in the case of belief, some core of intelligible similarity in desires, a pressure in the direction of agreement: “with desire as with belief, there is a presumption (often overridden by other considerations) that similar causes beget similar evaluations in interpreter and interpreted” (Davidson 1986, 208). These are known as Davidson’s principles of charity in radical interpretation. Radical interpretation is a thought experiment where we ask how we would interpret the action of a radically unknown agent, and charity means that we must initially attribute agent rationality in order to attain an interpretation. It may be objected that I misrepresent Riker. He did not say that it is impossible to know other minds, only that there are insufﬁcient data from voting choices to infer underlying preferences. He could say that we know others’ beliefs and desires well enough in private life and on the market, but not when we enter public life and the government. Incentives to misrepresent are at least as ubiquitous in private life as in public life, but leave

The doctrine of democratic irrationalism

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that problem aside. Riker’s claim is that if communication is limited to voting choice, then it is impossible to know underlying preferences. This may be so for each of our votes taken alone, but from that it does not follow that it is so for all of our votes considered together. A series of votes on similar issues would begin to generate enough data to allow inference of underlying preferences, presuming at the individual level logically consistent beliefs, their correspondence to objects, and transitively consistent desires, that are sufﬁciently similar. For example, suppose that we observe that a legislator votes for alternative C over alternative B in the ﬁrst stage of a plurality runoff among alternatives A, B, and C, and that alternative C wins the most votes in the ﬁrst stage. Then in the runoff between C and A we observe that the legislator votes for A, and that A is victorious in the runoff. So far, we have observed that the legislator chooses A > C > B. The next day a binary vote arises between alternatives B and C and the legislator votes for B over C , contradicting yesterday’s vote for C over B. At this point an observer can generate a number of hypotheses. Perhaps the legislator blundered or is irrational. If we assume that the legislator’s actions are rational, then one plausible hypothesis is that his true preference is B over C and that yesterday he was engaged in strategic (also termed “sophisticated”) voting: the legislator and his allies knew that the chamber’s distribution of preference orders was such that if they voted sincerely for B in the ﬁrst stage B would go into the runoff and defeat A their more favored alternative, so they strategically voted for C in the ﬁrst stage. Contrary to Riker, the possibility of manipulation has not obscured our inference of the legislator’s underlying preferences, rather, just the opposite, our knowledge of the possibility has enabled the inference of preference ranking. Now suppose that we are able to make a third observation and a fourth observation: the legislator votes for B over C and B over C . That strengthens the hypothesis that the legislator’s true preference is B over C. The foregoing is merely from assuming internal consistency of desires and understanding the logical properties of voting rules. Considerations of external consistency may improve the inference of an individual’s preference rankings. Suppose that alternative A is for high social-security payments, B is for medium social-security payments, and C is for low social-security payments. Then on the ﬁrst day’s vote we would be able to hypothesize that voting for C over B was strategic: although there may actually be occasional contexts where it makes sense to prefer high payments to low payments to medium payments, generally someone will prefer high over medium over low. Or suppose that alternative A is aid to the third world, B is labor organizing rights, and C is costly imperialist war

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Democracy Defended

memorials. From what we know about the coherence of ideologies we are again able to hypothesize immediately that the legislator’s true preferences are A > B > C and that his vote for C (imperialist war memorials) over B (labor organizing rights) was strategic in nature. The assumption of internal consistency alone permits some inference of underlying preference. Considerations of external consistency provide additional principles and data to ease the inference. Finally, public discussion surrounding the votes provides even more data with which to “triangulate” on a reading of others’ underlying preferences. Suppose that when the legislator voted for C over B he said out loud in a speech that his true preference is for B over C and that his vote was strategic in order to thwart the unfair attempt by the opposition to manipulate the outcome via agenda control. His announcement itself could have been a strategic lie, but it is a piece of evidence that gains strength from other considerations, for example if he later votes for B over C , or if he is known never to lie about such things. In discussion, individuals may sometimes misrepresent their desires and beliefs, but again enough must be true to give content to the rest (for a criticism of Rikerian skepticism about democratic discussion, see Mackie 1998). Sustained public deliberation over a series of contested issues involves a complex wealth of meanings that feeds intuitions about the intentions of others. The sum of evidence from all sources permits one to form judgments about what other people want and know, judgments that are fallible but reliable enough for human affairs. It is the peculiar misfortune of the skeptic that he is always forced to act as if his conclusions were false. The skeptical philosopher dresses warmly for cold weather and worries about what’s for dinner, even if all his experiences are just delusions. The skeptical political theorist infers preferences behind choices in every human situation, even, as it turns out, in making his case against the possibility of doing so. Riker uses the very methods of inference I have recited in his case studies that purport to demonstrate pervasive political disequilibrium and obscurity of preferences. I will argue that Riker’s inference of preferences in each of these cases was clearly mistaken, but that does not change my point against him on the knowability of preferences. My point is the transcendental one that he must assume that preferences are knowable in order to attempt his demonstration that they are not. Further, the fact that I am able to present reasoning and evidence that supports one hypothesized set of underlying preference rankings and undermines another hypothesized set of preference rankings shows again that inference of underlying preference from surface manifestations is not only possible but also a normal and uncontroversial everyday occurrence.

The doctrine of democratic irrationalism

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In his analysis of a 1956 Congressional vote over the Powell amendment involving school construction funds and school desegregation, Riker states: Since there were only two roll calls on the three alternatives, there is not enough information to specify complete preference orderings. But there is enough data from other roll calls in 1956 and 1957 and from the debate to show that some people probably voted strategically and that there were enough of them to generate a cycle. (Riker 1982, 153)

Riker’s further analysis of the Powell amendment makes an implicit auxiliary assumption that elected representatives represent the interests of their districts. He goes on to conﬁdently identify ﬁve “natural political groups”(!), almost the exact number of representatives in each group, and the preferences of each group over three alternatives (Riker 1986, 118–122). He seems to have forgotten, among other things, that on his account there is no such thing as a district interest that could be discovered by electing a representative. It is a delicious irony that his analysis is forced to assume that Congressional districts have identiﬁable interests. It was a similar problem, whether countries could be said to have an identiﬁable interest, that led Arrow down the path to his theorem which denied such a possibility (Amadae and Bueno de Mesquita 1999, 274). Yet, in his attempts to show the empirical relevance of Arrow’s logically possible result, Riker is forced to assume the empirical irrelevance of Arrow’s result. In another analysis, of the Wilmot Proviso, Riker conﬁdently identiﬁes eight factions and proposes an inference of the preferences of each over three alternatives: “There were not enough votes to ascertain preference orders, but it is easy to guess what they were” (Riker 1982, 227). Finally, from minuscule data in an obscure letter written 1,900 years ago by Pliny the Younger, Riker is able to identify and estimate the strength of three factions in the Roman Senate on an issue, involved in a process of voting that resulted in the socially better outcome, despite rampant manipulation: In general, parliamentary situations are like this. Leaders have the kind of [agenda-setting] power that Pliny exercised, but back-benchers can counter with strategic voting. So the fox can be outfoxed. And thus a balance can be maintained, often resulting, as here, in the selection of the . . . socially better outcome. (Riker 1986, 85)

There is one unfortunate difference between the skeptical philosopher and the skeptical political theorist. The philosopher would be ignored if he recommended that human institutions be designed as if his conclusions were true, but the political theorist might wrongly be heeded.

3

Is democratic voting inaccurate?

Democratic voting as inaccurate Simple majority voting on binary alternatives is not a problem for social choice theory, and indeed enjoys several desirable qualities that account for its paradigmatic appeal (May 1952; Rae 1969; Taylor 1969). Political issues are not somehow naturally binary, however, and all voting methods of reducing multiple alternatives to two alternatives are subject to manipulation. Thus, Riker (1982, 65–113) continues, fairness requires a decision rule that works with more than two alternatives. Any number of plausibly fair voting methods are available, but the problem is that, given a ﬁxed set of voters’ preference rankings, it is possible that the different methods would lead to different outcomes. The method of counting affects the outcome of counting; thus, voting does not accurately amalgamate voter’s values. For example, if preferences are as in Table 3.1, and if voting is sincere, then alternative A wins by plurality voting, B by plurality runoff, C by the Condorcet criterion, D by approval voting, and E by Borda count (Nurmi 1992, 465). The plurality rule is that the alternative with the most votes wins. If there were an election among alternatives A through E, those in the four-voter group would each cast his vote for A, those in the three-voter group would each cast her vote for B, and those in the two-voter group would each cast his vote for C: A gets the most votes (but not necessarily the majority) and thus is the winner under the plurality rule. The plurality runoff is a two-stage process. If one alternative wins a majority in the ﬁrst stage, that alternative wins the election; otherwise the top two vote-getters by plurality rule in the ﬁrst stage go on to face each other in the second stage. Here, the two winners in the ﬁrst stage would be A and B. For the second stage, four voters prefer A to B, but seven voters prefer B to A; thus B is the plurality runoff winner. The Condorcet winner is the alternative that beats all others in pairwise comparison. Refer to the pairwise comparison matrix in Table 3.2, which shows the number of votes a row alternative receives against each column alternative: B beats 44

Is democratic voting inaccurate?

45

Table 3.1. Five alternatives, ﬁve procedures, ﬁve winners 4 voters

3 voters

2 voters

A E D C B

B C E D A

C D E B A

Source: Nurmi 1992, 465.

Table 3.2. Five winners: pairwise comparison matrix and Borda count A A B C D E

5 5 5 5

B

C

D

E

(BC)

4

4 3

4 3 5

4 3 5 2

(16) (14) (21) (17) (22)

6 6 6

4 4

7

Note: Votes Favoring Row Alternative over Column Alternative. The rightmost column is the Borda count (BC), which is the row sum of the pairwise comparisons and alternative faces.

A by ﬁve votes, D beats B by six votes, E beats D by seven votes, and C beats E by ﬁve votes: C > E > D > B > A, and C is the Condorcet winner. In the proﬁle of voter preferences in this example there is a Condorcet winner and a transitive ranking of collective outcomes; this is not necessarily so for all proﬁles, as will be detailed below. Approval voting permits voters to cast a vote for each alternative that wins their approval. In this instance, assume that members of the four-voter group approve of the three alternatives they favor most: A, E, and D, and disapprove of the remainder; and that members of the other groups approve only of the two alternatives each favors most: B and C for the three-voter group; and C and D for the two-voter group. Now we just add up all approval votes for the result: alternative D wins with six approval votes, more than the votes received by any other alternative. Finally, if there are ﬁve alternatives as we have in this example, the Borda count assigns a score of zero to the last-ranked alternative, one to the fourth-ranked alternative, two to the third-ranked, three to the second-ranked, and four to the

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Democracy Defended

ﬁrst-ranked. The scores are summed and the alternative with the highest score is ﬁrst-place winner, and so on. The Borda count is also identical to the row-sums of pairwise comparison votes, as shown in Table 3.2. The Borda count assigns 22 votes to E the Borda winner, 21 votes to C, 17 votes to D, 16 votes to A, and 14 votes to B. Thus, from the same proﬁle of voter preferences, ﬁve different voting procedures, each of them reasonable and used in real-world contests, yield ﬁve different outcomes. The Borda count, which assigns one point (or any other equal interval) of difference between each alternative, is the most straightforward instance of a positional voting method. Plurality voting or negative plurality voting can also be construed as positional methods: plurality voting assigns one point to a voter’s top-ranked preference and zero points to her other preferences, and negative plurality voting assigns a zero vote to a voter’s bottom-ranked preference and one vote to each of her other preferences. An inﬁnite variety of positional methods is available; for example, suppose in our example above that instead of four points we assign seven points to the top-ranked alternative, and then the rest as in the Borda count – three to the second-ranked, two to the third-ranked, and so on. That method would yield A as a winner, in place of E the winner by the Borda count. There exist proﬁles of voter preferences that permit any outcome by monkeying around with positional weights. An example that would have delighted Riker: Saari (1995a, 112, 122) ﬁnds a 10-candidate voter proﬁle that permits 84,830,767 different election outcomes to arise by varying the choice of the positional method! Even if a method in wide use were justiﬁably fair, say in producing a Condorcet winner (the choice that beats or ties all other choices in pairwise comparison), Riker’s (1982, 66–114, 234–236) favored criterion, we would not be able to know that, because information on invisible preference orders is usually not sufﬁciently available from the visible data of voting choice, he argues. In other words, even if by luck we happened to possess an accurate voting method, it would not be possible for us to know that we did. Here Riker falls back, as usual, to his mistaken basic argument pattern. Possible but not probable It is possible that different methods will lead to different outcomes, but is it probable? Riker’s argument depends on demonstration of possibilities by example, but he concedes that: The moral and prudential standoff among methods would not in itself occasion difﬁculty for democratic theory if “most of the time” most methods led to the

Is democratic voting inaccurate?

47

same social choice from a given proﬁle of individual values . . . But it seems a safe conjecture that, if such a comparison [of commonly discussed methods] were made, the proportion of social proﬁles from which all the compared methods produced identical results would indeed be tiny. (Riker 1982, 235)

The evidence defeats Riker’s conjecture. We shall review studies that apply different voting rules to the same proﬁle of individual preferences, under different assumptions about the distribution of individual preference orderings. The ﬁrst assumption is that individual orderings are uniformly distributed, the second that such orderings resemble one another, and the third is the use of real data on voter preferences. Many of these same studies deal with the topic of the frequency of cycles, which will be considered in the next chapter. Nurmi (1992) tests the Condorcet efﬁciency (probability of a method selecting the Condorcet winner when one exists) of widely used voting methods by computer simulation. The impartial-culture assumption is widely used in simulations: every logically possible preference order is considered equally likely; or, given a number of alternatives A, all voters 1 are assigned with probability A! to each of the A! possible strict preference rankings over A (Nurmi 1992, 461). Under the impartial-culture assumption, the Condorcet efﬁciency of commonly used voting rules generally decreases with an increase in the number of alternatives, and decreases more slowly with an increase in the number of voters. For example, assuming an impartial culture, the plurality runoff with three alternatives and 5 voters has a Condorcet efﬁciency of 98 percent, with three alternatives and 999 voters 96 percent, with seven alternatives and 5 voters 77 percent, and with seven alternatives and 999 voters 67 percent. Discrepancies in choice between any two voting rules also generally increase with an increase in the number of alternatives, and increase more slowly with an increase in the number of voters. “Impartial-culture” assumes that each possible preference order among alternatives is equally probable, and thus that preferences have no relationship to any substantive considerations: one person prefers A, personal prosperity to B, the torture of kittens, to C, suicidal nuclear war, but each of the ﬁve remaining permutations of strong preferences is equally probable, for example, that another person prefers suicidal nuclear war to the torture of kittens to personal prosperity, and another the torture to nuclear war to prosperity, and so on. Even under the impartial-culture assumption, reasonable voting rules (Borda, plurality runoff, Hare, Coombs, but not plurality) applied to the same proﬁle of voters’ preferences tend to identical outcomes for three, four, or ﬁve alternatives and many voters. Plurality rule performs worst of all as numbers

48

Democracy Defended

of alternatives and voters increase, as one would expect; and unlike other rules the Borda count retains high Condorcet efﬁciency even as the number of alternatives greatly increases. The estimates of Condorcet efﬁciency and of choice discrepancies are similar under a bipolar-culture assumption (the ﬁrst third of the electorate has one preference order, the second third is assigned the impartial-culture assumption, the third has preferences in reverse order of the ﬁrst). However, a slight perturbation of impartial-culture towards unipolarity (assigning 5 percent of voters to identical preferences and 95 percent to impartiality under a ﬁrst condition, or 10 percent to identical preferences and 90 percent to impartiality under a second condition) makes a large difference, generally increasing the Condorcet efﬁciency of voting rules, and reducing the discrepancies between rules as the number of voters increase, both effects approaching perfection with the increase from 5 to 10 percent unanimity. For example, with seven alternatives and 999 voters, the Condorcet efﬁciency of the plurality runoff is 67 percent under impartial culture, is 96 percent under the 5 percent unanimity condition, and is 100 percent under the 10 percent unanimity condition (Nurmi 1992, 478, interpreted from Figure 7). Under the 10 percent unanimity condition, and assuming 999 or more voters and even up to 15 alternatives, there are zero choice discrepancies between plurality runoff and Hare’s system, and between six of the pairwise comparisons among Hare’s, Coomb’s, Nanson’s, and Copeland’s voting systems. Merrill (1988) conducted simulations using both impartial culture and, in a spatial model, multivariate normal distributions across dimensions. He tested both the Condorcet efﬁciency and the social utility efﬁciency of various voting rules under different assumptions. When candidate dispersion is equal to voter dispersion, then Black (a Condorcet-consistent rule which decides cycles by the Borda count – thus almost identical to Condorcet), Coombs, and Borda are of high Condorcet efﬁciency; Hare, plurality runoff, and approval are intermediate; and plurality is low. If candidates are less dispersed, more central, than voters, then Condorcet efﬁciency drops drastically for Hare, plurality runoff, and plurality. The simulated voters possess Von Neumann–Morgenstern utilities, and social utility of a candidate is the sum of all voter utilities for that candidate, arguably a more appropriate baseline than Condorcet efﬁciency. Social utility efﬁciency is highest (in the high 90s) for Borda, Black, approval, and Coombs procedures, lower for Hare and plurality runoff, and lowest for plurality (37). Such efﬁciency does not decrease with an increase in number of candidates for Borda, Black, approval, and Coombs; decreases with Hare and plurality runoff, and dramatically decreases with

Is democratic voting inaccurate?

49

plurality (36). Social utility, Condorcet (Black), Borda, approval, and Coombs yield almost identical results. These ﬁndings are strong under impartial culture, and much stronger under more natural multivariate normal distributions. Gehrlein (1995; see also 1997) is able to estimate analytically the relationship between Condorcet efﬁciency and social homogeneity. The more similar are voter’s preference orders, the more likely is it that a Condorcet winner exists. Further, for plurality rule, Borda count, and plurality runoff, Condorcet efﬁciency increases as voter homogeneity increases (negative plurality – vote against your least-favored candidate – is less Condorcet-efﬁcient as homogeneity increases). For lower levels of homogeneity, Borda count is more Condorcet-efﬁcient than plurality; at modest levels of homogeneity, plurality, Borda, and plurality runoff rules display high Condorcet efﬁciency; at higher levels of homogeneity, plurality is more Condorcet-efﬁcient than Borda count; at all levels of homogeneity, plurality runoff is more Condorcet-efﬁcient than either plurality or Borda. The simulations of Merrill and of Nurmi and Gehrlein’s estimates are robust enough to defeat Riker’s conjecture, and thus Riker’s dismissal of majoritarian democracy as necessarily inaccurate. We seldom possess ﬁrm data on voter’s preferences over all alternatives because the plurality methods we often use do not record them. Chamberlin, Cohen, and Coombs (1984) were able to obtain data on 5 different presidential elections of the American Psychological Association (APA), each involving 11,000–15,000 voters rank-ordering 5 candidates. The APA is an organization with cleavages: roughly half its members are academic psychologists and half are nonacademic psychologists, and further there are the theoretical, methodological, topical, and political divisions usual in a social science. We will also discuss the APA study in the section on cyclical majorities, for now we will look at the results the study obtains from hypothetical application of different voting rules to these real-world preferences. The authors use the Condorcet pairwise ordering as a baseline (there were no cyclical majorities present), and compare results that would obtain by applying plurality voting, Borda count, the Hare method, the Coombs method, approval voting with two votes per voter, and approval voting with three votes per voter. The various methods failed to select the Condorcet winner about 20 percent of the time; when they failed, however, they always picked the second-ranked candidate by the Condorcet ordering. The various methods also deviated from the complete Condorcet pairwise majority ordering about 20 percent of the time. All methods ranked the same two candidates ﬁrst or second 85 percent of the time. Some methods were better than others. Plurality rule deviated the most from the Condorcet winner and from the Condorcet

50

Democracy Defended

ordering, while Borda count and approval voting with two votes per voter were quite close to the Condorcet outcome. Feld and Grofman (1992) also examine rare data on full-rank ordering of multiple candidates from 36 elections held by nongovernmental associations in Great Britain, which also will be more fully presented in the discussion of cyclical majorities below. Voters per election ranged from 9 to 3,422 and candidates ranged from 3 to 29. Each election had a Condorcet winner. The Borda winner was the Condorcet winner in 34 out of 36 elections. Borda rankings differed from Condorcet rankings by about 6 percent. Levin and Nalebuff (1995) used some of the same data to compare nine different voting rules: plurality, single transferable vote, Borda, Copeland, min–max, Kendall–Wei, power ranking, minimum violations, and Young–Kemeny. All rules obtained similar results except for plurality; when rankings differed from one another it was because of a cycle somewhere in the ordering, but even then rules picked the same winner. “When voter preferences are sufﬁciently similar, a variety of voting systems lead to similar choices, and these choices have desirable properties,” they conclude (4). Felsenthal, Maoz, and Rapoport (1993) examine a mostly overlapping set of elections using a different approach. They argue that the Copeland method should be the normative baseline. The Copeland method selects the alternative which scores highest on the Copeland index, which for alternative x is the number of times x beats other alternatives minus the number of times x loses to other alternatives. The Copeland method gives the same result as the Condorcet method when there are not cycles, but provides an order when Condorcet reports cycles. They compared rankings by the Copeland method to ﬁve other voting rules: plurality with one vote, plurality with several votes, approval voting, the Borda count, and the repeated alternative vote procedure. Most of the elections under consideration were to ﬁll more than one post. Plurality with one vote allocates each voter one vote even if there are several slots to ﬁll. Alternatively, plurality with several votes allocates each voter one vote per slot to ﬁll. Approval and Borda we have already encountered. In the repeated alternative-vote procedure, a variation on the Hare procedure, each voter ranks at least one and as many of the competing candidates as she wishes. The votes are counted and if there is a majority winner then she wins. If not, then the candidate who is ranked ﬁrst in the fewest ballots is dropped from all the ballots, and the vote recounted. This process is reiterated until there is a majority winner (or a tie, randomly broken). If there is more than one slot to ﬁll, then the procedure is repeated on remaining candidates to ﬁll the second slot, then repeated on remaining candidates to ﬁll the third slot, and so on. The authors apply the six voting rules

Is democratic voting inaccurate?

51

to the proﬁles in each election, and then (Spearman rank-order) correlate the rankings generated by the Copeland method against the rankings generated by each of the ﬁve remaining voting rules. The median correlation between Copeland and plurality with one vote is 0.857, not bad but nevertheless the poorest performance, and this is not surprising as we know that plurality performs poorly with more than a few candidates (there was a median of nine candidates in these elections). The median correlation between Copeland on the one hand, and plurality with several votes, approval voting, Borda count, and repeated alternative vote on the other hand, was, respectively, 0.953, 0.976, 0.977, and 0.963. They also identiﬁed the candidates who would have won available slots under each of seven voting rules, and with Copeland as the baseline, measured the percentage of identical winners selected: 76.0 percent for plurality with one vote, and for plurality with several votes, approval voting, Borda count, repeated alternative vote, and single transferable vote, respectively, 88.8 percent, 89.8 percent, 89.0 percent, 90.7 percent, and 85.6 percent. In other words, the different procedures yielded virtually identical rankings and virtually identical winners (in elections with only three candidates the six methods were wholly identical in rankings and winners). They also measured the methods against other desiderata, such as whether they pick the Condorcet winner, or avoid the Condorcet loser. The methods do so from 35 out of 35 elections to 32 out of 35 elections, and again plurality with one vote is the worst performer. The mildly worse performance on all indicators by plurality with one vote for more than three candidates is something of an artifact, I believe. The data are from elections held under voting procedures which encourage large numbers of candidates. An actual election held under plurality rule with one vote would strategically induce a great reduction in the number of candidates, and plurality is more accurate the lower the number of candidates. Felsenthal and Machover (1995) explore an expanded list of 92 real elections that contains the 37 studied in Felsenthal, Maoz, and Rapoport (1993). They compare Condorcet winners and losers on the one hand to plurality voting, single transferable vote, and Borda count on the other hand. Plurality either fails to select Condorcet winners or does select Condorcet losers in 4.82 percent of instances, single transferable vote in 11.19 percent, and Borda count in 3.51 percent. Some of the elections studied select one winner, others from two to twelve winners. The Borda count’s fault rate was 9.52 percent for elections with one winner, but was much more well-behaved for elections with more than one winner. They also compare plurality, single transferable vote, and Borda by a measure of Copeland efﬁciency. The Borda count is, again, the best performing method.

52

Democracy Defended

Regenwetter and Grofman (1998) deploy a probabilistic model to infer underlying rankings from votes cast in elections decided by approval voting. The model was compatible with data in 7 of the 10 elections studied. The Borda ranking was identical to the approval-vote ranking in all 7 elections. The Condorcet ranking tended to be the same as the Borda and approval rankings. Regenwetter and Grofman conclude that what I call the irrationalist interpretation of social choice theory is “overstated” (530). They quote Tanguiane (1991) with approval: Many voting and decision making procedures proved to be efﬁcient for practical needs although they were poorly justiﬁed. The gap between theory and practice can be explained by the fact that every real situation deals with restrictions ignored by theory.

They argue that empirically testable cognitive models of social choice tested against real data should complement the purely theoretical models of social choice tradition. Kurrild-Klitgaard (2001b) directly examines Riker’s inaccuracy hypothesis with data from the Danish national election surveys. Randomly sampled respondents are asked to provide thermometer rankings on various Danish political topics. From the thermometer data, KurrildKlitgaard constructs rankings that would result from the application of up to seven voting procedures: Condorcet; plurality; Borda; the cumulative method (each voter is assigned the same number of points, say 100, to assign as she pleases across the alternatives; alternatives are ranked by total sum of points across voters); Bentham method (straight off the thermometer rankings); the Nash method (same as Bentham, but instead of adding voters’ point assignments, multiply them); approval voting assuming top two alternatives are approved; and approval voting assuming top three alternatives are approved. Rankings by all methods across all topics are virtually identical, and as usual plurality is the weakest performer. I shall calculate Spearman rank-order correlation in order to compare the results: 1.0 means perfect agreement in ranking; 0 means no relation in ranking; and −1.0 means perfect disagreement. Respondents ranked 11 parties in 1973, 9 in 1994, and 11 in 1998. I take the approximation of Benthamite utility as the normative baseline. For all three years rankings by Bentham, Condorcet, and Cumulative were identical; Borda was identical except for transposition of second and third places in 1994 (Spearman correlation −0.98). Spearman correlations for the Nash method were 0.99 (1973), 0.98 (1994), and 1.0 (1998); for approval with three votes from 0.95 to 1.0. Plurality was the worst performer: 0.68 in 1973, 0.78 in 1994, 0.85 in 1998.

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Table 3.3. Convergence of voting rules, Danish leaders Correlation with Bentham

1973

1994

1998

Condorcet Cumulative Borda Nash Plurality Approval (3)

0.98 0.99 1 0.99 0.72 0.95

1 1 1 0.88 0.76 0.95

1 1 1 0.96 0.88 0.96

In 1994 respondents ranked the policies of the 7 parties represented in Parliament. Bentham, Condorcet, Cumulative, Borda, and approval with three votes were identical (1.0), Nash was 0.96, and plurality was 0.86. Respondents ranked the leaders by name of 10 parties in 1973, 8 in 1994, and 10 in 1998. In Table 3.3, I present the Spearman correlations of various voting rules with the Bentham baseline. Respondents ranked the importance of 28 issues in Danish politics in 1987/1988. The correlation with Bentham was 0.98 for Condorcet, 0.95 for plurality, 0.98 for approval with three votes. Respondents ranked four important goals in 1994. The ranking by Bentham, Condorcet, plurality, and approval with two votes was identical. Voters ranked 12 public budget alternatives in 1990 and 20 such alternatives in 1994. We can reconstruct a ranking by the Condorcet method, by the plurality method (percent who say that too little is spent), and a third measure (percent who say too little is spent minus percent who say too much is spent). Rankings over the 12 alternatives in 1990 were identical across the three methods. Rankings over the ﬁrst 14 of all 20 alternatives in 1994 were identical, but there was a Condorcet cycle over alternatives 15–18. The Cambridge City Council is one of the few jurisdictions in the United States to use Hare preference voting, also known as the alternative vote or instant runoff when used to elect one candidate and as the single transferable vote when used to elect several candidates from the ﬁeld. Preference voters are required to rank-order candidates. Dave Robinson, information vice president for Californians for Electoral Reform, a group advocating proportional representation in American elections, hypothetically applied alternative voting rules to the votes cast in the 1999 Cambridge election, and posted his results to the organization’s webpage (www.fairvoteca.org/learn/cambcomp). There were 18,777 votes, which selected 9 councilors from a ﬁeld of 24 at-large candidates. The results by preference voting (Droop method) were identical to those by

54

Democracy Defended

preference voting (Hare method). Other methods – a simulation of conventional single-member-district plurality, single-member district plurality runoff, at-large plurality with one vote, and at-large plurality with nine votes – either were identical or differed by only one candidate from the preference-voting outcome. One could still favor preference voting on other grounds, for example, if it created a greater sense of legitimacy, increased voter turnout, or elicited a more moderate set of candidates. Finally, in the climax to his volume (1982, 227–232), Riker claims to show that the election of Abraham Lincoln in 1860 was the result of a cycle among the electorate and that different reasonable voting rules would have yielded different outcomes from the same proﬁle of preferences that he estimates. I shall show in detail below that the proﬁle he estimates for the Lincoln election is at its most important point erroneous, and thus that his claim that the 1860 election would yield different outcomes by different voting rules is mistaken. We know that to some extent alternatives are endogenous to voting rules, such that one voting rule might elicit different alternatives for consideration than another voting rule. When we hypothetically apply different voting rules to a set of preferences actually elicited by a particular voting rule, we are neglecting to consider the endogeneity of preferences. A critic could press that it is possible that somehow taking into consideration the strategic interdependence between rules and alternatives would decrease the convergence of outcomes that we ﬁnd when applying voting rules hypothetically to data on real preferences. We could respond that it is possible that such consideration would rather increase the convergence among voting rules, and indeed, that is my conjecture. If the critic pressed harder, we could reply that if endogeneity is a major problem for the comparisons that demonstrate convergence, then that would count more heavily against Riker’s claim of arbitrary divergence, because the slim and speculative evidence he produces – mostly contrived examples that show the logical possibility of divergence – ignore the endogeneity problem as well. If endogeneity bites, then no contrived example is persuasive. Even with the implausible assumption of impartial-culture, the reasonable voting methods converge when there not too many alternatives or too many voters. Convergence improves when resemblances among individuals’ preference orders are admitted, and improve further when real data are used. Further, it turns out that the impartial-culture assumption misleads us about what happens as the number of voters increases. Given certain assumptions, the Bentham method of summed cardinal utilities, Condorcet pairwise comparison, and the Borda count, almost certainly produce the same results as the number of (independent) voters increases,

Is democratic voting inaccurate?

55

according to Tangian (2000). What are the assumptions? There is more convergence as (1) the number of voters increases, (2) the distribution of voters’ preferences departs from the impartial-culture assumption, and (3) the less indifference there is among voters about the alternatives. Next, List and Goodin (2001) extend the Condorcet jury theorem to more than two alternatives. Suppose along with epistemic democrats that the aim of democracy is to track the truth about the general will or the public good. The jury theorem assumes that independent voters are better than random in selecting the true choice; this amounts to a departure, even if slight, from the impartial-culture assumption. If so, then commonly discussed voting rules – plurality, Borda, Condorcet, Hare, Coombs – are each good at tracking the truth, and further all are almost equally good at doing so, again as the number of voters increases (but plurality is not quite as good as the others). “We can afford to be relatively relaxed about [choice of voting rule] from an epistemic point of view” (294), they conclude. Finally, recall that Merrill’s (1988) simulations showed nearly identical performance by social utility, Condorcet, and Borda. Riker’s conjecture is that it is not the case that most of the time most reasonable voting methods lead to mostly the same outcomes. The evidence at hand is overwhelming that the conjecture fails. What is arbitrary? Are some voting rules better than others? Quite deﬁnitely so. The rule that Gerry Mackie decides everything is popular in some quarters but does not enjoy widespread acclaim. We want voting rules for free and equal citizens, and we are seeking a rule that is, one way or another, accurate and fair. Simple majority vote over two alternatives is not afﬂicted with the perversities identiﬁed by social choice theory, and possesses several properties: it is decisive (an alternative wins, loses, or ties – although, as the Bush–Gore race shows, a tie result may be frustrating); it is anonymous in that if voters trade names the result is unchanged (that is, it treats all voters alike and the Mackie rule is thus disqualiﬁed); it is neutral in that if alternatives trade names the result is unchanged (it does not privilege any alternatives – even if some, such as rights, should be privileged); and it is strongly monotonic (positive responsiveness), that is, if an alternative X is among the winners and if one voter changes her vote to X then X becomes the unique winner. Those four properties uniquely identify majority rule over two alternatives, but only because of the strong monotonicity requirement. The uniqueness claim for majority rule over two alternatives is much exaggerated in the literature. Several other voting

56

Democracy Defended

rules that operate over two or more alternatives (for example, the Borda count) are decisive, anonymous, neutral, and weakly monotonic (nonnegative responsiveness): if an alternative X is among the winners and if one voter changes her vote to X then X does not become a loser, it should never hurt an alternative to get more support. There is certainly a distinction between positive responsiveness and nonnegative responsiveness, but not much of one. Positive responsiveness says that if there are a million voters for Bush and a million for Gore, and one voter switches from Gore to Bush, then Bush wins – but this seems to be a formal rather than a substantive victory. Nonnegative responsiveness says that if there were a voting rule such that an increase in votes for Bush would make Bush the loser, then we would assess a defect in the voting rule – intuitively more compelling than positive responsiveness (see Nurmi 1987, 67). Further, it is possible, by varying the selection of axioms, to select any one of a number of voting rules as unique, for example, Young–Kemeny is the only rule that is anonymous, neutral, Pareto, and satisﬁes reinforcement and local independence of irrelevant alternatives (Young 1988); Borda the only rule to satisfy axioms labeled neutrality, cancellation, faithfulness, and reinforcement (Young 1974); and so on. Riker (1982, 99–101) proposes some additional criteria for evaluating voting rules: that the Condorcet criterion – rank alternatives by pairwise comparisons (if such a ranking exists) – should be the normative baseline; reinforcement, such that if two subgroups approve an alternative then so should the full group voting together; and independence of irrelevant alternatives (the social choice between two alternatives would not change if individual preferences over some third alternative were to vary, which I shall discuss below with respect to the Arrow theorem). Further desiderata might include contraction consistency (if a is the choice from {a, b, c} then a is the choice from {a, b}), and whether the rule picks the majority ( 12 + 1) winner. No rule I list satisﬁes Arrow’s strong independence of irrelevant alternatives condition, except that majority rule over two alternatives satisﬁes it trivially merely because it is limited to two alternatives. It trivially satisﬁes many of the conditions. Most rules of interest for three or more alternatives are Condorcet-consistent rules, positional (or scoring) rules (see Moulin 1988; Young 1988; Saari 1995a), or elimination rules such as plurality runoff and Hare. Positional rules satisfy decisiveness, anonymity, neutrality, weak monotonicity, and reinforcement, but not always the Condorcet criterion. Of the positional rules (including plurality), the Borda count may be most favorably distinct: it is the positional rule most likely to satisfy the Condorcet criterion, it is the one least likely to be subject to manipulation by small numbers of voters, it is the

Y

Y Y N

Y Y Y

Y Y

Y Y Y

N N Y

Y Y

Anonymous

Y

Decisive

Y Y

Y Y Y

Y Y Y

Y

Neutral

N N

Y Y Y

Y Y Y

Y

Weak Monotonic

Y Y

Y Y Y

Y N N

Y

Picks 50 percent + Winner

N N

Y Y Y

N N N

Y

Picks Condorcet Winner

N N

N N N

N N Y∗

Y

Contraction Consistency

N N

N Y N

Y Y Y

Y

Reinforcement

Note: Y means the voting rule in the row satisﬁes the axiom in the column, N means it does not. N means that failure is logically possible, but not necessarily empirically probable. ∗ = only if voter preferences “dichotomous.” Sources: Moulin 1988, Nurmi 1987, Nurmi 1998, Riker 1982, Young 1988.

Majority rule: 2 alt’s Positional: Plurality Borda Approval Condorcet-consistent: Condorcet Young–Kemeny Schwartz Elimination: Plural runoff Hare

Criterion Rule

Table 3.4. Some axiomatic properties of some voting rules

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Democracy Defended

Table 3.5. Pairwise comparison matrix to illustrate Young–Kemeny rule A A B C

27 35

B

C

33

25 42

18

one least likely to select a different winner if an alternative is dropped (Le Breton and Truchon 1997). The pure Condorcet method satisﬁes anonymity, neutrality, and monotonicity, but does not satisfy decisiveness or reinforcement if there is a cycle present. Condorcet-consistent rules generate the same ranking as pairwise comparison where there are no cycles, and each differs in the way it decides cycles. The Schwartz (1982) rule counts cycles as ties. Of the Condorcet-consistent rules, the Young– Kemeny rule may be most favorably distinct (Young 1997 dubs it the maximum likelihood rule; others have named it the Young–Kemeny rule; see Risse 2001 for arguments for its distinctiveness and Saari 2003 for a reply). The Young–Kemeny rule selects the ranking supported by the most number of votes in all pairwise comparisons within the ranking. Young–Kemeny agrees with Condorcet order when that exists, and, as does the Borda count, decides a cycle (it may report a cycle as a tie, which we count as decisive). For example, suppose a proﬁle of voters that gives rise to the pairwise-comparison matrix in Table 3.5 (Young 1997). There is a cycle: A > B > C > A. For any election with three alternatives there are six possible preference rankings: A > B > C; C > A > B; B > C > A; C > B > A; A > C > B; B > A > C. To ﬁnd the Young–Kemeny score for one of the six possible rankings, say A > B > C, we sum the number of pairwise votes for each of A > B, B > C, and A > C (33 + 42 + 25 = 100). We do this for all six rankings and discover that the ranking B > C > A has the highest sum (42 + 27 + 35 = 104) and this ranking is thus the Young–Kemeny ranking. The Young–Kemeny result can also be found by breaking the cycle at its weakest link: in the cycle here – A > B by 33 votes, B > C by 42 votes, and C > A by 35 votes – A > B is the weakest majority in the cycle A > B > C > A, hence we reverse the weakest majority from A > B to B > A and the noncyclical ranking B > C > A is our result. The Young–Kemeny rule satisﬁes anonymity, neutrality, and reinforcement. It also satisﬁes a condition labeled local independence of irrelevant alternatives, that is, it is not susceptible to manipulation by the addition or deletion of alternatives either above or below

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the given set of alternatives (but is still susceptible to such manipulation in between, as it were). Rules that are used in real-world settings include plurality, plurality runoff, variations on Hare, and, more rarely, approval and Borda count. The plurality rule was the weakest performer in the various simulations as the number of alternatives increased, and for good reason. Plurality rule has the virtue of being extremely simple for the voter and for the organizer of elections, works adequately if there are fewer alternatives and larger agreement among voters across the alternatives, but may err when there are more alternatives and larger disagreement among voters. Such errors appear now and then in American candidate elections (but such errors do not appear often, because plurality rule in single-member districts tends to strategically elicit no more than two candidates, an effect not captured by the simulations). In the American context, plurality-rule situations will be found when there is not a majority winner in a primary election (the ﬁrst stage of a plurality runoff when there are two parties in the general election) or when there are third or nth parties running in a general election and no majority winner amongst the candidates. I managed a campaign in a local nonpartisan primary election among fourteen candidates that resulted in the forwarding of two candidates to the general election whose selection made no sense to anybody on the scene save perhaps to the spouses of the two victors, and the spouses’ admiration was probably motivated by loyalty alone. In the 1972 Democratic primary elections McGovern beat Muskie by plurality rule, went on to win the Democratic nomination, and then was steamrollered in the general election against Republican Nixon. Because McGovern was the top choice for some Democratic primary voters but the bottom choice for many, Muskie would have beaten McGovern in the primary election under plurality runoff, Borda count, or the Condorcet criterion (Joslyn 1976, as reported in Mueller 1989, 122), and as more of a centrist probably would have done better against Nixon. In the 1970 presidential election in Chile, leftist Allende won with 36 percent of the vote, the centrist with 28 percent, and the rightist with 35 percent (Merrill 1988, 4), and Allende’s government and Chilean democracy shortly died at the hands of a rightist military coup. Colman and Pountney (1978) look at the 266 British members of Parliament in the 1966 general election who won by a plurality but not a majority of votes cast. They estimate that 15 of the 266 were Condorcet losers, that is, they would have ranked last if measured by the Condorcet method. Why does plurality rule tend to be unrepresentative as the number of alternatives increases above two? Because it throws away a lot of information about voters’ preferences. Suppose an election by plurality rule among

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Democracy Defended

three candidates: Rapscallion (A), Tweedledum (B), and Tweedledee (C). Six voters prefer A > C > B, ﬁve voters prefer B > C > A, and four voters prefer C > B > A. Tweedledum and Tweedledee espouse similar policies preferred by a strong majority of the population; Rapscallion espouses policies that motivate a minority at the expense of the majority. Plurality rule selects A, Rapscallion, and ranks the candidates A > B > C. Now let’s see what happens if the candidates face each other in pairwise contests. Nine out of the ﬁfteen voters prefer Tweedledum, B, to Rapscallion A. Ten of the ﬁfteen voters prefer Tweedledee, C, to Tweedledum, B. The results by Condorcet pairwise comparison (and by Borda count) are C > B > A, just the opposite of the plurality ordering. To make things worse, suppose that Rapscallion and his cronies entered the race only because they thought they would win under plurality, and would have stayed out otherwise – the majority has been thwarted. A different rule, plurality runoff, forwarding the two top plurality winners to a runoff election, will usually produce the Condorcet winner, and so is less vulnerable to minority outcomes than pure plurality. Unfortunately, in the Rapscallion example, plurality runoff happens to yield a ranking of B > A > C. The prospect of that outcome should deter Rapscallion A from entry, however; if so, then Tweedledee (C) would beat Tweedledum (B). Plurality runoff, an elimination rule, is a familiar method, so I will say no more about it. Imagine that we want to rank the quality of students in a school (example adapted from Saari 1995a). If the grading system is binary, such that for each course a student gains a pass or a fail, the obvious way to rank students is by the number of pass grades received (resembling majority rule over two alternatives). Suppose, however, that the grading system is rather the American one of A, B, C, D, and F, and that each student accumulates 30 courses over four years. Now, if we rank students only by the number of As they receive, the outcome of such plurality grading does not have to be fair, its fairness depends on how grades are distributed. If there are obvious top choices, one or two students who have attained 30 out of 30 As, then plurality grading picks the winners, but the remainder of the rankings might not be that fair: someone with one A and 29 Fs would outrank someone with 30 Bs. If there are not obvious top choices, then the potential for unfairness extends to the winners: someone with 15 As and 15 Fs beats someone with 14 As and 16 Bs. Using the Borda count to rank alternatives resembles using the grade point average to rank students: zero points are assigned for each F, one point for each D, two points for each C, three points for each B, and four points for each A (and so on, for more than ﬁve alternatives). If we only want to single out the top student, then plurality grading and Borda grading (grade point

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average) will yield similar results some of the time, but not all of the time. Notice also that different grading systems have different incentives, just as different voting systems can elicit different behaviors from candidates; for example, under plurality grading students would be more likely to seek easy courses and avoid hard courses (because a B under GPA would be the same as an F under plurality, it is foolish to risk a B). The plurality rule discards considerable information; but the Borda count utilizes all ranking information. Riker, Arrow, and many others, believe that the Condorcet criterion (the ranking, if it exists, that results from pairwise comparison of the alternatives) should be the normative baseline. However, there are strong arguments in favor of the Borda count as a normative baseline (Le Breton and Truchon 1997 calculate the Borda-efﬁciency of various voting rules). I agree with Dummett (1998) that: with reservations, the Borda count is in principle at once the best tool for reaching the decision most likely to be correct when the object is to reconcile different judgments about effective means to a common aim, and the most equitable method of determining a resultant of divergent desires.

Saari (1995a) uses accessible geometric methods that unify and simplify much of social choice theory; and his work argues, given ordinal data, that the Borda count is ideally “the unique procedure which always respects the ‘will of the people.’” His formal work is extended in Saari (2000a; 2000b, among others), and popular expositions, well worth a look, may be found in Saari (2001a; 2001b). One problem with the Condorcet criterion is that it is indecisive in the face of cycles (the possibility of a cycle is a consequence of insisting on the Condorcet criterion). Another problem with the Condorcet criterion is that it throws away information about preference rankings, sometimes with consequences that are intuitively undesirable. Here is an example. Suppose that 1,001 voters favor A > B > C and 1,000 voters favor B > C > A. Alternative C is no better than middle for all voters: it is the last choice of 1,001 voters and the middle choice of 1,000 voters, so is clearly not a contender. Alternative A is the ﬁrst choice of 1,001 voters but the last choice of 1,000 voters. Alternative B is middle or better for all voters: the middle choice of 1,001 voters and the ﬁrst choice of 1,000 voters. The Condorcet order awards the contest to A, the candidate ranked worst by almost half the population, rather than B the obvious Borda winner (adapted from Saari 1995a, 79). Riker’s argument for the Condorcet criterion is that “when an alternative opposed by a majority wins, quite clearly the votes of some people are not being counted the same as other people’s votes” (1982, 100). The same complaint can be lodged against the Condorcet criterion

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Democracy Defended

Table 3.6. Borda reversal 3

2

2

Y C B A

A Y C B

B A Y C

A A B C Y

5 3 3

B

C

Y

(BC) ABCY

(BC) ABC

2

4 2

4 2 0

(10) (9) (8) (15)

(6) (7) (8)

5 5

7

in this example, however. The fact that almost half the voters rank the Condorcet winner last is not being counted by the voting rule: B-voters’ bottom ranking is not treated “equally” with A-voters’ top ranking. Since Riker’s principle that some people’s votes be counted the same as other people’s votes can be construed to support both the Condorcet criterion and the Borda count, if not other voting rules, the principle fails to identify the Condorcet criterion as a uniquely justiﬁed and therefore superior voting rule. One major practical allegation against the Borda count is that it is sensitive to manipulation by the adding and dropping of alternatives (although it is least sensitive of all positional methods, including plurality, to such manipulation). Here is an example (adapted from Riker 1982, 92). Suppose the voter proﬁle and the resultant pairwise comparison matrix are displayed in Table 3.6. The Borda ranking for the four alternatives is Y > A > B > C. Suppose that alternative Y is removed. Removing an alternative shouldn’t make a difference (contraction consistency). With Y removed, the Borda ranking for the remaining alternatives is now exactly reversed: C > B > A. (Condorcet ordering stumbles on this proﬁle as well: it reports a cycle among either A > Y > C > B > A or A > C > B > A ). The Condorcet order, however, violates reinforcement. Suppose there is a club with two divisions, ten members in one and nine members in another, and there is a choice among three alternatives. In the Western division, six voters prefer B > A > C, and four voters prefer C > A > B. Reasonably democratic voting rules, including Condorcet pairwise

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comparison, select B as the winner in the Western division and rank the alternatives B > A > C. In the Eastern division, nine voters fall into three symmetric groups: three prefer A > B > C; three prefer C > A > B; and three prefer B > C > A. This is a cyclical proﬁle with an equal number of voters for each ordering, so a pairwise comparison would report that A > B > C > A, Borda count a tie, and Young–Kemeny a tie. Perhaps because of the confusion in the Eastern Division, the whole club of 19 members meets and votes together. The three blocs in the Eastern Division neatly cancel each other out, so why should they change the unequivocal result from the Western Division when the club votes as a group together? Under the Borda count, the outcome for the whole club is the same as that for the Western Division, B > A > C; adding the tied cyclical preferences from the Eastern Division changes nothing. By pairwise comparison, however, the outcome for the whole club is A > B > C > A, a cycle (the Young–Kemeny rule is tied between A > B > C and B > C > A). Under Condorcet ordering, what happened to the unequivocal ranking from the Western division? It’s as if by some magical stunt it has vanished. (Saari 1995a, 51–54 shows an easy way to construct examples like this). The Borda count and perhaps Young–Kemeny may be the most favorably distinct voting rules. How do they fare with respect to truth and fairness of amalgamation? First, truth: suppose that voting is an epistemic exercise, that there exists a best or correct decision for the decision-making group that the group seeks to identify by some method of voting. Say that each voter has the same probability p ( 12 < p < 1) of being correct. For two alternatives, simple majority rule is most likely to identify the correct outcome, according to Condorcet’s jury theorem. If the voters are on average better than chance in identifying the most correct of the two alternatives, and if voters’ judgments are independent, then the more voters there are the more likely correct is the aggregate judgment.1 For three or more alternatives, Young (1988, 1997) has demonstrated that the Young–Kemeny rule is the method with the maximum likelihood of identifying the correct ranking of alternatives. The story is a bit different if the task is to select the probably best choice rather than to choose the probably best ranking. Choosing the candidate with the highest probability of being best is not necessarily the same as selecting the most highly ranked alternative from the most probable ranking of alternatives. If p, the voters’ probability of being correct, is closely above one-half, then the Borda count is the method most likely to identify the best choice. If p is near 1, then the Young–Kemeny method is most likely to identify the best choice; although, as Young points out, if p is near 1, it is still very likely that the Borda winner is the best candidate even though strictly speaking

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not the optimum estimate of the best alternative that Young–Kemeny would provide. Second, fairness: if we have exhausted our epistemic deliberations and want to establish a mere compromise among voters then Young–Kemeny (the median of all rankings: Young 1997) and Borda count (the ranking with the minimum number of disagreements with alternative rankings: Dummett 1998; Risse 2001) remain highly attractive principles. Therefore, if accuracy of representation or exactitude of fairness are the only considerations, then the Borda count and perhaps the Young–Kemeny rule appear to be the most justiﬁed of democratic voting rules (compare Risse 2001 and Saari 2003). Riker (1982, 81) dismisses Young–Kemeny because, although it is based on “clever and defensible” ideas, so are other Condorcet-consistent rules such as Copeland’s and Schwartz’s. As for Borda count, it seems especially vulnerable to manipulation by the addition and subtraction of alternatives, different positional methods lead to different outcomes from the same proﬁle, and there are few arguments for selecting Borda count from among the inﬁnite number of possible positional rules (since Riker wrote, the uniqueness properties of especially the Borda count and perhaps Young–Kemeny have become more obvious). Riker (1982, 91) also mentions a practical difﬁculty for Young–Kemeny and Borda count: for much more than three alternatives voters might ﬁnd it difﬁcult to rank all candidates (I shall not cavil that rational choice theory requires voters to have complete preference orderings). Where Hare voting has been used, however, voters have been required to rank-order all candidates, and it has not been a major practical problem. Accuracy is one desideratum for a voting rule, and in some circumstances simplicity may be another desideratum. Moreover, the Borda count, perhaps the most accurate rule for aggregation of ordinal data, is not the simplest rule. Plurality rule is very simple for voters and election administrators but possibly vulnerable to rapscallions as in the example above, or even verges on randomness with a half-dozen or more candidates who are more or less evenly matched. Approval voting permits the voter to approve or disapprove each candidate. Say that the alternatives are A, B, C, and D – a voter can approve only A, or both A and B, or A, B, and C (the voter can also approve or disapprove of all four, but then she may not bother with voting). Approval voting can’t be manipulated in a three-candidate situation like that of Rapscallion above (Weber 1995), Rapscallion would be deterred. The simulations show generally that approval voting is more Condorcet-efﬁcient than plurality. Further, if voter preferences are dichotomous in the sense that voters divide the candidates into two sets, are indifferent among the candidates in each set, but rank one set above the other, then voters have no incentive to vote

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strategically; similarly, if voter preferences are trichotomous then voters will also be sincere (Weber 1995). If manipulation by agenda control is a major concern, then it appears that approval voting is the method that best resists such manipulation (Nurmi 1987, 192). In addition to accuracy and simplicity we must also consider how voters and alternatives strategically interact with a voting rule.2 Voting rules are such that a voter may ﬁnd it to her advantage to vote other than her true ranking – so-called strategic voting. An American leftist in 1992 might have preferred as President left-wing Democrat Jesse Jackson to centrist Democrat Bill Clinton to Republican George Bush. Assume for the argument that Jackson and Clinton were about even, and that Jackson would probably lose, and Clinton win, in an election against Bush. If our leftist and people like her vote for their most favored candidate Jackson then their least favorite candidate Bush wins, so they end up voting for Clinton – this is strategic voting. It arises under Borda count as well: calculations are a bit more complicated, but a voter might believe that the overall distribution of preferences is such that if everyone like her truly reports her second-ranked candidate then that second-ranked candidate would come in ﬁrst, so voters like her mark their second-ranked candidate as last in order to assure their ﬁrst choice a victory. Strategic voting may matter because of the possibility that strategic voters might outfox one another and unintentionally end up selecting an outcome that almost no one wants. Generally, but not always, the more simple a rule is, the more vulnerable it is to manipulation. Strategic voting will be discussed in greater detail in a chapter below. Elimination rules (Merrill 1988, 13) include plurality runoff, Hare and Coombs. The Hare procedure is called the alternative vote when used to select one winner, as in elections to the Australian House of Representatives, and single transferable vote when used to select several winners, as in elections to the Australian Senate. Voters rank all candidates once (in Australia, they might optionally select the ranking recommended by one of the parties). If no candidate receives a majority of ﬁrst-place votes, then the candidate with the lowest number of ﬁrst-place votes is eliminated from all ballots, and the tally is recalculated. The procedure is repeated until a majority winner is reached. The single transferable vote is more complex, and is implemented in several variations; it is used in multimember districts in Ireland. The US House of Representatives elects its speaker by successive elimination, which is structurally identical to Hare if voters do not change their votes from ballot to ballot: voters cast only their ﬁrstplace votes, and if no majority then the candidate with the lowest number of votes is eliminated, and then a new ballot is taken, until a majority winner is reached. Plurality runoff is equivalent to successive elimination if

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there are three candidates, and advocates for the alternative vote in the US call it the instant runoff. The Coombs method is like Hare, but instead it proceeds by successively eliminating the candidate with the most last-place votes. Elimination methods – especially Hare – are the least susceptible to manipulation by strategic voting, if that is a concern (Nurmi 1987, 192). Bartholdi and Orlin (1991) show formally that for more than a few voters and candidates it is practically impossible to manipulate the Hare vote by strategic misrepresentation of preferences. Nor is strategic misrepresentation observed where Hare is used. So far we have pretended that alternatives are naturally given, that they are some exogenous fact that would be the same from voting rule to voting rule. The alternatives offered, however, can depend on the voting rule, and here we are in for some surprises. As summarized by Myerson (1995), Cox (1987; 1990; also see 1997) makes the case that plurality voting with more than two parties (alternatives) makes for parties widely scattered across the spectrum, that negative plurality has parties clustering at some point within a wide portion of the spectrum, and that approval voting, Borda count, and single transferable vote compel parties to cluster in the center at the policies favored by the median voter. When parties are endogenized, according to Myerson, we ﬁnd that plurality rule creates a small number of parties, that Borda count and negative plurality encourage a large number of parties, and that approval voting, proportional representation, and single transferable vote can accommodate small or large numbers of parties. Plurality voting in single-member districts tends to encourage two parties, for example, because voters (or elites persuading them) tend to vote strategically. Why? If a voter believes or is led to believe that her ﬁrst-ranked choice has little chance of winning and that the race is probably between her second-ranked and third-ranked choice then she’ll likely vote for her second-ranked choice so as to deny victory to her third-ranked choice: this can lead to a so-called Duvergerian equilibrium with most support going to two candidates and the tendency to the two-party system. The voter wants to coordinate with other voters and a focal point in this coordination game is indicated by the expectation that more people will vote for her second-ranked choice than for her ﬁrst choice (some other kind of focal point would work as well so long as beliefs were reciprocal among coordinators). In the example with Rapscallion, Tweedledum and Tweedledee above, strategic voters could defeat Rapscallion’s manipulation: ten people prefer Tweedledee to Tweedledum, but only ﬁve people prefer Tweedledum to Tweedledee; thus, the ﬁve Tweedledum voters would vote strategically for Tweedledee in order to thwart Rapscallion, who would be deterred from entering the race by this expectation. A non-Duvergerian equilibrium can emerge only

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when the Tweedledee and Tweedledum voters are about equally divided and there are no other focal points that permit these voters to coordinate on one candidate against their foe, which is perhaps why the Rapscallion maneuver is not frequently attempted or achieved. To speculate, one could praise the Borda count for forcing parties to the median, yet dread a consequent confusing Trotskyite proliferation of one, two, three, many centrist parties; one could praise plurality for encouraging a clear binary choice between two distinct alternatives (Riker 1982, 88), but deplore the indeterminacy that permits those in society with the most resources to single out the focal points for each of the two parties (Myerson and Weber 1993). Further considerations include variations in voting and party systems, sometimes ﬁne ones, and also their interaction with other institutional features such as the executive and the constitutional court and their variations (Myerson 1995). Gametheoretic models, however, are notorious for delivering large changes in conclusions from small changes in assumptions (or even generating the same conclusion from a second model after the ﬁrst model is shown to be in logical error). Theoretical and especially empirical examination of the ancillary consequences of electoral systems – cabinet durability, number of parties, proportionality of representation, voter turnout incentives, descriptive representation of women and ethnic minorities, incentives for localism or generalism, among others – must also enter into the evaluation of voting rules.3 Culture, notably the particular distribution of voter preferences, should also be considered. Reilly (2001) compares in Papua New Guinea conciliatory politics under Hare-style preferential voting to conﬂictual politics there after adoption of plurality rule. Papua New Guinea is the most ethnically fragmented country in the world, and primary loyalties for many are to one’s own group. Thus, unlike in the US and UK, many candidates enter the plurality race – an average of 21.7 per seat in 1997 – and the winner is typically an arbitrary choice who obtains between 10 percent and 19 percent of the vote, as low as 6.3 percent. This worsens ethnic conﬂict, and Reilly recommends preferential voting for many divided societies, as it requires the successful candidate to campaign across ethnic groups for second and third preferences. Thus, deep historical understanding of single cases as well as comparative empirical analyses must weigh more strongly in our judgments than isolated models, and wisdom would help too. Given that there are many complex interactions and tradeoffs among many imperfectly measured and differently valued desiderata, it would not do to be overly dogmatic about choice of voting rule. For cardinal preferences – ignoring conceptual, empirical, and strategic misrepresentation

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problems – I believe that a sum of utilities voting rule which counted each citizen as one would most accurately and fairly amalgamate preferences (such summations are not necessarily true or right, however). For ordinal preferences, an ideal Borda count probably better satisﬁes accuracy and fairness than other rules, although most of the literature endorses the Condorcet criterion. Moving from the ideal to the practical, the Borda count may not be so accurate and fair if in reality it is much affected by strategic manipulation, an open question. Values other than accuracy and fairness – for example, proportionality, moderation of conﬂict, ease of use, among others – might also be thrown into the balance. The voting rules do not differ that much when aggregating from the same set of real individual preferences over alternatives; but the different rules may elicit different alternatives – as in Papua New Guinea plurality might elicit divisive candidates and preferential vote conciliating candidates. Generally speaking, pure plurality, widely used in the US and the UK, seems to be the worst of the commonly used rules – unless one puts a high value on seesawing extremes in government so as to promote innovation in public policy. Good arguments are made for the variants of Hare, and for approval voting, as practical voting rules. There are good arguments for Condorcet as an ideal rule, as a yardstick by which to measure the accuracy of other rules, and there are better arguments, I believe, for the Borda count. But as a practical rule the Borda count probably needs more testing by experience. Good electoral engineers, like their colleagues in physical engineering, want to test their models in practice and evaluate them ultimately by real-world consequences.4 The axiomatic criteria are superﬁcially appealing, but then Riker treats us to counterexamples (I have not repeated them here) illustrating that each voting rule violates one or several of the apparently innocuous criteria – and to this we can add the considerations arising from simplicity, from strategic responses from voters and from candidates, and from institutions and culture. In a way, the axiom game is rigged: we could happen on a voting rule that satisﬁed a maximum number of important criteria, but then anyone is free to devise a superﬁcially appealing criterion that the rule does not satisfy (e.g., does the rule exclude outcomes based on false beliefs? etc.), and then we are back to Riker’s alleged arbitrariness. Is the messiness indicated by these counterexamples and considerations sufﬁcient to justify Riker’s conclusion that the use of one voting rule over another is arbitrary? First, Riker himself does not mean that the choice is arbitrary among all possible voting rules, only among those that are arguably accurate and fair, those we have discussed such as plurality, plurality runoff, Hare, Condorcet order, Borda count, approval voting, and the like, and not among the plainly inaccurate or unfair such as the

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Gerry Mackie rule or a rule which said ﬁnd out what the majority wants and then do the opposite. If a social choice rule operates on all logically possible proﬁles to provide all logically possible nonempty outcomes, then how many different social choice rules might there be? With ﬁve voters and four alternatives, there would be 10235,000,000,000 such social choice rules, as compared to 1019 seconds in the universe since the big bang, according to Kelly (1988, 62). Someone who has encountered one or two voting rules in his lifetime might be bewildered to discover that variations on a dozen or so voting rules are used by humans across the world. Someone who knows that the number of possible social choice rules is beyond imagination might be impressed to discover that we use only a dozen or so. Second, among those rules that are arguably accurate and fair, there are many logical and empirical considerations that do permit us to say that one rule would be better than another under speciﬁed conditions. This is the beauty and usefulness of the work in social choice, that its many ﬁndings permit the cumulative reﬁnement of judgment on such matters. Nor are we at the end of history with respect to designing political institutions; conceptual and empirical advances, and yet uninvented technologies, will cause our evaluations to shift over time. Nurmi (1987) is the deﬁnitive work on comparing voting rules by how they satisfy various axiomatic criteria. After mustering far more complex considerations than I have here, and not mentioning Riker by name, he suggests two possible responses: (1) to conclude that no procedure is good enough for all purposes and, hence, we should revise our ideas of popular choices so that their results are viewed as nearly random and certainly more or less accidental, or, (2) to conclude that the differences in performances should be taken into account in choosing procedures for use in various settings. (191)

Nurmi drolly remarks that he ﬁnds the second conclusion more plausible. After a full survey of the logical possibilities associated with different voting rules, Nurmi concludes that the more important question is the comparative frequencies of undesirable faults in practical application. An instance of the confusion of logical possibility with empirical probability arose in the early 1990s in a British Labour Party working party on electoral reform.5 The group rejected single transferable vote (STV) ostensibly because of its lack of monotonicity – the logical possibility that increasing the vote for a candidate might cause her to lose. Widely used plurality runoff is also nonmonotonic, as a logical possibility. The chief electoral ofﬁcer of Northern Ireland responded that “the experience of the use of STV in Northern Ireland over the past 22 years, involving a

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range of election types and sizes, reveals no evidence to support in practice the lack of monotonicity.”6 Allard (1995) calculated that if STV were used in the UK, there would be less “than one incidence every century of monotonicity failure.”7 To go from plurality to STV would mean the cost of a speculative to slight chance of a nonmonotonic result in exchange for the beneﬁts of a voting rule extremely difﬁcult to manipulate and of a much more proportionally representative Parliament. Of course, the Labour Party presently beneﬁts greatly, and unfairly, from plurality rule in the UK, and would lose seats to other parties under STV. We have seen from simulations, even with uniformly distributed preference orders, and more so from mildly unipolar distributions, and decisively from empirical data, that the reasonable voting rules deliver similar results; if there is mild homogeneity among the population, choice of voting rule need not evoke exquisite anguish. There is no rule that is uniquely best for all purposes under all constraints; numerous considerations count for or against any rule; but this does not make choice of a rule arbitrary. For an analogy, consider the question of whether there is a single method of human transportation that is uniquely best across all conditions of variation. Obviously, there is not. We do know that circumstances favoring crawling or rolling are quite rare, and that teleportation always fails. As to whether one wants to walk, run, bike, drive one make or model of car or another, train, bus, plane, and so on, it always depends on purposes and constraints. Does the mere multiplicity of methods mean that when an individual chooses one method over another that her choice is arbitrary? No. Often there are reasons for one choice over another; and often we might be indifferent among some subset of choices, but there’s nothing at all wrong with considered indifference. And practically, sometimes a bicycle will have to do when a car would be much better. Riker himself recommends different methods for different circumstances, and gives reasons for his choices. Brieﬂy, he recommends for legislatures the amendment procedure for three alternatives (which yields the Condorcet winner if one exists, and otherwise the status quo), and Borda or Young–Kemeny for more than three alternatives. For elections of executives and of legislators presumably in the American case of singlemember legislative districts, he recommends plurality vote so as to encourage a two-party system, and approval voting for primary but not for general elections. The advice is not unreasonable. He goes on, however, to say that his recommendations are merely a matter of “my own taste,” rather than a matter of judgment. He must state that his recommendations are an arbitrary matter of taste, otherwise he undermines his central claim that choice among voting rules is arbitrary. He then reverts to the position that preferences are unknowable, the ultimate bulwark in each

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of his lines of argument, “Doubtless the results are often fair or true; but, unfortunately, we almost never know whether they are or not, (1982, 113): the basic argument pattern. A decision rule must work with more than two alternatives, but from the same proﬁle of voters’ preferences it is logically possible for different decision rules to yield different outcomes, according to Riker. It is logically possible that different rules yield different outcomes, but it is not empirically probable, we have seen. Simulations and voting studies show that, with more realistic distributions of preference rankings, the reasonable voting rules yield similar results. Moreover, an axiomatic approach does not identify a uniquely best decision rule, each voting rule violates one or another principle from a collection of apparently desirable a priori principles, Riker continues. The axiomatic approach does not identify one best rule, but it does narrow the ﬁeld to a handful of reasonable voting rules. That handful of rules yields similar results in real circumstances. If accuracy and fairness are the only criteria, then the Borda count is probably the best. Additional pragmatic criteria support more simple and already widely used voting rules, such as the plurality-runoff rule and even the plurality rule. The accumulation of social-choice results does not obscure judgment as to choice of voting rule for the purpose of institutional design; rather, the social-choice results inform and improve such design judgments. Next, we shall consider the claim that from the same proﬁle of preferences even the same voting rule might yield different results.

4

The Arrow general possibility theorem

Democratic voting as meaningless First, irrationalism claims that voting is arbitrary. Second, irrationalism claims that voting is meaningless: even if a voting method survives the ﬁrst claim as fair, it is yet meaningless, because: (a) the outcome of voting is manipulable; and (b) we cannot know that manipulation occurred since again there is not enough information available from the data of voting to know the preferences underlying choices expressed in voting. The second claim of meaninglessness presents and interprets results of social choice theory. We have already treated (in Chapter 2) the crucial premise that preferences cannot be known from choices. Now, we will begin examination of the premise that voting is manipulable. The premise of manipulability is derived from the possibility of majority cycling as shown by Arrow (1963/1951), the possibility of strategic voting as shown by Gibbard (1973) and Satterthwaite (1975), the possibility of agenda control as shown by McKelvey (1976) and Schoﬁeld (1978), and ﬁnally the strategic introduction of new issues and dimensions (Riker 1982). Over the next three chapters, we discuss the Arrow theorem. In this chapter, we review the origins of the Arrow theorem in the ordinalist revolution in economics, and distinguish social choice as welfare economics from social choice as voting theory. Next, we present the contents of the Arrow theorem, followed by discussion of claims of its empirical relevance by Arrow and Riker. Then we review all studies found on the question of the frequency of cycles, and conclude that the incidence of cycles is rare. Finally, we begin review of justiﬁcations of the conditions of the theorem.

The origins of social choice theory Classical economics emphasized the remarkable coordinating power of markets, and suggested that a policy of laissez-faire would best advance the wealth of nations. Bentham and the utilitarians embarked on 72

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a wholesale program of practical reform, which overturned traditional policies, and enacted new policies, many laissez-faire, intended to do the greatest good for the greatest number. Economists were still bedeviled by the value paradox – why should useful water cost less than useless diamonds? The marginalist revolution of 1871–1874 solved that problem. The price of something is related to its marginal utility, not its total utility – water has great total utility, but in normal circumstances one more unit has little marginal utility – and consumer satisfaction is maximized when the ratios of marginal utility to price are equal for each good. Further, goods have a declining marginal utility: after some point, each additional increment is worth less than the prior increment. The intersection of utilitarianism with marginal analysis in Marshall’s neoclassical economics yielded a conclusion distasteful to those fond of laissez-faire: if for each person there is a declining marginal utility of money, then it would increase overall social welfare if money were taken from the rich and given to the poor, up to the point equalizing marginal utility of each person in society. Efﬁciency would best be achieved by equality. Utilitarianism had assumed cardinal and interpersonally comparable utilities, and the utilitarian philosopher proposed pursuit of the greatest good for the greatest number, that society should maximize the total sum of utility. Cardinal utility counts it as meaningful to say that I want a holiday in Andalusia ﬁve times more than I do a holiday in Buffalo; interpersonal comparability counts it as meaningful to say that Paul likes playing the guitar more than Matthew likes doing the dishes. Although interpersonal comparisons of welfare are common in daily life, and in my view are quite meaningful, they are always open to skeptical attack, and it was once thought that there are insurmountable difﬁculties in devising satisfactory formal representations of such comparisons. Meanwhile, economists found that they could restate the basic propositions of market economics in terms of ordinal and noncomparable utility. The advantage is that these are less demanding assumptions, and there are not so many formal and conceptual problems as there are with cardinal utility, comparable utility, or both. Ordinal utility considers only the order of ranking of alternatives; in the ordinal framework I cannot say that I like Andalusia ﬁve times better than I do Buffalo, only that I like Andalusia better than Buffalo. Further, a notion such as that society should maximize the total sum of utility is not possible within an ordinal and noncomparable framework; for one thing, you can’t add what you can’t compare. The chief ideologist of the ordinalist revolution was Lionel Robbins (1937/1932), who wanted to establish economics as a “Science,” and to

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distinguish it from “Ethics.” The purpose of a distinction between facts and values, is, according to Iris Murdoch (1992, 25): to segregate value in order to keep it pure and untainted, nor derived from or mixed with empirical facts. This move however, in time and as interpreted, may result in a diminished, even perfunctory account of morality, leading (with the increasing prestige of science) to a marginilisation of ‘the ethical.’ This originally well-intentioned segregation then ignores an obvious and important fact of human existence, the way in which almost all our concepts and activities involve evaluation.

I agree that it is quite important to distinguish fact from value, but notice that the claim I just made involves an assertion of fact and an expression of value. Too often, the discourse which states that value claims are nonscientiﬁc (in the descriptive sense) is twisted into an insinuation that value claims are unscientiﬁc (in the evaluative sense), or merely arbitrary expressions ungrounded in reason. Robbins tends to do this himself, in imagining that a committee made up of an economist, Bentham, Buddha, Lenin, and the head of US Steel would be unable to agree on the ethics of usury, but that the same committee would be able to agree on the facts of the economic consequences of anti-usury legislation (1937/1932, 150– 151). Values are arbitrary, according to Robbins (150): “If we disagree about ends it is a case of thy blood or mine – or live and let live according to the importance of the difference or the strength of the opponents.” At the same time he does not seem to be aware that his recommendations as to what should count as science are matters of evaluation, not of fact. Robbins’s second move was to allege that the claims of the reigning material-welfare school in economics were not scientiﬁc but ethical, and not just ethical, but arbitrary because ethical. The material welfare school held, according to Robbins, that it is possible to compare the utility or satisfaction of one person to another person. But such comparisons are not needed in modern economic theory, he wrote; the comparison is essentially normative and has no place in pure science. There is no means of testing the magnitude of A’s satisfaction as compared with B’s. If we tested the state of their blood-streams, that would be a test of blood, not satisfaction . . . There is no way of comparing the satisfactions of different people . . . In Western democracies we assume for certain purposes that men in similar circumstances are capable of equal satisfactions . . . although it may be convenient to assume this, there is no way of proving that the assumption rests on ascertainable fact. And, indeed, if the representative of some other civilization were to assure us that we were wrong, that members of his caste (or race) were capable of experiencing ten times as much satisfaction from given incomes as members of an inferior caste (or an “inferior” race), we could not refute him . . . we could not

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show that he was wrong in any objective sense, any more than we could show that we are right. (Robbins 1937/1932, 139–140)

From this he concludes that the recommendation by the material-welfare school for equalization of incomes is unscientiﬁc. Notice that Robbins’s doctrine is radical skepticism rather than mere behaviorism: any objective correlate of satisfaction is prohibited. If we could measure some chemical in the blood (or these days, study an image of the brain’s activation), that would not do; we would be measuring blood, not satisfaction. Robbins’s objection seems to me to be one of postured philosophy rather than of ordinary science – science frequently estimates unobserved variables by way of indirect measures, without calling into doubt the theoretical usefulness of the unobserved entity. I agree with Robbins, though, that in any case the next step of saying that satisfaction or some other measure should be equalized – or any other policy recommendation, including that it should not be equalized – is a normative question. Cooter and Rappoport (1984) argue that Robbins and his followers misconstrued the material-welfare school they superseded. Generally, the material-welfare school understood that ordinalism is sufﬁcient for market economics, and that it may not be possible to compare the satisfactions of any two individuals. Where they differed was in judging that ordinalism is not sufﬁcient for welfare economics, and in thinking it is possible to compare the needs of representative persons: “If people typically desire what they need, and if needs are more urgent when people are poor, then it follows that additional income is more useful to the poor than the rich” (Cooter and Rappoport 1984, 517). In their social-welfare calculation, goods were evaluated objectively, by whether they contributed to a person’s physical well-being, they distinguished necessities from comforts from luxuries, and they measured variation among individuals in the supply of health, food, housing, clothing, and money. The welfare economist need not be conﬁned to the equalization of satisfaction, a mental state; the welfare economist could have an objective theory of the human good, justiﬁed in its own right, and not solely because it correlates with the desire-satisfaction of the typical individual. Sen (1999; see also 1982) says that the rejection of interpersonal comparisons in welfare economics was based on interpreting them entirely as comparisons of mental states. He argues that, “even with such mental state comparisons, the case for unqualiﬁed rejection is difﬁcult to sustain” (1999, 358). He continues that such comparisons need not be based only on mental states, but might directly be based on incomes, or commodity bundles, or resources more generally, and Sen’s theoretical and applied work in this area demands attention.1 To conclude, is giving food to the hungry better than giving

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opera tickets to the bored (Cooter and Rappoport, 1984, 519)? I agree with Robbins that such is an ethical claim, but disagree that it is arbitrary because ethical. As economists completed their ordinalist revolution in the 1930s, they sought in welfare economics to devise an ordinalist replacement for the utilitarian formula. They had the Pareto criterion, that x is better than y if every individual ranks x higher than y, but that criterion is radically incomplete: a policy change that helps a million people but hurts one is not a Pareto improvement, and further there is no way to choose among a multitude of Pareto-superior states. As it happens, voluntary market exchange satisﬁes the Pareto criterion, but collective choice short of unanimity does not, and thus any political distribution of endowments other than the inherited status quo is off limits. Notice that most voting schemes are ordinalist – voters are asked to rank-order alternatives, not to state intensities on some scale. There was a minor, almost forgotten, current of analytic consideration of alternative voting rules, involving Condorcet and Borda, and later Lewis Carroll, Hare, Nanson, among others, and culminating in Duncan Black. Ordinalist welfare economics intersected with voting theory, and from Arrow’s achievement social choice theory was born. Social choice theory spans at least three disciplines. Arrow’s theorem and much of the discussion of it is motivated by the concerns of welfare economics, that is, what advice should be given to an imaginary social planner who has the task of providing the greatest social welfare to a society (the discussion includes those economists who dispute the legitimacy of such a social-welfare objective). There is also, of course, a large philosophical literature on theories of justice, each of which aspires to provide thorough and coherent arguments about the best way to organize the basic institutions of a society. The concerns of the justice theories overlap somewhat with the concerns of welfare economics, but also typically assert standards of the public good (or some similar objective, such as justice) that are partly or wholly independent of individuals’ ordinary rankings of social states. Welfare economics purports to be merely descriptive (or at most to provide hypothetical advice), but theories of justice are frankly normative. Finally, political scientists interested in the formal and empirical exploration of voting and of other political institutions adapted the ﬁndings of social choice theory to their purposes. Much of the content of American political science in the last twenty years has been an elaboration of the analogy of political choice to consumer choice ﬁrst brought to prominence by Arrow and Buchanan in the 1950s. Immediately upon publication of Arrow’s Social Choice and Individual Values, Little (1952) objected that Arrow’s scheme was excessively general in

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lumping the economist’s interest in social welfare with the political theorist’s interest in voting, and Sen (1982, 158–200) later elaborated on the point. My emphasis in this volume is on voting, and I will mostly ignore the concerns of welfare economics and of theories of justice, not from lack of interest, but rather because it would take us too far astray even to state the many issues at stake. Immediately, democratic voting is different from social-welfare calculations in at least one important respect: it is widely although not universally accepted that citizens should be treated as political equals, in terms of voting that each relevant person should have an equal vote. The economist and the philosopher are free to muse, for example, that one person might be a hundred times better than another in converting life’s experiences into some form of satisfaction, so that in the pursuit of equality of welfare such a person deserves fewer resources or perhaps less political inﬂuence over the distribution of resources. Or one or the other of them also might propose that the demonstrably competent be granted more than an equal vote or the overly privileged less than an equal vote. The democratic theorist, however, is entitled to the working assumption of formal equality, one vote per one person. The economist or the philosopher might consider that assertion of political equality a defect of democracy as it is presently understood. That would deﬁnitely be a minority view, however, and even if it were a correct view I cannot imagine in today’s circumstances how the supposed defect would be remedied in practice: if one departure from formal political equality is granted, that only increases the demand that another be granted, escalating into a chaos of exceptions only resolved by a return to formal equality. Most practical voting systems in use are ordinal: generally, voters are asked to rank-order two or more alternatives and are not asked to express by voting intensity of preferences over alternatives, for example, that Rome is three times as good as Santa Fe and Santa Fe is twice as good as Gary. A cardinal voting scheme, the argument goes, may be vulnerable to misrepresentation: it is in each voter’s interest to exaggerate the intensity of her preferences for her favorite choices. Intensity of preference is expressed in informal discussions and in democratic debate. The fact that Susie hates seafood because she has a life-threatening anaphylactic reaction to shellﬁsh is enough to overrule a tepid majority’s preference for the seafood restaurant – unless Susie insincerely has such a story for every occasion. Susie’s claim also relies on some kind of comparability: her life-threatening reaction is much more important than Mark’s mild distaste for pizza. A minority’s demand to be free from arbitrary deprivation of life and liberty can persuade a majority to desist, perhaps because the majority is well-motivated or perhaps because

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the minority threatens to withdraw social cooperation. One member of Congress can tell another that she really needs this vote for her district and would gladly trade votes with others on issues she is nearly indifferent about; there is an element of comparability in that each legislator is allocated only one vote per question. There are voting schemes and practices that under one interpretation approximate cardinality but are not vulnerable to exaggeration: the Borda count (the Borda count need not be justiﬁed, however, as an approximation of cardinality), cumulative voting (the voter is allocated a ﬁxed number of points to distribute across alternatives), and under ordinalist majority rule vote trading across a series of issues. Because most voting schemes are ordinal in character, Arrow’s theorem and its many offspring are relevant to questions about the comparative desirability of alternative voting schemes and broader questions of institutional design. Any voting scheme assumes some kind of comparability: allocating the same voting power to each person as I have advocated, or weighting votes so as to favor one voter over another, justiﬁed by either welfare or nonwelfare considerations. Arrow’s theorem assumes ordinal and noncomparable preferences, and voting tends to be ordinal but imposes one or another conception of comparability.

Arrow theorem The Condorcet paradox of voting, recall, arises from a possible distribution of preference orders among the population such that the aggregate majority vote is a cycle A > B > C > A. Arrow’s possibility theorem can be understood as a generalization of Condorcet’s paradox, applying not only to simple majority voting but also to any social-welfare function that aggregates individual orderings of more than one person over more than two alternative social states. The theorem shows the joint inconsistency of several innocuous-sounding conditions on the social-welfare function. There are many ways to state, informally and formally, the conditions and the results. A good way to begin is with Arrow’s (1973) own informal summary of his theorem: I stated formally a set of apparently reasonable criteria for social choice and demonstrated that they were mutually inconsistent . . . The conditions on the social decision procedure follow: (1) for any possible set of individual preference orderings, there should be deﬁned a social preference ordering (connected and transitive) which governs social choices; (2) if everybody prefers alternative A to alternative B, then society must have the same preference (Pareto optimality); (3) the social choice made from any set of available alternatives should depend only on the orderings of individuals with respect to those alternatives; (4) the social

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decision procedure should not be dictatorial, in the sense that there is one whose preferences prevail regardless of the preferences of all others . . . The inconsistency of these conditions is in fact a generalized form of the paradox of voting . . . As in the original Condorcet case of simple majority voting, all that is meant by the paradox is that it could arise for certain sets of individual preference orderings. If individual preference orderings were restricted . . . then majority voting and many other methods would satisfy conditions (2) to (4).

I shall now state some preliminary deﬁnitions, and then the assumptions of the Arrow theorem, along with some interpretations of the formalisms. To begin with, there are alternative social states. A social state, according to Arrow (1963/1951, 17), is a complete description of the amount of each consumption commodity, of labor, of productive resources allocated in the economy, and amounts of all collective activities, ranging from municipal services, to diplomacy, war, “and the erection of statues to famous men.” There is an environment X of all alternatives, and a set S that is a subset of X. Arrow’s framework is quite general, and X could be all possible social states and S all feasible social states. In a speciﬁc application such as a presidential election X might be all possible presidential candidates and S all actual presidential candidates. Each individual has a preference ordering over all possible social states, and an individual’s preferences need not be egoistically oriented, according to Arrow. A weak ordering, R, is a generalization of the concept applied to real numbers of “greater than or equal to”; a strong ordering, P, is a generalization of “greater than.” Strong ordering can be deﬁned in terms of weak ordering: x P y is deﬁned as x R y and not y R x. In other words, to say that Italy is better than England is the same as to afﬁrm that Italy is at least as good as England and to deny that England is at least as good as Italy. Indifference can also be deﬁned in terms of weak ordering: x I y is deﬁned to be x R y and y R x. To say that Coke is as good as Pepsi is the same as saying at the same time that Coke is at least as good as Pepsi and Pepsi is at least as good as Coke. Arrow assumes that individuals have consistent preferences over all possible states of the world. A weak preference ordering is reﬂexive: x R x means that x is at least as good as itself. A weak ordering is also connected, or complete: for all x and y, either x R y or y R x. Someone might be indifferent between Coke and Pepsi, yet she could compare the two. A person who had no weak preference (or strong preference or indifference) between joining the ﬁrst space voyage to another inhabited planet and spending the same number of years with Socrates would have preferences that were not complete and thus not an ordering. A weak ordering is also transitive: for all x, y, and z, if x R y and y R z, then

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x R z. Arrow’s individual would never, for example, prefer Tocqueville to Marx to Mill to Tocqueville. The possibility theorem shows that, if we accept Arrow’s conditions, such individual orderings (by deﬁnition reﬂexive, transitive, and complete) cannot be amalgamated into a collective ordering (also by deﬁnition reﬂexive, transitive, and complete). For example, we have seen with the Condorcet paradox that transitive individual preferences can result in a social preference that is intransitive and thus not an ordering. Another voting rule could have the defect that it is incomplete; for example, a voting rule that required unanimity for every decision would in the abstract, if there were any disagreements, result in an incomplete social preference, and would be unable to report social preference or even indifference between some number of alternatives (because of this incompleteness, unanimity rules in practice favor the status quo). To continue with notation, individuals’ orderings are denoted R1 , . . . , Ri and a collective ordering is denoted R (without any subscript). Now I turn to Sen’s widely used formulations. r “An element x in S is a best element of S with respect to a binary relation R if and only if ∀y: (y ∈ S: → x R y). The set of best elements in S is called its choice set and is denoted C(S, R)” (Sen 1970, 10). To say that x is a best choice (in the set S with respect to the relation R) means that for all y, if y belongs to S then x is weakly preferred to y. The choice set contains the best elements. We might call them the winners of the contest. If collective preference cycles among the top alternatives, then there is no best element and the choice set is empty. r “A collective choice rule is a functional relation f such that for any set of n individual orderings R1 , . . . , Rn (one ordering for each individual), one and only one social preference relation R is determined, R = f(R1 , . . . , Rn ).” (Sen 1970, 28). For Sen, the collective choice rule is the more general case in which the social preference relation need not be an ordering; it is also made clear that a unique social preference relation is required. Now follows the Arrow theorem, which assumes rather a social preference relation that is an ordering. The conditions are labeled O, U, P, I, and D. r “A social welfare function (henceforth, SWF) is a collective choice rule f, the range of which is restricted to the orderings over X. This restriction is to be called condition O on f ” (Sen 1970, 41). The collective ranking of alternatives generated by the social-welfare function should be as a collective choice rule unique, and as a social welfare function both complete and transitive. r “Condition U (unrestricted domain): The domain of the rule f must include all logically possible combinations of individual orderings”

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(Sen 1970, 41). The social-welfare function should accept as input any and all possible individual preference orderings. r “Condition P (Pareto principle): For any pair x, y in X, [∀i: x P y] → i x P y” (Sen 1970, 41). For example, if every individual prefers Metallica to AC/DC, then Metallica is preferred to AC/DC in the social preference order. r “Condition I (independence of irrelevant alternatives): Let R and R be the social binary relations determined by f corresponding respectively to two sets of individual preferences, (R1 , . . . , Rn ) and (R 1 , . . . , R n ). If for all pairs of alternatives, x, y in a subset S of X, x Ri y ↔ x R i y, for all i, then C(S, R) and C(S, R ) are the same.” Condition I is the condition most difﬁcult to understand and the most frequently misunderstood. The social preference over any given pair of alternatives depends only on individuals’ preferences over the same given pair of alternatives; and if individuals’ preferences about some third alternative should change, that would not change the social preference over the given pair of alternatives. r “Condition D (nondictatorship): There is no individual i such that for every element in the domain of rule f, ∀x, y ∈ X: x Pi y → x P y” (Sen 1970, 42). If the social preference over every two alternatives is the same as one particular individual’s preference over every two alternatives, regardless of the preferences of other individuals, we could call that a dictatorship. r Arrow’s General Possibility Theorem: There is no social welfare function (an ordering) that satisﬁes the conditions of universal domain, Pareto principle, independence of irrelevant alternatives, and nondictatorship. Here is more on the independence condition. Suppose that we have two individuals, Napoleon who ranks b > a > c > d > e, and Josephine who ranks a > b > c > d > e. In order to rank a and b, what information does the social-welfare function that obeys Condition I take into consideration? Only that Napoleon ranks b over a and that Josephine ranks a over b, and nothing else. Intuitively, if this were the only information we had, and if we regard Napoleon and Josephine as equals, we would probably conclude that given those individual rankings the social choice between a and b should be a tie. Now suppose that as before Napoleon ranks b > a > c > d > e, but that Josephine is different and ranks a > c > d > e > b, for Josephine alternative b has dropped from second place to ﬁfth place. What information does Condition I permit to be taken into consideration? Again, only that Napoleon ranks b over a and that Josephine ranks a over b, and by simple majority rule a would tie with b. The alternatives deemed irrelevant in this illustration are any other than a and b. Someone might object: alternative b went from second

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to ﬁfth in Josephine’s preferences, it seems that Josephine really hates b, so it makes more sense now to say that a beats b rather than that a ties b. Condition I forbids that objection: the social-welfare function accepts only pairwise information from individual preference orders. My explanation of Condition I is not typical in the literature, which, if it offers any explanation at all, usually provides an example that makes violation of Condition I look silly. A good proof of the theorem can be found in Sen (1970, 41–46). Naturally, the proof logically depends on the assumed conditions. The work the universal domain condition, U, does in the proof is that by allowing any logically possible combination of individual orderings it allows as one possible instance a cyclical proﬁle of individual orderings such as that which gives rise to the Condorcet paradox. If the cyclical proﬁle is excluded for one reason or another, the proof does not go through, as Arrow himself notes in his informal remarks I quoted above. The work that the independence of irrelevant alternatives condition, I, does in the proof is to exclude information other than individuals’ preferences over pairs. If we could include information about individuals’ relative rankings over more than two alternatives, also the proof would not go through. Condition U excludes Condorcet voting. Condition I excludes Borda and many other methods. Condition D excludes the only remaining voting rule, the dictatorship of one. Just as the Condorcet paradox is used to shock at the elementary level of study, the Arrow possibility theorem is used to shock at a more advanced level. There are thousands of articles varying, extending, and elaborating the theorem. It is often said that the Arrow ﬁndings are robust to several variations in the assumptions, and that if the spirit of the conditions is accepted, then there is no magic bullet that puts the problems to rest. That is not quite right. Sen, the social choice theorist who later won the Nobel Prize (a criterion cited by the speakers in my hall of quotations), says that Arrow’s conditions are not inescapable commandments. The issue is not the absence of rationally defendable social decision procedures, but rather the importance of disparate conditions that pull in different directions as we evaluate diverse procedures, he says. “We are not at the edge of a precipice, trying to determine whether it is at all ‘possible’ for us to hang on” (Sen 1995, 11). The usual attention-getting way of stating the result is that the only social-welfare function that satisﬁes some simple and apparently fair conditions is a dictatorship. A more boring but in my view more appropriate way of stating the Arrow result is to say that if we are required to consider only individuals’ rankings of pairs when the collective choice is over more than two alternatives (I ), or if we must assume that there is no correlation among different individuals’

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preference orderings (U ), then there may be a cycle in the social choice. Before we interrogate justiﬁcations for the several Arrow conditions, we shall examine the crucial issue of empirical relevance. Throughout his career Arrow has asserted the empirical relevance of cycling, and he came to rely on Riker’s ﬁndings in support of that belief. In his ﬁrst major work, Social Choice and Individual Values (1963/1951, 3), he introduces the Condorcet paradox and asserts in a footnote that there were cycles in recent Congresses over no federal aid to education, federal aid only to public schools, and federal aid to both public and religious schools, but he does not develop or defend the assertion. In his 1963 (93) postscript to the 1951 volume, Arrow cites Riker (1961) as “the most complete and up-to-date summary of the problem of aggregation of individual choices into collective ones, with particular emphasis on political aspects.” Arrow (1963/1951, 120) repeats: “That an intransitive social choice mechanism may as a matter of observed fact produce decisions that are clearly unsatisfactory has been brought out . . . by Riker . . . Riker’s emphasis is on the possibility that legislative rules may lead to choice of a proposal opposed by a majority.” The work to which Arrow refers (Riker 1961) was written while Riker was visiting the Center for Advanced Study at Stanford, where Arrow was in the Economics Department, and Riker acknowledges the generous help and commentary of Arrow on the paper. The paper is a bibliographic survey, and concludes with a declaration of the Rikerian doctrine that many observed majorities are merely apparent because of underlying cycles, providing as examples Riker (1958) on a Congressional appropriations vote (which I show below to be mistaken) and a brief mention of Senate deliberations on the 17th Amendment (later developed in Riker 1982, and which I also show below to be mistaken). In the same passage, Arrow refers to a few pages in Dahl’s (1956, 39–42) A Preface to Democratic Theory. Dahl maintains that when roughly equal factions in a group favor mutually exclusive alternatives then democratic rule may be endangered. If democratic procedures do not provide a unique outcome, then the factions may pursue their goals by extrademocratic means, that is, by violence. Deadlock leading to violence would be avoided only if the groups valued maintenance of democratic rule more than they did the nondemocratic pursuit of their goals, according to Dahl. Indeed, “the closer a group approached to an equal division the less valid the majority principle becomes” Dahl believes (1956, 41). Although social choice theorists call majority rule “decisive,” that is only by means of the deﬁnitional ﬁat that a tie counts as a decision, in the real world ties are useless when collective action is urgently required.

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Dahl’s concern is illustrated by the confusion and anguish of the 2000 US presidential election; in the end it mattered less whether Gore or Bush won than that one of them should win (it had to be one of either Gore or Bush; in the circumstances selection of some third candidate would have been truly arbitrary). In a footnote, Dahl includes within his concern a cyclical collective outcome arising from three equally sized groups with a cyclical proﬁle of individual preferences. In other words, for Dahl, a cycle over more than two alternatives is a defect of the same type as a tie between two alternatives. The defect is easily remedied. First, as Dahl mentions, if the population favors democratic rule generally over the nondemocratic pursuit of goals in the particular circumstances of tied outcomes, then democratic stability follows. Second, if ties are a problem then a tie-breaking procedure should be institutionalized in advance: bias to the status quo alternative, or perhaps better a random procedure, or a Republican-majority US Supreme Court, or a neutral constitutional monarch. Notice, however, that the problem of deadlock is not conﬁned to tie votes in a majority-rule setting. If the constitution is of the presidential or Madisonian or Rikerian “liberal” variety, which in the name of checks and balances allows each of many different minorities a veto power over changes from the status quo, deadlocks will be more frequent and thus more dangerous, especially when the status quo is worsened by unanticipated exogenous factors, than if the constitution is of the parliamentary or majoritarian or Rikerian “populist” variety (Stepan and Skach 1994). Arrow (1960) observes that means of minimizing the deadlocks that arise from the paradoxes of collective choice have evolved in all democratic systems. These brief notes are interesting, because elsewhere Arrow seldom engages in empirical reﬂections. He rehearses the defects of plurality rule, including that the rule strategically elicits two alternatives and thus disguises possible cycles. Plurality runoff, he says, might exclude a Condorcet winner. Possible ties in US presidential elections are decided by the election going to the US House of Representatives – the theme, apparently following Dahl, is avoidance of deadlock. Finally, in a recent volume Arrow (1997, 5) says, “That there is nothing unlikely about [the Condorcet] paradox has been empirically documented by a number of political scientists beginning with Riker (1958).” It was suggested to me that Arrow’s theorem was not intended by its author, nor understood by its audience, to be of empirical relevance; rather it is merely a logical exercise that illustrates a limit case (which is how it should be understood, I believe). I have shown that Arrow himself was motivated by the empirical relevance of his theorem; and that no small part of his audience

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shares that motivation is demonstrated by the literature of Riker and his followers. Furthermore, consider Arrow’s (1963/1951, 21) methodological credo: the present author regards economics as an attempt to discover uniformities in a certain part of reality and not as the drawing of logical consequences from a certain set of assumptions regardless of their relevance to actuality. Simpliﬁed theory-building is an absolute necessity for empirical analyses; but it is a means, not an end.

I read that to mean that the model and its logic is of interest only to the extent of its empirical applicability. The later Arrow (1997, 4) asks, regarding social choice theory, “Does it say that democracy is impossible?” He answers that, “Social choice theory offers only a limited criticism of democratic procedures” (5). He says that although failure to satisfy the theorem’s conditions is a legitimate criticism of a procedure, since the failure is universal the theorem alone offers no basis for differentially evaluating alternative social choice mechanisms (8; including, I would add, the market). Instead, “In the case of real social choice procedures, we have to consider the frequency with which intransitivities [and other violations] occur. This is not the sort of result I like, but that is the way the world is” (8). Arrow implicitly rejects the claim by Riker and his followers that the general possibility theorem renders democracy impossible. Arrow explicitly accepts the claim by Riker and his followers that empirical cycles have been robustly demonstrated, and he has always held that the relevance of his theorem is an empirical question. What is the frequency of social intransitivities? [E]mpirical observations of a wide variety of actual collective decision-making processes indicate that cyclical majorities are very rare. Thus, cycles do not appear to be a real problem for group decision-making although some paradoxes may occur which may go undetected. (Feld and Grofman 1986)

Actual observations about majority cycling are scarce, because elections rarely generate data on pairwise comparison among all alternatives or a ranking of all alternatives (Gehrlein 1983). In the limited instances where such data were available from experimental subjects or by inference from a sample of actual legislative situations, the absence of a Condorcet winner tended to be infrequent, according to the summary by Gehrlein (1983). Since then, whenever good data were available and analyzed, cycles have been shown to be infrequent, as we shall now see.

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What’s the frequency? Dobra (1983) solicited real election data from the readers of the journal Public Choice. This is no random sample: the readers of Public Choice are motivated to notice and report cycles. The cases reported were mostly faculty searches and from a small experiment, with small numbers of voters (median 10, range 4 to 27) and larger numbers of alternatives (median 5, range 3 to 37). There were three cycles including ties (e.g., A > B > C ∼ A) and one cycle not including a tie out of the 32 cases. Although cycles were infrequent, Dobra holds that the infrequency does “not repudiate the work of the disequilibrium theorists” (247). Recall the study by Chamberlin, Cohen, and Coombs (1984) of ﬁve different presidential elections of the American Psychological Association (APA) where voters rank-ordered all candidates, permitting hypothetical comparison of voting rules. The data also permit examination of aggregated preference orders for the presence or absence of cycles. Only about half the voters in these elections ranked all ﬁve candidates; the authors generated complete ballots in one condition by ﬁlling in remaining preferences randomly (as if voters were indifferent to unranked candidates) and in another condition by ﬁlling in remaining conditions proportionately (as if voters were uninformed about unranked candidates). Either way, there was a transitive majority ordering of the candidates in all ﬁve elections. The actual APA preference orders yield zero cycles. With the same numbers of alternatives and voters as in the APA election, but rather an impartial culture, there would be a 24 percent expectation of cycles. There are no cycles in the APA elections because preference orders are not randomly distributed as they are under the impartial-culture assumption. Natural preference orders have some minimum of structure, such as to preclude cycles nearly all of the time. As mentioned above, alternative voting rules picked the Condorcet winner about 80 percent of the time, and the second-ranked Condorcet candidate the rest of the time, again because of minimal similarity among preference orders. Niemi and Wright (1987) looked at thermometer ratings (respondents rate 0 to 100 when 0 means very unfavorable and 100 very favorable) of 14 politicians who were potential or actual candidates for the 1980 American presidential election, from a nationally representative sample of US voters. If all preference orders within a group are single-peaked (to be detailed below) and thus unidimensional then no cycle is possible. If only one of the voter’s rankings within a group fails the single-peakedness criterion then a cycle is possible but it is most improbable; and the higher the proportion of single-peaked preference orders within the group the less likely is a cycle (Niemi 1969). For three-, four- and ﬁve-candidate

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groups, Niemi and Wright found that the observed proportions of unidimensional preference orders in each condition are much higher than what would be expected by chance under the impartial-culture assumption; and those observed proportions were such that the probabilities of cycles were 0.04 or less. Further, the ten three-candidate rankings with the worst unidimensionality were sampled 1,000 times each; there were 29 cycles in these 1,000 samples, and 22 of those cycles involved the most obscure ﬁgure of the 14 candidates (Lucey, John Anderson’s vice-presidential running mate). For the least unidimensional fourcandidate rankings, top cycles were found in 154 out of 1,000 samples, and 137 of those occurred in two of the ten rankings. They also found absence of a relationship between unidimensionality on the one hand and on the other hand more distinguishable candidates, voter education, voter partisanship, judging better-known candidates, longer campaign exposure, or within-party judgments. Curiously, however, the dimension used by voters in their data did not appear to be the standard left–right dimension, but rather perhaps one of likability. Some very good data from candidate elections in private organizations in Great Britain were analyzed by Feld and Grofman (1992). These 36 elections, with between 3 and 29 candidates and between 9 and 3,422 voters, were conducted by the single transferable vote procedure, which requires that voters rank-order candidates. The authors state that although strategic voting is possible in principle under single-transferable vote, the necessary calculations are too complex for it to occur in practice (Bartholdi and Orlin 1991 show that it is NP-complete, that is, too computationally complex, except in special cases, for voters to be strategic under single transferable vote). From the data of the voters’ rankorderings, pairwise comparisons can be constructed. Every one of the reconstructed elections had a Condorcet winner. In 34 of the 36 elections the Condorcet winner and the Borda winner coincided (so the results speak as well against Riker’s claim that democracy is inaccurate). Only 0.5 (one-half of one) percent of the linearly ordered triples in the sample universe were cyclic; 24 of the 36 elections had no cycles whatsoever, the largest percentage of cycles in any election was 2.0 percent; and almost all cycles were among alternatives adjacent in Borda scores (meaning that they were among close alternatives). Since many observers believe actual cycles are infrequent, with those asserting otherwise emphasizing the absence of data to make a conﬁdent determination, I agree with Feld and Grofman that their results are important. Felsenthal, Maoz, and Rapoport (1993) review a mostly overlapping set of elections, and make similar ﬁndings. They observe that among elections with eight or fewer candidates there is only one instance of a (minor)

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cycle, and among elections with more than eight candidates there are 13 out of 19 instances of (minor) cycles. Felsenthal and Machover (1995) consider an expanded set of 92 elections, and replicate the observation: 7.5 percent of elections with eight or fewer candidates contain cycles, but 56.4 percent of elections with more than eight candidates do, and they remark on the sharp jump in occurrence of cycles beyond eight candidates. I shall propose an explanation for this in the next chapter. Of the 92 elections, 26 contained cycles; no cycle involved all candidates, and only two were cycles at the top of the preference order. Of the 26 elections with cycles, winners were immediately obvious in 19 of the elections, either because the cycle was not at the top, the number of slots to ﬁll exceeded the length of the cycle, or indifference relations within cycles appropriately indicated winners. Radcliff (1993) reports high unidimensionality derived from studies of American presidential elections from 1972 to 1984: 77 percent to 85 percent single-peakedness in years with three major candidates in the primary and general elections (at 75 percent unidimensionality the expectation of a cycle is less than 1 percent, and at 80 percent the expectation is almost zero, Radcliff 1994); and 50 percent in 1980 when there were ﬁve major candidates. Radcliff (1993) also ﬁnds that most individual voters’ rankings are transitive but that individual intransitivities increase with number of candidates. If intransitive voters are removed from consideration in the ﬁve-candidate case, single-peakedness goes up to 70 percent. Radcliff (1994) uses data from the same election studies to examine the transitivity of collective rankings. There was a Condorcet ordering in each American presidential election studied (that is, no cycles); the ordering corresponded to the standard left–right dimension of understanding; and each actual election picked the Condorcet winner. Thus: 1972, Nixon > Humphrey > McGovern; 1976, Carter > Ford > Reagan; 1980, Reagan > (Carter ∼ Bush) > Anderson > Kennedy; 1984, Reagan > Hart > Mondale. Van Deemen and Vergunst (1998) continue the elusive quest for the empirical cycle. From the Dutch parliamentary election studies of 1982 (13 parties), 1986 (12 parties), 1989 (9 parties), and 1994 (9 parties) they have survey data on respondents’ preferences over the alternatives. If preference rankings were random, as under the impartial-culture assumption, then there would be about a 50 percent chance of cycles. There are, however, no cycles in their data, not anywhere in the rankings, not in any of the elections. The authors ﬁnd the results surprising: “for some reason or another cycles in large elections are scarce” (485). Kurrild-Klitgaard (2001a) investigates cycles in Danish national election surveys. Respondents ranked 11 parties in 1973, 9 parties in 1994, 11 parties in 1998;

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the policies of the 8 parliamentary parties in 1994; 10 party leaders in 1973, 8 in 1994, and 10 in 1998; the importance of 28 issues in Danish politics in 1987/1988, and of 16 issues in 1994; 4 important goals in 1994; 12 public budget alternatives in 1990, and 20 such alternatives in 1994. With the number of respondents and often large number of alternatives, the prediction from simulations based on impartial-culture assumption would be a large proportion of cycles. For example, with an impartial culture, many voters and 20 alternatives, the prediction is a 68 percent incidence of cycles (Gehrlein 1997, 179). There was, however, only one trivial cycle in this entire set. For the 20 budget alternatives in 1994 there was a Condorcet ranking for the ﬁrst 14 alternatives, and then a cycle over what would be alternatives 15 through 18, and then transitive order again over alternatives 19 or 20. Otherwise, no cycles. Finally, Regenwetter and Grofman (1998) used a probabilistic method to estimate rankings from data in seven out of ten real approval-vote elections, and found only a small chance of a cycle in one of the elections. We should remember the bias against publishing negative ﬁndings. No doubt many people over the last thirty years have thought that it would be intellectually and professionally satisfying to demonstrate a real instance of cycling, yet the positive claims of cycling we have from the entire political universe can be counted on one’s ﬁngers and toes (and, as we shall see, even these claims collapse under scrutiny). Where is the pervasive political disequilibrium? Shepsle and Bonchek (1997, 50–51) ask: Is [group intransitivity] merely an arcane logical possibility, a trick foisted on the unknowing student by professors, philosophers, and textbook writers? Or is it a profound discovery, the stuff from which important insights about political philosophy and social life are made. In our opinion, the answer lies much closer to the latter.

In my opinion, the answer is closer to the former rather than to the latter. Riker (1965, 52) warned that the Arrow theorem is no mere “mathematical trick without practical signiﬁcance” and set out to show that the paradox of voting does occur and is of tremendous importance in committees and legislatures. At ﬁrst, he estimated that whenever on important issues a proposal loses to the status quo, half the time it is due to a manipulated cycle. Later, Riker estimated that cycles afﬂict 10 percent of legislative votes (Bell 1974, 308). Still later, Riker (1982, 122–123) acknowledged there is a tendency to similarity among preference orders that reduces the likelihood of cycles: “there is good reason to believe that debate and discussion do lead to . . . fundamental similarities

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of judgment.” However, the possibility of manipulation increases the likelihood of cycles, he argues. The net result: there are few cycles on unimportant issues, but more cycles the more important the issue is to the manipulators. More precisely: quite a wide variety of rather mild agreement about the issue dimension guarantees a Condorcet winner . . . not all voters need display the agreement to obtain the guarantee . . . agreement about dimensions renders uncontrived cyclical outcomes quite rare . . . intransitivities only occasionally render decision by majoritarian decisions meaningless . . . at least when the subjects for political decision are not politically important. When, on the other hand, subjects are politically important enough to justify the energy and expense of contriving cycles, Arrow’s result is of great practical signiﬁcance . . . on the very most important subjects, cycles may render social outcomes meaningless. (Riker 1982, 128)

I will argue in Chapters 9 through 17 that Riker is unable to demonstrate the existence of a cycle on any issue, minor or major. Riker later (1990b, 179) granted that, “Poole and Rosenthal . . . have shown with large empirical studies of congressional voting that, in the absence of grand manipulation, a considerable part of political life is unidimensional.” Poole and Rosenthal (1997) dedicate their book to Riker, their “teacher, friend, and colleague.” Their spatial analysis of all roll-call votes in the 1st through 100th Congresses of the United States shows that about 85 percent of all votes can be accounted for in two dimensions. Moreover, “Except for two periods of American history, when race was prominent on the agenda, whenever voting could be captured by the spatial model, a one-dimensional model does all the work” (227). The ﬁrst and overwhelmingly important dimension is what we popularly understand as the standard left–right dimension. The second dimension explains only about 2 percent of the 85 percent captured. The second dimension varies from Congress to Congress, and varies from public works to currency to tariffs and other issues; but was most salient as slavery in the period before the Civil War (the 37th Congress in 1850 most poorly ﬁt the spatial model) and as race relations in the civil rights era of the 1950s and 60s. Testing for third, fourth, and greater dimensions on the whole does not explain meaningfully more than the two-dimensional model. Since the mid-1970s, the Congress has become increasingly and is now almost wholly unidimensional (Poole and Rosenthal 1999). A unidimensional issue space implies no cycles; and the mostly unidimensional issue space discovered by Poole and Rosenthal implies very few cycles. Originally, I suspected that this unidimensionality was somehow a product of the American two-party system and thus not evidence for

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a strong tendency to unidimensionality in politics. The Poole–Rosenthal (1999) methods, however, have recently been applied to votes in the European Parliament (1989–1997), the British Parliament (1841), the French National Assembly (1951–1956), the Czech Parliament (1993– 1997), the Polish Parliament (1995), and the United Nations General Assembly (1946–1996). The percentage of votes correctly classiﬁed by a single dimension of analysis ranges from 85.9 percent in the UN (1954–1969) to 94.2 percent in the Czech Parliament. The Czech Parliament is a multiparty system, and the United Nations comprises the diverse interests of six billion people. It is possible that the apparent unidimensionality is an artifact of the Poole–Rosenthal methodology. Budge (1993) and coworkers examined all party manifestoes or platforms from 1945 to 1981 in 23 democratic countries and applied factor analysis. They found that one dimension, the standard left–right dimension, best explained the data. After reporting the ﬁndings of Poole and Rosenthal and of Budge, Riker (1993, 4) acknowledged that “issue spaces tend to be one-dimensional over time.” He responded that second dimensions would be of relevance, presumably with respect to manipulation, in the short run. On his own terms, Riker’s claim of meaninglessness now stands only on incidents of grand manipulation. Even if, as Riker maintains, all cyclical manipulations are difﬁcult to detect, he must be able to demonstrate some instances from the rich universe of politics, especially since cycles are supposed to be associated with the most important issues on which we would have the most information. Otherwise, his claim would have nothing but the glory and the shame of an untestable empirical claim. If there are only a handful of such incidents, then the meaninglessness claim fails, and it utterly fails if the handful do not withstand scrutiny. Later we shall investigate in detail the topics of strategic voting and agenda manipulation; for now accept that an instance of legislation defeated by a killer amendment implies the presence of natural cycles or of the manipulatively contrived cycles that Riker stresses. With respect to strategic voting, Poole and Rosenthal (1997, 147) “found very few bothersome needles in our haystack of 37,000 roll calls.” The three instances of successful killer amendments identiﬁed in the political science literature are the three recited by Riker in Liberalism against Populism, known as the Wilmot Proviso, the Depew–Sutherland amendment, and the Powell amendment, and each does have to do with race, often the second dimension in American politics, according to Poole and Rosenthal (1997, 162). With almost ﬁfty years of controversy, and strong professional incentives for unveiling grand manipulations, these are the three that we have from the universe of American Congressional roll-call votes to support the

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proposition that democracy is meaningless. In later chapters, I will show that Riker’s accounts of these three events are mistaken. The jewel in the crown of Riker’s examples of grand manipulation (not related to Congressional roll calls) is his famous allegation of a cycle in the 1860 American presidential race that resulted in the arbitrary election of Lincoln and consequently the Civil War. As promised, I will later show that his account of that election is clearly mistaken and that there was no such cycle. In a review article on the subject, Enelow (1997) writes that, “cycling and majority rule is one of the most heavily researched areas of public choice” (149), yet, citing only Riker, he acknowledges that “basically, the empirical literature testing the theory we have described consists of a small set of examples” (160). If I succeed in showing that Riker’s and others’ examples are mistaken, then the cycling hypothesis must die from lack of evidence. Further, it would be shown that the Arrow theorem cannot be interpreted to conclude that democracy is meaningless.

Justifying the theorem’s conditions The deﬁnition of a social-welfare function requires that both individual and social preferences be orderings – complete and transitive ordinal rankings. Condition I goes beyond requiring individual orderings, and in addition requires that all voting rules proceed by pairwise comparison. These issues will be discussed in depth in Chapter 6. Condition P (if all voters prefer Metallica, then society prefers Metallica) is not as innocent as it ﬁrst looks. That’s because the Arrow theorem is not an engineering guidebook, but rather it is a logical exercise: it need not be that any of the conditions are actually violated, rather the transgression occurs if one of them could be violated. Condition P rules out such social-choice rules as: do whatever the Bible says to do. It may be that all voters want society to do what the Bible says to do, but the point is, if the citizens were to change their view about that, the socialchoice rule would still dictate doing what the Bible says to do. Consider, among other concepts, Rousseau’s concept of the general will, inalienable rights to life and liberty, the US Constitution, or Rawlsian justice. Each violates Condition P, to the extent that each is not based on aggregation of individual orderings into a social ordering. It could be that the unanimous will of all (aggregated votes) is identical to the general will (the true or right decision), but it could be that everyone is mistakenly opposed to the general will; and because it could happen, the general will as a decision rule is in violation of P. It may that everyone agrees that I have an inalienable right to life and liberty, but it is logically possible that

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everyone, including me, would vote to deny that right. Thus, the right is in violation of P. Condition D – no one person determines the social ordering regardless of the preferences of other individuals – is of direct normative relevance to democratic theory. The condition is quite thin, however. Other than Conditions P and D the Arrow theorem is noncommittal about democracy, as the theorem declares impossible both democratic voting rules that give each citizen one vote and undemocratic voting rules that give more weight to some classes or exclude other classes of persons or establish any dictatorship of two. Notice also that in the absence of some independent justiﬁcation, Arrow’s nondictatorship condition seems to bring a worry relating to the interpersonal comparison of welfare into the scheme, contrary to its logical positivist foundations. If there is no way of comparing the welfare of one person to another, then why should we object if one person gets to decide everything? It could be, and many dictators act as if it were so, that the satisfactions of the dictator are worth 1,000 times everyone else’s put together. That leaves Condition U, unrestricted domain, which says that the domain of the social-choice function includes all logically possible individual orderings of the alternative social states. When social preferences cycle, there is no social choice, according to the deﬁnitions. Condition U contributes to the impossibility result because only cyclical proﬁles of individual preferences yield cyclical social orderings. If the domain of individual preferences were limited so as to exclude cyclical proﬁles, then there would be no impossibility result. Two justiﬁcations typically are offered for Condition U. First, that Arrow’s theorem seeks generality, and U is the most general assumption. But that is not so. Condition U requires individuals to have complete and transitive orderings. Obviously they don’t in real life, and a more general condition would be to permit individuals to have some incomplete and some intransitive preferences. The problem with the more general condition is that it would detract from the rhetorical force of the Arrow result, since all that would be shown from the more general condition is that incomplete and intransitive individual preferences may aggregate into incomplete and intransitive social preferences. Second, it is said that to exclude some preference orderings would be tyrannical. Condition U has been interpreted to mean that “citizens should be free to prefer any policy option at all and to rank any options in any way they want, meaning that no institution should have power to declare certain choices out of bounds at the start” (Pildes and Anderson 1990, 2,132). Any domain restriction that would mitigate the Arrow theorem’s impossibility result would have harsh consequences for those whose

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preference rankings fall outside the domain restriction. We would have to “restrict entry into the community to those having preference orderings that do make collective choices possible” or if it is already too late “they must somehow be isolated and excluded from the community, or an impossibility result can again emerge” (Mueller 1989, 392–393). In the next chapter, I shall argue that if the question is about the public interest, then individual preferences are naturally sufﬁciently similar to one another’s to avoid cycling most of the time. And if the question is ﬁxed-sum redistribution, then destructive self-seeking preferences should be excluded from public consideration (as taught in kindergarten).

5

Is democracy meaningless? Arrow’s condition of unrestricted domain

Introduction Given theoretically predicted instability, why the empirically observed stability? There are several types of answers: that stability is an illusion because we are unable to detect the manipulation that occurs (Riker 1982); that stability is due to institutional devices (e.g. Shepsle and Weingast 1984); that such institutional devices are themselves pervasively unstable (Riker’s rejoinder 1980a); that stability is due to similarity in preference rankings among the population, and to preferences for fair distribution; or is due to some other defect in the models. The counterempirical outcome of Arrow’s theorem puts us on notice that one or another of its conditions must be misconceived. I begin with similarity among individuals’ preference rankings, a challenge to the realism of Arrow’s condition of unrestricted domain. The theorem’s impossibility result is a logical possibility but not an empirical probability, I shall argue. One kind of similarity in preference rankings is disastrous though: if majority-rule voters divide up a ﬁxed good, and if each is motivated solely by self-interest and not at all by fairness, then we are guaranteed instability. Contrary to theoretical prediction, however, democratic legislators are typically universalistic rather than factional on distributional questions. This may be due to uncertainty about the future, or a direct concern for fairness, or independently motivated reciprocity, or public deliberation, or due to some combination of these devices. Empirical work shows that citizens vote judgments of general welfare rather than personal welfare. An individual voter almost never affects the outcome of an election, hence she is free to express her disinterested sentiments rather than her interests, and this may explain the empirical ﬁnding. Further, there is empirical evidence that Americans overestimate the prevalence of self-interest. If there is not sufﬁcient fairness in the population to tame Condorcet-voting instability, I argue, then there are other acceptable voting rules that avoid cycles altogether. 95

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Table 5.1. Probability of Condorcet winner, impartial culture, strong preference order Voters’ Alternatives

3

5

7

9

49

Limit

3 5 7 25 Limit

0.944 0.840 0.761 0.475 0.000

0.931 0.800 0.704 0.379 0.000

0.925 0.785 0.682 0.345 0.000

0.922 0.776 0.670 0.327 0.000

0.914 0.752 0.638 0.281 0.000

0.912 0.749 0.631 0.270 0.000

Note: Table adapted from data in Gehrlein (1983, 174). It is important to distinguish two forms of the Condorcet Paradox: ﬁrst, when there is no Condorcet winner; second, when there are more than three alternatives, and there is a Condorcet winner, but there is a majority cycle on alternatives below the Condorcet winner. The Table, and the discussion, unless otherwise indicated, refer to the ﬁrst form of the paradox.

Simulations of homogeneity In the last chapter, we saw that voting cycles are rare in measures of realworld preferences. Why might that be so? Simulations suggest that it is because of natural similarities among individuals’ preference rankings. Unrestricted domain is any combination of individual preference orders. For lack of any more salient and tractable assumption, calculations of the probability of cycling therefore tend to assume an impartial culture, just as deﬁned in the discussion of Nurmi (1992) above: each of the A! orders of alternatives is equally likely. Under the impartial-culture assumption, the probability of cycling increases slowly as the number of voters increase, and increases more quickly as the number of alternatives increase, as seen in Table 5.1. Simulations assume strong preference orders (no indifference among alternatives) for computational convenience. If weak preference orders (voters may be indifferent among some candidates) and impartial culture are assumed, then the probability of a Condorcet winner changes. If we permit ties for top place, in the three-voter, three-alternative case the probability of Condorcet winners increases from 0.944 to 0.995 for weak preference orders (Van Deemen 1999). If we require a unique majority choice, then a Condorcet winner among weak preference orders is less likely than among strong preference orders with smaller numbers of voters, and a Condorcet winner among weak preference orders is more likely than among strong preference orders with larger numbers of voters (Jones et al. 1995). These gyrations are simply due to how the impartial-culture assumption behaves in the contrasting simulations; what is important, as

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we shall now see, is that the more similar are preference orders the less likely are cycles. Regenwetter, Adams, and Grofman (2000) remark that the empirical literature ﬁnds evidence of virtually no cycles, and that the few cycles observed tend to be over low-ranked alternatives not sharply discriminated among by voters. Tsetlin, Regenwetter, and Grofman (2001) demonstrate that for three voters the impartial-culture assumption maximizes the probability of cycles in samples drawn from an inﬁnite population of individuals with transitive weak preferences. In this setting, any departure from the impartial-culture assumption, realistic or not, reduces the probability of cycling. Recall that Tangian (2000) showed that as we depart from the impartial-culture assumption, and as the number of voters increases, then the outcomes selected by summed cardinal utilities, the Condorcet method, and the Borda method tend to converge. Since there are no cycles with summed utilities or with the Borda count, that implies that with a large number of voters cycles are extremely unlikely, according to Tangian. Similarly, List and Goodin (2001, Appendix 3) show that, given suitably systematic, however, slight, deviations from the impartial culture assumption, the probability of a cycle converges either to 0 (more typically), or to 1 (less typically) as the number of voters increases. The impartial culture assumption is often used in textbook demonstrations of the incidence of cycling (e.g., Shepsle and Bonchek 1997, 53, who on the assumption of impartial culture also claim that the likelihood of cycles goes up as the number of voters increases, contrary to Tangian), but it is the assumption most likely to yield cycles. There are several ways of conceptualizing the similarity of preference orders. I will begin with the probabilistic. Kuga and Nagatani (1974) develop an antagonism index, a ratio of the number of antagonistic choice pairs (e.g., x > y and y > x) to the number of pairs of persons in the population, normalized by the number of persons in the population. Under the impartial-culture assumption the antagonism index would equal one. When that antagonism index is 23 or less, there is no voting paradox (by analysis), between 23 and 1 the probability of paradox increases as antagonism increases (by simulation). Williamson and Sargent’s (1967, 811) probabilistic method concludes, “where unimodal preferences exist . . . and a large vote can be expected, the probability of intransitivity seems to vanish.” Berg’s Polya-type urn model claims to subsume most remaining prior measures of homogeneity of preferences, and conﬁrms prior studies: “greater preference similarity among voters, or stronger mutual inﬂuence among voters, leads to a lesser chance for the paradox of occurring” (Berg 1985, 379). The model contains a contagion or

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Table 5.2. Probability of Condorcet winner, increasing homogeneity, three alternatives Homogeneity parameter # of voters

0

3 5 7 Large

0.9444 0.9306 0.9250 0.91226

1 4

0.91919

1 2

1

2

3

10

0.9750 0.9665 0.9626 0.95493

0.9815 0.9602 0.9690

0.9952 0.9938

0.92578

0.9643 0.9524 0.9470 0.93750

homogeneity parameter, and as that parameter increases, the probability of a Condorcet winner increases. Suppose an urn with chips of six different kinds corresponding to the six strong preference orders resulting from three alternatives. When the homogeneity parameter is zero, voters are independent of one another, and chips are drawn from the urn with no replacement (known in the literature as the impartial-culture assumption). When the homogeneity parameter is one, we replace a chip drawn with one of the same kind (known elsewhere in this literature as the anonymous-culture assumption). When the homogeneity parameter is two, we replace a chip drawn with two of the same kind, and so on, reﬂecting the extent to which voters inﬂuence one another. Gehrlein (1995) further developed estimations of Condorcet efﬁciency and social homogeneity under the urn model. In Chapter 3 on the irrationalists’ claim that democracy is arbitrary, I argued that natural similarity among individual preference orders reduces divergence of outcomes among alternative reasonable voting rules. I argued that people have similar preference orders because they live in the same world and they have similar interests in that world; for example, most prefer prosperity to torture of kittens to suicidal nuclear war. If again we move from logical possibility to empirical probability, then the irrationalists’ claim that democracy is meaningless also seems to miss the target. Even if there is no similarity among individuals’ preference rankings, the probability of a cycle is very low. With a more natural similarity among preference rankings, such as what we found in our empirical examination in the last chapter, the probability of a cycle shrinks further. It is nature that provides the cycle-shrinking domain restriction, not human institutions. To relax the domain restriction does not require a crushing uniformity in the population, nor the horrifying picture of preference police hounding out those with topsy-turvy rankings. Should everyone have topsy-turvy rankings, then of course there is no mere aggregation

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Table 5.3. Egomaniacal redistributional instability Voter:

A

B

C

200 300 0 299 300

200 300 301 0 300

200 0 299 301 0

Coalition: 1. ABC 2. AB 3. BC 4. AC 5. AB

function that can bring order out of disorder. In that case, however, the fault lies in the distribution of preference rankings, not in the voting rule. Condition U was primarily intended as a matter of methodological convenience, according to Brennan and Hamlin (2000, 106–107). Whatever the intent, the condition is normative in effect, they continue. The requirement that all and only individual orderings be admitted for social choice is not neutral, but rather is a particular view on the question. The condition bites even if everyone were to agree to exclude some kinds of preferences – such as the unfair, the malevolent, or even the evil – from consideration. Such an agreement would violate the condition; the condition is imposed even if all citizens were to reject it. The imposition of a rule dictating the consideration of evil preferences is not normatively compelling. Condition U “imposes a substantive and questionable ethical view on members of society, while at the same time failing to reﬂect the patterns of common interest that might be expected to arise within genuine societies” (107).

Egomaniacal redistributional instability I said that natural resemblance of preferences from individual to individual almost eliminates cycling, but in another way similarity of preferences might force Condorcet instability. Asked what the disagreement was between himself and King Francis I of France, Charles V replied: “My cousin Francis and I are in perfect accord – he wants Milan, and so do I.”1 If Condorcet majority-rule voters are engaged in division of a ﬁxed good, let’s say pie, then instability is inevitable if each insists only on getting the most pie for himself (Sen 1995, 10). In Table 5.3 we begin in stage one with an equal distribution of 200 each among majority-rule voters A, B and C. But next in stage two the coalition AB can form, offering each of A and B more than they would receive under equal distribution. But

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in stage three, the coalition BC could offer each of B and C more than they would receive in stage two. But in stage four, the coalition AC could offer each of A and C more than they would receive in stage three. But in stage ﬁve, the coalition AB could return and offer each of A and B more than they would receive in stage four. And so on. Say that there are three piemen: Jaime, Lyman, and Simon. Any majority-rule coalition of two or three is unstable. Condorcet voting cannot transform the egomaniacal “more-for-me” preferences of these three into a fair outcome. Suppose that each of the three piemen has a preference in the ﬁrst rank of all the pie for himself, and then in the second and third ranks has random preferences over all the pie going to one of the two others, such that there is a cyclical proﬁle over the “more-for-me” alternatives, and in fourth rank has preferences for fair division of the pie. There is a cycle over the “more-for-me” alternatives, each of which is preferred over fair division. (In contrast to cycling with Condorcet voting, Borda voting would declare a tie among all-for-Jaime, all-for-Lyman, and all-for-Simon.) If, however, the ﬁrst rank remains the same, but fair division is moved up to everyone’s second rank, then fair division becomes the Condorcet winner, and the more-for-me alternatives cycle in the remaining ranks of the social ordering (Borda would rank fair division ﬁrst, and a tie among the all-for-me alternatives). Thus, even if everyone’s ﬁrst preference is more-for-me, if their second preference is fair division, then fair division prevails as the social decision. Impartial alternatives drive out partial alternatives. To illustrate more explicitly, assume there are ﬁve individuals, labeled 1 through 5. There are six alternatives: v gives the whole world to individual 1, w gives the world to individual 2, x gives the world to individual 3, y gives the world to individual 4, z gives the world to individual 5, and a divides the world equally among the ﬁve individuals. The collective ranking is a > (x > w > v > z > y > x). Fair division prevails (and would prevail even if fairness were anywhere in the upper half of the rankings). If preferences for fair division were originally ranked lowest, and if there were costs to cycling, then perhaps it would develop that preferences for fair division would come to rank higher. Since there are many redistributional issues in politics, some commentators are conﬁdent that there must be much majority-rule instability, even if it is difﬁcult to detect empirically. But I think they are making an empirical assumption, controversial and not widely warranted, that political participants do not at all value fair outcomes. As I have told the story, each voter could still in a childish way want all the pie for himself, but just so long as each ranks fair division better than random distributions of the pie then there is a tendency for the social choice to be fair division. They would also

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Table 5.4. Impartiality displaces partiality Individual:

1

2

3

4

5

v a z y x w

w a v z y x

x a w v z y

y a x w v z

z a y x w v

Ranking: First Second Third Fourth Fifth Sixth

Pairwise comparison matrix a a v w x y z

1 1 1 1 1

v

w

x

y

z

(BC)

4

4 1

4 2 1

4 3 2 1

4 4 3 2 1

(20) (11) (11) (11) (11) (11)

4 3 2 1

4 3 2

4 3

4

have to rank universalistic outcomes over majority-faction outcomes, but that would be likely if majority coalitions were unstable and themselves random in incidence. In earlier work based on cooperative game theory, Riker (1963) formulated his size principle: that in the majority-rule division of a ﬁxed good, only minimum-winning coalitions would form. If the voting rule is half the voters plus one, then all distributional measures would be won only by that margin. The idea is that adding more members to the coalition would dilute the amount of the good going to each member of the coalition. If there are 100 voters, dividing the pie among 51 of them gives each of the 51 more than she would get than dividing the pie among 52 or among all 100. A problem developed with the theory: actual legislatures infrequently passed measures by the minimum number of votes, rather they frequently passed measures by large, almost unanimous majorities, especially on distributional issues. Empirical studies concluded that “distributive policy making was characteristically associated with the development of an extremely large and at times unanimous coalition that included virtually everyone with a stake in the outcome” (Collie 1988, 430).2

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Congressional porkbarrel spending on projects at the CongressionalDistrict level resembles such a constant-sum game. If there is cycling, then spending by district should equalize over time, as losers can always create new winning coalitions; if there is no cycling, then spending by district should remain stable from year to year. Stratmann (1997) proposes a measure for this, applies it to federal-funding data, and infers an absence of cycles. If his ﬁnding is correct, it may be due to any number of reasons, for example institutional constraints in Congress, or perhaps there are substantive reasons for some districts consistently to obtain more funding than others, and it is not necessarily due to a similarity among preference orders. Additionally, Poole and Rosenthal’s (1997; 1999) data suggest that although the one dimension of importance in Congress is the struggle between the poor and the rich, still, redistributive struggles rarely take a multidimensional form. Brennan and Lomasky (1993, 44–45, 83) say that the instability story strains credulity: one never observes the degree of volatility in spending or taxation that the cycling model requires. The empirical tendency was termed the norm of universalism. Weingast (1979) sought to explain universalism within the inherited cooperative game-theoretic framework. The set of minimum-winning coalitions dominates all coalitions not in the set. But, Weingast argued, beneﬁtseeking legislators would be uncertain, as the vote approached, of which of the many possible minimum-winning coalitions would form and win. Because of this uncertainty, the chance of ending up in a losing coalition, each legislator beforehand would prefer the universalistic coalition to any other coalition. The Weingast model assumed that the beneﬁts of projects funded exceeded their costs, which, because of the view that many government-funded projects are economically unjustiﬁable, occasioned further models by him and others that would explain inefﬁcient projects.3 Ferejohn, Fiorina, and McKelvey (1987) modeled the same problems with noncooperative game theory. In the one-shot game, the cheapest projects would be funded, and by a minimum-winning coalition. If that stage game were indeﬁnitely repeated then, as with social-dilemma models of indeﬁnite repetition, any Pareto-optimal outcome is sustained in equilibrium, from minimum-winning to universalistic. Baron and Ferejohn (1989) modeled a sequential multilateral bargaining game. Now the pie rots as the legislators debate how to divide it up. Under a closed rule, a minimum–coalition wins. Under an open rule, the outcome can be universalistic, but only if the legislature is quite small in number of voters (or in blocs) and if the pie rots quickly. Glazer and McMillan (1982) propose a nifty noncooperative model that yields a universalistic equilibrium when legislators want to spend their limited time, in my metaphor,

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baking new pies rather than ﬁghting over the division of old ones. Groseclose and Snyder (1996) propose another model showing that supermajority coalitions can be cheaper than minimal-winning coalitions. There is an alternative hypothesis to explain the observed norm of universalism, however, which enjoys the advantage of consistency with a controlled experiment on the topic, and more importantly consistency with legislative discourse on redistributive taxing and spending tasks.4 The alternative hypothesis is that a sufﬁcient number of voters are directly concerned to attain a fair distribution. Miller and Oppenheimer (1982) conducted experimental tests of Weingast’s model of universalism. In controlled experiments, ﬁve-person committees were formed, and individuals’ preferences were induced by cash reward. Committees operated by majority rule, any three of the ﬁve members determined the outcome, after 15 minutes available for discussion; and subjects were prohibited from redistributing rewards outside the terms of the experiment. Coalitions of three or more could choose among one alternative that provided an equal distribution to all ﬁve committee members and other alternatives that would provide various payoffs to the members. In the ﬁrst experimental condition, the value to each member of equal distribution was $12.40, and, a` la Weingast, the expected value of belonging to any one of the decisive three-member coalitions was $8.40. If a threemember coalition were actually to win on any alternative other than equal distribution, each of its members would make more than $12.40. Subjects rapidly agreed that equal distribution was the best choice. Typically some members pointed out that three members could be made better off, and typically some members responded that an alternative three-member coalition could be formed leaving two of the three in the original coalition worse off, and then members would settle for the safety of equal distribution. Subjects were aware of the fragility of equal distribution, and typically truncated discussion so as to discourage temptation. Four of ﬁve committees were unanimous for equal distribution, in the ﬁfth, the vote for equal distribution was four against one economics student. In the second condition, the value of equal distribution was made $8.50, just above the expected value of belonging to any one of the decisive three-member coalitions. In four groups out of ﬁve, members chose the equal distribution. In the ﬁfth group, discussion secured unanimous consent to explore coalition formation, and a three-member coalition formed. Weingast’s model seems to be supported. Further experiments were run, however, with the universalistic alternative worth less than the expected value of $8.40 for belonging to one of the decisive three-person coalitions. In the third condition, equal distribution was worth $6.72. Still, in four out of ﬁve committees the universalistic alternative was chosen.

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In the ﬁfth committee, three members wanted universalism, and two insisted on coalition formation. In response, the three members who originally proposed universalism voted for their own three-member coalition, thereby punishing the two members for advocating an unfair outcome! In a fourth condition, equal distribution was lowered to $4.20. Again, four out of ﬁve committees chose equal distribution. The ﬁfth committee devised an alternative universalism: they decided to draw lots among all alternatives, with an expected value of $7.70 for each member. They then voted unanimously for the randomly drawn outcome. The third and fourth conditions do not support the Weingast model. In a ﬁfth condition, equal distribution was worth only $2.10; ﬁnally, members agreed that the equal distribution was not worthwhile. I have gone on at length because I think it is important to remember the possibility that on distributional questions many people are motivated directly by fairness. More than a decade of human-subject experiments, say Fehr and Fischbacher (2002), demonstrate robustly that many humans possess social preferences beyond material self-interest, and, they continue, some economic models that neglect this fact fail in their predictions. Although the models of economists permit complete heterogeneity of taste with respect to material consumption, they insist that individuals are motivated only by self-interest and dogmatically exclude heterogeneity in social preferences. The experiments show, however, that roughly 40 to 50 percent of subjects are motivated by reciprocal fairness. Moreover, the presence of a critical mass of those motivated by reciprocal fairness changes the incentives of the selﬁsh types, resulting in constraints and interaction patterns quite different from those that would result if the population were wholly selﬁsh. A reciprocal individual responds to kind action with kind action, and to hostile action with hostile action. Such reciprocity is carried out even if costly; it is not motivated by expectation of future material beneﬁt; it differs from retaliatory behavior in repeated interactions. It also differs from altruism, which is kindness in response to either kindness or hostility. The primary experiment in this paradigm is the ultimatum game. A pair of subjects are assigned the task of dividing a given sum of money, in an unrepeated, one-shot game. The ﬁrst makes an offer to the second of from 0 to 100 percent of the sum. The second either accepts or rejects the offer. If the second accepts, then the second gets the share offered, and the ﬁrst gets the remainder. If the second rejects, then both get nothing. The rational-choice prediction is that the ﬁrst will offer the smallest possible unit of money, say a penny, and the second will accept. The experiments show, however, that proposals offering less than 20 percent are rejected with 0.4 to 0.6 probability. Also, it appears that proposers anticipate rejection of lower offers, which motivates them to make higher

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offers. This is shown by comparison to dictator games, where the ﬁrst mover simply decrees the division. The rational-choice prediction is that ﬁrst movers would give nothing; in dictator experiments, however, some give, but on average less than in the ultimatum game.5 Henrich et al. (2001) conducted ultimatum, dictator, and social dilemma games across ﬁfteen nonindustrial cultures, and found that humans consistently deviate from the model of textbook economics. Many appear to care about fairness and reciprocity and reward cooperators and punish noncooperators, even when such actions are costly to the individual. Mean offer per culture in ultimatum games ranges from 0.26 to 0.58. The Los Angeles County Board of Supervisors, report Cox and Tutt (1984), formally adopted a rule that nonmandated federal funds be divided equally among the ﬁve supervisorial districts – again, the norm of universalism. Observe that any three supervisors superﬁcially have an incentive to vote to depart from the norm, but that they do not. One of the things I did before going to graduate school in political science was to serve for three years as the directly hired policy aide (aka political hack) to one of three elected commissioners of a county of about 250,000 people – the retail politics of roads, sewers, zoning, garbage, and dogs. The norm of universalism was common in allocative decisions, with arguments around the edges. One day, however, there was a palace revolution. We policy aides went into a meeting to discuss allocation of millions of dollars of CETA make-work funds among the many applicants. The previous year the norm of universalism was informally followed. In the year under discussion, a representative advisory committee had ranked proposals. In the meeting, the aides of the other two commissioners junked the advisory committee proposal, and devised a list of grantees which excluded any applicant of interest to the third commissioner, my boss. Moreover, the gang of two continued this exclusive collaboration on all further issues. Consider that when the norm of universalism is a possibility, everyone is strongly motivated to maintain comity. A permanent loser, however, has no such motivation and, spared some of the burdens of governance, has lots of spare time on his hands. There is more to politics than votes on propositions. My boss’s constituencies were extraordinarily mobilized because of the unfairness of the “CETA massacre,” he gained unexpected allies motivated solely by considerations of fairness because of it, and he triumphed against a well-funded opponent in his next reelection campaign. It also turned out that one of the gang of two became subject to a recall election. He survived the recall, but was permanently damaged politically, and later did not run for reelection. The other of the gang of two was accused of defrauding the county on a land sale; the criminal prosecution did not secure a conviction, but the political career

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of a gubernatorial aspirant was ended, and later a civil action against him to recover defrauded value did succeed. New commissioners after that operated more by the norm of universalism. Perhaps this is an example of reciprocity as a motivator of equal distribution. In the famous prisoners’ dilemma or social dilemma used widely to model many collective action problems, it is in each individual’s interest not to cooperate, which makes everyone worse off than they would be if all did cooperate. In terms of material payoffs, the problem may appear to be a social dilemma, but if there is a critical mass of individuals independently motivated by reciprocity to punish noncooperators, then the dilemma is transformed into a coordination game. In a coordination game there is more than one possible equilibrium, and the question is whether everyone will coordinate on an equilibrium that makes all or most better off or on an equilibrium that makes all or most worse off. In this model, cooperation could fail in one of two ways. First, given a critical mass of conditional cooperators, promoting cooperation involves management of people’s beliefs: “If people believe that others cooperate to a large extent, cooperation will be higher compared to a situation where they believe that others rarely cooperate” (Fehr and Fischbacher 2002, C16). Second, even if there is a critical mass of conditional cooperators, and people believe there is one, then it still may happen that people have inherited a welfare-inferior coordination equilibrium that can only be escaped by coordinated exit (see Mackie 1996). Notice that inheriting a welfare-inferior equilibrium, say a tradition of political corruption, might cause a false belief that there is not a sufﬁcient mass of conditional cooperators in the population, when in fact there are. A nice feature of a model like this is that it might explain both the presence and the absence of fair cooperation, for example, of democratic success in Australia, and of democratic failure in Argentina: identical institutions containing otherwise identical individuals might vary in fair cooperation just because people vary in their beliefs of what to expect from one another. This is one reason why some people deplore the rhetoric of the material-egoist version of rational choice theory: the more hegemonic is the theory, the more self-fulﬁlling it is, by causing people to believe that the proportion of unconditional and conditional cooperators in the population is less than it actually is, thereby making people worse off than they would have been in the absence of the theory. The correlation between self-interest (personal ﬁnancial situation) and voting in US presidential elections is usually 0.08, but after four years of self-interest rhetoric in President Reagan’s ﬁrst term of ofﬁce, and his call to “Ask yourself, are you better off today than you were four years ago?”, the correlation jumped to 0.36 (Miller and Ratner 1996, 31).

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Traditional social choice theory is solely concerned with voting, and excludes democratic discussion about the content of alternatives and reasons for favoring one alternative over another. Some strains of deliberative democratic theory seek to escape the social choice-problems of democratic voting by sole reliance on unanimous agreement attained by democratic discussion. In democratic institutions, I submit, voting and discussion are complements, not substitutes. A voting rule such as Condorcet’s is, or should be, adopted in the ﬁrst place due to considerations of fairness. Majority rule would be a hideous institution if it were conﬁned only to the casting of votes on alternatives without content, or if it were carried out by unfair people, or both. Sen (1982, 21) illustrates. In case A, person 1 is very rich, and persons 2 and 3 are very poor; 2 and 3 vote to take some from 1 and give to 2 and 3, reducing inequality. In case B, person 1 is very poor, and persons 2 and 3 are very rich; again 2 and 3 vote to take some from 1 and give to 2 and 3, increasing inequality. In the Arrovian noncomparabilist framework, Case A is identical to Case B. Some people might judge Case A to be morally wrong, but most people would judge Case B to be morally wrong. Recall Rousseau (1968/1762, 72): “There is often a great difference between the will of all and the general will; the general will studies only the general interest while the will of all studies private interest, and is indeed no more than the sum of individual desires.” If we could exclude egomaniacal preferences from consideration, then cycling would be of little worry. Is there some way to do this? Robert Goodin and Jon Elster propose that public discussion helps: The conceptual impossibility of expressing selﬁsh arguments in debates about the public good, and the psychological difﬁculty of expressing other-regarding preferences without ultimately acquiring them, jointly bring it about that public discussion tends to promote the common good. (Elster 1986b)

The full argument is found in Goodin’s (1995/1986) landmark essay, “Laundering Preferences.” Devices such as vested rights ﬁlter the output of collective decisions. Another kind of device is to ﬁlter the input to collective decision, via the exclusion of some individual preferences, the laundering of them. Acceptable grounds for laundering preferences include: for one individual, some preferences are more fully considered than conﬂicting others; some individuals agree amongst themselves to reciprocal forbearances, such as conditional toleration of the others; individuals may explicitly have preferences over what kind of preferences they should have, and the second-order preference should be honored over the ﬁrst-order preferences; individuals may implicitly have such second-order preferences; and ﬁnally, “our very choice of aggregating preferences as

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a way of making social decisions carries consequences for the kind of preferences that we can count” (140). Goodin suggests further that an individual might possess multiple preference orderings, selﬁsh or fair, material or moral, according to context, and that, in the context of collective decision making, role rationality dictates the expression of publicly oriented, ethical preferences and the suppression of privately oriented, egoistic ones. It’s pragmatically impossible to argue publicly that an alternative which affects others should be adopted solely because it is good for the arguer. Further, that someone is voting in the ﬁrst place indicates an ethical context, because voting is instrumentally irrational according to rational choice theory (to be discussed in the next section). In addition to these pragmatic mechanisms, some or many individuals may possess simply moral motivations to support impartial outcomes. Elsewhere, Goodin (1992) cautions against expecting too much from this model of publicity and discursive defensibility. If a body of people is such that, on redistributive questions, most individuals and factions politically insist at all costs on more than their fair share of the social ofﬁces and product, then there will be instability, probably trouble, maybe even violence. Formally, there would be Condorcet-voting instability, but that is not the main problem. The ﬂaw is in the egomaniacal preferences of the individual citizens, not in the fact that those unfair preferences are aggregated by majority rule. For example, Didymus Mutasa, organizational secretary of the ruling party in Zimbabwe, ZANU-PF, in response to accusations that his government was withholding food aid from famine areas which did not vote for it in the election, is reported to have said that, “We would be better off with only six million people [out of a population of 12 million], with our own people who support the liberation struggle. We don’t want all these extra people.”6 No aggregation procedure can turn unfair individuals into fair ones.7 For someone such as Mutasa, public discussion probably wouldn’t do much good either. Voting and self-interest The empirical evidence indicates that democratic voters are not motivated by material self-interest, or only minimally in limited circumstances. Kinder and Kiewiet (1979, 1981) were the ﬁrst to investigate “sociotropic” voting. Generally, Americans vote for incumbent candidates when the economy is good, and for opposition candidates when the economy is bad. Most earlier work had been done on an aggregate basis, and thus it was wrongly concluded that citizens vote their pocketbooks: I

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vote against the incumbent when I’m not doing well. Alternatively, citizens could be sociotropically motivated: I vote against the incumbent when the country is not doing well. By studying individual rather than aggregate responses, Kinder and Kiewiet (1979, 524) showed that: With respect to economic issues, voters appear to choose between congressional candidates “sociotropically.” Voters are not egocentric in any narrow sense – they do not vote their own pocketbooks. Rather, their preferences follow a more collective reckoning.

Many similar empirical investigations were undertaken in reaction to the rise of the materially self-interested rational actor in the social sciences. Lewin (1991, 45) reviews the literature on self-interest or public interest in western politics, and ﬁnds that the “the results point overwhelmingly against the self-interest hypothesis.” He suggests that it is odd that the self-interest hypothesis is so tenaciously adhered to, when the great bulk of evidence goes against it.8 An even more detailed and wide-ranging review by Sears and Funk (1991, 47; abridged in Mansbridge’s excellent 1990 volume on self-interest), including survey data on two dozen diverse issues, ﬁnds “that personal self-interest generally has not been of major importance in explaining the general public’s social and political attitudes.” There are a few exceptions, and “self-interest is most potent when the issue provides large, clear, certain, and salient costs or beneﬁts” (63). Citrin and Green (1990, 16) conduct a similar survey, and conclude that the literature reviewed appears to be “devastating for the claim that self-interest, deﬁned narrowly as the pursuit of immediate material beneﬁts, is the central motive underlying American public opinion.” A test of whether individuals are concerned about whether or not their own group is doing well found another sociotropic effect, that citizens are concerned about whether economic gains and losses are distributed equitably among groups (Mutz and Mondak 1997). There are a great many confusions and equivocations about self-interest in the rational-actor tradition. Current economic theory has it that individuals maximize their utility, but the only content that claim has is that an individual chooses the most highly ranked alternative feasible from her consistent ranking of alternatives. Those aims could be egoistic or altruistic, smart or stupid, or apparently random, just as long as their ordering is consistent. The traditional utilitarian idea that individuals somehow maximize an underlying satisfaction is wholly abandoned. Individual aims, if they are concerned about the well-being of others, are nevertheless contained within the individual’s preference ranking; thus, it is sometimes said that the theory assumes that individuals are self-interested. But they are self-interested merely by deﬁnition: any alternative that St. Francis

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chose, no matter how selﬂess, was self-interested in this tautologous sense (Riker 1990b). It is more useful to say that current economic theory assumes that people are purposive rather than that they are self-interested. This is sometimes called the thin theory of rationality (Green and Shapiro 1994, 17–19). A thick theory of rationality goes further, and assumes an underlying dimension to those choices, often of objective content, in contrast to the purely subjective value assumed by the thin theory. The paradigm is the proﬁt-maximizing ﬁrm in the competitive market. Economic competition forces the successful ﬁrm to pursue solely proﬁt and to do so with perfect information. The rationality of the ﬁrm is measured by the objective criterion of proﬁt, and there is a background theory as to why on average ﬁrms should possess this thick rationality. Confusion arises when we move from ﬁrms to ordinary individuals, however. It could be assumed as a matter of modeling and measuring convenience that on average ordinary individuals engaged in economic activity are concerned to maximize material-egoistic wealth. This is a limited theoretical simpliﬁcation, however, not a descriptive claim, and should never be permitted to mislead, especially outside the economic sphere. Casual observation suggests a tendency to selﬁsh wealth maximization. But only a tendency, and primarily in the economic sphere: many individuals are also motivated by many other aims, including relations with family and friends, morality, justice, honor, and self-expression. Unlike ﬁrms in perfect competition, there is no background theory as to why ordinary individuals should exclusively maximize material-egoistic wealth; individuals who do not, are not irrational. Those who do – the C. Montgomery Burns of the world – seem to be more pathological outliers than healthy specimens of humanity, or so the wisdom of the ages suggests. I hasten to add that both self-interest and the pursuit of material wealth, in proper proportion and place, are consistent with if not necessary to the moral life. The reign of self-interest in popular economics is all the more puzzling in that the intellectual founders of the economic tradition themselves opposed Mandeville’s simplistic reduction of all human motivation to selfinterest. Holmes’s (1990) marvelous essay on the history of self-interest teaches us that David Hume, Adam Smith, and their fellow travelers believed both that an ideal of commercial self-interest was better for the common good than the ideals it displaced of a passion for military glory and the religious dogma of original sin, and that calculated self-interest was one human motivation among many. Calculation is contrasted with destructive impulse and folly, and self-interest is contrasted with varieties of benevolence on the one side and varieties of malevolence on the other. Some disinterested motivations are good, and, Holmes teaches, plenty

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of disinterested motivations are evil: these days, one thinks of the selﬂess cruelty of suicide bombers. Olson’s logic of collective action assigns a certain preference ranking to each individual, together these preferences amount to a social dilemma, and thus nonrivalrous and nonexcludable public goods tragically are undersupplied, the story goes. Rational individuals, Olson claims, will not voluntarily contribute to public goods, instead they will free-ride on the efforts of others, a ﬁnding that irks many. Olson and his followers believe that, since the contribution of any one agent does not affect provision of the public good, each agent would ﬁrst prefer to avoid her own costly contribution while all others contribute, second prefer mutual cooperation, third prefer mutual defection, and last prefer being the only person to contribute. The social outcome is mutual defection, even though mutual cooperation is better for everyone. Pellikaan and van der Veen (2002) show that Olson’s logic wrongly assumes that the objective interest of ﬁrms in the competitive market should apply as well to ordinary individuals. The thick rationality of competitive ﬁrms, for whom that ranking is appropriate, is confounded with the thin rationality of ordinary individuals. They further show that on certain environmental questions Dutch citizens do not have the preference order leading to a social dilemma, in fact, many are shown to be unconditional cooperators, willing to contribute even if others do not, just as some moralities would recommend. We have seen assumptions of self-interest and perfect information justiﬁed within a model of ﬁrms in a competitive market unjustiﬁably transplanted into the ordinary individual. Next, one variety of public choice theory goes one step worse: it transplants these same assumptions into the voter, for whom they are not justiﬁed at all. There is no background theory as to why the ordinary individual should be a maximizer of material self-interest, but there is or should be a background theory of why the ordinary voter should not be a maximizer of material self-interest. If there are more than a few voters in an election, then it’s unlikely that my vote would make any difference to the outcome, and the more voters there are the more unlikely it is that I would be decisive. Since voting takes effort, no instrumentally rational person would bother, and according to rational choice theory almost no one would vote, which we shall term the paradox of participation. Goodin and Roberts (1975) may have been the ﬁrst to point out that this unleashes the ethical voter. As in the argument about public deliberation, suppose that the individual possesses multiple preference orderings, selﬁsh or fair, material or moral. Since the individual’s vote lacks decisiveness, egoistic preferences are made futile, and thereby expression of ethical preferences comes to the fore. This is fully developed by Brennan and Lomasky (1993). In the market, the agent is

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decisive; if she chooses A over B, she gets A and forgoes B. When the voter chooses A over B, however, the outcome is not a function of how she votes, but of how everyone votes. For each voter, electoral outcome is detached from electoral choice. The market responds to interests, but democratic voting invites the expression of disinterested ethical and ideological principles. Thus, the empirical ﬁnding of sociotropic voting may have a theoretical foundation in the account of voting as expressive rather than instrumental action. As we have learned from Holmes, however, and as Goodin, Roberts, Brennan, and Lomasky conﬁrm, the disinterested need not be the good: justice could be unleashed, but so could jingoism. All the more important then is sound public deliberation over the content of political alternatives. Sen’s (1995, 15) presidential address to the American Economic Association deplores a trend among some economists to reduce all socially motivated action to some kind of cunning attempt to maximize purely private gains, and wonders whether the trend is more prevalent in America than in Europe, citing Tocqueville (1969/1851, Book II, Chapter VIII): The Americans . . . enjoy explaining almost every act of their lives on the principle of self-interest properly understood. It gives them pleasure to point out how enlightened self-love continually leads them to help one another and disposes them freely to give part of their time and wealth for the good of the state. I think that in this they often do themselves less than justice, for sometimes in the United States, as elsewhere, one sees people carried away by the disinterested, spontaneous impulses natural to man. But the Americans are hardly prepared to admit that they do give way to emotions of this sort. They prefer to give credit to their philosophy rather than to themselves.

Miller and Ratner (1996; 1998) update Tocqueville’s observation. They undertook a series of social-psychology experiments which measured both the actual extent that self-interest guided action, and people’s estimates of the extent of self-interest motivation in the situation. For example, they asked subjects whether or not they would be willing to donate blood for free and whether or not they would be willing to donate blood for $15, and they also asked subjects to estimate what percentage of their fellow students would donate blood for free and for $15. Material payoff only mildly affected willingness to give: 73 percent said they would donate for a price, 63 percent would donate for free. But the same subjects underestimated by half the number of students willing to donate blood for free: they thought that 61 percent of the population would donate blood for a price, and that only 32 percent would donate blood for free. Similar experiments studied effect of gender on support for abortion coverage, effect of racial status on concern for minority needs, and effect of

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payment on willingness to participate in future experiments, and found the same overestimation of self-interested motivation. We are enthralled by a myth of self-interest, according to Miller and Ratner. Public discourse equating rationality with self-interest normalizes actions consistent with self-interest and pathologizes actions inconsistent with it. People experience discomfort when they take action inconsistent with self-interest: one study found that people’s decision about whether or not to pursue an injury claim was based much more strongly on expectations of ﬁnancial gain than on expectations of fair treatment, but that people’s satisfactions with the claiming process were based far more on fair treatment than on degree of ﬁnancial gain. Thus, people ignore their own sentiments in favor of the norm that material self-interest should predominate, and they are led “to willingly adopt decision strategies they know will not maximize their satisfaction” (1996, 35). People fear social isolation when they take actions inconsistent with self-interest. People justify their actions in terms of self-interest: they explain their charitable activity, for example, in instrumental terms – “It gave me something to do,” “I liked the other volunteers,” “It got me out of the house” (38). Miller and Ratner do not indicate awareness of Holmes’s message that there are worse things than self-interest. Otherwise, their ﬁndings suggest that a dominant ideology of self-interest does obscure recognition of motivations of benevolence and fairness in the population. It does not take saintliness to overcome egomaniacal redistributional instability. Merely a secondary preference for fair distribution, should one be unable to grab everything for oneself, would do. Further, among a small number of people, independently motivated reciprocity would maintain equal distribution. Empirically, legislators are universalistic on redistributional questions. Among a larger number of people, the inefﬁcacy of voting could liberate sentiments of fairness. Empirically, voters are sociotropic. If there is a worry that there is not enough fairness in the population to avoid egoistic redistributional instability under the Condorcet voting rule, then there are good voting rules that avoid cycles. Cyclebusters We have seen that cycles are rare. This section will offer two further claims. First, most cycles are trivial. Second, if there are cycles that are not trivial, then there exist accurate and fair voting rules that eliminate such cycles. The closer alternatives are to one another, the less structure there is between individuals’ preference orders. Permit me to explain. Suppose that the three alternatives under consideration are education appropriations

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of a, $110,000, f, $10,000 or g, $0. There are 99 people in our assembly, and all 99 rank a > f > g, $110,000 > $10,000 > $0; there is just general agreement that an education expenditure closer to $110,000 than to $10,000 is good for everyone in the community. Individual preference orderings are perfectly correlated with one another. As we introduce more ﬁne-grained alternatives the less structure there is between individual preference orders, but also the less does the absence of structure matter. Suppose now that the three alternatives under consideration are a, $110,000, c, $100,000, and e, $90,000. There is unanimity that educational expenditure should be within the range of $110,000 and $90,000, but there is not unanimity on a ﬁgure within that range: 33 voters rank c > e > a, 33 rank a > c > e and 33 rank e > c > a. On superﬁcial inspection the three different rankings don’t seem to resemble one another, but they are somewhat correlated and can be arrayed along one dimension; they enjoy the property of single-peakedness which will be elucidated below. The social ordering by Condorcet order and Borda count is c > e > a, which discloses the resemblance between the individual orderings. Now suppose that the three alternatives are b, $100,100, c, $100,000, and d, $99,900. Everyone thinks that $100,000 is about right, especially when compared to $10,000, but people’s preferences over these last three alternatives $100 apart from one another are not well-considered, there is no structure between individual preference orders, which happen to be perfectly uncorrelated for the sake of my illustration: 33 voters rank b > c > d, 33 rank d > b > c, and 33 rank c > d > b. The collective ordering is a cycle: b > c > d > b, which discloses the absence of structure between the individual preference orders. The closer alternatives are to one another, the less likely is it that individual preference orders resemble one another, the more likely is it that a social cycle results, but the more trivial is the resulting cycle. A cycle over closely adjacent alternatives is not as troubling as a cycle over remotely distant alternatives. I want to distinguish between benign cycles and malign cycles. This distinction would be meaningless in the framework of ordinal and noncomparable utility, but will be of interest to those whose common sense is intact. For the noncomparabilist, that a senator prefers highway expenditures of $15,000,000,000.00 to $15,000,000,000.01 to $14,999,999,999.99 carries just as much information as that a senator prefers a policy of preemptive nuclear war to isolationism to charitable internationalism – the only information the Arrovian permits is the order of preferences. For the Arrovian, a benign cycle among three alternatives a penny apart from each other on $15 billion in highway expenditures is indistinguishable from a malign cycle among world war, neutrality, and

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charity. I claim, however, that a cycle among three alternatives a penny apart is of no importance compared to a cycle among war, neutrality, and charity. If an arbitrary method of choice were applied to select one from the three highway expenditure alternatives, or even an unfair method such as one agent with unfair control over order of consideration of alternatives, it would be of no practical concern. If, however, a random method, or worse, an unfair method were used to select among the alternatives of war, neutrality, and charity, we would rightly be horriﬁed. My hypothesis is that what empirical cycles there are will much more likely be of the benign rather than the malign variety. Now we are in a position to propose a possible explanation for the sharp disjuncture identiﬁed by Gehrlein: almost no cycles with eight or fewer candidates, more cycles with nine or more candidates. Formal theory does not predict this disjuncture; the likelihood of a cycle should increase smoothly as we move from three to many candidates. Gehrlein’s data were mostly from single-transferable vote elections where voters must rank all candidates, regardless of whether their preferences are fuzzy, indifferent, or incomplete. There is a rule of seven, plus or minus two, for identiﬁcation of items by humans in short-term memory and in unidimensional absolute judgment tasks (e.g., sounds varying only in loudness, lights varying only in brightness, forms varying only in size; G. Miller 1994/1956; Baddeley 1994; Shiffrin and Nosofsky 1994). Beyond the capacity limit of about seven, humans commit errors, even on the simplest of tasks, and this is a most robust effect. I suggest that the voters in Gehrlein’s study committed such errors when judging nine or more candidates, and that these individual errors, structureless ranking over a portion of the range of candidates, sometimes aggregated to cycles. Humans bypass the information-capacity limit by means of three methods. First, relative judgment rather than absolute judgment. Rather than judging brightness on an absolute ten-point scale, instead make relative judgments, A is brighter than B, B is brighter than C, and so on; then we can string together the pairwise comparisons. Second, increase the number of dimensions along which stimuli can differ. We can identify hundreds of faces, but faces are sorted over multiple dimensions. Third, make a sequence of several absolute judgments in a row. With respect to memory, for example, a ten-digit phone number is impractical to remember, but chunked into three portions, an area code of three digits, a preﬁx of three digits, and a sufﬁx of four digits, it is practical to remember. A fourth method not mentioned by the psychologists cited is the use of external technologies. This is uncanny. As a speculative hypothesis, it seems that the capacity limit and the methods of bypassing the limit are both reﬂected by

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voting procedures, as are the intuitions that modelers of voting strive to formalize. Arrow is intuitively certain that compounding of pairwise comparisons should be the way to rank many alternatives – even when that drives him to dictatorship. Maybe the root of his intuition is a tacit understanding that absolute judgments cannot distinguish more than about seven items along a single dimension. Why did the spatial model of voting, based, so far as I can tell, on no evidence, arise and have such widespread appeal? Maybe the root of the intuition that underwrites the spatial model is again a tacit understanding that humans can better sort multiple alternatives by mapping them to several dimensions (even if those dimensions are highly correlated with one another). We also seem to like handling multiple alternatives by chunking them into sequential procedures: the amendment procedure in legislatures, plurality runoff elections, federalism. The formal models of voting may be appealing because they appeal tacitly to the capacity-limit problem, but otherwise be misleading because they do not expressly recognize and incorporate the problem. Here is a new concept. To return to the example of the education appropriations, if the alternatives available for consideration were those between $100,100 and $0, then the collective ordering would be (b > c > d > b) > e > f > g, a so-called top cycle simply because the cycle is at the top of the social ranking. The collective choice rejects $0 and $10,000, but cycles among the closely adjacent alternatives $100,100, $100,000, $99,900. Does this matter? It violates Condition O, which requires an ordering over all alternatives. It would matter perhaps if it resulted in a cyclic deadlock and no action (effectively choosing the lastranked $0 as the assembly’s votes cycled among the top three alternatives until the end of eternity), but that could always be remedied by an arbitrary method, and in most instances by a nonarbitrary method, as we shall see. The arbitrary method would be to deﬁne cycles as ties. Then the collective ordering would be b ∼ c ∼ d > e > f > g. Further, if a single outcome rather than merely formal decisiveness were required, then we could add the reﬁnement of some kind of fair, perhaps random, tie-breaking institution, and one of b, c, or d would be chosen. This – counting cycles as ties (without the tie-breaking reﬁnement) – is known as Schwartz’s method, or the method of transitive closure (Sen 1982, 162–163, 180–183). As a matter of logical possibility, it violates one or another of Arrow’s conditions. If the transitive closure is taken on the set of all possible alternatives X, then the relation satisﬁes contraction consistency, also called Sen’s alpha (to be explained in Chapter 6 ), and thus Condition O, but may violate Condition I. If the transitive closure is taken on the subset S of considered alternatives, then Condition I is

Unrestricted domain

117

satisﬁed, but Condition O may be violated. The Borda count behaves similarly. Suppose that on another issue our assembly had noncyclical preferences at the top of the social ranking, but cyclical preferences further down the list, for example: u > v > (w > x > y > w) > z. Does this matter? If the task is to select the best alternative for urgent action, then it does not. Again, Condition O is violated. Perhaps it would matter if alternatives u and v somehow became unavailable, but then we could turn to one of our cyclebusting methods. Also, if for some reason our purpose is to generate a complete ranking we can use a cyclebusting method, for example, transitive closure: u > v > w ∼ x ∼ y > z. Should cycles be a real problem anywhere, there are accurate and fair voting rules that resolve most of them, as we shall now see. I want to distinguish between balanced cycles and unbalanced cycles. The canonical example of cycling has three voters each with exactly the right three rankings that taken together will yield a cycle (A > B > C, C > A > B, and B > C > A together; or C > B > A, A > C > B, B > A > C together). For that proﬁle, or any other proﬁle where three numerically equal groups of voters inhabit each of the sets of three cyclical rankings, which we shall call a balanced cycle, the Borda count and Young–Kemeny rule, correctly in my view, declare a tie among the alternatives. The mathematician Donald Saari, a formidable advocate of the Borda count, reports that a class of fresh-minded fourth-graders patiently explained to him that the notorious three-voter cycle was nothing but a tie (Saari 1995a, 50–51). Now consider the four-voter two-alternative majority-rule case where the Condorcet paradox does not apply. Sometimes, perhaps even frequently for the sake of argument, the four-voter group will have a tie vote on two alternatives. Does the possibility of a tie thereby render all their choices meaningless? What if they have some neutral way of breaking ties – taking turns, ﬂipping a coin, precedent, or ongoing discussions of fairness? It may be discomﬁting for there to be a tie among two or three alternatives, but at least remaining alternatives have been eliminated from consideration. Once one understands that balanced cycles are merely the three-or-more-alternative analog to the two-alternative tie, much of the spookiness of cycling is exorcised. Most empirical cycles would be both benign and nearly balanced, in my view, and there are remedies for malign and unbalanced cycles. Here is an abstract example of an unbalanced cycle (adapted from Dahl 1956, 42). One individual ranks x > y > z, 49 rank z > x > y, and 49 rank y > z > x, and this is a cyclical proﬁle of preferences, x > y > z > x. Applying the method of transitive closure to this unbalanced proﬁle would yield x ∼ y ∼ z. There are 98 out of 99 voters, however, who favor z

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Table 5.5. An unbalanced cycle x x y z

49 98

y

z

BC

50

1 50

(51) (99) (147)

49

over x, and can we really say that the social relation between z and x should be one of indifference? If the one individual who ranks x ﬁrst were an evil agenda-controller among foolishly sincere voters, and she pitted alternative y against alternative z, then ﬁrst y would beat z and next y would lose to x. Alternative x would be the winner even though 98 of the voters favor z over x. The Borda count and the Young–Kemeny rule, however, properly identify z as the winner. For someone who believes in the Arrow theorem, it would make no sense to say that z is better than x. For someone without such beliefs, it seems unfair for z to lose. The method of transitive closure would be unsatisfying because the cycle is unbalanced, z is better than, not as good as, x. There are several remedies for this unbalanced cycle. If there is pairwise majority voting, if there is an open agenda such that any alternative can be proposed in any order, and if the members of the assembly prefer any choice over eternal cycling, then z will be selected. How? Before proceeding, an aside. The normative argument against cycling appeals to the intuition that it is bad for a voting procedure to cycle eternally among alternatives. That judgment is external to the model, however. Inside the formal setup no one loses anything from cycling. The normative argument illicitly appeals to our real-world experience that indecisiveness is wasteful – we could be doing something better with our time than cycling, and we also need a decision now. In order to bring the setup in line with our intuitions, we have to amend our description of preference orders. Call the costly absence of a decision arising from an eternal cycle alternative o. Now we have one individual who ranks x > y > z > o, 49 who rank z > x > y > o, and 49 who rank y > z > x > o. To continue, we will examine three agendas, one beginning with y against z, one beginning with x against y, and one beginning with x against z. I will show that z is the ﬁnal choice on each agenda. If the ﬁrst-stage contest is between y and z then y wins by one vote and if the voting is sincere the cycle will go on forever, the last-ranked choice of all of our voters. If, however, at least one of the 49 who rank y > z > x > o votes strategically against her ﬁrst-ranked y in the ﬁrst stage

Unrestricted domain

119

in order to obtain her second-ranked z in the second stage and overall avoid her last-ranked o, then z would win and the cycle would be broken. The incentive of the 49 who rank z ﬁrst and z > x > y > o overall is to vote sincerely in order to obtain z. If in a third stage x is moved against z, then z beats x 98 to 1. Thus, z is stable. Next, if the ﬁrst-stage contest is between x and y, then x wins the ﬁrst stage and loses in the second stage to z, if voters are sincere in the ﬁrst and second stages, and the third-stage vote is between y and z, and z beats y and the cycle is broken just as before. Would the 49 who rank z > x > y > o vote strategically in the ﬁrst stage for y over x? No, that would gain them y, their lastranked alternative and lose them z, their ﬁrst-ranked alternative. Would the one who ranked x > y > z > o vote strategically in the ﬁrst-stage for y over x? By doing so, this lone individual might gain y, her second-ranked alternative and avoid x, her last-ranked alternative. Therefore, she might contemplate voting strategically. If she did so, however, the next choice would again be between y and z, but we have already seen that z would win that contest among strategic voters for whom a cycle is costly, so she would refrain from voting strategically. Finally, if the ﬁrst-stage contest is between x and z, then z beats x by 98 to 1, and again z goes on to beat y among our strategic voters for whom any choice among x, y, and z is more important than no choice o. The most strongly favored alternative, z, is picked from the cycle by strategic voting. The same analysis holds if this were a barely unbalanced cycle: one who ranks x > y > z > o, two who rank z > x > y > o, and two who rank y > z > x > o. The balanced cycle is similar but not identical. Assume three voters each with orders x > y > z > o, z > x > y > o, and y > z > x > o. Say that the ﬁrst-stage vote is between alternatives y and z. The voter with ranking z > x > y> o could end the cycle by voting for her thirdranked alternative y in order to avoid her fourth-ranked alternative o. Why should she though? She would rather let y beat z and go up against x. Then the voter with ranking x > y > z > o can end the cycle by voting for her third-ranked alternative. Why should voter x > y > z > o be the one to make the sacriﬁce, however? And so on. The three face a situation resembling an assurance game. The three need to devise and justify in advance a fair tie-breaking institution, not any more challenging, practically or normatively, than to devise and to justify such an institution for conventional two-alternative ties. Informal recognition of cardinal but uncompared utilities may help decide ties or cycles arising from ordinal voting. This is the basis of logrolling. Ozzie prefers A > B, and Sharon prefers B > A. We take a majority vote over A and B only to disclose a tie. There are other things in life, however, than A and B. Suppose that Ozzie wants A much more

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Table 5.6. An almost balanced cycle 102

100

99

A B C

C A B

B C A

A A B C

99 199

B

C

(BC)

202

102 201

(304) (300) (299)

100

than some of those other things, but that Sharon wants some of those other things more than she wants B. Ozzie could trade some of those other things to Sharon in exchange for A, thereby breaking the tie. Now (example adapted from Hovenkamp 1990a) suppose a balanced cycle, full knowledge of one another’s utilities, and preferences and associated cardinal but noncomparable utilities as follows: Huey prefers A(6) > B(5) > C(1), Dewey prefers B(60) > C(40) > A(20), and Louie prefers C(600) > A(400) > B(200). Suppose the three nephews have no tie-breaking procedures, and that the value to each of perpetual cycling is zero. Then, Huey will vote for B, B will win, and Huey will get 5 rather than zero; and no cycle. Suppose the nephews do have a fair tiebreaking procedure. Then the expected value to Huey of voting for A is 1 × 6 + 13 × 5 + 13 × 1 = 4, and the expected value to Huey of 3 voting for B is 1 × 5 = 5; hence, Huey votes for B, B wins; and no cycle. There are good voting rules that remedy unbalanced cycles. When the number of voters inhabiting each of the three cyclical rankings are not exactly equal to one another, when there is an unbalanced cycle, then the Borda count almost always declares unique winners, not ties. Riker (1982, 120) is not clear about this property of the Borda count. In discussing the frequency of cycles he says that the Borda count produces a tie among cycled alternatives, but he does not note that the Borda count produces a tie almost always in the rare instance of a perfectly balanced cycle, an equal number of voters across the cyclical rankings. To further illustrate, in Table 5.6 there are 301 voters and three alternatives distributed across three cyclical rankings, followed by the pairwise comparison matrix. By pairwise comparison we have a cycle: A > B > C > A. The Borda count, however, ranks the alternatives A > B > C, and the

Unrestricted domain

121

Table 5.7. Another unbalanced cycle 23

17

2

10

8

A B C

B C A

B A C

C A B

C B A

A A B C

27 35

B

C

(BC)

33

25 42

(58) (69) (53)

18

Borda count tells us as well, if we are not dogmatic ordinalists, the social judgment is that there is not much difference between the alternatives (if the number of voters had been in three equal groups of 100, the Borda count would have yielded a tie). The Young–Kemeny rule has us break the cycle at the weakest link: the pairwise majority for C > A is 199 votes, less than either the 201 votes for B > C or the 202 votes for A > B, and thus the Young–Kemeny ranking is A > B > C just like the Borda count. In Table 5.7 there is a more ragged distribution of preferences (borrowed from Young 1997), together with the associated pairwisecomparison matrix, involving ﬁve of the six possible rankings of three alternatives, that more strongly distinguishes Borda and Young–Kemeny from Condorcet order. Pairwise comparison delivers a cycle: A > B > C > A. Should we stop there and either declare that democracy is meaningless or more humbly declare a tie? Or should we use the ranking information we have to try and ﬁnd a winner with a better method than pairwise comparison? The Borda order is B > A > C and the Young–Kemeny order is B > C > A (recall that on assumptions Borda picks the most likely winner and Young–Kemeny the most likely ranking). If cycles are indeed a threat to the very intelligibility of democracy, then shouldn’t we eagerly seek for voting rules that resolve cycles? If that is our quest, then the accuracy and fairness properties of Borda count and perhaps of Young–Kemeny are distinguished, and thus we should adopt one of those rules and thereby save the republic from Arrovian dictatorship. If, in contrast, the prospect of cycles is rare due to mild homogeneity among voters’ rankings of alternatives, and mild preferences for fairness in distribution, then we may relax, knowing that we

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could adopt a more accurate voting rule if required by circumstances, but otherwise conﬁdent that simpler voting rules may be adequate for many purposes. Why would anyone reject the cycle-busting voting rules? They violate Arrow’s independence condition, the subject of the next chapter.

6

Is democracy meaningless? Arrow’s condition of the independence of irrelevant alternatives1

Introduction The interpretation that Arrow’s Condition I, independence of irrelevant alternatives, prohibits the use of individuals’ intensities of preference in the construction of social choices is not precise. Rather, it is the socialwelfare function (as deﬁned in Chapter 4) which demands both individual and social orderings, and thereby prohibits cardinal utility inputs. Condition I, as Arrow wrote it, redundantly requires individual orderings, but goes further and demands that, even given the ordinal data from individual orderings, the social choice over any two alternatives not be inﬂuenced by individuals’ preferences involving any third alternatives.2 This is explicit in Arrow (1963/1951, 59, emphasis added): It is required that the social ordering be formed from individual orderings and that the social decision between two alternatives be independent of the desires of individuals involving any alternatives other than the given two . . . These conditions taken together serve to exclude interpersonal comparison of social utility either by some form of direct measurement or by comparison with other alternative social states.

Arrow’s is a strong independence condition. Slight weakenings of it allow the Borda count or the Young–Kemeny rule as possible social welfare functions and further weakenings permit further voting procedures. Barry and Hardin (1982, 217–218) agree that Arrow’s IIA is a powerful condition. “Part of its power is that one cannot easily intuit what it means or why it matters . . . Perhaps because of its subtlety, condition I is apparently the condition that is most readily taken for granted in the proof of Arrow’s and related theorems.” Its content is frequently misunderstood. Justiﬁcations of the condition are typically thin and dogmatic, often no more than an assertion that its appeal is intuitively obvious. My search for justiﬁcations of the condition found thicker arguments mostly by Arrow (1963/1951; 1952; 1967; 1987; 1997), Sen (1970; 1982), some by Riker (1961; 1965; 1982), and otherwise mostly repetition of points made by Arrow without further justiﬁcatory development.3 123

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Democracy Defended

The chapter proceeds as follows. First, I explain that historically many people have misunderstood the content of the independence condition (IIA(A)), believing it to be another condition (IIA(RM)), one that does not contribute to the impossibility result. My main point is that the independence condition can not be defended as intuitively obvious if sophisticated commentators have trouble grasping even its content. Second, I show by example that to violate either Arrow’s independence condition (IIA(A)) or the contraction-consistency independence condition (IIA(RM)) can be substantively rational. I point out that Arrow understands the simplifying assumptions of his model not as ends in themselves but as means to empirical analysis; the assumptions themselves have no descriptive or normative force, even more so when they are contrary to observation and intuition. Third, Arrovians defend the IIA(A) as forbidding the inﬂuence of irrelevant alternatives over the consideration of relevant alternatives in social choice. I explain that the condition has nothing to do with forbidding consideration of irrelevant alternatives in the ordinary sense of the term, but rather requires that social choice be carried out only by pairwise comparison, thereby delivering the impossibility result. Fourth, I continue discussion of the Arrow theorem as motivated to avoid interpersonal comparisons of utility, and argue that the IIA(A) is superﬂuous to that goal. I submit that the Borda and Condorcet methods are equivalent with respect to comparing or not comparing mental states, and that both are purely ordinal methods. Fifth, I examine Riker’s claims that the IIA(A) serves to forbid undesirable utilitarian voting rules, probabilistic voting rules, and consideration of irrelevant alternatives. I reply that it has not been shown that utilitarian or probabilistic voting rules are undesirable, but if they are then there are weaker independence conditions that forbid those voting rules but still permit other rules such as the Borda count. Also, I point out that the concern over irrelevant alternatives may be of importance in social-welfare applications, but is of no importance in most voting applications. Sixth, I challenge the Arrovian view that the Borda count is logically susceptible to manipulation by addition and deletion of alternatives but that the Condorcet method is not. I argue that both are logically susceptible to such manipulation, but that the susceptibility is of little practical importance. I conclude that the frailties of the reasonable voting rules have been much exaggerated, and that the time has come to move from a destructive constitutional “physics” to a constructive constitutional “engineering.” The wrong principle is defended Arrow is an economist, and analogizes political choice to economic choice. He explicitly considers voting and the market as special cases

Independence of irrelevant alternatives

125

of the more general category of social choice. Arrow borrows his basic conception from simple consumer economics. He distinguishes all possible or conceivable alternatives from all feasible or available alternatives. Suppose that the set X contains all possible or conceivable alternatives. S, a nonempty subset of X, contains all feasible or available alternatives. To anticipate, S contains the “relevant” alternatives and X – S contains the “irrelevant” alternatives. On any given occasion, the chooser has available to him a subset S of all possible alternatives [X ], and he is required to choose one out of this set [S ]. The set S is a generalization of the well-known opportunity curve; thus, in the theory of consumer’s choice under perfect competition it would be the budget plane. It is assumed further that the choice is made in this way: Before knowing the set S, the chooser considers in turn all possible pairs of alternatives, say x and y, and for each such pair he makes one and only one of three decisions: x is preferred to y, x is indifferent to y, or y is preferred to x . . . Having this ordering of all possible alternatives, the chooser is now confronted with a particular opportunity set S. If there is one alternative in S which is preferred to all others in S, the chooser selects that one alternative. (Arrow 1963/1951, 12)

This will be a crucial passage. Many people, including myself for many years, have misunderstood the content of Arrow’s independence condition. Indeed, about twenty years after ﬁrst publication of his theorem it was recognized that Arrow in 1951 at one point seemed narratively to justify a condition that was not the same as the formally stated condition necessary for his proof.4 Again on analogy to consumer choice, Arrow (1963/1951) argues that a social choice from a set of alternatives S, “just as for a single individual,” should be independent of alternatives outside S. He illustrates with a criticism of the Borda count: For example, suppose . . . an election system . . . whereby each individual lists all the candidates in order of his preference and then, by a preassigned procedure, the winning candidate is derived from these lists . . . Suppose that an election is held, with a certain number of candidates in the ﬁeld . . . and then one of the candidates dies. Surely the social choice should be made by taking each of the individual’s preference lists, blotting out completely the dead candidate’s name, and considering only the orderings of the remaining names in going through the procedure of determining the winner. That is, the choice to be made among the set S of surviving candidates should be independent of the preferences of individuals for candidates not in S. To assume otherwise would be to make the result of the election dependent on the obviously accidental circumstance of whether a candidate died before or after the date of polling. Therefore, we may require of our social welfare function that the choice made by society from a given environment depend only on the orderings of individuals among the alternatives in that environment. (Arrow 1963/1951, 26)

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Democracy Defended

Arrow’s “surely” is too quick. The election has already provided us with a social ranking. Rather than deleting the dead candidate’s name from each individual’s preference list, why not instead delete the dead candidate’s name from the social ranking? Arrow’s example is thus: two voters rank the alternatives x > y > z > w, and one voter ranks them z > w > x > y. The Borda ranking is x > z > y > w, Arrow’s focus is that x wins (the Condorcet ranking is x > y > z > w). Now candidate y is deleted. By the Condorcet method the ranking of remaining alternatives stays the same, x > z > w, and x would still be the winner. If the Borda method is reapplied to the remaining three candidates, however, then the Borda ranking changes to (x ∼ z) > w, and both x and z are tied for the win. Then, certainly, if y is deleted from the ranks of the candidates, the system applied to the remaining candidates should yield the same result, especially since, in this case, y is inferior to x according to the tastes of every individual; but, if y is in fact deleted, the indicated electoral system would yield a tie between x and z. Arrow (1963/1951, 27)

There are two problems. First, recall that in Arrow’s scheme the chooser, before knowing the set S, forms a ranking over all possible alternatives in X. Then the chooser encounters S, the set of all feasible alternatives. The chooser consults the list made from X and selects the highest ranking alternative or alternatives in S as the choice. Arrow analogizes social choice to the economic model of individual choice. If the analogy holds, then social choice should form a ranking over all possible alternatives X, and consult from the list made from X in order to decide the winner or winners in S. As this would apply to Arrow’s story about the Borda count and the dead candidate, the Borda count would be carried out on the set X of four candidates and the ranking x > z > y > w determined. Then y dies. We do not reapply the Borda count to the three remaining candidates in set S, rather we consult the ranking over four candidates, x > z > y > w, and delete y from the social ranking, for x > z > w, and x remains the winner. If we take the Borda count over X, call that the global Borda rule, and if we take the Borda count over some subset S, call that the local Borda rule. The general idea of Arrow’s scheme suggests that we should apply the global Borda rule to X, but in this instance Arrow says we should apply the local Borda rule to S. Why the inconsistency? The second and much bigger problem is that Arrow’s example does not illustrate the IIA condition used in the theorem, but rather a different condition confusingly labeled “independence of irrelevant alternatives” by Radner and Marschak (1954), also called by Sen “Condition ␣,” and also called “contraction consistency.”

Independence of irrelevant alternatives

127

IIA(Arrow): Let R1 , . . . , Rn and R 1 , . . . , R n be two sets of individual orderings and let C(S ) and C (S ) be the corresponding social choice functions. If, for all individuals i and all x and y in a given environment S, xRi y if and only if xR i y, then C(S ) and C (S ) are the same. (Arrow 1963/1951, 27) IIA(Radner–Marschak): If x is an element of the choice set of S and belongs to S1 contained in S, then x is also an element of the choice set of S1 , i.e., x ∈ C(S) and x ∈ S1 ⊂ S together imply x ∈ C(S1 ). (Ray 1973, 987, after Radner and Marschak 1954)

The two conditions are logically independent of one another (Ray 1973). In 1951, Arrow (1963/1951, 32–33) criticized by example the idea that summation of normalized von Neumann–Morgenstern cardinal utility functions might serve as a social-welfare function. His ﬁrst objection was an example that violated what is here called IIA(RM) or contraction consistency, and his second objection was an example that violated the IIA(A). In this passage, Arrow distinguishes the two conditions, but it seems that he does not in the passage justifying the IIA(A) by appeal to the example of the dead candidate in the Borda count (1963/1951, 27). Bordes and Tideman (1991) provide ingenious constructions that would make Arrow both accurate and consistent in his justiﬁcation of the IIA(A), and their interpretation is more than merely plausible. In the end, I do not join in Bordes and Tideman’s charitable reading, simply because Arrow (1987, 195) later acknowledged a mixup: Nash’s condition (adapted by Radner and Marschak 1954), he said, “refers to variations in the set of opportunities, mine to variations in the preference orderings . . . The two uses are easy to confuse (I did myself in Social Choice and Individual Values at one point).” The later Arrow (1997) explains that the key conditions of the theorem are Collective Rationality and IIA(A). For a given election the problems posed by the conditions are hypothetical or counterfactual, he says. First, what would have happened if we had added a candidate who wouldn’t have won or if we had subtracted a losing candidate? The addition or subtraction of such “irrelevant” candidates could have changed the outcome of the election, and this would be a violation of the Collective Rationality Condition, according to Arrow. The Collective Rationality Condition requires that “for any given set of [individual] orderings, the social choice function is derivable from an [social] ordering” (Arrow 1967, 70), which in turn requires IIA(RM). Second, what would have happened if voter’s preferences over noncandidates changed? Change of preference over “irrelevant” candidates could have changed the outcome of the election, and this would be a violation of the IIA(A) condition, according to Arrow. What “this argues is that the election rule was such that the result

128

Democracy Defended

Table 6.1. Violation of IIA(A) Actual # voters: Rank: 1st 2nd 3rd Condorcet Borda

2 A B C

2

Counterfactual 1

2

B C C A A B A>B>C>A B>A>C

A B C

2

1

C C B A A B C>A>B C>A>B

actually obtained might have been different although it should not have been” (1997, 5). Notice that Arrow’s conditions require that the social choice not change if individual preferences or availability of alternatives were to change. A more natural expectation would be that social choice may or may not change if individual preferences or availability of alternatives were to change. Consider simple majority rule over two alternatives – if one member of the majority changes her vote to the minority position, that may or may not change the social choice. It seems to me that, in response to changes in individual preferences or in availability of alternatives, any demand that the social choice should always change, or, the demand by the IIA(A) or IIA(RM), that the social choice should never change, carries the burden of justiﬁcation. I will now illustrate violation of IIA(A). Suppose that there are two voters who rank A > B > C, two who rank B > C > A, and one who ranks C > A > B. By the Condorcet method the collective outcome from the proﬁle is the cycle A > B > C > A and by the global Borda method the collective outcome is B > A > C. In order to investigate violation of the IIA(A) we are interested only in the rankings of two alternatives, say alternatives A and B. Suppose now, counter to the ﬁrst supposition, that the two who rank B > C > A instead rank C > B > A. By the Condorcet method the collective outcome changes from a cycle to C > A > B, and by the global Borda method from B > A > C to C > A > B. Focus on the Borda count. Under the ﬁrst supposition, the Borda count yields B > A. Voters’ preferences over the pair A and B do not change, but two voters change from ranking C second to ranking C ﬁrst. Then, under the second supposition, the Borda count yields A > B, a reversal from the ﬁrst supposition. The IIA(A) is violated. I will now illustrate violation of IIA(RM), or of contraction consistency. Suppose again that there are two voters who rank A > B > C, two who rank B > C > A, and one who ranks C > A > B. Again, by the Condorcet

Independence of irrelevant alternatives

129

Table 6.2. Violation of IIA(RM) Actual # voters: Rank: 1st 2nd 3rd Condorcet Borda

2 A B C

2

Counterfactual 1

2

2

B C C A A B A>B>C>A B>A>C

A B

B A A>B A>B

1

A B

method the collective outcome from the proﬁle is the cycle A > B > C > A and by the local Borda method the collective outcome is B > A > C. In order to investigate violation of the IIA(RM) we are interested only in the rankings of two alternatives, say alternatives A and B. Suppose now, counter to the ﬁrst supposition, that instead of the three alternatives A, B, and C, there are only two alternatives, A and B. By the Condorcet method the collective outcome changes from A > B > C > A to A > B, and by the global Borda method from B > A > C to A > B. Again, focus on the Borda count. Under the ﬁrst supposition, the Borda count yields B > A. Voters’ preferences over the pair A and B do not change, but alternative C is removed from the menu. Thus, under the second supposition, the Borda count yields A > B. B is an element of {A, B} ⊂ {A, B, C}, and B wins among {A, B, C}, but does not win between {A, B} – contraction consistency says that if B wins {A, B, C} then it should win {A, B}. The IIA(RM) is violated. In Arrow’s 1951 presentation (1963/1951), an axiom was presented that the individual preference relation is complete, and another presented that it is transitive, and it was further stated that a relation that satisﬁed those axioms was a weak ordering (12). Individual orderings and social orderings must satisfy the two axioms (19). A social-welfare function is a rule which for each set of individual orderings of alternatives states a corresponding social ordering of alternatives (23). A social-choice function C (S ) is the set of alternatives x in S such that, for every y in S, x is weakly preferred to y. A social welfare function determines a unique social-choice function, and the social-choice function satisﬁes contraction consistency (Bordes and Tideman 1991, 170). A voting rule that violates contraction consistency violates the requirements of the Arrow theorem. Hence, Arrow’s scheme does require that both IIA(RM) and IIA(A) be satisﬁed. Sen (1993) proved that an impossibility result can be reached even if the requirement for contraction consistency, IIA(RM), is dropped;

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a condition similar to IIA(A) must be retained, however. IIA(A) is the culprit in the impossibility result. Arrow’s possibility theorem shows that social ordering, universal domain, Pareto principle, nondictatorship and IIA(A) are inconsistent. Ray (1973) shows that social ordering, universal domain, Pareto principle, nondictatorship and IIA(RM) are consistent. All social-welfare functions satisfy IIA(RM), and at least one, the Borda method, satisﬁes the remaining conditions, according to Ray. All social-welfare functions satisfy IIA(RM) if, as Arrow originally suggested, they are taken on X: if we apply our voting rule to all possible alternatives and consult that ranking to order any subset S of X, then no contraction of the set of alternatives has taken place. If it is insisted that the voting rule be applied to X, and then be reapplied to S, then violations of contraction consistency are possible. The global Borda count, for example, taken on X, satisﬁes IIA(RM), contraction consistency, but may violate Arrow’s IIA(A). It satisﬁes contraction consistency because with the global Borda count there is no contraction from X to S. The global Borda count may violate Arrow’s IIA(A) as shown in the example in Table 6.1. The local Borda count, taken on S, satisﬁes Arrow’s IIA(A), but may violate IIA(RM). To determine the rankings of A and B, the local Borda count is applied only to A and B, C does not enter the picture, thus the local Borda count outcome is the same before and after the change by two voters from B > C > A to C > B > A – and there is no violation of Arrow’s IIA(A). The local Borda count may violate IIA(RM) as shown in the example in Table 6.2, where, contracting from three alternatives to two alternatives, the outcome changes from B to A. There is a wide discourse, illustrated in my hall of quotations, declaring that democracy is dubious because of the Arrow theorem. The problem I am getting at here is that many commentators have made this claim on the mistaken view that the Arrow theorem depends on the IIA(RM) rather than on the IIA(A) (see, e.g., Riker 1961; 1965). Some of these commentators spend time justifying IIA(RM), believing they are thereby justifying the impossibility result. But IIA(RM) is not essential to the impossibility result, rather it is IIA(A) that is essential, and IIA(RM) does not lead to impossibility. Would not such a discovery suggest a revision in views? Instead, what we see in some commentators (Riker 1982) is not a revision in view, but rather a new attempt to justify the newly understood IIA(A). The conclusion is driving the premises, the tail is wagging the dog. I have made many astounding errors in earlier drafts of this volume and I fear that, despite my best efforts, astounding mistakes and misunderstandings remain. Scholars more talented and diligent than I are

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bound to err, because the issues under consideration are difﬁcult. My purpose here is not to dwell on the errors of others. The purpose is to call into doubt the common assertion that the IIA(A) condition should be accepted just because it is intuitively obvious. How could the condition be intuitively obvious if many sophisticated commentators are confused even about its content, let alone its implications? The independence conditions are not always substantively rational Barry and Hardin (1982, 266) say that “Nobody has any immediate views about the desirability of, say, the independence of irrelevant alternatives, and we should refuse to be bullied by a priori arguments to the effect that we would be ‘irrational’ not to accept it.” Arrovians proceed as if IIA(RM) and IIA(A) were requirements of rationality. One or the other of the conditions is presented as intuitively obvious, and sometimes an example is presented that illustrates the absurdity of violating the condition. It is hinted, but never spelled out, that to violate the condition would be a logical contradiction. I grant that in a set of particular circumstances, it may well be that a violation of one of the conditions has absurd consequences. In another set of particular circumstances, however, it may be acceptable, or perhaps even reason would demand, that choice violate one of the conditions. A condition may be substantively applicable in particular circumstances, or it may be useful as a simpliﬁcation to assume that one or the other of the conditions applies, or to assume that it usually applies unless there are special circumstances. But neither of the conditions is necessary to practical reason in the sense that it should apply to each and every possible choice regardless of the particular circumstances. My goal is to show that the conditions are not requirements of rationality, are not justiﬁed by naked appeal to intuition, and to do so I present examples that illustrate the absurdity of obeying the condition. If I present plausible counterexamples to the conditions, then my argumentative goal is achieved. It should be understood that all Arrow (1952, 49) intends by the word rational is that “an individual is rational if his preferences among candidates can be expressed by an ordering; similarly, collective decisions are made rationally if they are determined by an ordering acceptable to the entire society.” Although the IIA(RM) is implicated in the ordering assumptions of Arrow’s theorem, the independence aspect of the IIA(A) is an additional requirement. To violate these narrow construals of rationality is not to violate the broader concept of rationality: of having beliefs and desires, and carrying out plans and actions, for good reasons. Acting

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for good reasons is prior to Arrow’s rational choice model, and in case of conﬂict it is the model that must go. Here is an example showing that violation of IIA(RM), contraction consistency, may be substantively rational. My example is inspired by Sen (1993), who argues that the concept of internal consistency of choice, exempliﬁed by the IIA(RM), is “essentially confused, and there is no way of determining whether a choice function is consistent or not without referring to something external to choice behavior (such as objectives, values, or norms).” To introduce and motivate his entire scheme, Arrow (1963/1951, 2) supposes a society that must choose among disarmament, cold war, or hot war. It is obvious to Arrow that rational behavior on the part of the community would mean, in analogy to the economist’s understanding of individual choice, that “the community orders the three alternatives according to its collective preferences once for all, and then chooses in any given case that alternative among those actually available which stands highest on its list” (1963/1951, 2). He then uses the Condorcet paradox of voting to illustrate the possibility that the community might cycle among the three momentous alternatives. Arrow’s scheme requires that choice among more than two alternatives be decomposed into pairwise comparisons. The example Arrow chooses, however, illustrates the folly of insisting on pairwise comparisons over social states. Suppose that there is an individual who prefers peace so long as it does not require surrender to the enemy. If she were to face all three of Arrow’s alternatives, then she would rank them Cold War > Hot War > Disarmament. She least prefers Disarmament as that would amount to surrender to the enemy, but also thinks Cold War is better than Hot War because there are fewer casualties in Cold War. If she were to face a choice between Cold War and Hot War, she would choose Cold War. If she were to face a choice between Hot War and Disarmament, she would choose Hot War. If she were to face a choice between Cold War and Disarmament, however, she would choose Disarmament. Why? If Hot War were off the menu of choice, if Hot War were no longer possible, then the peace of Disarmament would be preferable to the tension of Cold War and would not require surrender to the enemy. Her preferences over a menu of all three alternatives is transitive: Cold War > Hot War > Disarmament. Her preferences over menus of two alternatives differ, however, and to chain them yields a cycle: she would prefer Cold War to Hot War to Disarmament to Cold War. One may not agree with the order of her rankings, but one would have to agree that her rankings are substantively rational. Arrow’s argument about social choice is by analogy to individual choice. The Arrovian scheme seems to assume that for an individual’s

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choice to depend upon the menu of choices is irrational, but I have just shown by example that it is possible for a rational person’s preferences over alternatives to vary by the menu of alternatives available. If it is possibly rational for an individual’s choices to vary by menu, then, by analogy, it is possibly rational for a society’s choices to vary by menu. A collective might rationally rank A > B when those two are the only alternatives of interest, but rank B > A when alternative C is also available. Thus to demonstrate formally that a voting rule ranks A > B when A and B are under consideration, but B > A when A, B, and C are under consideration is not in itself an objection to the voting rule. One would have to go beyond formal rationality and further show that the reversal is substantively irrational in the concrete instance. Suppose that some reversals are substantively rational and some substantively irrational. Then, in the comparative evaluation of voting rules, we would want to know the probable frequency of substantively irrational reversals for each rule as conditions vary. Substantively rational reversals would be welcome. Now for the more important chore, to show that violation of Arrow’s IIA(A) may be substantively rational. Suppose that there is to be a reception and that the caterer will only provide one beverage, either beer or coffee.5 The overly rushed organizer of the reception copies a form from last year’s event that asks people to rank beer, coffee, water, tea, milk, and pop and e-mails it out. Attendance is by RSVP only. Five people from the business school will come, and each of them ranks beer > coffee > water > tea > milk > pop. Four people from the law school will come, and each of them ranks coffee > beer > water > tea > milk > pop. The organizer, a political scientist indoctrinated in the Arrow theorem, and a believer in the IIA(A) condition, tallies only preferences over beer and coffee, the two relevant alternatives. Five want beer rather than coffee and four want coffee rather than beer: beer wins by majority rule. Beer is the Condorcet winner, the alternative that beats all others in pairwise comparison: beer > coffee > water > tea > milk > pop. Beer is also the Borda winner. It turns out though that the four people from the law school cancel, and four people from the theology school will attend instead. Their ranking is: coffee > water > tea > milk > pop > beer. The ranking of the lawyers and the theologians is almost the same, except that the lawyers rank beer second and the theologians rank beer last. The organizer looks only at the relevant alternatives, coffee and beer: by pairwise comparison nothing has changed, beer is still the choice by majority rule. The Condorcet order remains identical as well. The theologians come to the reception and are furious. They are teetotalers and would rather have anything but beer. The organizer loses his job, all because of his dogmatic belief in the IIA(A) condition. If the political scientist had instead used

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Table 6.3. Substantively rational to violate IIA(A) 5 Business School

4 Law School

4 Theology School

Beer Coffee Water Tea Milk Pop

Coffee Beer Water Tea Milk Pop

Coffee Water Tea Milk Pop Beer

Note: Business School + Law School Condorcet: Beer > Coffee > Water > Tea > Milk > Pop Borda: Beer > Coffee > Water > Tea > Milk > Pop Business School + Theology School Condorcet: Beer > Coffee > Water > Tea > Milk > Pop Borda: Coffee > Water > Beer > Tea > Milk > Pop

the Borda count, he would have noticed that the theologians ranked alcohol last, and would have provided the Borda-winning beverage, coffee. The viewpoint of the Arrow theorem is that a social choice is derived from a social ordering that is aggregated from individual orderings over social states; “only orderings can be observed, and therefore no measurement of utility independent of these orderings has any signiﬁcance” (Arrow 1967, 76–77), and the IIA(A) condition enforces the ban on information other than individual orderings. What if there had been a discussion about the beverage to be served at the reception? Assume that the theologians have the same mere ordering of preferences. Before the decision, they explain that they are teetotalers, and would rather have anything but beer. Alternatively, suppose that they are prohibited from drinking beer as a matter of their religion, and that they have a right to be served a beverage at the reception that doesn’t offend their beliefs. The political scientist, our hapless believer in the IIA(A) condition, would have to reject this information and enact the social choice of beer. “Only orderings can be observed,” he would reply to the theologians, “and the only ordering that matters is between coffee and beer. That you would rather have any beverage but beer is irrelevant.” I have put the argument in terms of the Borda count because my focus is on voting rules aggregating from ordinal preferences. In principle, a utilitarian voting rule might be applied to cardinal preferences to obtain a more accurate social ranking (maybe beer would be last), but the qualitative features of the story would remain the same. Riker (Riker and Ordeshook 1973, 110–111) has an objection to the kind of story I have

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told. Adapting his objection to ﬁt the current example, what if the orderings remained the same, but the participants had cardinal utilities as follows. Each member of the business school would rank beer as 10, then the remainder of alternatives as in the Borda count, 4, 3, 2, 1, 0 and each member of the theology school as in the Borda count, 5, 4, 3, 2, 1, 0. With these cardinal utilities, although the Borda count would still select coffee, the utilitarian choice would be beer (51) over coffee (40). My ﬁrst response is that in the pure voting exercise all we have are ordinal data, and thus we cannot go beyond the Borda count. But if we had sound cardinal data then why not use it? My second response is that the Rikerian objection has changed the qualitative features of the story, now, although the theologians rank beer last, the business schoolers are crazy for beer. My third response is that if the Borda count generally is imperfect in approximating cardinal utilities, should that be a goal, then Condorcet is more imperfect at the task – in my original example Condorcet fails to detect that the theologians rank beer last. In the Rikerian example, Condorcet picks beer, but, in utilitarian terms, for the wrong reasons. My fourth response is that with increasing numbers of voters, Borda tends to the utilitarian outcome (as does Condorcet). To conclude, in practice, ardor or horror at beer is expressed in discussion, people vote in a fair-minded way to take account of intense preferences of others (and maybe entrench some relating to life and liberty as rights claims), and in more competitive environments may engage in logrolling (OK, no beer, you theologians, but we get to choose the main dish). Arrow does not defend his assumptions on logical grounds. As for the requirement of pairwise comparison for individual choice orderings, There seems to be no logical necessity for this viewpoint; we could just as well build up our economic theory on other assumptions as to the structure of choice functions if the facts seemed to call for it.18 18 Like Lange, the present author regards economics as an attempt to discover uniformities in a certain part of reality and not as the drawing of logical consequences from a certain set of assumptions regardless of their relevance to actuality. Simpliﬁed theory-building is an absolute necessity for empirical analysis; but it is a means, not an end. (Arrow 1963/1953, 21)

What are the facts of the matter? I suggest that almost everyone would ﬁnd the Borda winner normatively superior to the Condorcet winner, in other words, that they would ﬁnd it intuitively obvious that the IIA(RM) and the IIA(A) should be violated. Controlled experiments among a subject pool of Stanford students support this hypothesis (Davies and Shah 2003). Subjects were shown the preferences of various groups of voters and were asked, “Which

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alternative should be chosen for the group?” In one study, for example, the Condorcet ranking for one proﬁle of two alternatives and another proﬁle of three alternatives was X > Y. The Borda winner in the threealternative proﬁle, however, was Y, and 38 out of 39 subjects chose Y > X, in violation of the IIA(RM). In another study, individual pairwise rankings over X and Y were identical across two three-alternative proﬁles, and X > Y was the pairwise majority in each proﬁle. The individual rankings of Z were varied, however, such that X was the Borda winner in one proﬁle and Y was the Borda winner in the other proﬁle, and 41 out of 46 subjects chose Y > X in that other proﬁle, in violation of the IIA(A). These studies yield large effects, in response to minimal manipulations, are extremely signiﬁcant, and the basic result that large majorities choose in violation of the independence conditions is robust to variations in experimental design. Further replications across more conditions, researchers, and culture groups are needed, but I expect that the ﬁndings will stand. Here Arrow defends pairwise comparison as only a modeling convenience in the case of individual choice. And, his justiﬁcation for pairwise comparison in the case of social choice is only by analogy to individual choice. I have argued that it can be substantively rational to violate either IIA(RM) or IIA(A). Further, almost all experimental subjects choose as if it were normatively desirable to violate both conditions. There is no need to make fetishes of the conditions, they are model-building means, not normative ends. We should not let the simpliﬁcations of models mislead our larger judgments about, say, democracy. The irrelevance justiﬁcation is ﬂawed Arrow (1952) says that the IIA(A) condition has always been implicitly assumed in voting systems, but the claim is mistaken. He offers the example of a community deciding between construction of a Stadium and of a Museum. The community can afford one or the other, but not both, and the community cannot afford a University at all. Arrow believes that the choice between the Museum and the Stadium must be independent of preferences of community members between the feasible Museum and the infeasible University. “The essential argument in favor of this principle is its direct appeal to intuition” (51). It is true, as a matter of practice rather than of logic, that infeasible or irrelevant alternatives are usually not placed on ballots. But sometimes they are. It was notorious in the 2000 election that dead Democratic candidate Carnahan remained on the ballot for US senator from Missouri, and won the election against Republican Ashcroft. As expected, the Democratic governor appointed

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Carnahan’s wife as his successor. In Great Britain, the Ofﬁcial Monster Raving Loony Party is an irrelevant alternative that regularly appears on the ballot. In his narrative justiﬁcations Arrow uses an ordinary conception of irrelevance: voting systems should choose over available alternatives but not over conceivable alternatives, over feasible alternatives but not over possible alternatives, over relevant alternatives but not over irrelevant alternatives. I imagine that many people are against the mischief of irrelevance, and also against permitting preferences over irrelevant alternatives to inﬂuence wrongly decisions concerning relevant alternatives. The ordinary irrelevance that Arrovians deplore in narrative justiﬁcations is not the irrelevance formally stated in the IIA(A) condition, however. What if the community could afford a Museum, a Stadium, or a University, but not any two or all three of these alternatives, and further could not at all afford a Nuclear Missile? There would have to be a social choice among the three feasible alternatives. Does the IIA(A) work to permit consideration of the relevant Museum, Stadium, or College and forbid consideration of the irrelevant Nuclear Missile? Not at all. Arrow’s condition does not partition alternatives into the ordinarily relevant and the ordinarily irrelevant. The condition applies to all candidates x and y, let’s say in a set S. If there are four relevant alternatives, a, b, c, and d in S, then the choice among a, b, and c must be independent from preferences involving d. As we consider the three alternatives a, b, and c, the choice between a and b must also be independent from preferences involving c or d. The choice between a and c must be independent from preferences involving b or d, the choice between a and d must be independent from preferences involving b or c, the choice between b and c must be independent from preferences involving a or d, and the choice between b and d must be independent from preferences involving a or c, even though each of a, b, c, and d is ordinarily relevant. The IIA(A) condition always boils down to one that requires that the social choice between any two alternatives x and y not be inﬂuenced by individuals’ preferences over any third alternative. The IIA(A) would better be named the pairwise comparison condition, as it requires that choices among several alternatives be carried out only with information about choices between pairs. Arrow (1963/1951, 20) said as much in 1951: One of the consequences of the assumption of rationality is that the choice to be made from any set of alternatives can be determined by the choices made between pairs of alternatives. Suppose, however, that the situation is such that the chooser is never confronted with choices between pairs of alternatives; instead, the environment may always involve many alternatives . . . we can say that

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the choices made from actual environments can be explained as though they were derived from choices between pairs of alternatives; and, at least conceptually, it makes sense to imagine the choices actually being made from pairs of alternatives.

The IIA(A) means that if someone ranks x > y > z, we count that she likes x > y, count that she likes y > z, and count that she likes x > z, but we are not allowed to count that she likes x > y > z. Saari (2001b) argues that the information lost due to this prohibition is what drives the impossibility result. We can insist that voting procedures rely only on pairwise comparisons and end up with Arrow’s dictatorship result and with startling interpretations such as those in my hall of quotations, or we can more sedately interpret the Arrow theorem to mean that procedures for three or more alternatives require more information than pairwise comparisons (Saari 1995a, 88).6 Continue to suppose that any one of the Museum, Stadium, or the University is a feasible or ordinarily relevant alternative, but not any two or all three. The choice between the Museum and the Stadium cannot be affected by people’s preferences between the Museum and the University or between the Stadium and the University, according to the IIA(A), even though the University is a relevant alternative in the ordinary sense of the term. Voter preferences are distributed as in Table 6.4. Voters are asked to rank all alternatives. Begin with the “actual” scenario in Table 6.4. The Condorcet advocate insists that the Stadium should win, even though almost half the voters rank it last among all projects. The Borda advocate insists that the Museum should win, it is the ﬁrst choice of almost half the voters and the second choice of the other half. The presence of the third alternative of the University on the ballot assists in the decision because it discloses that the 99,000 voters rank the Stadium last. In choosing between the Museum and the Stadium, eliminating from consideration the genuinely relevant alternative of the University ensures that the Stadium wins, and conceals the fact that almost half the voters would rather build anything but the Stadium. The Condorcet rule does not violate the IIA(A), but in this example the Borda rule does violate the IIA(A). Compare the pair of the Museum and the Stadium, and inspect the “counterfactual” scenario in Table 6.4. Suppose the 99,000 voters change their ranking of the university from second to third. Then the social choice by the Condorcet rule would continue to be the Stadium, but the social choice by the Borda rule would change from the Museum to the Stadium – the IIA(A) is violated. Next, suppose that the university is infeasible, is an ordinarily irrelevant alternative. Nothing in the foregoing analysis changes, except that addition of the ordinarily

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Table 6.4. The relevance of irrelevant alternatives Actual

99,000 voters

100,000 voters

1st 2nd 3rd

Museum University Stadium

Stadium Museum University

Act

M

M S C

100 0

S

C

(BC)

99

199 100

(298) (200) (99)

99

Counterfactual

99,000 voters

100,000 voters

1st 2nd 3rd

Museum Stadium University

Stadium Museum University

Cﬂ

M

M S C

100 0

S

C

(BC)

99

199 199

(298) (299) (0)

0

irrelevant alternative would have made more information available for a better decision. The IIA(A) decrees that in all circumstances there is nothing to be said in favor of any method that considers information beyond pairwise comparisons. If the IIA(A) were strictly and literally applied, it would forbid the social-choice process even from considering any public arguments concerning the alternatives, as that would be information beyond the pairwise rankings of voters. The Arrovian tradition equivocates on “relevance.” The IIA(A) condition does nothing more than require that in a choice between two alternatives a third alternative should have no inﬂuence. Whether any of those alternatives are relevant or irrelevant, feasible or infeasible, available or unavailable, in the ordinary sense of those terms, has nothing to do with the IIA(A) condition. The choice could be among two ordinarily irrelevant alternatives, and the IIA(A) would forbid that a third ordinarily relevant alternative inﬂuence the choice between the two ordinarily irrelevant alternatives (then we would have to rename it the independence of relevant alternatives condition). The choice could be between ordinarily

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relevant alternative x and ordinarily irrelevant alternative y, and then the IIA(A) condition would require that the social choice between x and y not be inﬂuenced by preferences over some third alternative z, no matter whether z is ordinarily relevant or irrelevant. Arrow (1952) says that all actual voting methods respect IIA(A). It is true that most elections do not consider ordinarily irrelevant alternatives (and when they do voters mostly ignore them), but it is deﬁnitely not true that all voting methods proceed by pairwise comparison. For example, suppose there is a natural election among candidates, say there are six. There are certain qualiﬁcations for entry, such as residence and age, and to be eligible a candidate must declare before a certain date. The election is carried out by Hare preferential voting. This election does not violate ordinary irrelevance because no ordinarily irrelevant candidates are considered. It does violate IIA(A), however, because the Hare method does not proceed by pairwise comparison. Arrow (1967) contains a remarkable statement: For example, a city is taking a poll of individual preferences on alternative methods of transportation (rapid transit, automobile, bus, etc.). Someone suggests that in evaluating these preferences they also ought to ask individual preferences for instantaneous transportation by dissolving the individual into molecules in a ray gun and reforming him elsewhere in the city as desired. There is no pretence that this method is in any way an available alternative. The assumption of Independence of Irrelevant Alternatives is that such preferences have no bearing on the choice to be made. It is of course obvious that ordinary political decisionmaking methods satisfy this condition. When choosing among candidates for an elected ofﬁce, all that is asked are the preferences among the actual candidates, not also preferences among other individuals who are not candidates and who are not available for ofﬁce.

If the IIA(A) states that nonexistent alternatives should not be listed on ballots, then there would be no controversy about it. The IIA(A), of course, states something else entirely, that only pairwise comparisons should be inputs to social choice. Yes, the IIA(A) agrees with common sense by excluding the ray gun, but at the cost of excluding all but pairwise voting in consideration among the feasible alternatives of rapid transit, bus, automobile, etc. The IIA(A) way overshoots. It is as though someone in Canberra refuses to leave his room because he’s heard that there’s a dangerous snake somewhere in Sydney. We point out to him that he won’t get bit by walking around Canberra, but he replies that he wishes to get no closer to the snake. We must be careful here about confusing the IIA(A) and the IIA(RM). I don’t think that Arrow in the example is thinking of adding the ray gun to the menu of alternatives (possible violation of IIA(RM)). What he

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means, I think, is that preferences over the infeasible ray gun shouldn’t inﬂuence preferences over (any two) feasible alternatives (possible violation of IIA(A)). The way to avoid that inﬂuence is to decompose all social choice into pairwise comparisons, and then to string together the pairwise choices over alternatives of interest, but that remedy carries an immense price: dictatorship as the only acceptable social-welfare function. It is as though the obsessive Canberran chooses to starve himself to death rather than leave his house. Davies and Shah (1993) deﬁne a new condition of the independence of unavailable alternatives (IUA): that information be considered only from rankings of alternatives designated as available, and that information about alternatives designated as unavailable be ignored. In a betweensubjects experimental condition, the IUA was violated by a majority of subjects. In a within-subjects condition, and when voter proﬁles were presented in a pairwise manner, there was a tendency for subjects to respect the IUA. I suggest that the IUA is compelling in some contexts, but not in others. In 1963, Arrow (1963/1951, 110) commented that the austerity imposed by the IIA(A) “is perhaps stricter than necessary; in many situations, we do have information on preferences for nonfeasible alternatives. It can be argued that, when available, this information should be used in social choice.” My business school and theology school example shows this. Later, Arrow (1997, 5) said of an approach such as Borda’s that it is not willing to take the logical next step, of adding irrelevant alternatives to the list of candidates just to get extra information. I agree that people usually would not advocate adding noncandidates in order to obtain more information, but this is a practical consideration, not a logical one. I can conceive of circumstances where people would advocate consideration of irrelevant alternatives just to gain extra information. Suppose that a forestry workers’ cooperative is voting to select a site for a new ofﬁce. The ofﬁce subcommittee has searched diligently and presents to the membership the only two alternatives available on the market. One is small but centrally located, the other is remote but large. Discussion suggests that sentiment is stronger for the small ofﬁce, but a straw vote over small and large indicates a tie between the two. Discussion also reveals that a large majority would prefer an intermediate alternative if it were feasible. The situation reﬂects the following preference orders: 25 members rank small > intermediate > large; 50 members rank intermediate > large > small; and 25 members rank intermediate > small > large. The Condorcet rule and the local Borda rule over the feasible pair yields 50 votes for small and 50 votes for large. Someone suggests voting by the global Borda count over the feasible small and large alternatives and

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the infeasible intermediate alternative. The result is intermediate (175) > small (75) > large (50). If all along we had used the global Borda count over the three alternatives, then we would have violated the IIA(A) with respect to the two feasible alternatives. Global Borda says that small > large, but if the preferences of the 25 who ranked small > intermediate > large were to change to small > large > intermediate then the global Borda result would change to small ∼ large, in violation of the IIA(A). Adding consideration of the infeasible alternative of the intermediate ofﬁce shows both that an intermediate ofﬁce would be most favored, and that a small ofﬁce is favored over a large ofﬁce. As a result, the members instruct the ofﬁce subcommittee to pursue more aggressively intermediate alternatives, and, if none is found, to secure the small ofﬁce. The example shows that consideration of ordinarily irrelevant or of third alternatives can be substantively rational, and is even strongly advisable in some circumstances. Generally, though, irrelevant alternatives are not added to gain extra information. Why might that be? One reason, I suppose, is that in all contexts relevance is a compelling imperative. A stronger reason, perhaps, is that in many cases, unlike in my example of the cooperative, there is no motivation to include alternatives incapable of selection. What happens if the noncandidate wins? If the election is carried out by plurality rule, as many are, then the victory of a noncandidate would require a new election. I recall that once those of a rebellious bent proposed to place “none of the above” on American plurality ballots, but the proposal fell ﬂat because of the practical need to have a winner. Adding irrelevant alternatives has the air of frivolity and irresponsibility. Perhaps some would be motivated to add the noncandidate in order to manipulate the election and would not vote sincerely, but certainly even if many were to consider John Stuart Mill the best alternative for mayor few would bother to vote sincerely for that choice on the ballot. Arrow’s point is one of practical observation rather than of logical objection. Voting rules may be justiﬁed independently of interpersonal comparisons of utility Arrow (1952, 52) states that to violate the IIA(A) presents an “operational problem: preferences between impossible alternatives make virtually no sense, for they correspond to no action that an individual could imagine having to perform.” He must be speaking rhetorically, as immediately before he is speaking of logically possible alternatives or of imaginable alternatives, not of impossible alternatives. He must mean that individuals are required to have preferences over all possible alternatives X, in

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order to decide among feasible alternatives in some subset S, and then his argument would be that critics of the IIA(A) require people to have preferences over infeasible alternatives in X – S. If he is correct that it makes no sense to have preferences over infeasible alternatives in the context of applying a voting rule, however, then it would follow as well that Arrow’s entire social welfare perspective itself makes no sense, because in his larger scheme, “it is assumed that each individual in the community has a deﬁnite ordering of all conceivable social states” (Arrow 1963/1951, 17), which includes of course the infeasible, however that is deﬁned. In his 1963 addendum, Arrow (1963/1951) offers further justiﬁcation of the IIA(A). He begins with reference to ordinalism in economics and expresses the belief that ordinalism is desirable because it is based only on interpersonally observable behavior. The IIA(A), he says, extends the requirement of interpersonal observability a step further. One could observe all preferences over alternatives available to or feasible for society, but one could not observe preferences over alternatives not available to or feasible for society, demonstrating the practicality of requiring voting procedures to respect the IIA(A). Again, this calls into question the entire Arrovian scheme. Arrow (1967, 61) later directly mentions this inconsistency with respect to the social-welfare perspective: how can we “possibly know about hypothetical choices if they are not made”? His response is to “pass by” the issue. Arrow’s concern about observability arises from the doctrine of logical positivism, just past its apex of inﬂuence as Arrow wrote in 1951. Since 1951, logical positivism has fallen into disfavor in all disciplines outside economics, but inside that discipline its strictures linger to this day. “According to this doctrine, any statement is meaningful if and only if it is possible to specify a set of observations that would verify it; and the meaning of the statement is exhausted by the speciﬁcation of these observations,” write Barry and Hardin (1982, 249).7 The viewpoint of Arrow’s Social Choice and Individual Values (1963/1951, 9–11, 109–111) is the claim that the “interpersonal comparison of utilities has no meaning and, in fact, that there is no meaning relevant to welfare comparisons in the measurability of individual utility” (9). The only meaning that the concepts of utility can be said to have is their indications of actual behavior, says Arrow, and if such a course of behavior can be explained by a given utility function it can also be explained by a second that is a strictly increasing function of the ﬁrst. Von Neumann–Morgenstern utilities over alternative probability distributions are no way out, because the behavior explained by a given function of that type can also be explained by a second that is a positive afﬁne transformation of the ﬁrst.8 Even if such utility were measurable, says

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Arrow, which function out of an inﬁnite family should be selected to represent the individual, and which function should be selected to aggregate the individual utilities? The selection of the functions “requires a deﬁnite value judgment not derivable from individual sensations” (11). Sen (1970, 97) points out that the choice of one cardinal utility function or another is descriptively arbitrary, “but in an ethical argument one may wish to choose some particular scaling in spite of this ‘arbitrariness,’ on some other grounds that may be additionally speciﬁed.” Arrow seems to go in the other direction: “If there is no empirical way of comparing two states . . . there can be no ethical way of distinguishing them” (112). If the welfare of different individuals is empirically and hence ethically indistinguishable, then there is no reason to be more concerned for the poor than for the rich in social policy, as the rich are no better off than the poor according to the doctrine of noncomparability. Perhaps Arrow’s statement is not intended to carry outside the context of his criticism of Samuelson’s welfare function: even if the rich and poor were to be indistinguishable in terms of observed mental states, they are surely empirically and ethically distinguishable by objective measures. In 1963 Arrow criticizes Borda’s justiﬁcation of his method. Borda, says Arrow, gave equal weight to differences between adjacent rankings and gave equal weight to different voters. “The ﬁrst raises the problem of the measurability of utility, the second that of interpersonal comparability” of utilities (1963/1951, 94). Borda justiﬁed the ﬁrst claim with the argument that if a voter ranks B between A and C, then we have no information about whether the intensity between A and B is more or less than the intensity between B and C, according to Arrow. The second claim “is justiﬁed on the grounds of equality of voters,” an ethical claim. Arrow immediately contrasts the Borda method to the Condorcet method (“that a candidate who receives a majority against each other candidate should be elected”) and praises Condorcet as consistent with the IIA(A). We begin with Borda’s second claim. Notice that every democratic voting rule, including Condorcet, gives weight (usually equal) to each voter.9 If giving equal weight to voters in the Borda count offends the noncomparabilist doctrine, then so does the Condorcet method, and indeed any political aggregation which assigns weights, equal or unequal, to voters. In 1951 Arrow (1963/1951, 46) proved that the method of majority decision over exactly two alternatives does satisfy the conditions of his theorem, in other words, is a possible social-welfare function; the impossibility result pertains to three or more alternatives (when applied pairwise over three or more alternatives we call this the Condorcet method, which can cycle).

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He eludes the interpersonal comparability of utility problem by means of the following deﬁnition: By the method of majority decision is meant the social welfare function in which x R y [the social ranking] holds if and only if the number of individuals such that x Ri y [individual rankings] is at least as great as the number of individuals such that y Ri x.

Either counting the numbers of individuals for, against, or indifferent to an alternative violates the prohibition on the interpersonal comparison of utility, and all democratic voting is thereby rendered meaningless, or the assumption of one vote per individual has nothing to do with interpersonal comparison of utility. Reading Arrow charitably, it must be that one vote per individual has nothing to do with comparison of mental states. If one vote per individual is acceptable because it has nothing to do with comparison of mental states with respect to the method of majority decision, then it must be acceptable as well with respect to any other voting method, including Borda. Therefore, the Borda method does not necessarily rely on interpersonal comparison of utility. One variety of noncomparabilist might further urge that because of noncomparability, each voter should be given equal weight. One argument is Borda’s ﬁrst claim, as related by Arrow: just because the individual preference data are ordinal, it is best to assign equal weight to the differences between adjacent rankings. Neither the Borda count nor the Condorcet method is a utilitarian method of voting: each is an operation performed on ordinal rankings.10 That the Condorcet method (in the absence of cycles) ranks all alternatives does not necessarily make it a cardinal voting scheme, and the same goes for the Borda count. Some friends, and enemies, of the Borda count argue that it approximates a cardinal voting scheme, that it attempts to squeeze cardinal blood from the ordinal turnip (Mackay 1980, 73), but the same could be said for the Condorcet method. Another argument has it that as the number of voters increases, cardinal variations would tend to cancel each other out, and the Borda outcome would tend to the cardinal outcome (as would Condorcet, see Tangian 2000). The Borda count can be independently justiﬁed on purely ordinal grounds, however. It collects exactly the same information as does the Condorcet method, as can be seen in the pairwise-comparison matrix, but instead sums up the number of votes each alternative gets over every other alternative, and socially ranks by those sums. The alternative that gets the most votes over every other alternative is the winner. There is no reference to cardinality or to comparable mental states in this justiﬁcation

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of the Borda count. Arrow’s deﬁnition of the method of majority decision counts the number of individuals who prefer one or another of a pair of alternatives, and is phrased such that it does not necessarily have anything to do with comparable mental states. Counting the number of times an alternative is preferred by individuals to every other alternative, as does the Borda count, also does not necessarily have anything to do with comparable mental states. Objection: but that would make the outcome depend on the range of alternatives. Reply: just as the outcome should depend on the range of voters. Any democratic voting rule – Condorcet, Borda, other – weights voters (usually equally). Once that is conceded, the Borda count, just as the Condorcet method, is otherwise justiﬁed within the noncomparabilist framework. The deﬁnition of the social-welfare function requires individual and social orderings. The independence aspect of the IIA(A) is adventitious. Its purpose is to exclude voting rules otherwise compatible with ordinal input, and thereby deliver the impossibility result. The IIA(A) does too much Riker (1982, 101) describes the IIA(A) as requiring “that a method of decision give the same result every time from the same proﬁle of ordinal preferences.” He says that the IIA(A) “seems a fundamental requirement of consistency and fairness to prevent the rigging of elections and the unequal treatment of voters,” and that it has been disputed. In a footnote (271), he explains that the main reason for the dispute is that Arrow’s original discussion of the condition confused it with contraction consistency. The IIA(A) condition has three desirable consequences, says Riker. First, it prohibits utilitarian methods of voting. Second, it prohibits arbitrariness in vote counting, such as lotteries or other methods that give different social choice from the same given proﬁle of individual preferences. Third, it prohibits, when choosing among alternatives in a set S, inﬂuences from alternatives in X – S. I respond in turn. First then, we shall consider utilitarian methods of voting. Riker (1982, 118) thinks utilitarian voting “gives advantages to persons with ﬁner perception and broader horizons.” Would utilitarian voting, which on ethical grounds counted each voter equally, and which accepted intensities of preference from cardinal rankings, were it practical to carry out and resistant to misrepresentation of intensity, be undesirable? I think the main objection to utilitarian voting is its impracticality rather than its comparable cardinality; if it were a practical voting system, it might be an excellent one (it might be an excellent voting rule, but it would not necessarily deﬁne what is true or right). Another advantage of the IIA(A),

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according to Riker, is that it forbids “the arbitrariness of the Borda count.” As I have shown, the justiﬁcation of the Borda count need not depend on comparison of mental states. Furthermore, the Borda count avoids two problems of utilitarian voting: ﬁrst each voter is counted equally, and second the weighting of the alternatives is established by the voting scheme and thus avoids voter misrepresentation of intensity. Under the Borda count and with more than two alternatives, if an alternative is lowered in an individual ranking that may lower the social ranking of the alternative. Is this arbitrary? Riker (1982, 108) provides an example of how the Borda count violates IIA(A), but the example seems rather feeble, and arguably supports the opposite view that violation of the IIA(A) by the Borda count is a desirable attribute. Suppose that Larry ranks A > B > C, that Moe ranks C > A > B, and that Curly also ranks C > A > B. Then A and C tie with a Borda score of four points each, and are both preferred over B which has a Borda score of one point (the Condorcet outcome from the proﬁle is C > A > B ). The IIA(A) says that the social ranking of A and C should depend only on the individual rankings of A and C. Thus, if Moe changes his ranking from C > A > B to C > B > A, then, the IIA(A) decrees, the social ranking of A should not change. The Borda count after Moe’s change, however, is four points for C, three points for A, and two points for B (the Borda outcome is now C > A > B, and the Condorcet outcome remains C > A > B). The Condorcet method reports the same outcome for both proﬁles of individual preferences: C > A > B. Preferences with respect to only C and A are the same in each proﬁle, so the Condorcet method here is respecting the IIA(A) (there is no cycle in either proﬁle). The Borda method distinguishes the two proﬁles. Under the ﬁrst proﬁle, the Borda method ﬁnds that C is tied with A. Why does this differ from the Condorcet outcome? Condorcet reports that C is better than A, but the Borda count takes into account that although C is ﬁrst-ranked by two voters, it is last-ranked by one voter, and that A is ﬁrst-ranked by one voter and second-ranked by two voters. Under the second proﬁle, the Borda method ﬁnds that C is better than A. Why the change in the Borda outcome from the ﬁrst proﬁle to the second proﬁle? In the ﬁrst proﬁle, C is tied with A, but the change from the ﬁrst to the second proﬁle is that one voter changes A from second-ranked to last-ranked. The Borda method responds to this change, but the Condorcet method does not so respond. The IIA(A) says that a voting rule should never respond to that sort of change. Practical evaluation of alternative voting rules must consider actual frequencies of good and bad violations of the IIA(A). Second, the IIA(A) also excludes any probabilistic voting rule, according to Riker (1982, 118), because from the same given proﬁle of individual

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preferences it requires that a voting rule always return the same result. For example, imagine the rule that each of n voters writes down his ﬁrst preference among the alternatives on a ballot and then one ballot is randomly drawn to determine the social choice. Incidentally, such a rule would be strategy-proof, since each voter has the incentive to report her true preference, which is why the Gibbard and Satterthwaite theorems are limited to deﬁnite voting rules. Or suppose a rule such that if 90% of voters prefer x over y, there is a 90% chance that the social choice would be x over y; such a rule would be prohibited by the IIA(A). The missing premise in his argument is that Riker does not establish that probabilistic voting rules are normatively undesirable in all or in any circumstances. We would have to consider in detail, theoretically and practically, the consequences of various such rules. Third, “many people believe that judgments on alternatives in X – S are germane to judgments on S itself,” that is, they doubt the IIA(A) (Riker 1982, 129). To charitably reconstruct Riker’s argument, there is no formal method to decide actual relevance and irrelevance, thus, the only way to guard against the threat of irrelevant alternatives having an inﬂuence on decisions is by way of the pairwise IIA(A) condition. More precisely, there is no “wholly defensible method to decide on degrees of irrelevance. In the absence of such a method, Condition [IIA(A)] seems at least moderately defensible.” If, for whatever reason, one were motivated to satisfy Riker’s ﬁrst and second concerns, to disqualify utilitarian or probabilistic voting methods, then other approaches are available that would do the job yet would also permit some voting systems; and if there were somewhere a real human being concerned about wrongful inﬂuences from consideration of ordinarily irrelevant alternatives, then there are approaches that address that concern but avoid the impossibility conclusion. I begin with Hansson (1973), of whom Riker (1982, 275) is aware. If feasible and infeasible alternatives can be clearly identiﬁed, then one should simply conﬁne consideration to feasible alternatives (the IUA condition). For example, if the application of interest is a standard political election among candidates, then the feasible candidates are those who stand for the election. Infeasible candidates would not be considered just because they are infeasible candidates. Then the election would be independent of infeasible alternatives, not in Arrow’s sense of avoiding consideration of third alternatives, but rather in the ordinary sense of avoiding actually infeasible alternatives. Problem solved. Nor is this terminological trickery: the natural reaction to any proposal to include, for example, Napoleon and Confucius as extra candidates in the city council election is ridicule and rejection. This is a clear and simple solution

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to the IIA(A) problem with natural applicability in the political context. Because it is so simple, I take a moment to reiterate that people sincerely concerned about consideration of infeasible alternatives have no worries in this political context. One of Arrow’s (1952, 52) main concerns with respect to the IIA(A) is: If it is abandoned, a choice among a given set of candidates can be made only if each individual possesses a list of preferences containing more candidates than those which are really available. What will be the list of candidates that the individual will be asked to order? There is no natural limit except a vague universe comprising all logically possible candidates. It does not appear correct to make the choice among a very limited set of possibilities depend on all preferences among all “imaginable” possibilities.

Notice that this objection does not apply to the voting context discussed in the last paragraph. Perhaps it does apply in the social-welfare context, and perhaps welfare economists have more reason to worry about the IIA(A) than those in political studies. The worry is that the social-welfare function would have to consider not only actual alternatives, but also the analogs of Thomas Jefferson, Socrates, Buffalo Bill, ﬁctional people, animals, ﬁctional animals, androids, and rocks, and “it is costly in terms of resources to gather and process information about preferences – independence is a requirement that we conserve those resources” (Kelly 1988, 73). First, the costly resources argument is surprising. I think of the social welfare function as an idealization, not an exercise actually carried out in full. Decision theory constantly proposes simplifying models that it would be practically impossible for real agents to carry out, for example, because of combinatorial explosions. The practical impossibility of carrying out the calculation is seldom raised as an objection to the model. Second, it may well be, and I conjecture that it is likely, that the inﬂuence of irrelevant alternatives would be beneﬁcial, neutral, or trivial, especially with large numbers of voters and alternatives. Third, I am not aware of whether welfare economists have explored the concept of possibility with more philosophical rigor; if not, perhaps that would help clarify the problem. Hansson offers weakened independence conditions. Again, X is the set of all alternatives, nonempty subset S contains the feasible alternatives, and X – S contains the infeasible alternatives. IIA(A) would be violated if changes in preferences over two alternatives in X – S changed the social choice over alternatives in S, and also would be violated if changes in preferences over two alternatives, one in S, and one in X – S, changed the social choice over alternatives in S. Hansson’s “positionalist

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independence” (PI) condition, like IIA(A), forbids changes in preferences over two infeasible alternatives in X – S to inﬂuence the social choice, but it permits changes in preferences over two alternatives, one in feasible S and one in infeasible X – S (or both in S), to inﬂuence the social choice over the alternatives in S. This PI condition would void Arrow’s impossibility result for the Borda count, the Copeland method, and some other voting rules. He also offers a “strong positionalist independence” (SPI) condition. How much can you change individual orderings without changing the social choice between two alternatives x and y? Divide an individual’s rankings of alternatives other than over x and y into ﬁve groups: those below both x and y; those the same as y; those between x and y; those the same as x; and those above both x and y. IIA(A) permits that we can move around in individual orderings alternatives other than x and y as much as we like, from any group to another, without changing the social choice. The PI condition allows us to move around alternatives other than x and y only within each of the ﬁve subgroups. SPI is more generous than PI; it allows us to move alternatives from above both x and y to below both x and y, and from below to above, without changing the social choice. Although stronger, the SPI condition still permits the Borda count, that is, substituting SPI for IIA(A) in the Arrow theorem shows that the Borda count is a possible social-welfare function (but not the Copeland rule, etc.) Much more simply, Saari (1995a, 97) offers an “intensity IIA” condition. Suppose that we measure intensity of preference only by the number of candidates a voter uses to separate a pair, as in the Borda count. The intensity IIA requires that the ranking of any two candidates depends only on each voters’ ranking of those candidates and the intensity of that ranking. Again, the intensity IIA avoids Arrow’s impossibility result. Also, recall that Young–Kemeny, a Condorcetextension voting rule which resolves cycles, gets by with a local independence of irrelevant alternatives condition. The alternative independence conditions would entirely satisfy Riker’s ﬁrst and second concerns to forbid utilitarian and probabilistic voting rules. The device of considering only feasible alternatives when there is a clear boundary between the feasible and the infeasible, such as in many democratic-voting applications, entirely satisﬁes Riker’s third concern about avoiding inﬂuence from preferences over infeasible alternatives, even though it would violate Arrow’s IIA(A) if more than two feasible alternatives were considered. When the boundary between the feasible and the infeasible is less clear, the weakened independence conditions partially satisfy Riker’s concern that decisions be independent of infeasible alternatives, a concern about which he can say no better than that it is “moderately defensible.”

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Table 6.5. Borda manipulation, initial situation 3

2

X Y

Y X X

X Y

2

Y

(Borda)

3

(3) (2)

Independence is not a practical requirement Recall that Arrow believes that a positional method such as the Borda count is defective because it must consider some vague universe of all possibilities. The Borda method must consider all possible candidates, not merely actual candidates. The Condorcet method is independent of irrelevant alternatives, therefore it need not consider all possible candidates, but rather may consider only actual candidates, and thus is practically advantageous, the story goes. The Arrovian tradition has added that the Borda method is subject to manipulation by the addition and subtraction of candidates, but that the Condorcet method is not. Mueller (1989, 394) glosses Arrow: The outcomes under the Borda procedure and similar schemes depend on the speciﬁc (and full) set of issues to be decided. Thus, abandonment of the independence axiom raises the importance of the process that selects the issues to be decided in a way that its acceptance does not.

The supposed contrast is merely academic folklore, however. Notice that the violation alleged is of the IIA(RM), not the IIA(A). The IIA(A) takes alternatives considered as given, and varies preferences over alternatives; the IIA(RM) takes preferences as given, and varies alternatives considered. Both the Condorcet and the Borda methods depend, although in a tenuous way, on the set of issues to be decided. And both the Condorcet and the Borda methods are susceptible to manipulation by addition or deletion of candidates. The Borda count is theoretically subject to a special case of manipulation (Dummett 1998) – by adding new candidates from outside the given set a manipulator might be able to change the outcome. Let’s begin with a proﬁle of ﬁve voters and two alternatives, and the accompanying pairwisecomparison matrix, as in Table 6.5. Obviously, X is the Borda winner. If

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Table 6.6. Borda manipulation, ﬁrst step 3

2

X Y Z

Y Z X X

X Y Z

2 2

Y

Z

(Borda)

3

3 5

(6) (7) (2)

0

Table 6.7. Borda manipulation, second step 3

2

X Q Y Z

Y Z X Q X

X Y Z Q

2 2 0

Y

Z

Q

(Borda)

3

3 3

5 2 2

(11) (7) (6) (6)

2 3

3

the Borda count is the voting rule, then supporters of Y can boost Y to ﬁrst place, however, by introducing an alternative Z that is very similar to Y but just below it in everyone’s preference rankings. See Table 6.6. This little trick changes the Borda order from X > Y to Y > X > Z, a violation, of course, of contraction consistency. Dummett proposes a ﬁx for this eventuality that shall not detain us here. Another ﬁx is strategic deterrence: the partisans of X can restore X to ﬁrst place with an identical maneuver: they just introduce alternative Q that is similar to X but just below it in everyone’s rankings. So we are back again to X > Y, just where we started. Why would the partisans of Y introduce manipulative alternative Z, if they anticipated that the partisans of X would respond

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with the introduction of countermanipulative alternative Q? The result if everyone manipulates is the same as the result if no one manipulates, and if there were transaction costs to adding alternatives then would anyone bother with this ploy? Assume, however, that the Borda method is guilty as charged. The same charges can be laid against the Condorcet method. In order to carry out a proper Condorcet ranking one has to rank all alternatives feasible and infeasible.11 Why? Suppose that the two feasible alternatives are x and y, and that the social preference over the set S of x and y is x > y and thus that the social choice appears to be x. That is not sufﬁcient to determine the social choice, however. We also have to examine all infeasible alternatives z in X – S in order to determine that it is not the case that the social preferences are z > x and y > z. Because if it happens that for some alternative z that z > x and y > z, then there is a cycle z > x > y > z. If there is such a cycle, then the choice set is empty. When we apply the Condorcet method only to feasible alternatives x and y, the choice between x and y is x. When we apply the Condorcet method to all alternatives feasible and infeasible, then it may be that there is no social choice between x and y. The Condorcet method seems to be especially absurd here: society would prefer relevant x to relevant y despite irrelevant alternative z, but the possibility of irrelevant alternative z prohibits choice between relevant x and relevant y. If the objection is tenuous against the Condorcet method, then the objection is tenuous as well against the Borda method. How do the Condorcet and Borda methods compare with respect to the manipulative addition and deletion of alternatives? Someone who would manipulate by addition or subtraction of alternatives needs a vast amount of information. She needs to know in advance, before the vote, the preference rankings of all of the voters. If she is a manipulator by way of addition of alternatives, which I will show is the more important case, she also needs to know not only the voters’ preference rankings over the “relevant” alternatives naturally under consideration but also their rankings over some number of “irrelevant” alternatives in order to be able to select from the “irrelevant” alternatives the one or more that would permit her manipulation to succeed (assuming that the one or more irrelevant alternatives she needs exists). Again we stumble across an inconsistency in Arrovian tradition. On the one hand, change of preference over an “irrelevant” alternative may suspiciously change the outcome. On the other hand, the ordinalist revolution requires that welfare judgments be based only on interpersonally observable behavior, according to Arrow (1963/1951, 110), “that, ideally, one could observe all preferences among the available alternatives, but there would be no way to

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observe preferences among alternatives not feasible [irrelevant] for society.” On the one hand, the possibility of manipulation is a threat. On the other hand, the information required for the manipulation is not available. If an aspiring manipulator has the requisite information, then a new problem will arise in many circumstances. With more than a few voters and a few alternatives it is quite complicated to calculate the manipulative strategy. The calculation of a strategy may take such a long time that it is not practical to carry out, and in the extreme it may be exponentially hard to carry out, that is, it would take more time to calculate than there is in the universe, for example. Bartholdi, Tovey, and Trick (1989) showed that for more than a few voters or alternatives it would be computationally impractical (NP-hard) to calculate the election outcome by the Dodgson method or the Young–Kemeny method. Bartholdi, Tovey, and Trick (1992a) showed that a version of the Copeland method is computationally resistant to manipulation by strategic voting; Bartholdi and Orlin (1991) showed the same for the single transferable vote. Bartholdi, Tovey, and Trick (1992b) compared the manipulability of plurality rule to the Condorcet method with respect to adding candidates, deleting candidates, partitioning candidates, adding voters, deleting voters, and partitioning voters. Although plurality is logically susceptible to the ﬁrst three manipulations, it is computationally resistant to such manipulations; Condorcet is logically susceptible to the second three manipulations, but is computationally resistant to them. There is the magniﬁcent and crisp issue of whether a manipulation is calculable in the lifetime of the universe that Bartholdi and coworkers consider, and there is also the modest and fuzzy issue of whether a manipulation is practically calculable by real humans in real time in real settings, that could only be decided by empirical investigations. It is important to distinguish whether the option of manipulation by addition and deletion of candidates is open only to one actor or is open to all. If it is open to one unconstrained monopoly actor, then no matter what reasonable voting rule is in force, she can just delete all candidates she doesn’t like and add the one candidate she does like, which is equivalent to agenda dictatorship. Practically, the addition of alternatives must be relatively open, and the subtraction of alternatives must be relatively closed (or made on the basis of criteria selected well in advance under veil-of-ignorance conditions, otherwise one would face the conundrum of needing to apply the voting rule in order to decide which candidates to subtract from consideration by the voting rule). If we posit that an actor has a manipulative advantage arising from her unconstrained monopoly power to delete candidates we have not demonstrated that a voting rule

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has unfair consequences. We have said nothing different than it would be unfair to give 99 of the voters one vote each while giving one special voter 100 votes to cast; we have quietly assumed violation of voter equality in order to publish loudly a violation of voter equality. Perhaps it is meant that a trusted and accountable authority would delete a candidate in order to manipulate by stealth. Suppose that information and calculability are not problems. Deﬁne the criterion of manipulation to be changing a winner into a nonwinner by the addition or deletion of alternatives. Then the Condorcet method is just as vulnerable to manipulation by deletion of candidates as is the Borda method. The manipulating Condorcet chairperson simply deletes all alternatives that in pairwise comparison would defeat her favored alternative. It may be objected that what is meant is that the manipulator would be able to succeed by stealth under the Borda method but not under the Condorcet method. That smuggles in a new assumption, however: not only would the manipulator have monopoly control over the deletion of alternatives, the manipulator would also have a monopoly control over information about the distribution of preferences and over calculative capacity. Then all we have shown is that those with unfair power have unfair inﬂuence. Manipulation by deletion of alternatives does not seem to be a plausible scenario. The Condorcet method is as vulnerable to manipulation by addition of candidates as is the Borda method. If in the absence of manipulation the social choice would have been x > y, the Condorcet manipulator – as with Borda, any of the voters, not only the chair – simply adds an alternative z that creates a cycle x > y > z > x, and x is no longer the Condorcet winner. It may be objected that there may not exist an alternative z that would allow for the manipulation, but the same could be said for the Borda count, that there may not exist an alternative the addition of which would change a winner to a nonwinner. We have established that both Condorcet and Borda are susceptible to manipulation by addition or deletion of alternatives. Finally, there is an additional complexity. Manipulation begets countermanipulation. Someone contemplating the strategic addition of an alternative also has to consider the strategic response of other actors. It may be that strategic addition by all actors would cancel out and the outcome would be the same as in the absence of strategic action, it may be that strategic addition by all actors would lead to an outcome intended by no one, it may be that strategic actions are impractical to calculate. These issues are not well settled. Gibbard (1973) and Satterthwaite (1975) showed that voting procedures that satisfy the IIA(A) are immune from strategic voting, but those

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that violate the IIA(A) are susceptible to strategic misrepresentation of preferences. This breathes new life into the IIA(A) and the Arrow theorem. While admitting the attractive qualities of the Borda count, Mueller reports that “its Achilles heel is commonly felt to be its vulnerability to strategic behavior” (120). But the Gibbard–Satterthwaite theorem shows that all voting methods of interest share this defect of being susceptible to manipulation by strategic misrepresentation of preferences, including Condorcet pairwise comparison among three or more alternatives (but only if the proﬁle of voters’ preferences is such as to yield a cycle, which I have argued is rare). It may be that the Borda count is more practically and irremediably susceptible to strategic misrepresentation of preferences than other reasonable voting rules; it may be not (see Chamberlin 1985, Nitzan 1985, Saari 1990). Conclusion The Arrow theorem is a great piece of work. It illustrates an abstract limit case. It is a logical exercise, it does not describe the real world. The conditions of the theorem, especially IIA(A), are methodological assumptions, with no descriptive or normative force of their own. That a democratic voting rule violates IIA(A) is nothing to be feared, as such violation has not been established to be normatively undesirable, all the more so given that insistence on the conditions leaves the dictatorship of one as the only possible voting rule. Any democratic voting rule forces a comparability assumption, or requires a nonwelfarist justiﬁcation of voting weights, and a democratic voting rule, whether Condorcet or Borda, assigns equal inﬂuence to each citizen. If there is someone who believes that the idea of cardinal ranking of alternatives is unintelligible, or judges that it is impractical, she still might be able to endorse either the Condorcet or Borda methods, which work on ordinal rankings. If there is someone who fears the threat of Condorcet cycles, she still might be able to endorse the Borda count as a method that avoids cycles. If there is someone who worries about inﬂuence from irrelevant alternatives, she can recommend that elections only consider actual candidates, and when the boundary between feasible and infeasible is fuzzy she can recommend the Borda count as a method that satisﬁes a slightly weakened independence condition. These, and other considerations in this chapter, are not a plea for the widespread adoption of the Borda count. Natural similarity among preference rankings means that in most circumstances the differences in outcomes among the reasonable voting rules are practically minimal. If there is someone concerned about manipulation by strategic misrepresentation of

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preferences, she might choose the single transferable vote, which experience has shown to be practically unmanipulable in this regard. Even our most inaccurate voting rule, plurality, might be desirable because of its simplicity. The alleged irrationalities of voting are greatly exaggerated. It is time for a shift from constitutional “physics” to constitutional “engineering.” Newton’s ﬁrst law of motion, another great intellectual achievement, says that an object in motion tends to stay in motion and an object at rest tends to stay at rest, unless the object is acted upon by an outside force. An inattentive interpreter of physics may advise engineers that it is futile to try to make anything go, or try to make anything stop, because of Newton’s ﬁrst law. The inattentive interpreter has failed to notice the qualifying clause: unless the object is acted upon by an outside force. Arrow’s theorem says that there are no social welfare functions that satisfy his conditions. Yet we observe that there are social decision processes (discussion, institutions, voting) that work satisfactorily to translate what individuals would prefer into democratic social outcomes, and there are social-welfare functions (voting) that work satisfactorily in practice. That means that they do not satisfy one or another of the Arrow conditions. That does not make democracy impossible, irrational, arbitrary, meaningless, and the rest. There is another important issue of constitutional engineering. It is no longer enough to show that a voting rule is logically susceptible to manipulation by addition of alternatives, deletion of alternatives, addition of voters, deletion of voters, partitioning of voters, agenda control, strategic voting, and so on. It is no longer of interest to interpret such logical susceptibilities as relevant to global normative judgments about democracy, the trick is just worn out. The era of destructive social choice theory is past. Rules that are logically susceptible to manipulation may not be practically susceptible at all, some rules may be more practically susceptible than others, susceptibility may vary with the actual distribution of preferences in the population, the strong logical susceptibility of one rule might be more practically remediable than the weak logical susceptibility of another rule, and so on. The constructive social choice theory of the future would work on the comparative practical susceptibility of rules to unfair manipulations, and the identiﬁcation or invention of institutions to remedy them, rather than on denunciations of democratic choice.

7

Strategic voting and agenda control

As we have seen, Riker (1982, 122, 128) acknowledges that debate and discussion lead to similarities of judgment, that “a wide variety of rather mild agreement about the issue dimension guarantees a Condorcet winner,” that uncontrived cyclical outcomes are “quite rare,” so that “intransitivities only occasionally render decision by majoritarian methods meaningless.” His remaining objection then is that outcomes may be manipulated by strategic voting, agenda control, and contrived introduction of new alternatives and dimensions. “Manipulated outcomes are meaningless because they are manipulated, and unmanipulated outcomes are meaningless because they cannot be distinguished from manipulated ones” (Riker 1982, 237). To introduce his concern, consider the following exercise. Suppose that a majority of 60 percent favors A over B, and a minority of 40 percent favors B over A. The minority faction could contrive a cycle if it has some idea of the distribution of preferences over original alternatives A, B, and new issue C. Issue C splits the majority. See Table 7.1. With C on the scene, A beats B by 60 percent, B beats C by 70 percent, and C beats A by 70 percent. Then, the minority can propose C against A, which C wins, then C against B, which B wins, thus, the minority view favoring B over A prevails (but only if the majority is somehow incapacitated from continuing the cycle by proposing A against B which of course A would win, ad inﬁnitum). If the majority faction were to have unconstrained monopoly control over the order of consideration of issues, then the majority could defend against the contrived cycle by putting B against C, which B would win, and then B against A, which A would win, vindicating the majority view (with agenda control, the majority prevents the minority from proposing C against A). But wait, if the minority were thwarted by majority agenda control it could vote strategically: rather than voting its true preference B when B is posed against C, it could instead vote for C, putting the minority back at the start of its winning cycle, assuming that the majority lacks its 158

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Table 7.1. Contrived outcomes Before contrived cycle %

After contrived cycle %

After intramajority logroll %

60 A > B

30 A > B > C 30 C > A > B 40 B > C > A

30 A > A-100 > B > C 30 A+100 > C > A > B 60 B > C > A

40 B > A

own strategic capacity, and so on. The majority faction also could resist the cycle by logrolling in its own ranks, if, say, its ﬁrst subfaction (A > B > C ) could compensate its second subfaction (C > A > B) with sufﬁcient cash (or, more likely, in implicit obligation), when alternative A minus the cost of compensation is still better than B for the ﬁrst subfaction and alternative A plus the beneﬁt of compensation becomes better than alternative C for the second subfaction. The contrived cycle in my example is inspired by Riker’s (1982) examples; the logrolling by Tullock (1992). Strategic voting, logrolling, agenda control, and multidimensional issue spaces are each topics that have inspired vast, challenging, and unsettled literatures. There are hundreds of models, considerable variations in assumptions, and divergent results arising from alternative assumptions. I do not propose a comprehensive review of these topics. Instead, the focus will be on looking over ﬁndings relevant to the normative conclusions of Riker’s positive political theory: that multidimensional issue spaces make the concept of a majoritarian democracy meaningless and that associated opportunities for manipulation make democracy arbitrary, viz.: “Outcomes of any particular method of voting lack meaning because often they are manipulated amalgamations rather than fair and true amalgamations of voters’ judgments and because we can never know for certain whether an amalgamation has in fact been manipulated” (1982, 238). If the issue space is multidimensional, does that mean, in principle, that there is no determinate public good? How frequent are opportunities for manipulation? When there is an opportunity, how often are manipulations attempted? When manipulations are attempted, how often do they lead to unfair and inaccurate outcomes (which I shall call harmful manipulations), and how often do they preserve fair and accurate outcomes? Are there practical remedies available to deter harmful manipulations, and if so, how often do they work? This boils down to the crucial question: how frequent is irremediable and harmful manipulation? Finally, does the possibility of manipulation make the inference of preference orders so obscure that we are unable to distinguish manipulated from unmanipulated outcomes?

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The answer to the ﬁnal question is necessarily no, due to an internal contradiction in Riker’s argument. In order to succeed at strategic voting, logrolling, agenda control, or the manipulative introduction of new alternatives and dimensions, the manipulator needs conﬁdent knowledge of the distribution of preference rankings in the population to be manipulated. This is evident from the foregoing exercise (and such complete information is assumed in the formal models). To contrive the cycle, the minority faction would need to know the preference rankings both among its own members and the members of the majority faction over the original alternatives, A and B, and also their rankings in relation to the manipulative new alternative C (a side issue that calls into question the practicality of contriving a cycle is if the alternative is “new,” how would the manipulator know the population’s rankings of it?). The majority faction’s attempted manipulation of the sequence of the agenda also requires complete information about the preference distribution, as does the minority faction’s attempted response at strategic voting. As well, to succeed at the logroll, the majority faction would need to know the distribution of preferences in its own ranks. Riker’s argument is that the possibility of manipulation makes it impossible to know the preferences of others (his defense of this premise and its failure is examined in detail in Chapter 2 on the basic argument pattern), and since the preferences of others cannot be known then it is impossible to distinguish manipulated outcomes from unmanipulated outcomes. Manipulation is not possible, however, without knowledge of others’ preferences. Thus, we arrive at the contradiction: manipulation is possible only if preferences are known; but if manipulation is possible, then preferences are unknown. If p then q; if q then not-p; one or another of these propositions must go, and it must be the second one: the statement that “if manipulation is possible, then preferences are unknown” must be false. Therefore, the second half of Riker’s argument, that harmful manipulations are necessarily impossible to detect, fails. Only the ﬁrst half of his argument remains: that harmful manipulations are frequent, an empirical assertion. Strategic voting Recall that strategic voting (also known as sophisticated voting) comes about when it is advantageous for one not to vote for one’s sincere preference, as illustrated by the minority’s maneuver in the exercise above. Another example: in a plurality runoff system, one might vote against one’s ﬁrst choice and for one’s second choice in the primary election as the best candidate to defeat one’s third choice in the general

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election: don’t throw away your vote. Recall that there is a connection between Arrow’s theorem and the possibility of strategic voting. Say that a vote is sincere if it represents the voter’s sincere preference, and a vote is strategic if it misrepresents the voter’s sincere preference. If Deborah and all remaining voters vote sincerely, we label the outcome the sincere outcome (in this context, insincerity should be read without pejorative connotations). If Deborah votes strategically, and all remaining voters vote sincerely, we call the outcome the strategic outcome. A voting procedure is strategy-proof if there is no strategic outcome that Deborah prefers to the sincere outcome. Arrow’s possibility theorem showed that any nondictatorial social-choice procedure for three or more alternatives must violate the condition of the independence of irrelevant alternatives (IIA(A)). If a procedure is strategy-proof then it satisﬁes IIA(A), and if a procedure satisﬁes IIA(A) then it is strategy-proof. This is the theorem of Gibbard and Satterthwaite (as paraphrased by Hinich and Munger 1997, 165): “No voting rule that can predictably choose one outcome from many alternatives is strategy-proof unless it is dictatorial.” (A voting lottery such that each voter marks a ballot and then one ballot is chosen randomly is strategy-proof, here there is no reason for Deborah to mark her ballot insincerely, thus the Gibbard–Satterthwaite theorem is limited to predictable voting rules.) Therefore, nearly all rules of interest for three or more alternatives are susceptible to strategic voting. One immediate qualiﬁcation: again, this susceptibility is a logical possibility, the theorem does not show that the susceptibility is an empirical probability. Riker (1982, 280) notes that “if there is enough similarity in voters’ preference orders, many voting systems are strategy proof,” but does not develop the point. I conjecture that again it would be a matter of probability, the more similar are preferences, the less the susceptibility. We do know for sure that if the distribution of preference orders is such that they are single-peaked, the Gibbard–Satterthwaite theorem does not apply, there is no chance for strategic voting to succeed (Dryzek and List 2003). So far, we have assumed that only Deborah is capable of strategic voting and thereby bringing about the strategic outcome that otherwise would not have prevailed. What happens if other voters possess strategic capacity as well? If all voters vote strategically, and if preferences are separable (that is, if a voter’s reaction to changing levels of one alternative is independent of the expected level of any other alternative, Hinich and Munger 1997, 243), then the outcome is just the same as if all voters vote sincerely. In these circumstances, sophisticated votes cancel each other out in a manner of speaking, and our true and fair outcome is thus restored. The incidence of manipulation could be universal under these

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conditions, but the incidence of harmful manipulation would be zero. This is not too surprising; after all, a model that grants strategic capacity only to one actor violates the democratic ideal of voter equality. The model gives one actor an unfair advantage and then, in a manner reminiscent of Captain Renault’s discovery of gambling in Rick’s nightclub in the movie Casablanca, is shocked to discover that an unfair advantage leads to an unfair outcome. How important is strategic voting? We’ll look at two aspects of the question: voters selecting among candidates, and members of a committee selecting among alternatives. I think it is uncontroversial that voters, for example in American primary elections, engage in strategic voting. That voters have this capacity constrains the entry of candidates in such a plurality election (if voters won’t waste votes on losers, then it is unlikely that more than two strong candidates will enter), and thereby reduces the incidence of strategic voting. Cox (1997, 37–148) has shown empirically the incidence in particular circumstances of strategic voting under a variety of voting systems. Again, potential candidates’ anticipation of strategic voting should deter entry and thereby reduce the incidence of strategic voting among voters. Another sort of constraint on strategic voting is that it requires a lot of information; undoubtedly, sometimes there is both enough information and the requisite circumstances for voters to vote strategically, but that such information is available defeats Riker’s argument that manipulation makes preferences unknowable. Although hypothetical examples of harmful manipulation are available, I know of no sustained argument, theoretical or empirical, that the potential for strategic voting among voters actually leads to irremediable, frequent, and harmful outcomes. Now suppose a committee using standard parliamentary amendment practice (or any other binary agenda procedure), whose members have complete information including knowledge of each other’s preferences, and where members are free to offer amendments. Austen-Smith (1987) showed that in these circumstances, and whether or not there is a Condorcet winner, strategic voting and sincere voting are observationally equivalent. If all voters are strategic their votes are the same as if they were all sincere. That is because those offering proposals would anticipate strategic voting and would only offer those proposals that would beat previous proposals under sincere voting. Under these circumstances, an empirical survey would disclose zero instances of strategic voting. Nor would the strategic outcomes differ at all from the sincere outcomes, and thus the incidence of harmful manipulations would be zero. To draw out an implication, only if some actors are unfairly constrained from responding strategically might an unfair decision come about.

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Logrolling Riker brieﬂy treats vote trading as another opportunity for strategic voting with the potential for harmful manipulations, and my rejoinder will be brief. Recall the example I provided as a normative objection to the Condorcet criterion: the Red Party of 1,001 voters favor A > B > C and the Green Party of 1,000 voters favor B > C > A. Pairwise comparison gives the contest to A, the candidate ranked last by the Green Party who make up almost half the population. If we are operating by pairwise-comparison majority-rule voting this is an ideal opportunity for vote trading. Those in the Red Party of 1,001 voters prefer A to B, some fanatically, some just barely; and all those in the Green Party of 1,000 voters rank A as the worst of all the alternatives. A few of those in the Greens should go to a few individuals in the Reds who least intensely prefer A to B (the cheapest votes, as it were), and propose a trade: you Reds who mildly prefer A to B, vote for B so we Greens can avoid our lastranked candidate, and we’ll owe you for it. When the tables are turned and there is some X you intensely prefer to a Y while we only barely prefer Y to X, we’ll return the favor. Pairwise comparison ignores information about the relative intensity of preferences, so carrying debits and credits between issues brings intensity back into the decision system. It would seem that vote trading makes everyone better off, is welfare-enhancing (Coleman 1990). So it would seem, but by varying behavioral assumptions we can craft one model that shows logrolling to be welfare-enhancing and another model that shows logrolling to be welfare-reducing. Riker chooses the assumptions that portray logrolling as welfare-reducing. Since the theoretical models can’t settle the controversy, we can only rely on empirical evidence. The empirical evidence is not weighty, but what there is goes more towards the proposition that vote trading is welfare-enhancing.1 Additionally, the experimental evidence, according to Mueller’s (1989, 94) summary, shows that logrolling does not lead to welfare-reducing outcomes, and generally that “the outcomes from committees that use majority rule tend in practice to be more stable than the theoretical literature on majority rule leads one to expect.” How might vote trading be welfare-reducing? In ﬁve ways. First, before vote trading we might have two independent binary votes, one pitting X against Q and another pitting Y against Q. Binary votes are not subject to cycling. If the issues are joined by vote trading, however, that yields four alternatives for each voter: XY, QY, XQ, QQ. Cycling is possible with more than two alternatives, and vote trading created four alternatives where before there were two, so vote trading

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introduces the possibility of cycling where there was none before. As I always must add, this is a possibility, not a probability. A cycle either generates costly instability or permits a monopoly agenda-setter to dictate the outcome.2 Second, if vote traders renege on their commitments then there is instability as voters drift from one doomed coalition to another. Third, if to enhance their bargaining power some voters exaggerate their support or opposition on an issue so as to claim more credits than they are due then that might decrease welfare. Fourth, it is possible for a majority bloc to vote trade among its own members in a fashion that beneﬁts them but imposes greater costs on the minority not included in the logroll. Fifth, a linked series of such trades could end up making everyone in the legislature worse off as each individual ends up the minority victim of a different externality-imposing majority (Riker 1982, 161–165). In conclusion, “vote-trading enormously expands the potential for strategic voting in legislatures.” He acknowledges that vote trading can enhance welfare “even for a majority,” but adds that “possibly more frequently in the real world, cases also exist in which vote-trading makes more people worse off than are made better off.” The argument is insulated by opaque qualiﬁers. Vote trading expands the potential for strategic voting, but does it actually increase the incidence of strategic voting, and if so, would any harm result? Logrolling is on net welfare-reducing, possibly; which means that it is also possibly welfare-enhancing. The ﬁrst and second objections smuggle in an exogenous assumption, that instability is welfare-reducing. Endogenizing the costs of instability changes the incentives for the actors; if cycling or unstable coalitions shrink the pie then at some point it becomes worthwhile to stick with one alternative or coalition over another, and if instability doesn’t shrink the pie then instability is not a problem. The ﬁrst and second objections alternatively rely on the assumption that a monopoly agenda-setter unfairly imposes an outcome (to be criticized in the next section). The second and third objections assume that legislators will be happy to cheat and lie on all occasions and that there are no cheap institutional remedies to control such naked sociopathy. The fourth objection has the most bite, and surely there are welfare-reducing logrolls such as perhaps the SmootHawley tariff or the American military budget. What governmental action is welfare-enhancing and what welfare-reducing is controversial, however, and judgment is often colored by ideological prejudices. America certainly seems greatly undersupplied with public goods compared to Western Europe. Were the following governmental actions net enhancements or net reductions of welfare: the controversial establishment of public education in the early nineteenth century, the tariff, rivers and

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harbors legislation, freeing the slaves, railroad land grants, the national park system, the GI bill, the defense establishment, and its spinoffs such as the internet? The ﬁfth objection assumes that voters will myopically march to disaster. There is a social dilemma aspect to the second through ﬁfth objections. The immediate incentive for each individual actor is to cheat, lie, and beggar his neighbor such that everyone is cheated, lied to, and beggared in the end. We observe elsewhere that social dilemmas are sometimes (but not always) resolved, and there are many mechanisms by which this may come about (see Ostrom 1990; Lichbach 1996). Perhaps the least controversial mechanism to suggest in this setting is that a repeated social-dilemma supergame permits an equilibrium where no one cheats, lies, or beggars his neighbor. It seems that among legislatures facing the same kinds of temptations, some succeed at self-regulation and some fail. Koford (1982, as related by Stratmann 1997), makes assumptions that produce a result more congenial to my taste, but I must emphasize that as far as I know the behavioral realism of his assumptions is not established. In Koford’s model legislators trade through party leaders who act as clearing houses of credits and debits. Such leaders are in a position to prevent cheating and lying and thereby deliver efﬁcient vote trading. Competition for leadership posts is over who is best at maximizing welfare from trades. Leaders from different parties form a collusive duopoly that maximizes joint gain and then struggles over division of the gain. The majority party colludes with the minority party; otherwise the minority has nothing better to do than to destabilize the majority. Leaders only pass bills whose beneﬁts exceed the costs, and leaders select those rank-and-ﬁlers who are cheapest to obtain for passage of a measure. Stratmann (1997) states that endless cycles are not observed in the real world of legislatures. Outcomes do not differ much from one session to the next, and differences are attributable to the replacement of legislators. Once legislation is enacted it is usually many years before it is revisited. Budget allocations do not lurch from one activity to another from year to year. Cycling dogma would predict that there is usually a majority that would defeat an incumbent legislator in her home district, yet the longevity of incumbents is notorious. As for vote trading, there is evidence of logrolling and of stable logrolling coalitions in the US Congress. There is evidence of intense minorities winning over mild majorities, and there is evidence that those who are least opposed to the measure are most likely to switch votes, implying the occurrence of vote trading. Moreover, “to date, empirical ﬁndings appear to point to stable coalitions . . . Further, reciprocity in vote trades has been found,

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indicating no widespread reneging . . . So far, the scarce evidence on vote trading appears to be consistent with the hypothesis that leaders efﬁciently organize vote trades” (Stratmann 1997, 340). The issues are not settled, but there is no evidence for the Rikerian proposition that logrolling permits manipulations so frequent, irremediable, and harmful as to render democracy meaningless. Agenda control While strategic voting is usually unobservable, agenda control is often obvious and its incidence can in principle be estimated, Riker continues, and its incidence is “surely very high, for the consequences of agenda control are apparent in some degree in the content of almost all social choice” (emphasis added, 1982, 169). Riker reckons that there are two types of agenda manipulation, one exercised by leaders in controlling the agenda, the other exercised by the capacity of nonleaders to introduce new alternatives for consideration. This section concentrates on the ﬁrst type, the power of leaders to add, subtract, and order consideration of alternatives. Although it is identiﬁable and supposedly ubiquitous, Riker makes no attempt to estimate the frequency of agenda control in any actual political arena; not even one anecdote of harmful actual agenda control of the ﬁrst type is reported. If the agenda-setter story were valid, say Brennan and Lomasky (1993, 45), then democratic politicians would directly appropriate a signiﬁcant portion of the public budget. They would be the richest members of the community, but this is not what we observe. Riker sharply qualiﬁes his argument. Leaders, he concedes, do not have unconstrained power. Leaders may nominate candidates, but nonleaders vote on them. Typically, the rank and ﬁle can challenge rulings of the chair. Leaders are elected because of their adherence to local norms of fairness, and most comply with those norms. Chairs recognize opponents, accept proposals for consideration that they oppose, and so forth. Therefore, leaders’ control is seldom challenged, but there is a “subtler reason” for the observation: to challenge the procedure is to challenge the leadership and thus leaders have “some, though constrained” control over the agenda. To draw out Riker, presumably, nonleaders would tolerate such control either if it were more welfare-enhancing for the body than some next-best institutional alternative or if the manipulated issue was of major importance to the leader but of minor importance to most other folks. This would not cohere, however, with Riker’s other claims that logrolling is welfare-reducing (1982, 167) or that contrivance of cycles and manipulation by agenda control emerges on the most important

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issues (1982, 122). Either agenda control is harmfully ubiquitous, or it is trivial; it cannot be both. Assume, however, an unconstrained monopoly agenda-setter, otherwise we have no bone on which to gnaw. It is just the Captain Renault demonstration again: one actor is quietly given an unfair advantage and then loudly discovered to have unfairly distorted the outcome. We are shocked to discover that someone with dictatorial power attains a dictatorial result. Let’s consider the one-dimensional case before going on to the multidimensional case. Suppose that the distribution of preferences is such that at one end a voter wants the status quo of 0 schools, the median voter wants 50 schools, at the other end a voter wants 100 schools, and the agenda-setter prefers 10 schools. The agenda-setter proposes her preference for 10 schools and this passes since it wins the vote of everyone who wants 10 or more schools, even though everyone who wants more than 10 schools is damaged by the agenda-setter’s unfair exercise of control. When presented in its simple one-dimensional version the agenda-control story is quite feeble. We immediately recognize either that an unconstrained agenda-setter has undemocratic power or that if such an ofﬁcial were herself constrained by threat of reelection or by appeal of the ruling of the chair or by some similar device then she would be constrained to permit the median proposal. The multidimensional version is recondite, and so it is not so immediately obvious that the same objections hold, but they do. If there is a cycle, and if there is an actor with unconstrained monopoly agenda power, then the agenda-setter can select the outcome by ordering the sequence of pairwise voting. Suppose there is a cycle A > B > C > A and the agenda-setter favors alternative A. Then the agenda-setter pits B against C which B wins, and then B against A which A wins; each alternative has been voted on and A is the winner. If the agenda-setter favors alternative B, then she ﬁrst pits C against A which C wins, and then B against C which B wins; and so on. If the cycles were of what I termed the balanced type, such that the numbers who rank each alternative ﬁrst are equal, then the agenda-setter has simply broken a tie. If there are a series of ties of various sorts and the leader settles them always in an unfair way then she will face the consequences among those who elected her. If, as is much more likely, the preferences are such so as to be a cycle by pairwise comparison but are determinately ordered by the Borda count, or by some intuitive apprehension of the intensities of preference, then the agenda-setter would again have to face the consequences. Suppose that only the agenda-setter ranks C ﬁrst and C > A > B, that ten others rank C second and B > C > A, and that ten others rank C last and A > B > C. That proﬁle yields the pairwise-comparison matrix

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Table 7.2. Unfair agenda setter A A B C

10 11

B

C

(Borda)

11

10 20

(21) (30) (12)

1

in Table 7.2. By pairwise comparison, A > B, B > C, C > A, or A > B > C > A, a cycle. The unconstrained agenda-setter sets A against B, which A wins, and then C against A which C wins. The ranking by Borda count, by Young–Kemeny, and by intuitive apprehension of intensities, is B > A > C. The agenda-setter has thwarted the victory of her least-favored alternative, but the otherwise most popular, B in order to enact her most-favored alternative, the otherwise unpopular C. Assume for the moment that the voters have no counterstrategy against the agenda-setter. If the agenda-setter were exogenously imposed, then the voters would have no choice but to acquiesce to her tyranny. If the agendasetter faced reelection to ofﬁce by the voters, then she would be deterred from cycling mischief. The voters do have a counterstrategy, however, which deters even the unconstrained agenda-setter: what the ten voters with the ranking A > B > C need to do when the agenda-setter proposes A against B is to ﬁnd at least one among their ranks to strategically vote for B. The strategic voters’ choice of their last-ranked alternative helps B win the contest against A; then when B goes against C, B wins by 20 votes to 1. Anticipation of voters’ strategic response would motivate the agenda-setter to refrain from wasting time on a maneuver that would fail. Harmful outcomes can be concocted if we assume an asymmetry: that one voter controls the agenda and others do not, that some voters know others’ preferences and some do not, or that some voters have strategic capacity and some do not, and the like. Formally, to make some actors unequal and then deplore the unequal outcome amounts to the weeping of crocodile tears. Practically, if there are unjustiﬁed asymmetries they can and should be institutionally remedied. By far the worst asymmetry in American politics, say, as compared to Europe, arises from the ineffective regulation of campaign contributions from interested parties. Those with a passionate concern for conserving democratic equality of voice might lend their talents to the cause of campaign-ﬁnance reform. Riker (1982, 173–181) provides two pieces of empirical evidence for his hypothesis of the “universality of agenda control.” One is from Pliny

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the Younger, acting as chair in the Roman Senate on a case deciding an alleged crime. There were three factions in the Senate: one favored A, acquittal, one favored B, banishment, and one favored C, condemnation to death. If Pliny had offered the customary agenda, guilt against innocence, then factions B and C would have voted together and defeated A; then in the choice between B and C banishment would have won. Pliny favored A and as agenda-setter put the three alternatives simultaneously because A had the plurality of votes. The C voters, however, responded by strategically voting for B, the choice of the median voter, which won. Agenda control was foiled by strategic voting. The manipulative attempt failed. The second is from “the contemporary laboratory.” Plott and Levine (1978, as related by Riker 1982, 174–181) induced in subjects preferences over ﬁve alternatives by cash reward. Each experimental group had the identical distribution of preferences but faced a different agenda sequence. Each subject was informed only of her own preferences, not of others’; and subjects were encouraged to discuss the decision but forbidden from disclosing information about their payoffs. From pretests Plott and Levine devised a behavioral formula that predicted how subjects would choose in such circumstances; they then ran the main test and discovered that their predictions were conﬁrmed, with one exception out of ﬁve trials. If the agenda-manipulator knows everyone’s preferences, and possesses the behavioral formula, and subjects are kept ignorant about one another’s interests (note the requisite asymmetry), then the agendasetter can indeed bring about any outcome. The exception is of major signiﬁcance, however. In one of the ﬁve groups the chair permitted a straw vote early in the discussion, thereby disclosing preferences, and this led the subjects away from Plott and Levine’s manipulative outcome and to the Condorcet (and Borda) winner. Riker says that he replicated the experiment, and again one out of four groups escaped Riker’s manipulation by recourse to a straw vote. “The experiment was successful enough to show fairly conclusively that conscious manipulation could change outcomes,” Riker comments (emphasis added, 1982, 175). Another way of describing the implications of the result, however, is that agenda control is possible only if two conditions apply: the agenda-setter has unconstrained power over the sequence of consideration and the agenda-setter has unconstrained power over the distribution of information about preferences. What has been shown is that birds can’t ﬂy if you chop off their wings. Riker’s theory is one of pervasive disequilibrium: “An equilibrium of tastes and values is in theory so rare as to be almost nonexistent. And I believe it is equally rare in practice” (1982, 190). So why don’t we observe pervasive disequilibrium? “Individuals . . . are constrained by institutions

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that are intended to induce regularity in society. And it is the triumph of constraints over individual values that generates the stability we observe” (190). Institutions are responsible for stability, and prominent among those institutions is agenda control, an observable institution of “very high” incidence. Riker’s colleagues wrote stylized models of agenda control in the US Congress that attempted to demonstrate this point. The stylizations, however, did not capture Congressional reality, according to the summary by Strom (1990, 83–91).3 There were four proposed institutions of agenda control. First, it was alleged that Congressional committees enjoy a gatekeeping power which allows them to prevent legislation from being considered in full chambers. There are rules, however, which permit the full chamber to discharge a committee from consideration of a bill. Successful discharge votes are quite rare, but game-theoretic insight suggests that this would only mean that the discharge rule is an effective deterrent to committee attempts to defy majority will. Most bills die in committee, but that reﬂects their original lack of majority support in the full chamber. The second form of agenda control is the so-called closed rule in the House, which prohibits amendments on a bill reported by committee, which would permit the committee to bundle the issues according to its own predilections. The closed rule is seldom invoked, however, for example only once over the six years of the 97th through 99th Congresses. The Senate does not permit the closed rule, yet there is no difference in legislative success between House and Senate committees. The third form of agenda control is the closed rule on bills reported from a conference committee. By one measure 86 percent of bills were passed with no conference, however; what happens is that one chamber accedes to the other chamber’s version, or amended versions are sent back and forth. The fourth is that it is costly for members to formulate and propose alternatives, and thus the specialists serving on the committee have an advantage on issues within the committee’s jurisdiction. Evidence for this proposition is that committee bills have great success on the ﬂoor, and half of ﬂoor amendments come from committee members. A more plausible interpretation of this evidence, however, is that committees craft only legislation that will obtain majority support in the full chamber. “It would thus appear that agenda explanations are not very successful or fundamental in accounting for the . . . stability of legislative outcomes” (Strom 1990, 91). Riker believes that in a multidimensional issue space there is no majority-rule equilibrium and thus that agenda control arbitrarily determines the outcome of the voting process (his interpretation of the McKelvey and Schoﬁeld chaos theorems, the topic of the next chapter).

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He concludes (1982, 237) that empirical evidence of a concern over agenda content demonstrates the presence of disequilibrium that enables manipulation and its arbitrary outcomes: Since we also know from a vast amount of conventional analysis of political institutions that much political dispute concerns control (and presumably, manipulation) of the agenda, we can be fairly certain that this kind of manipulation is utterly commonplace.

Riker (1993, v) edited and introduced a volume on agenda formation. “Agendas foreshadow outcomes: the shape of an agenda inﬂuences the choices made from it,” he begins (1993, 1), “making agendas seems just about as signiﬁcant as actually passing legislation.” Empirical evidence of concern over agenda content does not demonstrate disequilibrium, however. There is an alternative hypothesis which is much more plausible. Political deliberation takes place in real time, which is cruelly ﬁnite. There are multitudes of potential political issues, but at any one session there is time to consider only a few, we hope the most panoptic and the most urgent. At the margin of public attention there is sure to be a sharp contest as to which issues deserve to be on a time-limited agenda. Imagine that I propose the Mackie theorem, which postulates one actor with an unconstrained monopoly capacity for persuasion. In my model the persuader can change any other actor’s preferences, but the other actors can’t change the preferences of the persuader. Therefore, on any issue, the persuader can determine the collective outcome, proving the arbitrariness of democracy. Evidence of the truth of the Mackie theorem is the fact that people in legislative assemblies devote a great deal of time to persuasion. Have I made my case? Summary Strategic voting, logrolling, and agenda control permit the manipulation of outcomes, according to Riker, and it is impossible to distinguish manipulated from unmanipulated outcomes because of the unknowability of preferences. The models of manipulation, however, require that manipulators have full knowledge of preferences, in contradiction to Riker’s claim that the possibility of manipulation makes preferences unknowable. As for strategic voting, if all voters are strategic then their votes are the same as if they were all sincere. Whether or not logrolling is welfare-enhancing or welfare-reducing depends on behavioral assumptions; and limited evidence leans towards the conclusion that it is welfare-enhancing. Riker believes that agenda control is ubiquitous, although he concedes that the unconstrained monopoly agenda-setter in his models is not found

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in reality. An unconstrained monopoly agenda-setter might have unfair power over outcomes, but agenda-setters are constrained, and further voters can defeat agenda control with strategic voting. Empirical incidence of agenda control has been much exaggerated. The next chapter continues the study of opportunities for manipulation, in multidimensional issue spaces.

8

Multidimensional chaos

Chaos in multidimensional issue spaces Black (1958) showed that if alternatives can be represented as points along one line and if voters’ preferences are single-peaked, indicating resemblance, then a majority-rule equilibrium results. The position of the median voter on the line will beat any other alternative in majorityrule voting. This is normatively attractive because a central alternative prevails. In Figure 8.1 there are ﬁve voters with preferences over alternatives A, B, C, D, and E. Each voter’s preference curve has only a single peak. Voter 3 has the median preference C, and C will beat by majority vote any alternative that it faces. For example, if D is pitted against C, voters 1 and 2 prefer D > C, voters 3, 4, and 5 prefer C > D, and thus C wins by majority vote. There are no cycles. The preference orders need not be so neat as portrayed in the ﬁgure; each only needs to be singlepeaked. Figure 8.2 shows a proﬁle of preferences that is not single-peaked because one of the voter’s rankings, in this portrayal #2, has two peaks (single-peakedness and its lack are impervious to rearrangements of the labels). Recall that given three alternatives, there are six possible strongpreference rankings, and that given three voters, one each with cyclical rankings 1 (A > B > C ), 3 (C > A > B ), and 5 (B > C > A ), or with rankings 2, 4, and 6 together, the result of majority voting is inconsistent, that is, A beats B, B beats C, and C beats A. The non-single-peakedness illustrated in the ﬁgure is just a portrayal of a proﬁle with cyclical rankings 1, 3, and 5. Single-peaked preferences are not cyclical, and non-singlepeaked preferences are cyclical. If the relevant political issue space is in two or more dimensions, however, and given a number of other usual assumptions, then there is no equilibrium: the majority-rule outcome can be anywhere in the issue space, “anything can happen,” as Riker says frequently. This is Riker’s interpretation of the so-called “chaos” theorems of McKelvey (1976) and Schoﬁeld (1978). The chaos theorems are interesting and impressive 173

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1 Utility

2 3 4 5

A

B

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D

E

Figure 8.1 Single-peaked

Utility

1 2 3

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Figure 8.2 Non-single-peaked

exercises in the abstract. Instructors are fond of demonstrating them on the blackboard because of their gee-whiz qualities. The theorems, however, are normatively tangential, their predictions are falsiﬁed, and standing alone they are empirically irrelevant for understanding the world of politics. The theorems are, of course, logically true, given their initial premises, but the theorems fail as models. They are not simplifying

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abstractions from reality but are rather befuddling negations of reality; they fail as models because their premises are unrealistic and because they abstract away from essentials. Schoﬁeld (1995) offers the metaphor of the frictionless oscillator, such as a spherical pendulum. In the absence of friction most initial states result in nonstationary orbits or cycles that would continue forever in disequilibrium. But with the tiniest epsilon of friction all initial states lead to a stationary outcome in equilibrium. What’s missing in the early models is the metaphorical friction that obtains in real-world circumstances. It is a mistake to argue that the counterfactual world of no friction somehow reveals a more fundamental truth about the world of friction. What we have is one set of assumptions with disequilibrium consequences and another set of assumptions with equilibrium consequences; the former is not a deeper version of the latter. If there is to be any hierarchy among the theorems it must be one that privileges the more realistic assumptions, and those happen to tend towards equilibrium. Advice based on the counterfactual is absurd; it would be as if I said I am going to the store to buy some milk and my interlocutor fresh from his physics lesson warned me that in the absence of friction I would not be able to proceed because my feet could not grip the ground. The points I am about to rehearse are old news to everyone who follows this literature. Several writers in the Rochester tradition are quite scrupulous about resisting Riker’s interpretations and emphasizing the qualiﬁcations attendant to various results.1 McKelvey (1986) and Schoﬁeld (1995) themselves have devoted later work to models of democratic processes tending to stable outcomes around the center of the distribution of preferences. Nevertheless, Riker’s interpretations remain strangely inﬂuential, perhaps because of his memorable examples, and the chaos theorems are still widely promulgated as if they revealed a deeper truth: that apparent representativeness and stability is but an illusion concealing perpetual arbitrariness and instability lurking underneath the surface of democratic politics. “There is always an intense struggle, beneath the apparent stability, to induce a genuine disequilibrium of tastes” (Riker 1982, 190). If the distribution of voters’ ideal points is pairwise symmetric then there is a majority-rule equilibrium in two or more dimensions. Imagine ﬁve voters in a two-dimensional issue space, with voter ideal points distributed in an X-pattern, with four voters at the vertices of the X and one voter at the intersection of the two lines making up the X. The equilibrium point is at the ideal point of the voter inhabiting the intersection. This equilibrium is most fragile, if any one of the ﬁve voters changes position ever so slightly the equilibrium vanishes. The Plott pairwisesymmetry condition is sufﬁcient for a majority-rule equilibrium, but it is

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not necessary. The more general condition is due to Enelow and Hinich (Hinich and Munger 1997, 65), that a point is a Condorcet winner if it is the median in all directions: if every line drawn through the point divides the ideal points of all voters so that at least half are on either side of the line, including voters whose ideal points are on the line in both groups. In one dimension the median is inevitable, but in more than one dimension the Condorcet winner would almost never exist and would be fragile if it did. McKelvey showed that, if the decisions are made by pairwise majority rule, if the distribution of voters’ preferences falls in two or more dimensions, if as is almost certainly the case in two or more dimensions there is no Condorcet winner, and if voters are not strategic, among other assumptions explicit and implicit, then there exists an amendment agenda that would lead from any one point in the issue space to another and back again. In other words, with repeated votes the majority-rule voting outcome is entirely indeterminate. Again, an unconstrained monopoly agenda-setter could determine the outcome by choice of agenda sequence. Normatively tangential This does not mean in a multidimensional issue space that there is no normatively attractive point. Say that there is a dimension of concern X ranging from 0 to 100 and voters with a median preference, 42, along single dimension X, and that there is a second dimension Y on which the same voters have a median preference of 53 and a third dimension Z with a median of 62. The intersection of these medians in the three-dimensional space is the point (42, 53, 62). The problem is that with frictionless pairwise majority-rule voting neither that normatively attractive point nor any other is in equilibrium; there exist sequences of votes such that every point could defeat every other. The theoretical instability of majorityrule voting in multiple dimensions can be seen by imagining three voters, A, B, and C, in two-dimensional space, each with a bliss point surrounded by circular indifference contours, as in Figure 8.3. Say that the status quo happens to be the normatively attractive point, the intersection of medians. The circular indifference contours intersecting through that point generate three petals which deﬁne a so-called “win-set,” denoted W(Xmed ) in the diagram, and all the points in each of the petals is preferred by two out of the three voters to the status quo that we started from. Choose any arbitrary point P in W(Xmed ), and from there three new petals form, W(P ). And so on. An agenda-setter can move the outcome through the issue space, and even outside the Pareto set.

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Project 2 budget (millions of $)

XB

Xmed : Intersection of medians

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(X

) ed m

XA

Pareto set

W (Xmed)

XC Project 1 budget (millions of $)

Figure 8.3 Win-sets of intersection of medians Source: Hinich and Munger (1997, 63)

Suppose we have something so simple as the division of the question rule, that a motion is in order to divide a bundled proposal into parts, or a germaneness rule, that an amendment to a proposal must be germane to the proposal. In many parliamentary rulebooks, any one member may force division of the question. If issues do inhabit a multidimensional space then these rules constrain voting to one dimension at a time – voting ﬁrst along dimension X and next along dimension Y and so on – and there is no chaos (Strom 1990, 98–113). The sequence of votes will uniquely select the intersection of medians. This statement requires several qualiﬁcations. Recall that preferences are separable if the voter’s preference along one dimension does not depend on her preference along another dimension; and are nonseparable if there is such dependence. If preferences are separable, and if voters are either sincere or strategic, then dimension by dimension voting will select the intersection of medians as the equilibrium choice. If preferences are nonseparable, then dimension by dimension voting will necessarily select that equilibrium, unless voters are sophisticated. Finally, if, rather than the forward-moving agenda (deﬁned shortly below) we have tacitly assumed, we instead assume the more

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realistic backward-moving agenda, then again there is no equilibrium if voters are sophisticated (Strom 1990, 104). To continue, dimension by dimension voting is an exemplar of structure-induced equilibrium, the idea of Riker’s students that a number of political institutions function to force stability upon chaos. Further examples of structure-inducing devices are the four agenda-control institutions in the US Congress discussed in the last chapter. One objection to the story about division of the question and germaneness is that the motions these rules permit are almost never observed and thus they are irrelevant. If, however, there exist rules that can induce an equilibrium at the intersection of medians, yet these rules are rarely invoked, then one alternative explanation would be that there is rarely a practical disequilibrium for the rules to subdue, and another alternative explanation would be that the threat of invoking the rule is sufﬁcient to deter those who would otherwise join dimensions. Experimental and empirical failures Riker seeks to avoid the empirical problem of observed stability by means of his basic argument pattern, to the effect that the possibility of cycling, agenda control, and multidimensional issue spaces makes it impossible to know preferences, which was criticized in Chapter 2. If natural empirical observations are controversial because of the obscurity or incompleteness of preference data, then we must turn to experimental settings where preferences are known because they are induced by cash reward. Typically, a number of human subjects are recruited for an experimental game in a laboratory setting with nonexperimental factors controlled to the maximum extent feasible. For example, subjects might be assigned different ideal points in a two-dimensional space and then be rewarded with more money the closer the group voting outcome is to their ideal point; or subjects might be candidates who are rewarded if their platform is chosen by the majority of artiﬁcial subjects assigned to ideal points; subjects might be forbidden from disclosing their ideal point or otherwise communicating so as to ﬁx nonexperimental variables. Subjects will then vote under various experimental conditions, such as a distribution of preferences with an equilibrium compared to one without an equilibrium, with an agenda-controller compared to without, with issue-by-issue voting (division of the question rule) compared to without, with low payoffs compared to high payoffs, with a low number of voters compared to a high number of voters, and so on, and in various combinations. Green and Shapiro (1994) devote a useful chapter to “Legislative Behavior and the Paradox of Voting” on the cycling question; and their

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discussion of the experimental evidence (120–146) is especially splendid and indispensable, although too stern for my tastes. It would be redundant to summarize all their reﬂections, but I do want to borrow a few points. If the theories of equilibria and disequilibria in an issue space are true or useful, and if experiments are sufﬁciently controlled so as to be internally valid, then when there is an equilibrium or a core the voting process should select the equilibrium and when there is not an equilibrium or no core then the voting process should select any outcome in the space. There are two problems. First, although when there is an equilibrium it tends to be selected by the voting process, the success rate differs across different experimental conditions (preference conﬁgurations and voting tasks) in no pattern forecast by theory (Green and Shapiro, 128). In some experiments the predicted equilibrium is selected less than 50 percent of the time, in others more than 90 percent of the time; with one team of experimenters the success rate varied from 33 to 100 percent depending on variations in structure of the game that should not matter according to theory. Second, theory predicts that in the absence of an equilibrium different legislatures with identical preference conﬁgurations would choose different policies. But, according to Green and Shapiro (1994, 134): coreless games do not produce markedly more unstable outcomes than do games with cores (Fiorina and Plott 1978; Laing and Olmstead 1978), and sometimes the distinction between the two game forms is hard to detect at all (Laing and Slotznick 1987, 1991). To be sure, the dispersion of outcomes is typically greater for noncore games, but the difference is not as striking as the McKelvey result (1976) and subsequent commentary (Riker 1980[a]) might be taken to imply . . . If the existence of the core does not have an appreciable effect on the observed instability in experimental outcomes, then one of the central empirical claims motivating game-theoretic analyses of legislative behavior – the inﬂuence of majority rule equilibrium on legislative stability – receives little support.

McKelvey and Ordeshook (1990, 127) review a decade of experimental research on the spatial theory of voting, their own work and that of others, and are more optimistic than Green and Shapiro. Among their conclusions, however, is that “the absence of a core does not imply incoherence or chaos – patterns to the data warrant explanation.” Further (1990, 138): With the discovery that Condorcet winners are rare with spatial preference and that cyclic social preferences can extend across the entire set of feasible alternatives (McKelvey 1976, 1979), some scholars were led to the belief that political processes are inherently unstable and unpredictable (Riker 1984). Others,

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believing that only the possibility of rendering unique predictions is removed if a game’s core is empty, and the like, began the development of alternative equilibrium notions such as the uncovered set and the competitive solution. Experimental research supports this second view.

Although there are several equilibrium concepts that might account for the experimental ﬁndings none is clearly superior or widely accepted. Strom’s (1990, 76) textbook remarks that “it is currently unclear the degree to which real legislative decision making is characterized by unstable chaotic outcomes. There is the additional problem . . . the predicted chaos is not observed in controlled experiments.” Strom summarizes Fiorina and Plott (1978) who ran three conditions, two with an equilibrium and one without. In all conditions outcomes clustered in the center although were more dispersed in the disequilibrium condition. Fiorina and Plott did not notice any behavioral differences between equilibrium and disequilibrium conditions. According to Strom (1990, 74), “It almost appears as if the subjects were imposing their own equilibrium.” I speculate that although people may have to vote by ordinal pairwise majority rule, they possess enough knowledge of individual rankings of alternatives to identify a central point nearby the intersection of medians, and, if need be, they can use strategic voting to get into that center. Strom (1990, 75) reports that “the experimental results have not been accepted as sufﬁcient to discredit the theory.” There have been few experimental tests of the theory, he says, and there may yet be auxiliary equilibrium hypotheses offered that will save it. The experimental results speak directly to the theory, as the experiments induce distributions of preferences, either in equilibrium or disequilibrium. Strom continues that the apparent lack of agreement between the theory and natural empirical evidence on legislatures is more signiﬁcant and has more motivated the invention of auxiliary structural hypotheses to explain stability. I must add that real legislatures may have nearly unidimensional distributions of preferences that are already in equilibrium without additional structural constraints. Is observed stability in a real legislature due to a unidimensional distribution of preferences or due to a structural constraint such as the division of the question and germaneness rules? It cannot be claimed that a structure induces equilibrium unless the empirical investigation ﬁrst establishes, not assumes, that the distribution of preferences is in disequilibrium. Further, contrary to theory, experimental committees in multidimensional space pick stable central points in the absence of any “structure.” How then can structure be offered as an explanation for why a real committee stably chooses central points? Moreover, there is a bemusing abundance of structural devices, including elements of the constitutional setup, rules of procedure,

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and unwritten customs, that are often nonexclusive. Green and Shapiro (1994, 114–120) go so far as to call the devices of structure-induced equilibrium “post hoc accounts of stability.” A single empirical legislature will be structured by dozens of devices. If observed stability in a legislature is not due to the distribution of preferences, or is not due to the descriptive failure of the theory, then is it due to one nonexclusive structural constraint or due to another? Green and Shapiro charge that there is a tendency to nonfalsiﬁability in the empirical testing of spatial theory: if the data ﬁt the model, then structurally induced equilibrium has been demonstrated, but if the data do not ﬁt the model then the model is declared to be stylized and yet untested. Not only are stability-inducing rules often nonexclusive, worse, Strom (1990, 105) shows by example that stability-inducing rules are not necessarily additive. The spatial model assumes a forward-moving agenda, that is, the status quo is the ﬁrst issue put to the vote, and in the abstract this yields outcomes anywhere in the issue space; but legislatures use a backward-moving agenda, the status quo is the last issue put to the vote, and in the abstract this yields outcomes not in equilibrium but in the win-set of the status quo, a region less than the entire issue space. Then there is the division of the question rule we have already discussed that yields an outcome in equilibrium. In a legislature of sophisticated voters with both a backward-moving agenda and a division of the question rule, however, the outcome is no longer in equilibrium. The conclusion is that “to explain legislative equilibria requires the simultaneous examination of a whole constellation of procedural rules.” This would require an analytic model of unimaginable complexity, beyond the capacities of our era. Thus, due to modeling intractability and overdetermination of data, it is extremely difﬁcult, if not impossible, to test the spatial model in natural settings. I think that what Riker’s followers call positive political theory enriches with analytic insight, but will never become a grand-theoretical substitute for, an astute and informed commonsense understanding of politics. The multidimensional disequilibrium version of spatial theory does not, so far, survive experimental testing. Even if we ignore experimental falsiﬁcation, the basic empirical assumption of the enterprise, that the distribution of preferences is multidimensional rather than unidimensional is not established. Even if we ignore the evidence that the distribution of preferences is mostly unidimensional, empirical testing of the theory in natural empirical settings is extremely difﬁcult. Historically, I think, much of the motivating passion and prestige of the model is a result of Riker’s charismatic anecdotes of empirical cycling. When it comes time for empirical illustration of theoretical chaos, the only evidence Strom

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(1990, 68) can muster is three of Riker’s anecdotes and an article of Blydenburgh’s (1971), each of which I will later show to be mistaken. If those anecdotes do not survive then the spirit of the enterprise is deﬂated. Positive political theory is a worthy academic undertaking, but it is not entitled to grand normative claims to the effect that democracy is arbitrary and meaningless or that particular political views are blessed by political science.

Structured preference orders; alternative voting rules If the distribution of preferences is single-peaked and unidimensional then there is no cycling, no disequilibria, no instability. To eliminate any possibility of cycling, every single preference ordering in the population must satisfy the single-peakedness condition (Kramer 1973). For a period it was believed that this rendered the single-peakedness restriction empirically irrelevant, and that belief lingers: “any optimism associated with preference restriction theorems was dealt a heavy blow by Kramer (1973),” says Enelow (1997, 155). The simulation by Niemi (1969), however, which we have already examined, showed, starting from an “impartial culture” assumption of equiprobable preference rankings, that the greater the proportion of preferences that are single-peaked the more likely is a transitive group ordering, and that the probability of a Condorcet winner increases with the number of voters. Later, Niemi (1983) suggested the concept of semi-single-peakedness: a set of preference curves is semi-single-peaked if they can be arranged so that a majority of curves slope down to the left away from a given alternative A and a majority of curves, not necessarily the same ones, slopes down to the right of that given alternative A. If the set of curves is semi-singlepeaked, then A can beat all other alternatives in pairwise voting; and is the median voter’s preference. The concept of partial-single-peakedness was developed by Feld and Grofman (1986, 73): “small perturbations from the impartial culture assumption will virtually guarantee transitive majority preferences.” Here is their argument. Take the six strong preference orderings over three alternatives. For any individual preference ordering A > B > C, deﬁne opposite preference ordering as C > B > A. Deﬁne net preference ordering as the number of orderings A > B > C minus the number of C > B > A. Positive net preference orderings are the excess of orderings A > B > C over orderings C > B > A. The majority decisions of a group are transitive if and only if, (a) the positive net preferences are single-peaked, or (b) one positive net preference ordering has a majority of the positive net

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preference orderings. Why? There are three different opposite preference pairings: 1. A > B > C and 4. C > B > A, 2. A > C > B and 5. B > C > A, and 3. C > A > B and 6. B > A > C. 1, 3, and 5 together permit a cycle, so do 2, 4, and 6 together. Opposite preference orderings cancel each other out, and positive net preference orderings remain for each of the opposing pairs 1:4, 2:5, 3:6. There is no cycle if positive net preference orderings are not 1, 3, and 5 together or 2, 4, and 6 together; in other words, if the positive net preference is for one of the left side and two of the right side of the opposing pairs (e.g., 1:4, 2:5, 3:6 ), or vice versa (e.g., 1:4, 2:5, 3:6), then preferences are single-peaked, showing (a). (Under impartial culture, 23 of orderings of three alternatives are single-peaked, but for positive net preferences to be single-peaked, only a mere majority of individual orderings need be single-peaked). If the left side of each opposing pair (1:4, 2:5, 3:6), or the right side of each opposing pair (1:4, 2:5, 3:6 ) has the positive net preferences, and if one of those orderings has a majority, then it is the group majority preference, showing (b). The result is extended to more than three alternatives by reformulating it as a condition on every triple of alternatives. Given large numbers the impartial-culture assumption becomes simply the uniform distribution of preferences, and then positive net preferences are zero, Feld and Grofman (1986) continue. Then any small group epsilon whose positive net preferences are single-peaked imposes a transitive majority preference ordering identical to its own, so that coherent ordering prevails over incoherent ordering. Of course, multiple cyclically opposing small groups would negate that result. But if some larger group were able to subsume the cyclically conﬂicting coherences of small groups into a higher-order coherence, stability would prevail again. Generally, the more similar, even mildly similar, are preference rankings, the less likely is instability. Also, for more dissimilar preference rankings a larger than 50 percent (supermajority) voting rule can provide stability. For example, at the extreme, if there were a full cycle, a consensus rule would be stable at the status quo (although stability at the status quo may not be normatively desirable). Can we say how big a supermajority rule would have to be – 51 percent, 67 percent, 95 percent – in order to guarantee an equilibrium given various distributions of preference rankings? To a certain extent, yes. There are several approaches. Caplin and Nalebuff (1988; 1991; see also Ma and Weiss 1993) demonstrate a mean voter theorem. The mean voter’s preference is unbeatable

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under 64 percent majority rule, and no cycles are possible, if the voters’ preference rankings are sufﬁciently similar. On their ﬁrst go (Caplin and Nalebuff 1988) they demonstrated stability if the density of voters’ most preferred points is a concave function, in other words, if more voters favor intermediate positions than the average of those favoring extremes. On their second go, they demonstrated that the 64 percent rule chooses the mean voter’s preference for all log-concave densities and for further distributions as well. The large class of distributions with log-concave density includes the uniform, the normal, the truncated normal, exponential, and Weibull functions, among others. The work of McKelvey and Schoﬁeld (1986) as reﬁned by Saari (1997) relates the dimensionality of the issue space to the size of the supermajority required for an equilibrium and to the number of voters. Ignore some untroubling special cases, skip over the distinctions and deﬁnitions, and glance past some stratospheric mathematics. Suppose that there exist q-rules for n number of voters, 2n < q < n, such that qn votes are needed for a proposal to win, for example, an assembly might require a 23 (q = 2, n = 3) vote to change its procedures; and suppose there are k dimensions in the issue space. Roughly speaking, there is stability if k ≤ 2q−n. Thus 67 if there were a hundred voters and a 100 rule, then the outcome is stable if there are less than 2.67−100 = 34 dimensions in the issue space. In other words, the maximal dimension of the issue space with stability is about equal to the number of voters needed to defect from one winning coalition and join another. If 67 cardinals voted for the pope and 33 against, then 34 of the 67 must defect and join the 33 in the minority in order to make a new supermajority. Further, for any supermajority rule there is a large enough number of voters such that there will be stability. This is one of those half-empty, half-full controversies. One can say that given a number of voters we can increase the number of dimensions to the issue space until there is instability, or one can say that given a number of dimensions to the issue space we can increase the number of voters until there is stability. We can also deﬁne supermajorities as ␣ rules, 1 < ␣ < 1, such that an ␣ proportion of voters is needed to win the 2 election, for example, 0.67 of the voters. Saari (1997) gives the example that with a voting rule of ␣ as low as 0.5001 there is stability in a hundred dimensional issue space with around a half million voters. I must reiterate that all this commotion arises from insistence on Condorcet pairwise majority-rule voting. It is immediate that the Borda count returns a result at or very near the intersection of medians. If instability is a major problem, and the evidence is that it is not, then democratic bodies can resort to voting methods other than the Condorcet – Borda,

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approval, Hare, Young–Kemeny – and be spared the grief. If instability is feared in a constant-sum distribution such as a budget allocation, and comity is lacking, then institutional designers can propose various fairshare procedures, perhaps point voting, voting by veto, or probabilistic majority rule (discussed by Mueller 1996, 160–166), or other innovations that might be devised by theory and recommended by experience in the future. Adding back friction In a two-dimensional issue space with an odd number of voters the McKelvey agenda-setter can move the outcome from any one point to another. A few questions: Do we know that the political issue space is multidimensional? Is the issue space actually continuous, so that actors would be motivated to choose between alternatives $100,000.01, $100,000.00 and any proposal in between? An unconstrained monopoly agenda-setter is an unrealistic assumption and such an institution would be patently unfair, even in the one-dimensional case as we have seen. Further, would an agenda-setter be able to propose a sequence of proposals, inconsistent with one another and with her past positions, without exciting suspicion or destroying her credibility? Why would the voters, who are assumed to be sincere, passively let themselves be rolled; is that rational? What if the number of voters is even? Then there is an equilibrium in two dimensions, but disequilibrium in three dimensions. Is this a condition with any empirical content, do newspapers report that legislative observers are worried because there are two dimensions under consideration and an odd number of voters in the chamber? Why do we have to use ordinal pairwise voting? Of course these questions verge on silliness, but no more so than the story that democracy is arbitrary and meaningless because of the McKelvey theorem. The problem with the chaos theorems is that they are not supported by experimental and empirical observations of instability. The various amendments intended to construct models that predict observed stability are exceedingly scholastic and are only speculatively connected with reality. It would go beyond my budget of time and space to present each of them in a detailed manner, and they are more ably explained by others (Miller, Grofman, and Feld 1989; Ordeshook 1986; Schoﬁeld 1995; Strom 1990, 114–126). Because of their tenuous status I shall provide only the briefest of guides to these ideas. Kramer (1977) presented a dynamical model of political equilibrium. Two parties compete in a multidimensional policy space. The parties compete for voters in an inﬁnite series of elections, offering platforms

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as points in the space. The voters choose the platform closest to their respective ideal points; the platform with the most votes wins; followed by a new election. The trajectory of successive platforms leads to a set of alternatives closest to being majority winners; these alternatives are termed equilibria and may be contained in a small region rather than the entire space as in the McKelvey theorem. “Does Kramer’s elegant model save us from devastating disequilibrium?” Riker (1982, 191) asks. “Unfortunately, I think not because at least three of its assumptions are extremely unrealistic,” he continues. Riker says that the assumption of two parties is “unrealistic and unfair,” and that the assumption that parties are motivated by vote maximization is unrealistic. He also complains that it is unrealistic to assume that dimensions are ﬁxed over time. This objection is founded in Riker’s contention that elite political actors can add dimensions at will, which will be explicated and disputed at a later point. What is of interest here is Riker’s insistence that the criterion for a model’s success is its realism. If we accept the realism criterion, then a generalization follows. If a model is unrealistic, and even more so if a model’s predictions are contrary to observations, then the model must be rejected. The McKelvey theorem is unrealistic and it fails as a predictive model. Why then is it the foundation of Riker’s theory of democracy? Recall that a point is a Condorcet winner only if every line drawn through the point divides the ideal points of all voters so that at least half are on either side of the line, including voters whose ideal points are on the line in both groups. These lines are termed median lines. There is inevitably an equilibrium in one dimension, but the distribution of voter ideal points in multidimensional space will almost never be such that all median lines intersect at exactly one point. Ideal points will typically be distributed in a manner, however, such that there will be a small central region through which all median lines pass; this circular region is termed the yolk. With an unlikely distribution of ideal points the yolk will be a single point, that is, the equilibrium point. With other distributions the yolk may be large, but for many distributions the yolk will be small. The chaos theorem still holds so far; outcomes can be anywhere inside or outside the yolk. We shall return to the yolk. Suppose a point X in multidimensional space. All the alternatives that are majority-preferred to X we call the win-set, W(X ), the petals I mentioned earlier.2 Let Y be an element of W(X ), in other words Y is preferred to X. Now suppose a Z that is an element of W(X ) and also an element of W(Y ). This Y is said to cover X. There is no cycle because Z beats Y, Y beats X, and Z beats X. Sophisticated voters will not adopt X over Y if Y is an element of the agenda. If Y covers X it will also be closer

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to the center of ideal points than X. This is a chink in the McKelvey theorem. The McKelvey theorem says, assuming sincere voters, that an agenda-setter can move from any one point to any other. Now with sophisticated voters, and if X is covered by Y, an agenda-setter could not construct an agenda that starts with Y and ends with X. If we add a backward-moving agenda process – the status quo is voted on last – to this brew, then we get the result that sophisticated voters can constrain an agenda-setter to the points in the win-set of the status quo. Now depose the agenda-setter and assume that any voter can make proposals. We need a new concept, the uncovered set. Suppose an issue space S. Take an alternative X; there are alternatives in S that X does not cover and these are called the uncovered set of X, or UC(X ). Take an alternative Y; its uncovered set is UC(Y ). Take an alternative Z; its uncovered set is UC(Z). Find the uncovered set for every point in the issue space S, and then ﬁnd the intersection of all those uncovered sets. That intersection is the uncovered set for issue space S, UC(S ). All alternatives not in the uncovered set must be covered by UC(S ). The points inside UC(S ) cover all the points outside UC(S ). If B is inside the uncovered set of the issue space and A is outside the uncovered set of the issue space, then B covers A. As above, if B covers A, then sophisticated voters will not select A. The uncovered set always exists for an issue space. If there is a unique Condorcet winner then that single point is UC(S). The minimum size of the uncovered set is a point; otherwise its size depends on the distribution of ideal points and the shapes of voters’ indifference curves. It may include the entire space; on a purely distributional question, the outcome could be anywhere. If preference curves are circular (Euclidean) then the uncovered set is contained within a circle centered in the yolk with a radius four times that of the yolk. Depending on the distribution of ideal points and the shapes of indifference curves, the uncovered set is probably a small set near the geometric center of the ideal points. With sophisticated voting, an open agenda, and a forward-moving agenda process, outcomes will be restricted to the uncovered set. The intersection of medians will be in the uncovered set, and the sophisticated outcome will be there or nearby. Things are a bit different with the more commonly seen backward-moving agenda process. With a backward-moving agenda the only points that can win are in the win-set of the status quo, W(Q). If the win-set W(Q) and the uncovered set UC(S) have elements in common, then the outcome will be in both W(Q) and in UC(S), and thus the outcome will be in the uncovered set, that is, probably in the normatively attractive center of the distribution of ideal points. If the win-set W(Q)

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and the uncovered set UC(S) do not have elements in common, then the outcome is in W(Q) but not in UC(S), and thus the outcome is not in the uncovered set. In sum (Strom 1990, 124): if legislators use sophisticated voting strategies, outcomes will generally be located at not too great a distance from the geometric central point of the ideal points of the legislators. Moreover when legislators have Euclidean preferences, these outcomes will be conﬁned to a relatively small centrally located set. This does not mean that the joint median [intersection of medians] will be selected, but it does imply that signiﬁcant deviations from this outcome are not to be expected.

There are other ways to add friction back in. Tovey (1995), assuming sincere voters, proposes an ∈-core. The incumbent or status quo has some amount of advantage, ∈ > 0, over alternatives. One can interpret this as friction in moving from one alternative to another; new alternatives that are extremely close to where we are are just not worth the effort of moving. For Tovey, the yolk is an asymmetry measure of the distribution of ideal points; the smaller the yolk the more symmetric the distribution. Then, if ∈ is sufﬁciently large compared to the yolk radius, there are no intransitivities. Schoﬁeld (1995, 189) proposes a centrally located set he calls the electoral heart, and argues that “for large electorates, the operation of direct democracy is well behaved.” This is related to the example above of stability with a voting rule of ␣ = 0.5001, a hundred dimensional issue space, and around half a million voters. Another way to add friction to models of candidate competition is with probabilistic voting. Standard models assume that voters’ ideal points are deterministic, each will vote certainly for the candidate with the platform closest to her ideal point, and instability obtains in multidimensional space. If instead, for whatever reason, ideal points are construed as probabilistic (an ideal point is metaphorically the peak of a probability mountain falling away in all directions), then two candidates competing for votes will converge on an equilibrium (Mueller 1989, 196–216). This equilibrium will be within the Pareto set, and with stronger assumptions in a center of the distribution: if the probabilities depend on differences in expected utility, then competition drives candidates toward the (weighted) arithmetic mean of the voters’ utilities, if the probabilities depend on the ratios of the utilities then the equilibrium is driven toward the geometric mean (Mueller 1989, 202). Hinich and Munger (1994, 1997) combine formal rigor with an admirable concern for empirical content. Looking for the moment at mass elections (rather than committees) voters have very little information about the multitude of political issues, the connections among issues,

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and the positions of candidates or parties on each of the issues. Voters are rationally ignorant, according to Downs (1957); one individual’s vote does not change the outcome of an election and hence voters have no incentive to gather political information. I would add to Downs that even if voting is expressively motivated, the typical voter is still not motivated to express a detailed position on all possible political issues, but rather more of a general stance or ideology. One cheers on the football team even if one does not understand every jot and tittle of the play. Voters, whether instrumental or expressive, are looking for information shortcuts. Ideology – in the neutral sense of the term – is such a shortcut. Hinich and Munger (1997, 191) say that ideology is an internally consistent set of propositions. I think it would be better to call it a coherent set of propositions. Even a hard science will contain, despite the most heroic efforts, theoretical elements that are not consistent with one another and certainly observations that are not consistent with the theory or with one another. We do not ﬁnd the one consistent system of beliefs, rather we ﬁnd that one system of beliefs is more coherent, has more elements in harmony, than another. Coherence can be formalized and measured in principle with parallelconstraint satisfaction models (Thagard 1992), but that is a topic to be pursued elsewhere. Issues are connected to one another by three webs, according to Hinich and Munger (1997, 193). The ﬁrst is communication. Just as a science simpliﬁes abundant observations, an ideology simpliﬁes abundant issues so that information can be conveyed with economy. In appealing to a voter in a mass election a candidate’s message can be as simple as a single slogan (see Popkin 1991). The second is commitment. The declaration of a mere set of issue positions that a candidate promises to enact lacks credibility. Positions require reasons and explanations; those reasons and explanations cohere into a system with a few principles and values at the apex of its hierarchy; to credibly express a commitment to principles and values requires that they be sincerely applied to issues both old and new. The third is budget. Spending more on one thing means spending less on another. Issues are linked by budgetary constraint and by opportunity cost. If there are two parties, then due to ideology the effective issue space collapses to one dimension; if a few parties then a few dimensions. They work this out as an extension of the spatial theory of voting. Poole and Rosenthal’s work showing that the issue space in the US Congress is mostly unidimensional is “fundamental,” according to Hinich and Munger (1997, 196), and is consistent with their model of ideology. Poole and Rosenthal are also able to locate each representative and each senator respectively at a point in the issue space of each two-year House

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or Senate session. Remarkably, the correlation of members’ coordinates from Congress to Congress is 0.95. They also calculate the annual movement of members in an issue space. Such ideological movement declines with length of service. There is little movement early in the 200-year period and even less later on, such that: Contemporary members of Congress do not adapt their positions during their careers but simply enter and maintain a ﬁxed position until they die, retire or are defeated. Indeed this stability is so great that, even in their last Congress, members typically do not alter their liberal/conservative positions. Similarly they generally don’t alter their positions if they are redistricted. The major change in behavior is that exiting members vote less often. (Poole and Rosenthal 1997, 74)

They suggest that the absence of ideological movement by individual legislators since World War II is due to increased scrutiny of reputation by expanding mass media. Further, political change in Congress results from replacement of legislators, not from ideological changes in individual legislators. It does not seem to be the inﬂuence of one’s fellows in the caucus, because there is a 0.90 correlation between a member’s position as a representative and her position if she is later elected to the Senate. The few party-switchers, however, make dramatic moves in the issue space, as if they had undergone ideological conversion. This suggests to me that a concept of ideology would apply not only to mass elections such as in Hinich and Munger’s concept, but also to committee settings such as the US Congress. Poole and Rosenthal (1999) also report that the issue space of multiparty parliaments is mostly unidimensional, which would not be explained by Hinich and Munger’s two-party explanation for the American data. The models I have summarized are far more complicated and qualiﬁed than I have been able to indicate. What I have said, although abstruse to novices, will seem dismayingly casual to devotees. To continue the initial metaphor, my purpose is merely to sketch some of the more realistic frictions that have been proposed to account for the observation that the pendulum always comes to rest. How these models will develop, and how they will fare comparatively in empirical tests, I don’t know. It is possible that we are not adding frictions, but rather adding epicycles to explain in Ptolemaic terms the looping motions of planets while we await a Copernican revolution of a more parsimonious approach to the theory of political preferences and their collective reconciliation, but I don’t know that either. What is warranted, however, is a rejection of the McKelvey chaos theorem as a realistic (Riker’s criterion) model and hence a rejection of the normative implications for democracy that Riker draws from it. Finally, those who remain convinced that ordinal pairwise

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voting does have terrible consequences can adopt an alternative voting rule without the believed problems, such as the Borda count. Riker’s argument resumed Riker’s driving image is the petals of the win-set that emanate from any given point in a two-dimensional issue space (and their multidimensional analogs). If the issue space is multidimensional and if we decide by pairwise majority rule, then no matter where we are there is always a majority that prefers somewhere else to where we are and thereby has an incentive to get there; politics is in pervasive disequilibrium. Riker (1982, 241) confounds, however, the absence (given certain assumptions) of an equilibrium with the absence of a public good: “The popular will is deﬁned only as long as the issue dimensions are restricted. Once issue dimensions multiply, the popular will is irresolute.” There is, as we have seen, a normatively attractive point of aggregate subjective welfare, the intersection of medians; it is just not in majority-rule equilibrium given ordinal pairwise voting, multiple dimensions, and the unrealistic assumptions of the basic model of spatial voting. Riker must reconcile theoretical instability with empirical stability (1982, 188–192). We see only an “apparent stability,” he says, but it is really an “incremental disequilibrium.” The idea of Riker’s students that institutions constrain chaos turns out to be quite helpful to his overall scheme, as it provides a useful explanation for frequently observed stability. Institutions that induce equilibrium are themselves a matter of choice, however, and in multidimensional space there will always be dissatisﬁed majorities with the incentive to overturn such institutions, Riker argues, and this conveniently explains revolution as well as stability. Furthermore, we are told that “revolution is not infrequent,” and the example he provides is the US Civil War, which he will illustrate was a consequence of political disequilibrium. Since revolution occurs and is admissible in a theory of stability, it follows that some kind of theory of disequilibrium is a priori empirically superior to a theory of equilibrium. The advantage of theories of disequilibrium is that they both admit long periods of apparent stability (often indistinguishable from incremental change) and episodes of catastrophic revolution. (Riker 1982, 189)

But that is to neglect alternative hypotheses. A major alternative hypothesis to explain change in aggregated preferences over time is change in individual preferences! At one point, the US government favored canals, later railroads, and still later highways. Is this due to cycling among aggregate preferences over ﬁxed alternatives? Isolationist sentiments were

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strong in the United States before World War II. Did Roosevelt induce a cycle in order to declare war on Japan, or did preferences in the population change after the attack on Pearl Harbor? The US was friendly with Iran, then the US was hostile to Iran, and now the US is trying to be friendly with Iran: is this due to changes in conditions or due to disequilibrium of tastes in the population? Pick any example you please of change in a collective’s choice, and almost always the Riker hypothesis of preferences in disequilibrium will be among the least plausible as an explanation. Holding an individual’s preferences ﬁxed over time is assumed as a convenience for the usual formal models because they can handle changes in only one parameter at a time. Just because it is a modeling convenience does not mean that it is a truth about humans, that their preferences are ﬁxed at birth never to change. Even if we stipulate the ﬁction that all humans have identical underlying desires (Stigler and Becker 1977), even under that scheme preferences not only differ between individuals, they also differ across time for an individual because of differences and changes in beliefs. It is incorrect, and contrary to the principle of methodological individualism that Riker endorses, to assert that a territorial population of individuals, largely replaced by births, deaths, and migration over decades of time, somehow has a ﬁxed distribution of preference orders over decades of time, as he tends to do in his analysis of the slavery issue in nineteenth-century American politics. He attempts to explain contrasting political decisions forty years apart as due to disequilibrium arising from unchanging preferences of the population and the mathematical curiosities of ordinal pairwise voting (his argument inadvertently appeals to preference change, but he intends it to be an argument from disequilibrium). Stability is sometimes real but only when “it is imposed by institutions [and] not the product of preferences and values. If we consider only values, then disequilibrium seems inherent in majority rule” (Riker 1982, 191). Riker’s dismal vision is that, “In the end . . . institutions are no more than rules and rules are themselves the product of social decisions. Consequently the rules are also not in equilibrium” (Riker 1980a, 444–445). All is chaos. “Anything can happen” (Riker 1982, 191). Such is the doctrine of democratic irrationalism. Consider Riker’s proposition that even the constraining institutions are arbitrary and unstable. The ﬁrst of his errors is to imagine that political passions and political forces are exclusively channeled by the sluice of ordinal pairwise voting. No matter what Arrow’s independence condition demands, individuals are motivated by rankings of preference rather than by pairwise comparisons. If a society were at the central region of the distribution of preferences in the issue space, how would a conspiratorial attempt to move to some extreme by

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means of pairwise voting maneuvers be received? No doubt by a mobilization of opinion, agitation, organization, contribution, and the like, even revolution, all forces exogenous to a model of simple majority-rule voting. Also, a discrete and insular minority may have its vital interests oppressed, but when the opportunity arises the intensity of its concern may overwhelm the less-aroused numerical majority. The second error is to assume that individuals have conﬁdent knowledge of all of their own and of others’ interests far into the future. Constitutions, rules of procedure, precedents, are often established behind practical veils of ignorance (imperfect to be sure), and are usually guarded from myopic disturbances by requiring supermajorities or other devices for going beyond the rules. The garden club does not adopt Roberts’s Rules of Order because some of its members calculate that those procedures will ensure their victory in the controversy over the tulips six years hence. On a particular issue one might be tempted to change the rule in one’s favor, provided of course that others are denied similar opportunities; but one’s feasible long-term interest among free and equal citizens is that no one be allowed to change the rules in an opportunistic fashion. We need not assume any extraordinary virtue motivating the creation and maintenance of fair institutions; modest virtue along with some ignorance of future position is motivation enough. How frequent is harmful manipulation? Common sense tells us that strategic voting and agenda control are possible, but that such manipulations, harmful or not, are rare: the literature on sophisticated voting exhibits a proclivity toward theoretical possibilities rather than empirical realities. Theoretical research suggests that opportunities for strategic manipulation of agendas should occur frequently and that, to counter the power of the agenda-setter, congressmen are often forced to cast sophisticated votes. However, agenda manipulation and sophisticated voting are rarely mentioned in the most detailed accounts of congressional decision making. Of the half-dozen or so papers which are exceptions to this rule, at least four focus on the same set of roll-call votes. (Krehbiel and Rivers 1990, 549)

Poole and Rosenthal (1997, 164), commenting on their spatial study of all roll-call votes over 200 years of the US Congress, conclude that “strategic behavior appears to be a destabilizing force only very rarely.” The rare exceptions that they extract from a review of political science literature are the votes on the Powell amendment, the Depew amendment, and the Wilmot Proviso, each as identiﬁed and portrayed by Riker in Liberalism against Populism (1982). I shall show in each of the three cases that Riker’s

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analysis is ﬂawed and hence that there are no well-established cases of harmful manipulation in the political science literature. The controversial hypothesis that harmful manipulations are frequent requires an empirical demonstration. The assertion that they are so frequent as to render democracy meaningless requires a robust empirical demonstration; as Hume said, it takes far more evidence to establish that a man has been resurrected from the dead than to establish that a healthy man has died inexplicably: When anyone tells me, that he saw a dead man restored to life, I immediately consider with myself, whether it be more probable, that this person should either deceive or be deceived, or that the fact, which he relates, should really have happened. I weigh the one miracle against the other; and according to the superiority, which I discover, I pronounce my decision, and always reject the greater miracle. If the falsehood of his testimony would be more miraculous, than the event which he relates; then, and not till then, can he pretend to command my belief or opinion. (Hume 1975, 116, sec. X, Part 1)3

There is no frequency demonstration, fragile or robust, not when Riker wrote, and none since by any of Riker’s followers on this question, which is why Riker needed the second but self-contradictory half of his argument (that manipulated outcomes cannot be distinguished from unmanipulated outcomes): if preferences are unknowable, then empirical demonstration of frequency or infrequency is obviated. In other words, the second half of Riker’s argument attempted to guarantee that if the frequency hypothesis were true it could not be empirically tested. It resembles the hypothesis that Satan planted false evidence of fossils in the earth so as to tempt the faithful to abandon their belief in recent creation: if the hypothesis were true, it couldn’t be tested. Riker’s fallback position would be that, even if possible in principle, nevertheless an empirical test of frequency would be practically impossible, because data are not sufﬁcient to permit testing of a proper random sample from some natural universe of democratic decision making. Strategic voting is an ineradicable possibility, he says, but the factual question of whether people take advantage of such possibilities is difﬁcult to answer because we must infer preferences, but “considering the real-world examples I have offered, it does seem likely that strategic voting occurs quite frequently” (Riker 1982, 167). Thus, his argument comes to rest on the citation of a few spectacular examples. These miracles are the glimpse that thereby proves the existence of a supernatural world otherwise hidden to us. Green and Shapiro (1994) accuse Riker (108–113) and rational choice scholarship in general (42–44) of problems with the selection and interpretation of evidence: a tendency to adduce conﬁrming instances, a

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tendency to project evidence from theory, and inattentiveness to competing explanations. First, they say, Riker’s theory of the generic instability of majority rule is consistent with any pattern of empirical observation of political decisions, since Riker’s theory explicitly predicts no change, incremental change, or revolutionary change (“Anything can happen,” Riker 1982, 191). The theory is conveniently unfalsiﬁable. Second, Riker’s method of proof by spectacular example is contrary to methodological standards that require unbiased sampling procedures and forbid extrapolation from small numbers of instances. Riker claims that his four stories of manipulation are not isolated examples but typical of democratic politics (1982, 195). Green and Shapiro (1994, 111) say that Riker adduces conﬁrming instances of harmful manipulation, but fails to adduce disconﬁrming instances, such as “the strategically ill-conceived Smith Amendment to the 1964 Civil Rights Act” (the Smith amendment, intended to kill the Civil Rights Act, prohibited discrimination on the basis of gender). Third, Riker’s narrative about the Depew amendment (to a resolution establishing the direct election of senators which eventually became the 17th Amendment to the US Constitution), for example, is poorly established and not strongly argued (the Depew amendment will be considered in full below). Fourth, the illustrative narratives fail to consider and reject alternative hypotheses; yes, parliamentary contrivance occasionally forestalls or defeats the majority will, but is the source of such outcomes necessarily manipulation of multidimensional issue spaces or is it more simply just blunder or short-sightedness, or other factors? Green and Shapiro’s objections are enough, I believe, to convince anyone but the faithful that Riker fails to establish his controversial hypothesis about the frequency of cycles and harmful manipulation. Green and Shapiro’s complaints resemble those that Hume brought against the existence of miracles: even if there is some evidence in support of the miracle we have to weigh that against the enormous evidence in support of an overwhelming absence of miracles generally. “I should not believe such a story were it told to me by Cato, was a proverbial saying in Rome, even during the life of that philosophical patriot. The incredibility of a fact, it was allowed, might invalidate so great an authority” (Hume 1975, 113). I go one step further and show that the evidence alleged in support of the cycling miracles is deluded: not merely is it improbable that Vespasian’s spittle cured a blind man in Alexandria, to use one of Hume’s examples (122), but also I’ll show that Vespasian was nowhere near Alexandria at the time alleged and that the man in question died blind. Therefore, let us momentarily accord Riker’s argument the most generous charity. Suppose, only for the sake of argument, that it is theoretically or practically impossible to estimate the frequency of

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harmful manipulations, that all we can rely on are some convincing examples, and that if those examples were established then the failure to observe instances of harmful manipulation is an illusion. I am not saying that I will take on all examples from all comers; that is impractical. We may fairly presume, however, that Riker’s examples in Liberalism against Populism (1982), and those in his refereed articles (1958, 1984), often repeated in political science training today, represent his best attempt to establish his case. If his examples fail, then so must his case, on its own terms. Summary Riker originally maintained that the Arrow theorem implied pervasive instability in democratic politics. Stability rather than instability is observed, however, and Riker responded that we usually do not have enough data to determine whether or not a cycle has occurred. Then it was demonstrated that cycles are unlikely with mild similarity among preference rankings. Riker responded that although natural cycles are rare, political actors manipulate the outcome by means of strategic voting, agenda control, and introduction of new issues and dimensions. Strategic voting and agenda control tend to cancel each other out, however. Thus, the McKelvey and Schoﬁeld chaos theorems of total disequilibrium in multidimensional issue spaces promised to rescue Riker’s disequilibrium hypothesis. Now observed equilibrium is no longer the consequence of mildly similar preference rankings, but is rather the result of imposed institutions (themselves in ultimate disequilibrium) that arbitrarily select an outcome from amidst the chaos. In this chapter we have seen that there is a normatively attractive point, the intersection of medians, in multidimensional issue space. We have seen that controlled human-subject experiments do not support the predictions of the Rikerian “chaos” interpretation of the McKelvey and Schoﬁeld theorems, and that empirical investigations in support of such an interpretation would be difﬁcult to impossible to carry out. Structured preference orders, and supermajority rules, each reduce the likelihood of instability. Adding realism to the spatial model – strategic voting, friction in moving from one alternative to another, probabilistic voting, or constraints of ideological coherence – tends to return the outcome to the normatively attractive center of the population’s preferences. Riker believes it sufﬁcient for his case that he demonstrate the possibility of manipulation by way of empirical illustrations, which we begin to examine in the next chapter.

9

Assuming irrational actors: the Powell amendment

Introduction Riker’s ﬁrst spectacular example is the 1956 school-construction bill in the US House of Representatives. A bill to fund school construction was amended to forbid segregation of white and black students in areas receiving aid. The amended bill failed. Riker offers two versions of this story; Krehbiel and Rivers (1990) a third; my running commentary challenges Riker’s interpretations and adds more ﬂesh to the bones of the Krehbiel and Rivers model. The majority that wanted school aid was thwarted by the desegregation amendment, according to Riker. Riker’s ﬁrst version argues alternatively that there was a natural cycle or that there was strategic voting by opponents of school aid that defeated the majority and hence is an instance of harmful manipulation. The second version drops the natural-cycle claim, revises the strategic-voting claim, and presents revised estimates of the distribution of preferences in the chamber. Since strategic voting can be countered by strategic voting the question arises as to why those who favored both school aid and desegregation failed to vote strategically against the desegregation amendment in order to retain school aid. Riker’s answer in his second version is that these legislators were constrained by the irrational preferences of their constituents. The same issues came to a vote in 1957, however, and the same legislators who failed to vote strategically against the desegregation amendment in 1956 did vote strategically against the desegregation amendment in 1957, which destroys Riker’s second interpretation. Krehbiel and Rivers offer revised estimates of the distribution of preferences in 1956, which were incompletely known according to their model, a game with a Bayesian Nash equilibrium. The Northern Democrats who voted for the desegregation amendment mistakenly believed that Republicans would join them in supporting an amended school-aid measure. After votes were revealed it was plain that there was not a majority for school aid, with or without the desegregation amendment. I add to Krehbiel and Rivers’s 197

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already convincing exposition additional evidence in support from the Congressional record and newspaper accounts. Particularly, their model would predict that, with complete information about the distribution of preferences, as in 1957, supporters of school aid would vote strategically against the desegregation amendment. I show that this is exactly what happened in 1957, and that the actors openly declared that their votes were “strategic.” The Powell amendment It is 1956, the Republican Eisenhower is President and facing reelection, the Democrats control Congress, and the postwar baby boom is well underway. Two years before, the US Supreme Court, in Brown v. Board of Education (litigated by the National Association for the Advancement of Colored People, or the NAACP) had declared school segregation unconstitutional, but neither the local and state governments responsible for segregation nor the federal government responsible to the Constitution had taken any steps of any kind to implement the decision. In the United States education is traditionally a state and local concern, in policy and in funding, but as the election approaches it looks like it will be politically popular to offer a one-time ﬁve-year program of federal aid for the construction of new schools. The Eisenhower administration proposes a bill for federal school aid in 1956, and a Democraticamended version of the legislation eventually arrives on the ﬂoor of the House of Representatives. Adam Clayton Powell, the African-American Member of Congress from Harlem, offers an amendment to the schoolfunding bill. The amendment proposes to deny the new school aid to any school district that doesn’t conform to recent “Supreme Court decisions,” in other words, a school district that accepted federal funds would be required to desegregate. The Powell amendment comes to a vote, and passes 229 to 197. The school-aid bill as amended by Powell comes to a ﬁnal vote and is defeated, receiving 199 afﬁrmative votes and 227 negative votes. Riker argues that voters who were both against school aid and against the desegregation mandated by Powell’s amendment voted strategically for Powell’s amendment in order to defeat the entire school-aid bill. The manipulators would be betting that southern members of Congress who wanted school aid would not be able to vote for a bill mandating desegregation. The upshot is that Powell and his liberal allies who prefer school aid to no school aid are thwarted, that they could have had their way if they hadn’t passed the Powell amendment. A cycle has been contrived. A harmful manipulation has succeeded.

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Table 9.1. Distribution of votes, 1956 Original

Powell

Yea Nay Total

Yea 132 67 199

Nay 97 130 227

Total 229 197 426

There are three alternatives under consideration: O: The Original school-aid bill. P: The school-aid bill amended by Powell so as to require desegregation. Q: The status Quo of no school funding. The recorded votes are as displayed in Table 9.1. From the recorded votes it is obvious that P > O, the Powell amendment beats the original schoolaid proposal (by 229 to 197, Congressional Record Roll-Call Vote No. 90, Congressional Quarterly Vote No. 46). Also it is obvious that Q > P, the status quo of no funding beats the school-aid bill as amended by Powell (by 227 to 199, Congressional Record Roll-Call Vote No. 92, Congressional Quarterly Vote No. 48). That leaves O against Q, the original proposal against the status quo, to account for. The 199 representatives who voted yea on ﬁnal passage of the Powell-amended school-funding bill, P > Q, could order the original bill, O, in one of three ways: r P > O > Q and O > P > Q. Notice that such voters prefer federal school aid (with or without the desegregation amendment) over the status quo. r P > Q > O. These are voters who rank school aid with desegregation over no school aid over school aid with segregation. Next, “nothing in the ideological circumstances of 1956 rendered [P > Q > O] likely . . . so I conclude that the 199 who voted for ﬁnal passage [P ] had either [P > O > Q or O > P > Q] and thus all preferred [O > Q]” (Riker 1982, 154). Some Southern Democrats, he argues, must have preferred school aid without desegregation over the status quo of no school aid over school aid with desegregation (O > Q > P ). Further, according to Riker, 18 Democrats, including 15 from southern and border states, who voted to defeat school aid with the Powell amendment in 1956, voted for a school construction proposal lacking the Powell amendment in 1957. The reader should be alert that we take data sometimes from a 1956 vote and sometimes from a 1957 vote. Altogether then, the 199 who voted for ﬁnal passage of the Powellamended school-aid bill must have preferred O > Q, and there are at least another 18 others whom the 1957 evidence indicates ranked O > Q, so

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that 199 + 18 = 217 > 209, O > Q. A cycle has been demonstrated: from the recorded votes, P > O and Q > P, and from inference based on the 1957 vote O > Q, in all we have Q > P > O > Q, a cycle. Does an alleged cycle show once again that the aggregation of preferences is incoherent? No. The Borda count for the three alternatives assuming Riker’s counts above is Q > P > O, the status quo is ranked ﬁrst, the Powell-amended school aid is ranked second, and the original school aid-bill is ranked last. The Young–Kemeny method reports the same ranking. Moreover, the Borda ranking survives even if we help Riker’s cycle assertion along by supposing that everyone, 426 > 0, favors O > Q. If there is a cycle, then the problem is not with the preference rankings, the problem is with pairwise voting procedure. I have claimed, however, that cycles are rare so that we don’t have to worry too much about the defects of pairwise voting. I shall now show that Riker’s calculations are erroneous, and that there was not a cycle as he imagined. Riker does not give a citation to the 1957 vote on school construction, but the only roll-call vote on the issue in 1957 took place on July 25 (Congressional Record Vote No. 154, Congressional Quarterly Vote No. 56). After some parliamentary maneuvers that I shall recount later, an opportunity arose to vote on school aid without a desegregation amendment, a pure contest between O and Q. The vote was 208 > 203 (actual votes – if we count pairs, announced votes and Congressional Quarterly-polled votes – would be 215 > 209) for Q over O . Federal aid to schools was killed in 1957 and thereafter dropped off the national agenda. Unfortunately, Riker’s use of the 1957 data is miscalculated. He states that 18 Democrats, including 15 from southern and border states who voted to defeat school aid with the Powell amendment in 1956, voted in 1957 for the school construction proposal lacking a Powell-type amendment. This is mistaken. There are only 14 Democrats who satisfy these constraints. Also, 7 of those were from Alabama, and for local reasons in 1957 7 out of 8 voting Alabama representatives voted for federal school aid, even though 31 out of 33 representatives in the immediately neighboring states of Florida, Georgia, Mississippi, and Tennessee were against federal school aid.1 The fact that 7 out of the 14 Democrats are the anomalous Alabamans who were most likely O > P > Q casts doubt on the story that a sufﬁcient number of southern Democrats naturally had the preference ranking O > Q > P. Further, recall that Riker dismisses the preference order P > Q > O as unlikely. Consider, however, that ideologically there might be some Republicans who would uphold civil rights even if encumbered by school aid, P, but otherwise would not support increased federal spending, Q > O. If we check the 199 who voted for P > Q in 1956, we discover that

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among them there are indeed 13 Republicans who voted Q > O in 1957: these 13 are unequivocally P > Q > O . Therefore, Riker’s calculation of 199 + 18 = 217 > 209, O > Q, must be corrected to 199 + 14 − 13 = 200 < 226, Q > O. What happens if we look for all voters, Democratic and Republican, who voted to defeat school aid with the Powell amendment in 1956 and voted in 1957 for the school construction proposal lacking a Powell-type amendment? We ﬁnd that there are 24 who satisfy these constraints, including the 14 Democrats already identiﬁed.2 We should also look for all voters, Democratic and Republican, who voted to pass school aid with the Powell amendment in 1956 and voted in 1957 against the school construction proposal lacking a Powell-type amendment. There are 18 who satisfy these constraints, including the 13 Republicans already identiﬁed.3 With these new ﬁgures, the calculation would be 199 + 24 − 18 = 205 < 221, again Q > O. From the 1956 recorded votes we have P > O, Q > P, from consistent use of the 1957 data we have Q > O, and thus we have Q > P > O which is not a cycle. The assertion of a natural cycle depends on inconsistent data selection and therefore fails. The status quo is preferred to the Powell amendment, is preferred to federal aid to schools, just as history played out in 1956, 1957, and in long run. Riker (1982, 156) alleges alternatively that there was probably strategic voting sufﬁcient to contrive a cycle on the vote; that opponents of school aid voted strategically and thus succeeded in bringing about its defeat (Riker 1986 is the stronger version of his argument for the presence of strategic voting, so I postpone exposition and criticism of his strategicvoting argument for the moment). The problem with the contrived-cycle argument on the assumptions given in Riker (1982) is that if the opponents of school aid had voted strategically, then so could have the proponents of school aid. Remember that if everyone votes strategically the outcome is the same as if everyone votes sincerely. For the contrivedcycle argument to succeed, some voters would have to vote strategically and others vote sincerely. So, why would the proponents of school aid fail to vote strategically? This problem is not addressed, let alone stated, in Riker (1982). If the reader think me unfair, allow me to point out that my conclusion that there was no natural cycle in 1956 is supported by Denzau, Riker, and Shepsle (1985)and Riker (1986). In their second version of the Powell amendment story the assertion of a natural cycle in 1956 is dropped, quietly and without explanation. In the second version, the cycle (and consequent harmful manipulation) is alleged to be contrived by strategic voting. Since the new argument is conﬁned to strategic voting, their

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major explanatory challenge becomes to account for why the majority of the proponents of school aid voted in a sincere and thus self-defeating fashion. In 1982 the assertion was that the 199 who voted for the Powell amendment had either the preference ranking P > O > Q or O > P > Q. In 1986 the assertion was that those 199 are divided as follows. The 132 who voted both for the Powell amendment and for the ﬁnal passage of the Powellamended school-aid bill (we shall label groups with two letters, the ﬁrst their yea or nay votes on the Powell amendment, the second their yea and nay votes for passage of the amended school aid bill, hence these 132 are labeled YY ) had the preference ranking P > O > Q, they preferred school-aid-and-desegregation to school-aid-and-segregation to the status quo of no-school-aid-and-segregation. Call the 132 in YY the Powellites. The 67 who voted against the Powell amendment but for the Powellamended school-aid bill (NY ) rank O > P > Q, the unamended schoolaid bill over the Powell-amended bill over the status quo of no school aid. Call the 67 in NY the School-Aiders. In 1982 Riker’s assertion was that segregationist southern Democrats ranked O > Q > P, that their ﬁrst-best was school aid with no Powell amendment, their second-best the status-quo of no school aid, and their worst the desegregating Powell amendment. In Riker (1986), the 130 who voted against both the Powell amendment and against ﬁnal passage of the Powell-amended school bill (NN ) are said to rank O > Q > P. Call the 130 in NN the Southerners. That leaves the 99 Republicans who voted for the Powell amendment but against the Powell-amended school-aid bill (YN). In 1982 Riker asserts that some of them rank Q > O > P and some rank Q > P > O. In 1986 Riker divides them in half: 48 Segregationist Republicans rank Q > O > P, no school aid over some school aid, over school aid with desegregation; and 49 Desegregationist Republicans rank Q > P > O they prefer no school aid, but if there is school aid it should be with a desegregationist amendment rather than without one. According to the 1986 version of the distribution of preferences, there is no natural cycle: O > Q, 329 to 97; Q > P, 227 to 199; and O > P, 245 to 181; O > Q > P. The cycle is contrived by the 48 Segregationist Republicans. They are said to sincerely prefer Q > O > P. If they vote according to their sincere preferences, the outcome is their second-ranked preference, a school-aid bill without a Powell amendment. If these Segregationist Republicans instead vote strategically as if they were Desegregationist Republicans, that is, Q > P > O, then a cycle is contrived: O > Q, 329 to 97; Q > P, 227 to 199; and P > O, 229 to 197; O > Q > P > O. We know that if there is a cycle, then the pairwise outcome

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Table 9.2. Riker’s estimates of factions and preference rankings, 1956 Recorded Votes

How Many

Nickname

Ranking

YY NY NN YN YN

132 67 130 48 49

Powellites School-Aiders Southerners Segregationist Republicans Desegregationist Republicans

P>O>Q O>P>Q O>Q>P Q>O>P Q>P>O

Table 9.3. Pairwise comparison matrix: Riker (1982), Riker (1986) P 1982 1986 Sincere 1986 Strategic P 1982 1986 Sincere 1986 Strategic O 1982 1986 Sincere 1986 Strategic

Q 1982 1986 Sincere

197 + 48 = 245 − 48 = 197 227 227

O 1982 1986 Sincere 1986 Strategic

Q 1982 1986 Sincere

229 − 48 = 181 + 48 = 229

199 199

199 + 18 = 217 – 18 + 130 = 329

209 + 18 – 130 = 97

Note: Boldface type in data indicates the estimates made by Riker in (1982), italic type indicates sincere preferences estimated by Riker (1986), and underlined type indicates sophisticated preferences estimated by Riker (1986).

depends on the sequence of the agenda. The sequence of voting supposedly foreseen by the manipulating Segregationist Republicans was, ﬁrst, P against O, the Powell amendment against the original bill, P > O, 229 to 197, P wins; and the second was thus Q against P, the status quo against the Powell-amended school-aid bill, Q > P, 227 to 199, and Q wins. By voting strategically, the Segregationist Republicans have avoided their second-ranked outcome, O, an unamended schoolaid bill, and achieved their ﬁrst-ranked outcome Q, the status quo of no school aid.

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If the Powellites had anticipated that the Segregationist Republicans would vote strategically, however, then they could themselves have voted strategically and thereby have avoided their bottom-ranked outcome, Q, the status quo, and instead have achieved, O, school aid, their secondranked outcome. To achieve their second-ranked outcome rather than their third-ranked outcome the Powellites, anticipating the strategic response of the Segregationist Republicans, should not introduce the Powell amendment or should vote against any similar amendment introduced by the opponents of school aid. Then the contest is between O and Q, and by Riker’s estimate O > Q, 329 to 97. So why did the Powellites vote sincerely and thus against their own interests? In fact there was major public controversy among nonsouthern Democrats about the Powell amendment. The NAACP supported, and was indeed behind, the measure. The liberal National Education Association opposed the desegregation amendment, fearing that it would kill the school-aid bill. The trade union federation, the AFL-CIO, originally supported and later opposed the Powell amendment. Mrs. Roosevelt opposed the amendment, as did former President Truman, ﬁgures with records of early and strong support for African-American civil rights. In an open letter, Truman stated exactly the Riker hypothesis: The Powell amendment raises some very difﬁcult questions. I have no doubt that it was put forward in good faith to protect the rights of our citizens. However, it has been seized upon by the House Republican leadership, which has always been opposed to Federal aid to education, as a means of defeating Federal aid and gaining political advantage at the same time. I think it would be most unfortunate if the Congress should fall into the trap which the Republican leadership has thus set. That is what would happen if the House were to adopt the Powell amendment. The result would be that no Federal legislation would be passed at all, and the losers would be our children of every race and creed in every State in the Union. (Riker 1986, 126)

Thus it is absolutely certain that the NAACP, Adam Clayton Powell, and those we have labeled the Powellites, were aware of this estimate of the situation. So, why did they ignore advice such as Truman’s and act in an apparently self-defeating manner? Riker’s second version of the Powell amendment story solves this problem by positing that the Powellites were constrained by their electoral interests to vote sincerely. They would be unable to explain a strategic vote against a desegregation amendment to their constituents who favored desegregation. Denzau, Riker, and Shepsle (1985) take this homely little solution and drape it in yards and yards of formalism, almost as if they believe along with Keats that beauty is truth and that is all you need to know. Curiously, 44 of the 46 references in their paper on the Powell amendment

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are to work by rational-choice scholars, yet there is not a single reference in support of the historical facts of the case. They acknowledge that the Powellites’ “image-enhancing activity, which discourages strategic behavior, comes ultimately at the expense of constituent welfare” (1,132). They do not explain why the Powellites’ constituents are irrational. Although Riker seems not to have realized the problem at the time of writing, his ﬁrst version of the story implied that some legislators are irrational and that some are not. His second version of the story saves legislator rationality with the assumption that the voters in Powellite districts are uninformed and irrational, although voters in Segregationist Republican districts are informed and rational. According to Riker, Powell himself was motivated by expressive rather than instrumental concerns: “Powell’s motive was, undoubtedly, to force some representatives to stand up for the symbolism he created . . . His amendment said to the Democratic leadership, ‘We blacks must be treated with dignity’” (1986, 128). Powell, and more so the NAACP behind the amendment, had an enviable record of instrumental accomplishment, however. Their successes against formal segregation are well known, and I am sure it is safe to say that they would be quite unhappy if all this activity turned out to be merely an expressive exercise. That the Powell amendment was not merely expressive but rather also instrumentally motivated is shown, for example, by the fact the NAACP did not seriously push for a school-desegregation amendment in Congress until after they had won Brown v. Board of Education in 1954. It is extraordinary that a rational-choice explanation of a political event ends up requiring the assumption that a large number of actors are not instrumentally rational. It suggests that a failed hypothesis is being saved by any means necessary. There is an insurmountable problem for Riker’s second version of the story. The failure of the 1956 school-aid bill was front-page news and became a major issue in the 1956 Presidential and Congressional election campaigns: Republicans blamed Democrats for the failure, and Democrats blamed Republicans. If ever in 1956 the Powellites had second thoughts about their alleged irrationality, however, all they had to do was reintroduce O, school aid without a desegregation rider. Riker’s ﬁrst version of the story ﬁnds that O > Q, and his second version ﬁnds that O > Q by an overwhelming margin, 329 to 97, and we can add on Riker’s behalf that the 1956 outcome of Q > O would be evidence of grossly harmful defeat by manipulation of the supposed Condorcet winner O. As I said though, in 1957 the Northern Democrats brought about an opportunity to vote on school aid without a desegregation amendment, a pure contest between Q and O , and Q beat O by 215 > 209. There were distributional differences between O in 1956 and O in 1957, but they only strengthen

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my argument. O in 1956 was a Democrat-favored distributional formula that Republicans claimed caused them to vote against P on ﬁnal passage, but O in 1957 was the Republican-crafted distributional formula, so the Republicans’ excuse was no longer available (the Republicans’ needbased formula favored the South because of the South’s lower incomes). To reiterate, O lacked a desegregation amendment, and possessed the Republican-sponsored but South-leaning distributional formula, but it was the Southern Democrats and the Republicans who killed O . Riker (1986) predicts O > Q by a margin of 232 votes, but as revealed in 1957, Q > O by six votes, so the Riker prediction is off by 238 votes out of a possible 426 and is in the wrong direction. Riker appeals to the 1957 data in his attempt to demonstrate a natural cycle in his ﬁrst version of the Powell amendment (Riker 1982), so clearly he is aware of the nature of the 1957 data, nor could he claim that it is illegitimate for another researcher to look to the 1957 deliberations for more data points. The failed prediction means that something must be seriously wrong with Riker’s (1986) second estimates of preference rankings, but what? The major problem, it turns out, is with the Republicans. He estimates that the 97 Republicans who voted YN, yea for the Powell amendment but nay against passage of Powell-amended school-aid, are 48 Q > O > P and 49 Q > P > O. Krehbiel and Rivers (1990) estimate that these 97 Republicans are either P > Q > O or Q > P > O, in other words, that the Republicans must have ranked O the unamended school-aid bill last. Why? First, the Powell-amended school-aid would be more distributionally advantageous to the Republicans, for the simple reason that money denied to segregationist school districts in the south would ﬂow north to Republican districts, so most Republicans would rank P > O. Second, and more importantly, the Republicans were the party who fought the Civil War over slavery and consistent with that tradition in the 1950s tended to support civil rights legislation, so few would rank O > P. Krehbiel and Rivers compare votes on the 1956 school-aid bill with votes on the unencumbered Civil Rights Act of 1956 and ﬁnd that only 10.4 percent of Southerners (NN on the Powell amendment and on ﬁnal passage of the Powell-amended school-aid bill) supported the Civil Rights Act of 1956, 94.5 percent of Powellites (YY ) supported civil rights, 90.2 percent of School-Aiders (NY ), and 81.5 percent of Republicans (YN ). Thus, 79 of the 97 YN Republicans voted for an unrelated civil rights measure. According to Riker’s estimation of the natural distribution of preferences, P > O by 245 to 181, so that to reverse this ranking for a contrived cycle requires that there exist at least 33 Segregationist Republicans who would vote strategically (245−33 = 212 < 214 = 181 + 33, P < O), but the unrelated vote on the unencumbered civil rights measure

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suggests that at best there were only 18 such Segregationist Republicans. Finally, the Republicans are the party of lower taxes and less government, so we are uncertain about their ranking of Q and P, even though they rank both above O. There is also a problem with the (NN ) Southerners who Riker has ranked as O > Q > P. Clearly, they rank desegregation, P, last, but how do they rank O and Q? They might like federal school aid out of distributional advantage (O), or they might dislike it altogether because of their suspicion of federal involvement in state issues, an issue that they had already fought and lost a war about (Q). So, we conclude that we are uncertain about their ranking of O and Q, even though they rank both above P. There is a ﬁnal problem with the Northern Democrats, the 132 Powellites (YY ), and the 67 School-Aiders (NY ). Riker says that the Powellites rank P > O > Q and that the School-Aiders rank O > P > Q. In the ﬂoor debates, however, the School-Aiders state that their ranking is P > O > Q but that they are voting O > P > Q for strategic purposes to obtain the otherwise unavailable O. Further, during the debate, Powellites “explicitly acknowledged the strategic logic of liberal opponents of the Powell amendment [the School-Aiders]. Yet the Powell amendment passed three times” (Krehbiel and Rivers 1990, 564). So we shall consider that the 199 Northern Democrats – Powellites and School-Aiders – who voted for ﬁnal passage of Powell-amended schoolaid ranked P > O > Q, but that 97 of the 199 expressed O > P > Q in a strategic maneuver that failed due to mistaken estimate of the distribution of preferences. With these new assessments of the preference rankings, including the uncertainty about the preferences over P and Q among the Republicans and the uncertainty about preferences over O and Q among the Southerners, Krehbiel and Rivers (1990) write a game of incomplete information with a Bayesian Nash equilibrium. There are four players. Both the Powellites and the School-Aiders rank P > O > Q, but we allow cardinal utilities because the players are making probability estimates. The Powellites very much prefer the desegregation amendment above the two remaining alternatives but also prefer school aid to no school aid, P O > Q. The School-Aiders prefer school aid with desegregation to school aid without desegregation, but very much prefer school aid of any kind over the status quo, P > O Q. The Southerners are O > Q > P with probability s and Q > O > P with probability 1 − s. The Republicans are P > Q > O with probability r and are Q > P > O with probability 1 − r. There are three blocs, the 199 Northern Democrats (Powellite and School-Aider), the 130 Southerners and the 97 Republicans, and the fusion of any two blocs makes for a winning majority.

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The vote on any bill, P or O, against the status quo, Q, comes last in any agenda, and there is never a reason to vote strategically on the last vote. The Northern Democrats thus become pivotal; if they adopt O, school aid with segregation, then the Southerners will vote between O and Q (the Southerners rank P last). If the Northern Democrats adopt P, school aid with desegregation, then the Republicans will vote between P and Q (the Republicans rank O last). A Northern Democrat legislator strategically votes for O if he thinks that s, the probability that the Southerners are of the type O > Q > P (rather than the type Q > O > P ) is larger than the probability r that the Republicans are of the type P > Q > O (rather than the type Q > P > O). A Northern Democrat votes for P if she thinks that the probability s is smaller than the probability r. To put it another way, a Northern Democrat votes against the Powell amendment if he thinks it more likely that he’ll get votes from the Southerners for an unamended school-aid bill than that he’ll get votes from the Republicans for Powell-amended school aid. A Northern Democrat votes for the Powell amendment if she thinks she’s more likely to get votes from Republicans for Powell-amended school aid than she is to get votes from the Southerners for unamended school aid. According to the model, a Northern Democrat for whom the Powell amendment is much more important than the remaining two alternatives (P O > Q) will play boldly and take a greater risk of losing by insisting on the Powell amendment, and a Northern Democrat who much prefers federal school aid to the status quo (P > O Q) will play cautiously and vote against the Powell amendment. Krehbiel and Rivers (1990) present data showing that Northern Democrats from states that lose redistributionally (state gets back less federal aid than the income tax it pays in) tend to vote for the Powell amendment, and Northern Democrats from states that win redistributionally tend to vote against the Powell amendment. They present further data showing that, controlling for redistribution and demographic variables, Democratic legislators are more likely to vote for the Powell amendment the more AfricanAmericans there are in their district. Only after the vote is it apparent that the Northern Democrats could not have won by adopting the Powell amendment and counting on Republican support; it is revealed that the Republicans are of the type Q > P > O. The 1956 vote reveals that 97 Republicans prefer Q > P and 97 Republicans prefer P > O. We already know that 81.5 percent of these Republicans voted on record in favor of civil rights on another bill in 1956 (P > O), and the ranking inference Q > O is further conﬁrmed by the clean vote in 1957 on school aid without desegregation versus the status quo; by my calculations, 86.3 percent of those 97 Congressional Districts

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voting YN in 1956 voted for Q > O in 1957 (even when including 13 replaced legislators and legislators with unknown 1957 rankings in the total). From the larger context it also becomes apparent that for emergently understood distributional reasons most Southerners will not support federal school aid under any circumstances, and thus the Northern Democrats could not have won by rejecting the Powell amendment and counting on Southern support either. From an account a few days after the vote: The position of the Southern Democrats is perfectly simple. They are opposed to any legislation which might be used, directly or indirectly, to ease them into obeying the Supreme Court’s decision against racial segregation in the public schools. They used every parliamentary device in the book to keep this schoolaid bill from passing for this reason: they knew that once this bill was on the books, it would have been easy next year for some Northern Senator or Congressman to tag onto the appropriation bill for the Department of Health, Education and Welfare an amendment stating that none of the funds in the bill could be allocated to states that had not carried out the Supreme Court’s integration decisions. Once this were done, the Southerners would have been disarmed, for they could not ﬁlibuster an appropriation bill without cutting off all funds for the Department of Health, Education and Welfare, including Social Security funds, and nobody is prepared to do that. (Reston 1956)

Their political friends wondered why Powell and the NAACP were so insistent on their amendment when it seemed likely that the Senate would ﬁlibuster any aid bill that carried a desegregation rider. The African Americans may have been one step ahead on this question. Powell conﬁdently dismissed the ﬁlibuster problem in Northern Democratic forums, and eventually the Southerners came to understand the basis of his conﬁdence. Powell’s insistence on his amendment would reveal a majority in the Congress willing to enforce Brown v. Board of Education. Once this objective was accomplished, federal school aid could be pursued on its own merits. During the 1956 debate Representative Roosevelt (D-CA), from the context clearly privy to Democratic strategy, stated that the Powellites would stand up and ﬁght for civil rights, “even at the cost of temporarily delaying the necessary money to ﬁnish some of our schoolrooms” (Congressional Record, July 3, 1956: 11761). I suggested that if Riker’s version of the story were correct, then the Powellites could quickly come back, propose O, win O, as Roosevelt seemed to have in mind, and be the heroes in the upcoming Presidential and Congressional elections. After the distribution of preferences was revealed by the ﬁnal vote, however, it became clear to the Democrats that they should not bother to raise the issue again; there were not enough votes to win school aid with or without a Powell amendment. How did

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the Democrats let it get to the ﬂoor in the ﬁrst place? Originally the preference orders of other legislators were not fully known. The SchoolAiders expected that enough Southerners would support federal school aid without desegregation (incorrect), and the Powellites expected that enough Republicans would both support civil rights (correct) and support school aid (incorrect). Federal aid for local school construction was a big election issue for Republican President Eisenhower. Incidentally, it is disturbing that Riker’s narratives fail to mention that federal school aid was Eisenhower’s proposal (it was at ﬁrst called the Hobby bill after the Republican secretary of health, education, and welfare), for example, “The story I have to tell involves a bill for federal aid to education, a bill sponsored by the Democratic leadership of the House of Representatives in 1956. (It was clearly not a bill put forward by the administration, which was of course Republican)” (Riker 1986, 117). Failure of school aid was described as a “major defeat” for Eisenhower (Morris 1957a). The silence of the President during this week’s debate is extremely interesting. Ever since his ﬁrst inaugural address, he has talked about the “urgent” need for “prompt action” in this ﬁeld, but with his own party divided and wavering on what to do, he did not send a single word to Congress during this week’s debate, though he had repeatedly and publicly urged the Congress to adopt his views on foreign-aid legislation the week before. (Reston 1956)

The Northern Democrats expected that Republican Eisenhower would deliver his own troops and were surprised when he did not. The failure of the school bill was “little expected by most students of Congress until the sudden House debacle this week” (Lewis 1956). Brief investigation of secondary historical literature shows that the NAACP strategy was not stubborn and foolish as in the Rikerian versions of the story. As Powell’s biographer (Hamilton 1991, 224) put it, the NAACP and other civil rights organizations faced a constant dilemma in the 1940s and 1950s: “How far should one go in insisting that segregation and discrimination be totally eliminated? Should the beneﬁts projected under less than full elimination of segregation be accepted as the best that could be obtained? When was the latter a ‘sellout’ of one’s principles?” If they were too reasonable in pursuing their desegregation objectives then nothing would change, and if they were too unreasonable then they would lose the allies they needed to succeed. From 1950 on, the NAACP and Powell routinely proposed, but selectively lobbied for, desegregation amendments to legislation. After winning Brown v. Board of Education in 1954 the NAACP sought to have the decision implemented. The Eisenhower administration was repeatedly evasive on implementation and suggested that the remedy was with the Court or with Congress.

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It was at that point that the NAACP decided to demand Congressional support for the desegregation of schools with the Powell amendment, which they backed with extensive lobbying. Pro-segregationists claimed that the Powell amendment would kill the school aid bill, and SchoolAider liberals tended to believe this claim. There was quite a controversy among northern liberals. The NAACP politely yet persistently required that its friends rally to the Powell amendment. What motivated their stand? According to Hamilton (1991, 234), Mitchell, the NAACP strategist, wanted a public recorded vote of who was willing to stand up for civil rights, and if the Powell amendment had been withdrawn then there would have been no such record. I would add that if, as was likely, the NAACP won a costly-to-attain majority on desegregation in the Congress, then from that point forward everyone would be on notice that school desegregation was ﬁnally onto the national agenda. One representative said, during the 1956 debate, “This is the day each Member pays a price for his civil rights vote. He has to decide whether the individual welfare of 15 million Negroes is more important than a vague risk of losing a $400 million federal plum” (Brownson (R-IN), Congressional Record, July 3, 1956: 11766). I surmise that the NAACP expected Eisenhower Republicans to help pass the school-aid bill in 1956 and were as surprised as everyone else by the outcome. One NAACP board member who publicly supported the Powell amendment circulated a caustic memorandum to other members of the board. He wrote that “We have been made to look like political suckers and amateurs because passing the Amendment was exactly what the enemies of Federal aid for schools wanted” (Hamilton 1991, 235). Nevertheless, the NAACP did demonstrate a costly majority with the Powell amendment in 1956, the ﬁrst civil rights bill since Reconstruction was passed in September 1957, a few weeks later President Eisenhower felt compelled to order federal troops to Little Rock, Arkansas to enforce a federal court school desegregation order, and the great civil rights revolution was underway. In the larger context, the Powell amendment in 1956 was instrumentally rational for the NAACP. It would be desirable to examine NAACP documents for details of their strategy in 1956 and 1957, but that is not possible in this project. I do not have any direct information about the NAACP’s stand in 1957, but the adroitly rational nature of its strategy can be inferred from the remainder of the school-aid story. If the incomplete-information outcome in 1956 was a tragedy, the complete-information outcome in 1957 was a farce. The Krehbiel and Rivers model would predict that in circumstances of more complete information most of the Northern Democrats (those we labeled Powellites and School-Aiders above) should strategically vote against any

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desegregation amendment, and that prediction is exactly conﬁrmed by 1957’s events. The alternative hypothesis of Denzau, Riker, and Shepsle (1985), that the Powellites were constrained by irrational constituents, is thus utterly demolished (it is distressing that these authors do not mention the 1957 vote directly contrary to their hypothesis even though at least one of them is aware of it). The Republicans rejected the Democratic formula for the level and distribution of funds in 1956, and so a smidgen of uncertainty remained for the Northern Democrats: would enough Republicans support their own Administration’s school-aid proposal? After all, three weeks before the 1957 vote Vice President Nixon addressed the National Education Association, and rather confusingly stated that although President Eisenhower strongly urged adoption of the school-aid bill there was virtually no chance that it would pass (Fine 1957). It is not apparent when reading the record of the 1957 debate forward innocently, but reading it backwards, with knowledge of the denouement, it is plain that the Northern Democrats, hoping for success but expecting failure on school aid, are full of mischief and mockery towards their Republican colleagues. Eisenhower won the 1956 election and on January 28, 1957 reproposed school-aid legislation. The legislation came to the ﬂoor of the House on July 23, 1957. The 1957 bill was a 50–50 compromise between Democratic and Republican positions on level and distribution of funding. Representative James Roosevelt (D-CA), liberal light and son of President and Mrs. Roosevelt, seemed to be central to the formulation and declaration of Northern Democratic strategy. Shortly after the bill arrived in the chamber, Roosevelt, who had spoken and voted for the Powell amendment in 1956, took the ﬂoor, indicated that Representative Powell was absent from the House, and declared that, “We believe that this year there should be a clear-cut determination of the fundamental issue of aid to school construction, and that it should not be clouded by another civil-rights debate . . . We hope that no one on either side of the aisle will force the committee to consider any amendment which would distract in any way from the fundamental purpose of the bill” (Congressional Record, July 23, 1957: 12482). Representative Diggs (D-MI), one of the three African-American members of the House, “conﬁrmed” the position of Roosevelt, and announced that he would vote “present” on any Powell-type amendment. He said, “This is not in any way to be construed as a retreat from our advocacy and support of the principle enunciated by the 1954 Supreme Court decision. It is rather to be interpreted as a strategic withdrawal from using the present proposed school-construction measure as a vehicle to supplement that decision . . . [Americans] can examine the record after the vote on this bill and determine who is for

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and who is against this proposal without any complications” (emphasis added, ibid., 12483). On the second day of debate, one Republican after another came to the ﬂoor to denounce federal aid on the grounds of economy. In response, Democrats gleefully quoted the 1956 Republican platform’s endorsement of school construction aid and quizzed equivocal Republicans as to the President’s position on the measure before the House. Udall (D-AZ), who sat on the committee of jurisdiction, pressed, “Is the President back of the Committee bill or not? Because if he is not, then the work of the committee is a shambles, and none of us know where we are. We are adrift here” (Congressional Record, July 25, 1957: 12723). McGovern (D-SD, 12722) poured on some delicious political rhetoric from the sidelines: I have often wondered how it is possible for a man in public life to be so popular with such a variety of people as is this man from Abilene [Eisenhower, aka Ike]. I think, however, after listening to the explanations of the President’s position on Federal assistance for the public schools that I know why everybody likes Ike. It is simply this: Ike, himself, likes everybody so well that he embraces with equal good humor all possible sides of issues on which there are sides to embrace. Those who favor Federal aid to education . . . are sure that Ike agrees with them. Those who are opposed to Federal aid are equally sure that the President is opposed, or at least lukewarm, about bringing the Federal government into this ﬁeld . . . Ike . . . no sooner signals with the left-turn indicator than we notice that the right-turn indicator is also blinking. Just about the time we wonder whether the Presidential car is swinging right or left, the brakes go on and we are left dead center in the middle of the road. Little wonder that even sophisticated Washington reporters get into trouble when they try to follow the Presidential car too closely.

Congressional Quarterly Almanac (1957, 592) devoted a boxed aside to the vexing question of Eisenhower’s true position on the subject, and in his ﬁrst news conference after the 1957 defeat of the school-aid bill Eisenhower professed that he had “never heard” that Democrats were willing to compromise on the legislation. Representative Powell was conveniently on the Riviera during the debate (reportedly, Congressional Record, July 25, 1957: 12735), and it was obvious that no other Democrat would be offering a desegregation amendment. On the third day of debate, Stuyvesant Wainwright (R-NY), who had voted for the Powell amendment and against ﬁnal passage of school aid in 1956 (YN ), moved a Powell-type amendment (Congressional Record, July 25, 1957: 12482). The Democrats fell in line, and one after another of the committee Democrats declared that the Wainwright proposal was a killer amendment and demanded a strategic vote for its defeat. The Democrats added some scarcely believable justiﬁcations, that the situation was different in 1957 than in 1956, that the Wainwright

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amendment was deﬁcient in craftsmanship, and so on, and were taunted with charges of inconsistency and hypocrisy by some of the Republicans. Wainwright, incidentally, said that although he was very much against the proposal now on the ﬂoor he would vote in favor of a bill that contained the original Eisenhower formula for level and distribution of aid, and he explained that he had been sincere in voting for the Powell amendment but against ﬁnal passage in 1956 (12599). This is worth noting because conservative Republican Wainwright’s YN vote is cited as prime evidence of strategic voting in 1956 (the point related but not endorsed by Krehbiel and Rivers 1990, 564). Allegedly, Wainwright was a hypocrite in 1956 for promising, in response to a query from Powell, that he would vote for the Powell-amended school-aid bill to demonstrate his respect for the civil-rights cause. Actually, Wainwright in 1956 promised to vote for a Powell-amended school-aid bill only if it contained the Republican distributional formula; the ﬁnal 1956 bill did not contain the Republican formula, and so he voted against it (Wainwright’s 1956 statement is a bit muddy in isolation but if one reads the surrounding debate it is clear that his promise was contingent on the ﬁnal bill containing the Republican aid formula, Congressional Record, July 3, 1956: 11758). In 1957, Wainwright proved he was true to his word; when a clean proposal containing the Republican distributional formula came to the ﬂoor he voted in its favor. Then something very peculiar happened. The killer Wainwright amendment came to a voice vote and the Chairman announced that the nays won – the Wainwright–Powell amendment was defeated, temporarily. A teller vote (a fast counting of votes without recording names) was demanded, and the outcome was reversed: there were 136 yeas for the Wainwright amendment and 105 nays against it. Notice that only 241 out of 426 representatives recorded votes on the amendment. We know from a news report (Morris 1957a) that only about a dozen Democrats voted for the Wainwright amendment, that the remainder voting yea for the Wainwright amendment were Republicans, and that Southern Democrats ﬂed to the cloakrooms, strategically absenting themselves from the vote so the killer amendment would pass (if the Southern Democrats had remained and voted sincerely against it, the Wainwright amendment would have failed). Then Ayres (R-OH, and a YN voter in 1956) offered a substitute bill containing the original Eisenhower formula for level and distribution of funding, which would also have the effect of striking the Wainwright– Powell amendment, and he promised that if his substitute were adopted no new Wainwright amendment would be offered by Republicans. The Northern Democrats swiftly rallied to the Ayres amendment and

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promised to support it, even though they had gone from 50–50 compromise to 10–90 compromise on the contents of the bill. For a moment there was a sliver of hope for the legislation, because the bill under consideration favored the south distributionally and lacked a desegregation clause. Then Smith (D-VA, and an NY voter in 1956) moved to report the bill from the Committee of the Whole to the House with a recommendation that the enacting clause of the legislation be stricken. The motion to strike takes precedence, usually only stated formally so as to obtain the right to speak, but, Smith continued, he really meant it on this occasion. This was a motion to kill the legislation with no further deliberation, and it succeeded, Q > O . A yea vote means to kill the bill and a nay vote means to support the original Republican proposal with no desegregation amendment (Congressional Record Roll-Call Vote 154: Congressional Quarterly Almanac Vote 56). The recorded votes were 208 yea (for Q) and 203 nay (for O ). Wainwright kept his promise to support a clean bill. Of the 208 votes to kill school aid, 97 were from Democrats and 111 were from Republicans. Of the 203 votes to save school aid, 126 were from Democrats and 77 were from Republicans. Bills usually don’t come to the ﬂoor unless they are expected to pass, so why did this one come to the ﬂoor? Representative Martin (R-MA), the only one of the three Republican leaders to vote to save school aid explained, “One group wanted to bring it out because this was the time to kill it. The other wanted to put the Republican party on the spot” (Morris 1957b). Calvert and Fenno (1994) offer a brilliant analysis of a 1986 US Senate Resolution providing for television coverage of Senate proceedings. The complete-information model of Austen-Smith (1987) showed that strategic voting and sincere voting are observationally equivalent, in other words that strategic voting is unidentiﬁable. The Calvert and Fenno model allows for probabilistic beliefs about the agenda sequence and about the distribution of preferences in the chamber. If legislators learn more about the distribution of preferences in the period between making proposals and voting on them, then there is a chance for identiﬁable sophisticated voting. They claim to identify 22 sophisticated votes on an amendment to the television-coverage resolution, but an attempt to thwart the majority through agenda manipulation failed. They argue that senators possess a clear consciousness of the possibility of agenda manipulation and sophisticated voting, even if it is infrequently observed in actual practice. Other than a general statement of faith that cycles are theoretically pervasive on distributional issues, the authors do not claim that harmful manipulation is frequent. Indeed it is instructive that their effort to demonstrate an instance of identiﬁable sophisticated voting was forced to rely on an example that lacked a harmful outcome.

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Riker’s ﬂawed interpretation of the Powell amendment, by the way, is one of the major examples intended to convince us that democracy is meaningless: “considering the real-world examples I have offered, it does seem likely that strategic voting occurs quite frequently. If it does, I conclude that the meaning of social choice is quite obscure” (Riker 1982, 167). The examples are all we have, and if the examples fail then the conclusion fails. It turns out that Riker is only able to demonstrate an instance of harmful manipulation by mistakenly assuming irrational actors. He makes the same error in his study of the Depew amendment, the topic of the next chapter.

10

Assuming irrational actors: the Depew amendment

Introduction Riker wants to demonstrate, with a story about the Senate deliberations on the 17th Amendment to the US Constitution, that manipulation by introduction of new alternatives is typical of democratic politics. The 17th Amendment would establish the direct election of US senators. Riker claims that in 1902 Chauncey Depew, a senator from New York, added a voting-rights rider to the direct-election proposal that introduced a disequilibrium. Depew is alleged to have contrived a cycle that prevented action on the direct election question for nine years, until 1911. I provide historical background on the election of senators controversy. I offer an alternative analysis, which shows that there was no cycle in 1911 and hence no cycle in 1902. The 17th Amendment failed to pass the 61st Senate early in 1911 due to lack of sufﬁcient votes for either the version with another voting-rights rider or the version without such a rider, not due to a cycle. The 17th Amendment passed the 62nd Senate later in 1911 due to the election of new senators who supported the Amendment. Altogether, I identify 11 errors of fact and interpretation in Riker’s account. Riker’s tale Although there may be equilibria in politics, they are extremely fragile to manipulation by the introduction of new alternatives, because of the McKelvey–Schoﬁeld ﬁndings about the indeterminacy of outcomes in multidimensional issue space, according to Riker (1982, 192). His explication of the US Senate vote in 1911 on the topic of the direct election of senators, he says, is intended to illustrate that fragility. The US Constitution originally provided that the legislatures of each state appoint two senators as the representatives of the state in the US Senate. The 17th Amendment to the Constitution provides that senators are elected by the people of their state, just as representatives are elected by the people of each Congressional district. The controversy over direct election 217

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of senators was originally one along a single dimension with an equilibrium point, but clever parliamentary tacticians invoked at least two other dimensions, one of party loyalty, the other of racism, in order to destroy the equilibrium and generate cycles to their advantage, he says. Beginning about 1890 a coalition of forces emerged demanding a constitutional amendment providing for the direct election of senators. The US House of Representatives passed several resolutions to that effect, each of which quietly died in Senate committee, because senators selected by state legislatures were reluctant to change the rule to one of election by the people. But, says Riker, by 1902 political pressure was such that the Senate could no longer ignore the issue. A Republican senator from New York, Chauncey Depew, disrupted the equilibrium outcome in favor of direct election by proposing in committee an amendment to the direct-election proposal that would establish a uniform national standard for voting rights. Depew’s motive, says Riker, was to divide the proponents of reform. The People’s Party, various progressives, and Western Republicans wanted direct election due to populist sentiments among their constituencies. Self-proclaimed white-supremacist Democratic senators in the south wanted direct election, because of white populism and because the system of primary nominations in the one-party south was yet another way to disenfranchise African–Americans. Depew’s proposed voting-rights amendment in committee threatened those voting rules and practices in the south designed to deny the vote to African–Americans. The South would not buy direct election of senators at that price, so Depew had single-handedly blocked the Constitutional Amendment. The issue did not get to the Senate ﬂoor in 1902, Riker tells us, but it did ﬁnally in February 1911 (numbered and italicized statements mark erroneous readings of the historical record), and (1) “This time the progressive proponents of reform protected their Southern allies against the DePew maneuver by adding a proviso to guarantee white supremacy” (Riker 1982, 194). (2) “The opponents of direct election moved to delete this sentence” (1982, 192). (3) “The motion to delete was known as the Sutherland amendment, and it was a negatively stated version of the DePew amendment” (1982, 192). Thus, there were three alternatives: r S, for South, the proposal to provide for the direct election of US Senators as reported from committee to the ﬂoor of the Senate. r N, for North or for No Change (to be made clear shortly), proposal S as amended by Sutherland; white supremacists claimed that N was a threat to their voting practices and “peculiar” way of life. r Q, for the Status Quo, no proposal to provide for the direct election of Senators.

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Because it was a proposal to amend the US Constitution, a successful resolution would require a two-thirds favorable vote. The vote on the Sutherland amendment was between N and S, and N won on a majority vote of 50 yeas to 36 nays (N > S ). The vote on the amended resolution, between N and Q, obtained 54 yeas and 34 nays, failing to attain the requisite two-thirds supermajority and so the resolution failed (Q > N ). Further, all 54 who voted for N over Q must “presumably” have favored S over Q, Riker contends. Also, at least ten Southern Democrats who voted for Q over N “presumably” favored S over Q. Together that makes 64 out of a total of 86 or 88 senators favoring S over Q, over two-thirds and satisfying the supermajority requirement, and thus the collective choice if it had come to a vote would have been S > Q. We have N > S, Q > N, S > Q, or N > S > Q > N, a cycle. Hence a small minority of 24 won by generating a cycle arising from the introduction of a new alternative in a new dimension, showing the empirical relevance of McKelvey–Schoﬁeld. He adds in a footnote, (4) “But in June 1911, the Democrats had a clear majority and defeated the Sutherland amendment, so the constitutional amendment passed. [(5)] Thus, the cycle was broken, but it had lasted more than ten years” (1982, 287). A later version of the tale, after introducing the Condorcet paradox of voting, continues by informing the student that: When tastes are circular (and if there are three or more alternatives and two or more voters, then almost always tastes are at least potentially circular), then the outcome depends as much on the procedure of amalgamation as on the tastes of the participants. Hence it is always possible to manipulate the outcome by manipulating the agenda. (emphasis added, Riker 1986, 10–11)

The hurried or untutored reader would conclude from this that manipulation by agenda control is possible in all circumstances. As we have seen, and as Riker himself conceded except for major issues, cycles and the attendant possibility of agenda control are naturally rare. Note the wobbling from almost always and at least potentially to always. Similarly, in the second version of the tale, we now learn that it was “conceivable – unlikely but conceivable” that a proposal for direct election without the Depew amendment would have passed in 1902 (1986, 14), in other words, a cycle in 1902 was unlikely. In 1902, the majority Republicans in the Senate would favor voting rights for African–Americans: Hence, there was, possibly, a cycle: The DePew amendment beat the Constitutional amendment which – perhaps – beat the status quo, which in turn beat the DePew amendment . . . It may seem to some readers that this is a rather fanciful tale to tell about a motion that never even got to the ﬂoor of the Senate. But we

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can be pretty sure it is just about true because the Constitutional amendment did get to the ﬂoor nine years later. (emphasis added, Riker 1986, 15)

We glide from unlikely to true quite quickly! He continues with a repetition of the tale of 1911; the argument is that since there was a cycle in 1911 there was probably one in 1902. In 1911 we have 50 to 36, N > S, 54 to 34, N < Q as in the ﬁrst telling. In the second telling we have the 54 (or perhaps 53 of them) who voted for N > Q favoring S > Q, and this time 8 (rather than 10) Southern Democrats who would have voted for S > Q if offered the choice, generating the same cycle as in the ﬁrst telling. Riker adds a new inference of preference orders for four groups in 1911. If a senator voted yea for the Sutherland amendment (N > S ) and yea for ﬁnal passage (N > Q) we call him a YY voter, and so forth. (6) The 20 Northern and Border Democrats and 8 Western Republicans who voted against Sutherland but for ﬁnal passage (NY ) must have ordered S > N > Q, according to Riker. (7) The YY voters, 25 Republicans and one “confused” Southern Democrat who voted for both the Sutherland amendment (N > S ) and for ﬁnal passage (N > Q) could have ordered either N > S > Q or N > Q > S. (8) “These 25 Republicans were exactly those who were being manipulated” (Riker 1986, 16). (9) They wanted the Constitutional Amendment for direct election of senators, but “they were constrained by their identiﬁcation as Republicans” to vote for the Sutherland amendment. (10) Thus, they must have ordered N > S > Q (and not N > Q > S). Riker needs for these 25 Republicans to be N > S > Q; if about eight or more of them were N > Q > S, then he would have no cycle and his larger argument would collapse. Finally, (11) “A few months later Democrats, now with an absolute majority, could prevent the DePew–Sutherland maneuver. Since over half of Republicans were also in favor of direct election, it was then easy to pass the Seventeenth Amendment, even without the protective clause” (Riker 1986, 17). The ﬁrst thing to notice is that, exactly as with his ﬁrst version of the Powell amendment, Riker is unaware that his supposedly rational choice account assumes irrational voters. Why? He labors to convince us that 25 Republicans were N > S > Q; if that is so then he gets his cycle. Recall that there is no incentive to vote strategically at the last stage of an agenda sequence. There are two possible last stages, S against Q or N against Q. The ﬁrst stage prior to either of these is a vote between N and S. Riker tells us that if it had come to a vote S would have beaten Q under the two-thirds rule, and as for the other possibility we know that the actual vote was Q > N. In the ﬁrst stage, the 25 Republicans vote between N and S. If they vote for their ﬁrst-ranked choice, N, then N > S, and the contest becomes one between N and Q, which Q wins, but this is

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the 25 Republicans’ last-ranked choice. If, however, at least 8 out of the 25 Republicans would have voted for their second-ranked choice S in the ﬁrst-stage contest between N and S, then S would have won; S then would have beaten Q in the last stage, and the 25 Republicans would have attained their second-ranked choice and avoided their last-ranked choice. If Riker’s story were true, then the 25 Republicans voted irrationally for their last-ranked choice over their second-ranked choice. Clearly, something must be wrong, again. Historical background What is wrong is an egregious misreading of the historical record. Haynes (1938) is the main source on the subject. Senatorial selection by state legislatures was tainted with abuses, and dissatisfaction steadily increased. Even after Congress regulated the process in 1866, nearly half the states experienced serious deadlocks in choosing a senator; the multiplicity of candidates sometimes made the outcome no better than chance; bribery, riot, assault, and martial law were not unknown; among other abuses (95). Earlier in the nineteenth century sporadic proposals for direct election were made, and they began to increase in the 1870s. By 1893, the House passed a joint resolution with the requisite two-thirds approval, calling for direct election. A Constitutional amendment requires approval by two-thirds of the House, two-thirds of the Senate, and then threefourths of the state legislatures. If Congress fails to act, two-thirds of the state legislatures can call for a Constitutional convention; however, such a convention would not be constrained to consider a single topic, raising serious apprehensions about utilizing this alternative. The House passed similar resolutions in 1894, 1898, 1900, the margin of approval ever increasing to unanimity in 1902 (there were abstentions). In 1896, the Senate Committee on Privileges and Elections favorably reported a direct-election amendment, but it never came to a vote. More than two-thirds of state legislatures passed memorials and petitions urging Congress to propose an amendment. There were no proposals from the House in the 58th, 59th, and 60th Congresses (1903–1908). As Byrd (1988, 398) explained, “After 1902, the House stopped trying, for nineteen resolutions submitted over three decades had quietly submerged in the still waters of the Senate Committee on Privileges and Elections.” Riker maintains that it was Depew’s maneuver in 1902 that halted Congressional consideration of direct elections. The standard story, however, is that there were not enough votes in the Senate for the proposed amendment to the Constitution. According to Haynes (1938, 98), “it would have been useless to force a new joint resolution through the House

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as long as opposition within the Senate was presenting an impassable barrier.” Thwarted in Washington, the movement found devices at the state level. A party’s state convention might nominate a candidate, although this is far from direct election. In the 1890s, many states turned to the direct primary election, and the practice in the one-party South became for the legislature to endorse, often unanimously, the winner of the primary election even if it had been hardfought. In the West, where there were two parties, Oregon developed a system that after 1909 was rapidly adapted by many states. Those running for the state legislature were permitted to include endorsement of either Statement No. 1, pledging the legislator to always vote for the people’s choice for US senator regardless of individual preference, or Statement No. 2, stating that he was free to disregard the people’s choice. Further, a petition was circulated among Oregon citizens whereby each pledged not to vote for any candidate who did not endorse Statement No. 1. The incentives for politicians are clear. In 1909, the people’s choice for senator was Chamberlain, a Democrat, and the people also elected a majority of Republicans in each house of the state legislature The pledges held and Democrat Chamberlain was selected by the Republican legislature, and thus the Oregon system passed the acid test. By the end of 1910, 14 out of 30 newly elected US senators were designated by popular vote, not to mention the incumbents previously selected by popular designation. Out of 46 states, 29 had already instituted the direct Senatorial primary election most with Oregon-type constraints on legislatures, and another 8 allowed for expression of popular preference in primaries (Hoebeke 1995, 150). Meanwhile, fresh Senatorial election scandals arose in nonreformed states. One short of the requisite number of state legislatures had applied to Congress for a Constitutional convention, which may have motivated some diehards in the Senate to act on an amendment so as to prevent a convention, but this is speculation, as the dangerous call for a convention was likely a bluff (see Caplan 1988, 61–65). Haynes, a professional political scientist whose major works were on state selection of senators and two volumes on the history and practice of the US Senate, believes that the most important factor in explaining the emergence of the issue in the Senate was the increasing number of senators who had been designated by popular vote. Not one of them “could antagonize the proposed amendment without seeming to stultify himself and to affront his constituency” (1938, 107). A similar psychology afﬂicted the older Republicans who opposed reform. They had been selected by state legislatures, and how could they repudiate the procedure that had placed them at the pinnacle of the nation’s esteem (there is some testiness on the point from them in

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the record, e.g., Congressional Record, January 24, 1911: 1339)? Borah, the most tenacious champion of reform, had been defeated by the Idaho legislature in 1903, but in 1907 was designated by popular election and became a US senator. “I have great affection for the bridge which carried me over” he said (Haynes 1938, 108). Haynes does not say that reform was thwarted by Depew in 1902, rather he refers to opposition in the Senate from 1902 to 1911 (106) and change by replacement in the Senate (107). Indeed, no author except Riker considers, or even mentions, any 1902 “DePew maneuver” as a factor in deterring Senate vote on the issue until 1911 (Byrd 1988; Caplan 1988; Haynes 1938; Hoebeke 1995; King and Ellis 1996; Kyvig 1996; Zywicki 1994). To be sure, the old guard in the Senate did work to thwart the reformers, not that hard a job given their seniority and the supermajority requirement, but as the old guard was replaced by senators pledged to the reform a breakthrough was bound to happen. Bristow (R-KS) recently become a senator by virtue of designation by popular election, offered a reform resolution in December 1909, which never got out of committee, and his discharge motion was obstructed. But early in the next session, January 1911, Borah favorably reported out of the Judiciary Committee the earlier Bristow proposal with a new committee amendment. The committee amendment, however, originating from Rayner (D-MD), was of great consequence. The effect of Bristow’s proposal was only to change the method of selection from state legislature to state popular election. Rayner’s committee amendment added a provision prohibiting federal regulation of Senate elections, in other words, to put in the Constitution a provision forbidding regulation of the South’s white-supremacist voting practices with respect to choosing senators, and if that were successful a movement to remove federal right of control over elections to the House would likely follow. At the end of the Civil War the victorious North enacted the 13th Amendment to the Constitution, forbidding slavery; the 14th Amendment, which guaranteed due process of law to all persons in the United States, among other things; and the 15th Amendment, which provided that “The right of citizens of the United States to vote shall not be denied or abridged by the United States or by any State on account of race, color or previous condition of servitude.” The Civil War was followed by a decade of Reconstruction, which involved military and political rule of the South by Republican forces. The South resisted northern efforts at reform and eventually drove African–Americans from participation in government by terrorist methods. Gradually, the vicious forces in the South regained their power, and cut down northern institutions such as active government and public education, and around the turn

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of the century the movement culminated in laws requiring strict segregation of the races, and imposing literacy tests, poll taxes, and all-white primary elections designed to disenfranchise African–Americans, setting in place the segregationist South that endured until the 1960s. This was the venomous atmosphere in which the Senatorial debate on voting rights took place. In 1890, as the white supremacists began to seek legal dress for their segregationist crusade, the Republicans in the Senate sought to establish federal regulation of elections in order to enforce the 14th and especially the 15th Amendments, and although they had a majority in the Senate they were thwarted by “the most impassioned ﬁlibuster in Senate history” (Hoebeke 1995, 163). The southerners labeled this the “Force Bill,” and advertised that it foretold a return to hated northern military occupation of the south. Meanwhile, the Republican Party was weakened nationally by corruption scandals and the national Democratic Party regained some strength. The ﬁrst House Joint Resolution calling for direct election of senators in 1894 contained a provision supported by the majority Democrats in the House and opposed by its Republican minority (Voteview 53rd House, Roll-Call #293, July 20, 1894).1 The provision denied to the federal government the authority to regulate election of senators, at best an undermining and at worst an implicit repeal of the 14th and 15th Amendments. Only some reform proposals contained this extraneous provision: widespread public opinion favored direct election but only the minority of white supremacists sought to insert race into the controversy. To remind the reader of the rancor and the righteousness associated with that extraneous issue of Negro voting rights in the South, I excerpt from the debate on the 17th Amendment remarks by Bacon (D-GA): there is no question concerning public affairs . . . in which the people of the South are so vitally interested . . . as their determination to preserve white supremacy, and it is no use to mince words about it . . . we have fought the battle . . . through the darkest night through which a people ever passed. We have rescued our civilization by the sacriﬁces and the trials which we then endured. We have not only rescued the civilization of the South, but we have rescued this entire Nation from the destruction of civilization which would have undoubtedly ensued if a Haiti had been made of the South. With civilization and order overthrown in the South, the deadly poison would have extended to the entire country. (Congressional Record, February 27, 1911: 3532)

Percy (D-MS) explained that in his county there were 5,000 white people and 44,000 negroes, and then boasted that: the framers of the constitution of 1890 in Mississippi met to frame a constitution under which a white man’s government could be maintained . . . There was

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no concealment about the object sought to be attained. It was to obstruct the exercise of negro suffrage to the point where it would not be a menace to the government. That object was avowed . . . “Restrained by the Federal Constitution from discriminating against the negro race, the convention discriminates against its characteristics and the offenses to which its members are prone.” (Congressional Record, February 27, 1911: 3541)

The young Depew was an elected Republican ofﬁcial during the Civil War, and his response to the southern maneuver was: This resolution virtually repeals the fourteenth and the ﬁfteenth amendments to the Constitution. It validates by constitutional amendment laws under which citizens of the United States, constituting in the aggregate more than one-tenth of the electorate, are to be permanently deprived of the right of suffrage . . . when it comes to deliberately voting to undo the results of the Civil War, when it comes by constitutional amendment to permanently taking from 10,000,000 people the rewards of education and intelligence, that reward being in a free government the right to vote, I can not assent to or be silent upon the proposition. (Congressional Record, January 24, 1911: 1336)

“Although Depew was opposed to popular Senate elections on any account, and was not above trying to defeat the proposal by offering an amendment unacceptable to the South, there was no affectation in his desire to retain the federal [right to] control of” elections (Hoebeke 1995, 163). Riker has it exactly backwards. It was not that the movement for direct election was sailing merrily along until 1902 when Depew cleverly introduced an amendment designed to split the supporters of direct election which sank the ship of reform. Rather, it was the segregationists beginning in 1894 who sought parasitically to attach their nationally unpopular cause to the nationally popular cause of direct election. Many of the northeastern Republican senators were politically formed by the Civil War. They sincerely opposed direct election from a sense of traditionalist elitism, and since they fought a bloody war over the matter they sincerely opposed mistreatment of African–Americans in the South. Naturally, they would vote against both proposals, whether bundled together or not. The Republicans in 1902 bundled in an extreme northern position on voting rights as a counterweight to Democratic attempts to bundle in an extreme southern position on the same question. Riker does not realize that there was another alternative available in 1902, or in any other year, and that would be a joint resolution calling for direct election that would also preserve the status quo with respect to federal right to regulate elections. As all commentators except Riker observe, the main problem for the cause of direct election in the Senate had been traditionalist opposition by men who had been favored by selection by state legislatures. Riker presents

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no evidence, repeat, none, and there is no evidence in the other secondary literature nor in the debates of 1911, for the linked propositions that direct election could have passed the Senate in 1902 and thus that there was a cycle for ten years (his ﬁfth incorrect claim) – we shall see that there were not enough votes for either form of direct-election amendment (N or S ) even as late as February 1911. In 1899, well before the alleged “Depew maneuver” of 1902, a special committee of the Pennsylvania legislature concluded that the US Senate would never act on direct election until confronted with applications for a constitutional convention from two-thirds of the states and set about organizing the states to that end (Caplan 1988, 63). Riker’s only support for 1902 is the assertion of a cycle in 1911. He is aware that in 1911 “there was much more support for reform” (1982, 194) than in 1902, but does not notify the reader that this fact impairs his claim for a cycle in 1902. Riker is also misinformed as to the content and nature of the various amendments pertaining to voting rights. Bristow’s was a neutral, status-quo proposal with respect to the federal regulation of elections. That is what went into the Senate Judiciary Committee. What came out was a proposal to abandon the federal right to regulate the election of senators (see Table 10.1). The Bristow proposal was neutral, the Rayner addition from the Judiciary Committee departed from the status quo towards the extreme southern position, and the former Depew amendment departed from the status quo towards the extreme northern position. The old Depew amendment was offered but ignored in 1911 deliberations: The qualiﬁcations of citizens entitled to vote for United States Senators and Representatives in Congress shall be uniform in all the States, and Congress shall have power to enforce this article by appropriate legislation and to provide for the registration of citizens entitled to vote, the conduct of such elections, and the certiﬁcation of the result. (Riker 1986, 14)

Not until the Voting Rights Act of 1964 were measures similar to this enacted and enforced. How did the Rayner addition come about? Surely after some backroom negotiations the Bristow proposal ended up in a Judiciary subcommittee of three members chaired by Borah. Rayner (D-MD) was the swing vote and insisted upon removal of federal right to regulate elections (Kyvig 1996, 212). The price for Borah to get direct-election to the ﬂoor was the addition. This was no mystery. “This amending doubtless served to get for the resolution a favorable report from the committee, but in the Senate it at once raised a new issue that proved most divisive,” according to Haynes (1938, 109). It was not that opponent Depew strategically split

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Table 10.1. Bristow and Rayner amendments compared Original Constitution

Proposed amendment

Bristow (N )

Paragraph 1, Section 3, Article I. The Senate of the United States shall be composed of two Senators from each state chosen by the legislature thereof for six years; and each Senator shall have one vote.

Rayner addition to Bristow (S )

Paragraph 1, Section 4, Article I. The times, places, and manner of holding elections for Senators and Representatives shall be prescribed in each state by the legislature thereof; but the Congress may at any time by law make or alter such regulations, except as to the places of choosing Senators.

The Senate of the United States shall be composed of two Senators from each state, elected by the people thereof for six years; and each Senator shall have one vote. The electors in each state shall have the qualiﬁcations requisite for electors of the most numerous branch of the State legislatures. The times, places, and manner of holding elections for Senators shall be as prescribed in each State by the legislature thereof.

Source: Congressional Record, January 21, 1911: 1218.

the ranks of direct-election supporters, rather it was the extreme southern wing of the supporters promising to bolt the coalition unless they had their controversial proviso. Carter (R-MT) complained on the Senate ﬂoor: It was manifestly used as a ﬂoat to bring the main amendment out of the committee room. Those who accepted that mode of transportation had more zeal than knowledge, for if the ﬂoat does not serve as a sinker in either branch of Congress it will surely prove a deadly weight in more than one-fourth of the state legislatures. (Congressional Record, January 21, 1911: 1218)

Nor, according to Carter, was there any mystery about the import of the Rayner amendment: The occasion demands plain speech and forbids evasion . . . The adoption of the amendment would give substantial though limited national sanction to the disfranchisement of the Negroes in the Southern States. In their disfranchisement we now passively acquiesce, but with this supine attitude some Senators are not content; they ask us to actually strip Congress of the power to question election methods and actions in so far as the election of United States Senators may be concerned. (Ibid.)

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Riker’s claim (1) that the progressive proponents of direct election protected their southern allies against the Depew maneuver by adding a proviso to guarantee white supremacy is incorrect: Rayner, the author of the proviso, was a border Democrat, not a progressive Republican. The huge majority of progressive proponents of direct election, such as Carter just quoted above, detested and opposed the Rayner amendment, as evidenced by their votes for the Sutherland amendment to void Rayner. What was the Sutherland amendment? Sutherland (R-UT) was a progressive proponent of direct election who voted both times for ﬁnal passage of a direct-election resolution. His motion was simply to strike the pro-southern Rayner addition and thereby return to the neutral Bristow proposal. Thus, Riker’s claim (2) that it was the opponents of direct election who moved to delete the Rayner amendment is as false as it could be, as it was the proponents of direct election who did so. Further, Riker erroneously claims (3) that the Sutherland amendment was a negatively stated version of the Depew amendment. This is not so. Look at the actual language of the amendments displayed in Table 10.1. The Depew amendment was the more pro-northern position on federal regulation of elections, the Sutherland amendment (or Bristow proposal) was the neutral position that left the status quo undisturbed; and the Rayner amendment was the more pro-southern position. Both the Depew amendment and the Sutherland amendment were proposed on the Senate ﬂoor; they were not equivalent, the ﬁrst was ignored in 1911, and the second was passed. This is manifest in the record, and not just by implication. Rayner (D-MD) warned that the Depew amendment “goes much further” than the Sutherland amendment, “and it goes much further than the force bill attempted to go” (Congressional Record January 20, 1911: 1163). The Sutherland amendment passed by a healthy majority, 50 yeas to 36 nays (N > S ), but then the restored Bristow proposal failed to get the requisite two-thirds majority in the 61st Congress. This is supposedly the great manipulative delay due to a contrived cycle. Notice, however, that unlike usual legislation that Congress may repeal at any time this was a resolution to propose a Constitutional amendment for the approval of three-fourths of the state legislatures. If a proposal failed among the state legislatures it would be unlikely that the issue would be considered again soon; if the proposal succeeded among the state legislatures and became part of the Constitution it would be nearly impossible to amend. Thus if a senator believed that the composition of the Senate were changing in favor of his position, he would be better off to delay the vote to a newly elected Congress. Riker’s great manipulative obstruction lasted a scant six weeks, when the issue was revived again

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in the 62nd Congress. In the new Congress the Democratic-controlled House passed the Rayner version of the resolution; a motion in the House like the Sutherland amendment to strike the southern demand for unregulated state election of senators failed, receiving 190 Democrat nays and 120 Republican yeas, a pure party-line vote (Voteview 62nd House, Roll-Call #4, April 13, 1911). The House resolution was referred to the Senate Judiciary Committee which reported it out in half an hour. In the 62nd Congress it was Bristow who proposed the ﬂoor amendment to strip the resolution of the Rayner provision. The Bristow amendment in the 62nd Congress was identical to the Sutherland amendment in the 61st Congress. In the 61st Congress, Bristow had voted against the Sutherland amendment to restore Bristow’s original proposal (S > N ) and for ﬁnal passage of the direct-election resolution (N > Q). Yet in the 62nd Congress Bristow proposed the same amendment he had voted against in the last Congress. This is an important clue. Senators from the Lower South, smelling defeat of their cause in the air, attempted to bully Bristow for his inconsistency. Bristow’s explanation was simple: in the 61st Congress he had voted strategically. He is worth quoting at length, because the entire strategic situation is disclosed without any doubt that my interpretation is distorted. When this [current, 62nd] Congress met I went over the membership of the Senate as it is now composed and ascertained that 10 of the Senators who had voted against the joint resolution [N > Q] when the roll was called on February 26 [in the 61st Congress] were not now Members of the Senate, and from inquiry I was convinced that more than a sufﬁcient number of the 10 new Senators would have voted for the joint resolution if they had been Members of the Senate to have carried it . . . the joint resolution would have been adopted instead of having been rejected . . . I believe . . . it can get more votes in this body in that form [N ] than in any other form in which it can be presented . . . that it will command more support from the people of the United States in the form we voted on it [in the 61st Congress, N > Q]. (Congressional Record, June 12, 1911: 1904) I voted against the Sutherland amendment [for S > N ] in the last session of Congress because I was advised by the Senator in charge of the joint resolution [Borah] and by other Senators whose judgment I had conﬁdence in [LaFollette?] that it would be safer with that amendment defeated than with that amendment adopted . . . I believed at the time I voted against the Sutherland amendment that the resolution would be stronger if that amendment was defeated. I think now that I was mistaken that it was stronger with the Sutherland amendment incorporated in it than it would be if not so amended, and it received more votes than it would otherwise have received. I believe further, it is stronger before the people now, in that form, than it would otherwise have been. (emphasis added, Congressional Record, June 12, 1911: 1905)

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Bristow also explained that if his neutral proposal on the question of federal regulation of state election were referred to the states that would occasion controversy only in the (Lower) South, but that if the pro-southern proposal were adopted that would cause controversy and loss of support in the much larger remainder of the nation (Congressional Record, June 12, 1911: 1906). In short, Bristow was saying that he strategically voted against the Sutherland amendment in the 61st Congress because he thought that otherwise direct election would not get enough votes from southern senators. After all, Rayner (D-MD), who had prevailed on Borah in the Judiciary Committee to include the southern proviso, had thundered on the ﬂoor upon the introduction of the Sutherland amendment: “Suppose that every Southern State is in favor of the joint resolution the way we reported it, and that every Southern State is against it the way the Senator from Utah [Sutherland] proposes to amend it” (Congressional Record, January 20, 1911: 1163). But after votes were recorded on N > Q Bristow realized that Rayner was all thunder and no lightning: it was not the South but only the Lower South that had blustered on the issue, and when N came to a vote, the Upper South supported it over Q. Next, Bristow said, he polled the replacement senators coming into the 62nd Congress and that further strengthened his belief that victory was possible for N > Q and so this time around he would vote sincerely for N. Bristow was correct. In the 62nd Congress, the Bristow (Sutherland) amendment passed, 45 to 44; a southern proposal to substitute a less extreme pro-southern provision failed; and the direct-election resolution (N ) received more than two-thirds approval, 64 yeas and 24 nays. The amended joint resolution was sent back to the House, which would not concur. The Senate voted (along party lines) to insist on its amendment and to ask for a conference. The conference committee met sixteen times without success. Eventually an exhausted House concurred in the Senate version. In the House the northern Democrats had been supporting the southern Democrats against the Republicans on state regulation of elections; in the end the northern Democrats joined the Republicans to defeat a southern-Democratic motion to amend the Senate version (Voteview 62nd House Roll-Call # 139, May 13, 1912). Then the House voted for the Senate version (N > Q), 238 votes for and 39 votes against, the scattered nays from Virginia and parts of the Lower South (Voteview 62nd House Roll-Call # 131, May 13, 1912). The state legislatures responded swiftly, by May 31, 1913 more than three-fourths had voted their approval and the 17th Amendment to the constitution was adopted. Only Utah voted against ratiﬁcation. As the three-fourths threshold was crossed it was mostly states in the Lower South who had yet failed

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to act: Alabama, Delaware, Florida, Georgia, Kentucky, Maryland, Mississippi, Rhode Island, South Carolina, and Virginia. Alternative interpretation The fact that two different Congresses recorded votes on the same two issues gives us an abundance of data points from which to infer preferences (see Table 10.2). For those senators participating in both the 61st and 62nd Congresses, we ﬁnd consistency that is almost perfect, but with one major and revealing exception, we shall see. Senators similar to Depew (who did not return to the 62nd Congress), 15 Republicans mostly from the Northeast, voted for the Sutherland and Bristow proposals to retain federal right to regulate elections (N > S ), but both times against referring the proposed amendment to the states (YNYN, Q > N > S ). Warren (R-WY), the only inhabitant of cell YNYY, is a telling case. Right before the vote in the 62nd Congress he explained that he believed that a popularly elected Senate would be unwise, but that he must bow to the opinion of the people in favor of the reform, a pitifully incoherent position probably inspired by the dramatic electoral defeats of anti-reform Republicans all around him (see Hoebeke 1995, 184). Most of the various progressives – Border, Midwestern, and Western Republicans – 21 of them, voted for the Sutherland and Bristow amendments and both times for referring the proposed amendment to the states (YYYY; N > S > Q or N > Q > S). Democrats from the Upper South, 20 of them, voted against the Sutherland and Bristow amendments but nevertheless for the amended referral of direct election to the states (NYNY, S > N > Q). The Insurgent Republican leaders, LaFollette and Borah, voted with the Upper South Democrats. Eight Lower South Democrats voted against everything, and said that they would have voted for direct election if they would have obtained their Jim Crow proposal (NNNN, S > Q > N ). The Insurgent Republicans were a distinct minority faction in the Congress from 1909 to 1916. A typical insurgent had migrated to a western state as a youth, had been a small-town lawyer, had identiﬁed with postbellum Republicanism, but had moved from right to left with political maturity along with his populist rural constituency. The insurgents wanted a progressive income tax and an inheritance tax, control or defeat of the corporate interests, and the extension of popular government. At the end of the 61st Congress, the established insurgent core in the Senate contained Borah (NYNY ), Bristow (NYYY ), Clapp (NYYY ), Crawford (YYYY ), Cummins (NYYY ), and LaFollette (NYNY ); Gronna (NYYY ) was new but core; and Bourne (NYYY ),

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Table 10.2. Votes on 17th Amendment compared 62nd Congress:

YN

YY

NY

NN

61st Congress: YN

15 mostly northeastern Republicans

YY NY

Warren (YNYY, R-WY)

21 Border midwestern, and western Republicans 6 insurgent-Republican rank-and-ﬁle

NN

20 Upper South Democrats 2 insurgentRepublican leaders 8 Lower South Democrats

Key: Y = Recorded vote, Yea Y = Paired vote, Yea 0 = Not voting YYYY means: Y = Yea vote on 61st Senate Roll-Call #244 (N > S ) Y = Yea vote on 61st Senate Roll-Call #248 (N > Q) Y = ∗ Nay vote on 62nd Senate Roll-Call # 25 (S > N ) Y = Yea vote on 62nd Senate Roll-Call #26 (N > Q) etc. YNYN: Brandegee (R-CT), Burnham (R-NH), Crane (R-MA), ∗ Dillingham (R-VT), Gallinger (R-NH), Heyburn (R-ID), Lorimer (R-IL), Oliver (R-PA), Page (R-VT), Penrose (R-PA), Richardson (R-DE), Root (R-NY), Smoot (R-VT), Wetmore (R-RI). YNY0: Lodge (R-MA). YYYY: Bradley (R-KY), Briggs (R-NJ), Burton (R-OH), Clark (R-WY), Clarke (D-AR), Cullom (R-IL), Curtis (R-KS), Dixon (R-MT), DuPont (R-DE), Gamble (R-SD), Guggenheim (R-CO), Jones (R-WA), McCumber (R-ND), Nelson (R-MN), Nixon (R-NV), Perkins (R-CA), Smith (R-MI), Stephenson (R-WI), Sutherland (R-UT). Y0YY: Crawford (R-SD). YY0Y: Frye (R-ME). NYYY: Bourne (R-OR), Bristow (R-KS), Brown (R-NE), Clapp (R-MN), Cummins (R-IA), ∗ Gronna (R-ND). NYNY: Bailey (D-TX), Borah (R-ID), Chamberlain (D-OR), Culberson (D-TX), Davis (D-AR), Gore (D-OK), LaFollette (R-WI), Martin (D-VA), Newlands (D-NV), Overman (NYNY, D-NC), Owen (D-OK), Paynter (D-KY), Rayner (D-MD), Shively (D-IN), Simmons (D-NC), Smith (D-SC), Smith (D-MD), Stone (D-MO), Swanson (D-VA), Taylor (D-TN), Thornton (D-LA), Watson (D-WV). NNNN: Bacon (D-GA), Bankhead (D-AL), Fletcher (D-FL), Foster (D-AL), Johnston (D-AL), Percy (D-MS), Terrell (NNNN, D-GA). NN0N: Tillman (D-SC). ∗ The motion to adopt the Bristow amendment (N > S, 62nd Senate Roll-Call # 24) tied at 44–44 and the Vice President broke the tie in its favor, making 45–44 for passage. Lower Southerners unsuccessfully objected to the Vice President’s tie-breaking vote. Lower Southerners also immediately moved a compromise that would have voided the Bristow amendment (S > N, 62nd Senate Roll-Call # 25), which failed 43–46, and it is this vote that is displayed in the table. Adjusting for polarity, the only changes between the two votes were: Dillingham (R-VT) paired yes for the northern position N on the ﬁrst vote and was recorded in favor of the northern position N on the second vote; Gronna (R-ND) voted against the northern position on the ﬁrst vote, but voted in favor of the northern position on the second vote. Source: Constructed from votes reported in Voteview.

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Brown (NYYY ), and Dixon (YYYY ) were in the insurgent penumbra (Holt 1967, 3). The exception to consistency is six Insurgent Republicans who followed faction leaders LaFollette and Borah in the 61st Congress and voted against the Sutherland amendment but for ﬁnal passage, but who in the 62nd Congress departed from LaFollette and Borah (NYNY ) to vote for the Bristow amendment and for ﬁnal passage (NYYY ). One of these was Bristow himself, and we have heard his explanation. The other ﬁve were Bourne, Brown, Clapp, Cummins, and Gronna. These six voted strategically against the Sutherland amendment in the 61st Congress because they believed they needed votes from the South for the success of the direct election cause. After the vote was revealed, however, as Bristow declared, it was plain that they had enough votes from the Upper South for success and would be better off voting sincerely to ensure the victory of N on the next occasion. Most of these six, since they voted strategically, must have had the preference order N > S > Q. What about the 21 other progressive Republicans who voted YYYY ? Were they N > S > Q or N > Q > S ? Riker gets his cycle by inferring, “presumably,” that none of them was N > Q > S. But if they were N > S > Q as Riker wants them to be, then they should have joined with their fellow progressive midwestern and western Republicans – certainly the Bristow six, and probably Borah and LaFollette – and voted strategically against the Sutherland amendment (NY ), especially given that their fellow progressive Republicans who voted strategically failed in their objective to defeat N in order to avoid Q. Many of the 21 must have been N > Q > S. This follows from Bristow’s statement that direct-election would enjoy more support with N than with S, reiterated by Bristow when a pro-southern senator (Percy, D-MS) wheedled that together the Democrats and the progressive Republicans could pass S > Q: “The Senator [Percy] is under the impression,” Bristow replied, “that a majority [50 percent rather than 23 ] can pass the resolution . . . the Senator’s mathematics are badly wrong” (Congressional Record, June 12, 1911: 1905). Riker does not understand that the preference order that he thinks unlikely, N > Q > S, makes sense: Bristow himself came close to changing from N > S > Q to N > Q > S. Why does N > Q > S make sense? If one wants direct election, and if one believes that N would attract the votes of three-fourths of the state legislatures and be adopted, but that S would fail to win the votes of three-fourths of the state legislatures and fail to be adopted, then one would rank the issues in the Senate N > Q > S. One’s position would be: don’t send a direct-election amendment to the states unless it is one that will succeed. Finally, we know that two senators stated on the record that their ranking was N > Q > S (Curtis, R-KS, and Jones, R-WA, cited in Haynes 1938, 111).

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Table 10.3. Replacement senators, from 61st to 62nd Senate 62nd Senate YN 61st Senate YN

YY

NY NN

YY

NY

NN

NY, Aldrich CT, Bulkeley (R) to 5 Republican seats (Y 0, R) to McLean (R); to Democratic, 1 Lippitt (R) MI, Burrows (R) Republican stays to Townsend (R) Republican IA, Young (R) to 4 Republican seats Kenyon (R) to Democratic, 1 Republican stays Republican FL, Taliaferro (D) to Bryan (D)

MS, Money (N N, D) Williams (D)

Key: YY means: Y = Yea vote on 61st Senate Roll Call #248 Y = Yea vote on 62nd Senate Roll Call #26 etc. YN to NY: CA, Flint (R) to Works (R); ME, Hale (R) to Johnson (D); NJ, Kean (R) to Martine (D); NY, Depew (R) to O’Gorman (D); VT, Dick (R) to Pomerene (D); WV, Scott (R) to Chilton (D). YY to NY: IN, Beveridge (R) to Kern (D); MO, Warner (R) to Reed (D); NE, Burkett (R) to Hitchcock (D); MT, Carter (R) to Myers (D); WA Piles (R) to Poindexter (R). Source: Constructed from votes reported in Voteview.

It remains to examine the replacement senators (see Table 10.3). There were 17 incoming senators. The Republicans lost nine seats, the Democrats lost none. Three seats retained by the Republicans went from opposing direct election to supporting direct election of senators. Five seats lost by the Republicans to the Democrats went from opposing direct election to supporting direct election. One seat retained by the Democrats went from opposing direct election to supporting direct election. Altogether then, nine seats converted to direct election; six seats retained a commitment to direct election; two seats remained against direct election; and no seats converted from support of direct election to opposition. There is a trend towards support of direct election. At the same time, the supporters of the Bristow–Sutherland amendments for neutrality on the question of federal regulation of elections declined by a whopping 11. An enactment of a direct-election amendment had become inevitable, but the Republicans may have calculated that the 62nd Congress was their last chance to attain N over S, which may explain their tenacious and

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Table 10.4. Riker’s inference of 61st Senate vote on 17th Amendment N

S ∗ 50

N S Q

36 ∗ 34

Q 54

∗ 64

24

Notes: ∗ = winner (it takes > 2 to beat Q) 3 italic = winner by majority rule

Table 10.5. Mackie’s estimates of distribution of preferences in 61st Congress Vote

#

Label

Ranking

YN YY NY NY NN

24 25 8 20 9

Northeast Republicans Sincere progressive Republicans Strategic progressive Republicans Upper South Democrats Lower South Democrats

QNS NQS NSQ SNQ SQN

triumphant refusal over almost two years to compromise with the House on the Bristow–Sutherland amendment. The ﬁnal task is to examine whether Riker’s assertion of a cycle in the 61st Congress is correct. He assumes, without mention or justiﬁcation, that all voters are sincere. His data and inferences would yield the pairwise-comparison matrix in Table 10.4. We see that N > S, S > Q, Q > N; a cycle, N > S > Q > N. I infer that all voters were sincere except for the Bristow six and perhaps Borah and LaFollette among the progressive Republicans. Most of these eight voted strategically S > N, against their sincere preference N > S, because they mistakenly believed that was the only way they would get enough votes to avoid their least-favored outcome Q and gain their second-ranked outcome S. As I have argued, many of the remaining progressive Republicans were N > Q > S; otherwise they would have voted strategically with their colleagues. Those who voted YN unambiguously ranked Q > N > S, and 25 of those who voted NY unambiguously ranked S > N > Q. If all we knew were the two roll-calls, those who voted NN could have been Q > S > N, but they said they were S > Q > N and there is no evident motive for misrepresentation. If they were capable

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Democracy Defended

Table 10.6. Mackie’s inference of 61st Senate vote on 17th Amendment N N S Q

S ∗ 57

29 ∗ 33

∗ 49

Q 53 37

Notes: ∗ = winner (it takes > 2 to beat Q) 3 italic = winner by majority rule

of strategic voting, those who voted NY would have been N > Q > S. Up to eight of those who voted NY were of the type N > S > Q voting strategically for S > N. Then we simply tally these preferences into a pairwise-comparison matrix (see Table 10.6). If the Senate operated by simple majority rule on the question, then the outcome would have been N > S, N > Q, and Q > S, for an overall noncyclical ranking of N > Q > S. Under the rule for referring a Constitutional amendment to the state legislatures, a two-thirds vote to overcome the status quo, and if all would have voted sincerely in the 61st Congress, then the outcome would have been N > S, Q > N, Q > S, for an overall ranking of Q > N > S. My conclusion, novel to the literature reviewed, is that there were not enough votes in the 61st Congress to pass a Constitutional amendment under any circumstances, implying that it was the replacement of senators in the 62nd Congress that was crucial to success of the 17th Amendment. In the 61st Congress S could not have beaten Q, and N was strongly favored over S, but there were not more than two-thirds who favored N over Q. Riker’s belief that Republican manipulation rather than simple lack of votes caused the defeat of direct election in the 61st Congress may just be an uncritical transmission of Democratic electioneering propaganda on the issue. If my assertion that many of the 25 sincere progressive Republicans were N > Q > S is controversial, consider a sensitivity analysis. In order to avoid Riker’s cycle, I need that only ﬁve in that category have the ranking N > Q > S, and the rest could rank N > S > Q as Riker would have them. I have already established that N > Q > S is a reasonable preference order, and shown that it has support in the record. There was no cycle in 1911, and since the claim of a cycle in 1911 is Riker’s only evidence for asserting a cycle in 1902, his claim (5) fails, that Depew had contrived a cycle in 1902 that delayed consideration of direct election for ten years.

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Table 10.7. Mackie’s estimates of distribution of preferences in 62nd Congress Vote

#

Label

Ranking

YN YY NY NY NN

16 22 16 25 8

Northeast Republicans Strong progressive Republicans Weak PRs & new N.Democrats Other Democrats Lower South Democrats

QNS NQS NSQ SNQ SQN

Table 10.8. Mackie’s inference of 62nd Senate vote on 17th Amendment N N S Q

40 16

S

Q

∗ 47

∗ 71

∗ 30

47

Notes: ∗ = winner (it takes > 2 to beat Q) 3 italic = winner by majority rule

How did the replacement of senators from the 61st Congress to the 62nd change the distribution of preference rankings? Here my inferences are less conﬁdent since I do not have two votes on the same issue for the replacement senators; but the conclusion of no cycle in the 62nd Congress is robust to reasonable variation in the estimates of preference rankings. I assume that all voters voted sincerely (there is no reason or evidence to assume otherwise) and that where there is a doubt a new senator voted like his geographic neighbors. That yields the estimates in Table 10.7, and the labels must change somewhat to reﬂect lack of strategic voting and the big Democratic gains in the North. That translates into the pairwise matrix in Table 10.8. That gives us under the actual voting rule N > S, N > Q, Q > S, or the noncyclical ranking N > Q > S. I assume that all 22 Strong Progressive Republicans are N > Q > S; and if 10 out of those 22 have the ranking I assume the conclusion stands. If 11 or more of the 22 instead rank N > S > Q, then the collective ranking would be the noncyclical N > S > Q. In neither case is there a cycle. Of course, we know that N won in the actual vote. My analysis does not concentrate on the ultimate causal factors behind the passage of the 17th Amendment. I favor the view that it was one step in

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Democracy Defended

the relentless march of democratization, that the Amendment came about because that’s what the people wanted. A second, complementary, factor was the deadlocks, corruption, and disorder associated with selection by state legislatures. In an excellent paper, King and Ellis (1996) show that before adoption of the 17th Amendment in 1913 it was easier relative to the House delegation to elect a Republican senator, but that after 1913 it was easier to elect a Democratic senator relative to the House delegation. The explanation offered is that aggregation by direct election mobilizes different interests than does aggregation by indirect election through the state legislature. Of course, the Democrats did more zealously seek the amendment than did Republicans, and that is the third factor disclosed by King and Ellis. Zywicki (1994) offers a rent-seeking explanation of the reform – that it allowed “special interests” such as workers and farmers to better work their will on the Senate – but the data he provides in support are not conventionally signiﬁcant. Now we are in a position to further elucidate Riker’s errors. He claimed (6) that the eight western Republicans who voted NY in the 61st Congress ranked S > N > Q. However, I have shown that six of these Insurgent Republicans including Bristow voted strategically for S > N in the 61st Congress and sincerely for N > S in the 62nd Congress, and thus that they ranked N > S > Q. Borah, the carrier of the resolution on the ﬂoor was constrained to S by the commitment he made in committee to get the bill to the ﬂoor, and on the ﬂoor said he would even support proposals to strip the Congress of the right to regulate House elections (Hoebeke 1995, 165), although this is suspicious since not one other Republican in the Congress held this position. LaFollette, the leader of the Insurgent Republicans, I surmise was also constrained to S by an early commitment he made as a factional leader to southern Democrats to get the bill onto the ﬂoor; Stephenson, LaFollette’s ideological sidekick from Wisconsin, never once voted for S. To continue the surmise, in the 62nd Congress LaFollette would keep his own commitment but plausibly claim that his troops were out of control given the contribution of his party’s obstruction of direct-election legislation to heavy Republican election losses. That the Insurgent Republicans were strategizing together on the measure is suggested by Gronna’s (R-ND) instant conversion in the 62nd Congress from voting against the Bristow amendment one minute and in the next minute casting a vote equivalent to favoring the Bristow amendment with the intended effect of providing its margin of victory. Riker claims (7) that southerner Clarke (D-AR) was possibly confused because he voted YY in the 61st Congress against the southern position (he voted N > S, N > Q). Clarke was quite unusual, but he was not confused, for he again voted YY in the 62nd Congress. Riker claims (8) that

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it was the group that I label the 25 sincere progressive Republicans who were being manipulated by the so-called Depew–Sutherland maneuver (9) because they were constrained by their identiﬁcation as Republicans. But, as we have seen, there was no such identity constraint on the Bristow six, the strategic progressive Republicans, nor on prominent progressive Republicans Borah and LaFollette. So why are some Republicans irrationally constrained by identity and some not? To throw an unjustiﬁed “identity constraint” into a rational choice model again suggests ad hoc hypothesis rescue. And how can it be said that the 25 sincere progressive Republicans were harmfully manipulated, given that they won their topranked alternative in the next Congress? Riker is misled because he does not detect that it is the Bristow Republicans making the (failed) strategic maneuver and because he does not understand that N > Q > S is a feasible preference order. That is Riker’s tenth incorrect claim, and the one that gives him his cycle, to assume that all 25 sincere progressive Republicans “presumably” had the preference order N > S > Q. I have shown that there is reason to believe that many did not. Riker also claims (4) that in the 62nd Congress in June 1911 the Democrats had a clear majority and were able to defeat the Sutherland amendment thereby permitting the Constitutional amendment to pass out of the Senate. This is ﬂat wrong. The Republicans were still the majority party in the 62nd Senate. Although the Senate did not vote on the Sutherland amendment in the 62nd Congress, they did vote on the identical Bristow amendment, and they did not defeat Bristow– Sutherland as Riker claims; instead they passed it. Alternatively, Riker claims (11) “A few months later Democrats, now with an absolute majority, could prevent the Depew–Sutherland maneuver. Since over half of Republicans were also in favor of direct election, it was then easy to pass the Seventeenth Amendment, even without the protective clause” (Riker 1986, 17). Again, this is quite wrong. The reader by now will understand that the Depew amendment was not seriously considered in 1911, and that the Bristow–Sutherland “maneuver” succeeded and made possible the passage of the proposed constitutional amendment out of the Senate. And how did the clause protecting the southerners disappear from the resolution except for something like the Bristow–Sutherland amendment? Riker concludes that the case of the 17th Amendment, “is not, I believe, an isolated example of manipulation, but a typical instance” (Riker 1982, 195). His account of the Powell amendment, intended to show harmful manipulation arising from strategic voting, failed because it assumed irrational actors. His account of the Depew amendment, intended to show harmful manipulation arising from the contrived introduction of new

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dimensions, failed again because it assumed irrational actors, and also because of egregious misreadings of the historical record. With the next two cases Riker will attempt to demonstrate a case of grand manipulation. Beginning from the Wilmot Proviso in 1846 and culminating in the election of Lincoln in 1860, he argues, the US Civil War arose in response to arbitrary manipulation of political disequilibrium. If not argumentatively then rhetorically, these two cases sustain Riker’s hypothesis of pervasive disequilibrium. The reader is led to believe not only that cycles happen, not only that democratic politics is arbitrary and meaningless, but also that the most cataclysmic event in American history is an instance of such disequilibrium. The lesson is powerful and unforgettable. It is also wrong.

11

Unmanipulating the manipulation: the Wilmot Proviso

Introduction I begin with a summary of Riker’s two claims of disequilibrium relating to the politics of the Wilmot Proviso. In 1846 President Polk requested an emergency appropriation in effect to commence the acquisition of the northern half of Mexico. The Wilmot Proviso was an amendment moved by northern Democrats in the House of Representatives to prohibit slavery in the lands to be acquired from Mexico. Riker’s ﬁrst claim of disequilibrium is that initially the least-desired alternative of no appropriations and no antislavery proviso prevailed in the House. His second claim of disequilibrium is that there was a cycle among legislators’ preferences among the status quo, the acquisition appropriation, and the appropriation proposal with the antislavery amendment. Then I present a more far-ranging and critical review of Riker’s second claim and then of his ﬁrst claim. The problem with Riker’s second claim is that he misreads the vote in the Congressional record. A corrected reading shows that there was no cycle. The problem with Riker’s ﬁrst claim is that it lacks context. A more thorough investigation discloses that the appropriation initially failed not due to some profound disequilibrium, but rather due to mischiefs and blunders. Finally, I present my own interpretation of the votes in question. By means of analysis of roll-call votes I am able to offer a fresh interpretation of the Wilmot Proviso controversy in Congress, including an explanation of how the Proviso was defeated.

Riker’s story Northern Democrats were annoyed by the southern tilt of the Democratic President Polk, says Riker, and opportunistically reintroduced the slavery issue into national politics. The motives of the northern Democrats are evidenced by Polk’s diary: this “remarkably astute observer, intimately acquainted with events and personalities honestly assessed the slavery issue as opportunism on both sides” (Riker 1982, 224). Wilmot did not care 241

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about slavery, he only wanted to protect free labor from slave competition, and the Wilmot Proviso was devised to protect the northern Democrats against Whig agitation on the slavery issue, according to Riker. The Mexican war was underway, and Polk sought a special two million dollar appropriation in order to bribe the Mexican army to accept a war settlement favorable to American interests. Wilmot moved as an amendment to Polk’s appropriation a provision prohibiting slavery in any territory acquired from Mexico. Almost all northerners voted for the Proviso and almost all southerners voted against it, whether Whig or Democrat. The Whigs, by the way, were the more commercial party, and the Democrats were the more agrarian party, and both parties were bisectional. The outcome involved disequilibrium in two ways, says Riker. There are three alternatives under consideration: OA, the Original Appropriation proposed by Polk WP, the original appropriation as amended by the Wilmot Proviso SQ, the Status Quo, no appropriation. Riker says that Polk almost certainly ordered OA > WP > SQ, and that the Senate had agreed to OA in secret session so that it must have preferred either OA > WP > SQ or OA > SQ > WP. The House did indeed pass WP, which it must have preferred to the alternatives. Riker recounts some estimated rankings of factions in the House that are useless to reiterate here because, as we shall see, they are mistaken. What he is trying to establish at this point is that SQ was the least-desired alternative in the House, which I agree is correct. We can again strengthen Riker’s argument by noting that just as OA was introduced but before WP was offered, several motions with the effect of immediately killing OA failed (Congressional Globe, August 8, 1846: 1212; Voteview Roll-Call Votes, 29th House, #450, #451, #452). The House passed WP, and WP went to the Senate where it was ﬁlibustered by an antiwar northern Whig who top-ranked SQ, and SQ prevailed due to the ﬁlibuster. Thus the least-desired alternative, SQ, won, “clearly an outcome in disequilibrium” (Riker 1982, 225). There was also a second disequilibrium within the House itself, according to Riker. First, by revealed vote a majority in the House ranked WP > OA. The Wilmot amendment to Polk’s appropriation carried. This conclusion is correct (but Riker’s warrant is not, we shall see). Second, OA > SQ, by inference, says Riker: it’s reasonable that the Democrats, a majority in the House, would support their President Polk’s request. This conclusion is correct. As I said, in the August 8, 1846 deliberations leading up to the Wilmot Proviso several motions to table OA failed; and in a clean vote on OA without any Wilmot Proviso on March 3, 1847,

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OA > SQ by a recorded vote of 115 for, all but two of those from Democrats, to 82 against including only ten Democrats (Congressional Globe, March 3, 1847: 573; Voteview, 29th House Roll-Call #637). Third, by inference, says Riker, SQ > WP: a coalition of ﬁrst, all southerners, Democratic or Whig, would oppose WP because it contained the prohibition of slavery, and second, the northern Whigs would oppose WP because it contained an appropriation for a war that the Whig Party opposed. We have WP > OA, OA > SQ, and SQ > WP, or WP > OA > SQ > WP, a cycle. Review Riker further estimates the ranking of the three alternatives by each of eight natural factions in the House, which taken together again conﬁrm the cycle, he says. The ranking estimates, however, are pure fantasy, because Riker’s inference that SQ > WP is directly contradicted by the revealed votes in the record. Riker wrongly believes that the vote he reports of 79 yeas and 93 nays was on adopting the amendment to the original appropriation, WP > OA (“Display 9–1, “The Vote on the Motion to Lay on the Table the Motion to Engross the Wilmot Proviso,” Riker 1982: 226). In fact, the vote that he refers to was on passing the amended appropriation, WP > SQ. There is no doubt that Riker’s estimates of rankings of the eight natural factions is based on mistakenly reading WP > OA for WP > SQ. His listing of the factions’ rankings (227) clearly builds from his Display 9–1 of the misinterpreted vote. The Display asserts that 93 legislators ranked WP > OA and 79 ranked OA > WP, when in fact 93 legislators ranked WP > SQ and 79 ranked SQ > WP. The estimates assert, for example, that seven northern administration Democrats rank OA > WP and 51 northern Free Soil Democrats rank WP > OA, when in fact the vote he references would have his seven northern Democrats voting SQ > WP and his 51 northern Democrats voting WP > SQ. If it is shown by ﬁve revealed votes that WP > SQ, then, I submit, a weakly warranted inference that SQ > WP must be mistaken. If we correct Riker’s error we have WP > OA, OA > SQ, and WP > SQ, or WP > OA > SQ, and no cycle whatsoever. Yes, the great cycle that initiated the disequilibrium that culminated in the Civil War is all based on a simple misreading of the record. The vote he reports is not on tabling engrossment of the Wilmot Proviso (WP > OA) but is on tabling engrossment of the Wilmot-amended appropriation (WP >SQ). Riker (1982, 290) cites to Congressional Globe, 29th Congress, 1st Session, 1218. He says (225) that the Wilmot Proviso was voted on eight times on August 8, 1846, but the largest and crucial vote was on a

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Table 11.1. Datum and warrant, Wilmot Proviso Riker

R. Warrant

Mackie

M. Warrant

WP > OA

Revealed vote “Motion to Lay on the Table the Motion to Engross the Wilmot Proviso,” August 8, 1846∗

WP > OA

OA > SQ

Inference “All Democrats, 60 percent of the House, supported the administration on the war” Inference All southerners, D or W, opposed the WP, and northern Whigs opposed the war WP > OA > SQ > WP

OA > SQ

Revealed vote Two voice votes, August 8, 1846; one recorded vote, February 15, 1847. (Recorded vote March 3, 1847 for OA > WP)∗∗ Revealed vote Three recorded votes, August 8, 1846; one recorded vote, March 3, 1847. Revealed vote Three recorded votes, August 8, 1846; two recorded votes, February 15, 1847. WP > OA > SQ

SQ > WP

Full Rank

WP > SQ

Notes: ∗ Riker’s claim of WP > OA is correct, but his warrant is not. He erroneously believes that the vote he cites is on WP > OA, when in fact it is on WP > SQ. ∗∗ In the end seven northern Democrats changed their votes from yes to no on the Wilmot Proviso (not mentioned in Riker’s story), for sound strategic reasons emergent on March 3, 1847.

motion to lay on the table a motion to engross, which was defeated by 79 to 93. There is not any motion to engross nor any vote resembling 79 yeas to 93 nays on page 1218 of the record. There is a vote to table engrossment on page 1217 of the record, with 78 yeas and 93 nays (Voteview 29th House, Roll-Call #456). Quite clearly this vote is on the whole bill, as are three further votes with the same effect of endorsing WP > SQ on page 1218 (one unrecorded and two recorded, Congressional Globe, August 8, 1846: 1218; Voteview, 29th House, Roll-Calls #457 and #458). The whole controversy replayed again on February 15, 1847, when WP > SQ by a vote of 115 to 106 (Congressional Globe, 425; Voteview, 29th House, Roll-Call #582). Altogether that makes ﬁve revealed votes showing that the House of Representatives ranked WP > SQ. Because I will be doubted, it is probably best to review the parliamentary action, beginning at page 1217. We are in the Committee of the Whole House. McKay, who is carrying Polk’s OA (House Resolution 534A), moves a perfected version. Ingersoll moves a substitute for OA (perhaps to confuse procedurally newcomer Wilmot). Wilmot moves WP,

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his amendment to OA. A point of order is made against WP that it is not germane. The chair overrules the point of order, and his motion is appealed. The decision of the chair is sustained by a teller vote (no recorded names) of 92 to 37; this test vote suggests a majority for WP over OA. Wick moves to amend WP with an extension of the Missouri Compromise: slavery permitted in the southern portion of the new territory but prohibited in the northern portion. The Wick amendment to Wilmot’s amendment fails, with 54 yeas and 89 nays. Then we get to a point of the main action, a vote on Wilmot’s amendment (WP > OA) which passes by teller vote, 83 yeas and 64 nays, “so the amendment was adopted.” Perry offers an amendment to the bill that is rejected. Constable offers an amendment that is rejected. McHenry adds a technical amendment that was adopted with 36 yeas and 0 nays. Hunt, Bell, and Ashmun offer amendments that are rejected. The Ingersoll substitute for OA is in order. Wilmot moves to amend the Ingersoll substitute with his Proviso, and Wilmot’s amendment to Ingersoll passes by teller vote of 77 yeas and 58 nays. The Ingersoll substitute is defeated by voice vote. “The committee, on motion, rose and reported the message, together with the bill to the House. The bill was read a ﬁrst and second time by its title” (emphasis added). The US House of Representatives operates by more time-saving rules when it meets as the Committee of the Whole. The Committee of the Whole works out the wrinkles on an accelerated basis, and then reports its result to the members, meeting as the House of Representatives. The ofﬁcial House functions by more cumbersome and time-consuming rules, and here major controversies may be replayed. The rules of the House also require that a bill be read three times before a vote. This bill was most unusually introduced on behalf of President Polk earlier that day, on the next to the last day of the Congressional session. The next order of business after the amendments are completed, then, is a motion to engross (record) the bill. Tibbatts moves “to lay the whole subject on the table” (emphasis added), and if this motion succeeds the bill is killed (effectively WP against SQ). There was a roll-call vote with 78 yeas and 94 nays. This is the vote that Riker misinterprets as a vote to amend the McKay bill (WP against OA). In fact, it is a vote about the Wilmot-amended McKay bill (WP against SQ), and “the House refused to lay the bill on the table” (emphasis added; WP > SQ). Now that the motion to table has failed, the motion to engross is in order, and a roll-call vote is taken on the motion to engross and it passes 85 yeas and 79 nays (CR page 1219, indicating that WP > SQ). Thus, the motion to engross is adopted and the bill goes to third reading. Now, “the question being on the passage of the bill ” (emphasis added), the vote on the bill is by division of the House (names

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not recorded) with 87 yeas and 64 nays (WP > SQ). Next, Brinkerhoff moves to reconsider the vote by which the bill was passed, and this fails on a recorded vote of 70 yeas and 83 nays (WP > SQ). (An immediate motion to reconsider is offered on controversial measures because otherwise the vote remains open to a reconsideration motion and mischief can thus follow; also, this is probably why, to save time, they took an unrecorded vote on passage, knowing that a recorded vote on reconsideration would be coming next). Altogether there were two unrecorded votes showing WP > OA (strictly speaking, the second of these was WP as an amendment to the Ingersoll substitute which also contained the two million dollar appropriation). There were one unrecorded and three recorded votes showing WP > SQ. Riker mistakenly believes that all six of these votes are about WP > OA, which is nonsensical because the last vote of any bill passing out of the House on its way to the Senate must be against the status quo. Theoretically, any reader should be able to detect the nonsensical error embodied in Riker’s claim that SQ > WP even without going back to check the references to the records of Congress, yet for almost twenty years many intelligent people have repeated this story without reporting the error. I feel that it is my reluctant duty to report a problem with public-choice style of explanation. This style of explanation is often not immediately intuitive yet is gilded with an abstract formalism that suggests that something important and believable is being said. I am not the ﬁrst to suggest that there is no necessary relationship between formalism and profundity, and that it is just as possible that such models obscure as that they reveal. Now, return to the ﬁrst claim of disequilibrium. The story was told in a great hurry, but we need to rerun it again in slow motion and keep our eyes closely on the cards. Riker’s account reads as if the House added the Wilmot Proviso to Polk’s appropriation proposal (OA) at the very last minute, as if the House were up to something hasty and duplicitous that foolishly brought about its bottom-ranked alternative, SQ, no appropriation. The standard history is quite different.1 The 1844 Democratic Party convention could not obtain the requisite two-thirds majority for presumptive candidate former President Martin Van Buren of New York (because he had offended the South by opposing the annexation of Texas) nor other leading ﬁgures, and James Knox Polk of Tennessee emerged as an unexpected compromise ﬁgure, the ﬁrst “dark-horse” presidential nominee in American history. During his campaign Polk forthrightly promised the annexation of Texas and the maximum claim against the British over the Oregon Territory (the famous slogan “Fifty-Four Forty or Fight!” originated after the campaign). Polk

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was the youngest, and most effective, President to that time in the history of the republic, but died three months after ﬁnishing only a single four-year term. The annexation of Texas with a contrived boundary claim that doubled its size sparked war with Mexico, and Polk manufactured provocations so as to make the war of territorial conquest appear to be defensive in nature. Land-hungry expansionist Democrats, especially in the South, supported the war; Whigs opposed it from sincere republican principle, economy, commercial motives, and partisan advantage; and northern abolitionists suspected that the land grab was engineered by the southern slave conspiracy to enlarge southern political and economic power. Radical northern suspicions were not entirely imaginary, for example, the Charleston Courier, in South Carolina, the state that started the Civil War fourteen years later, declared: “Every battle fought in Mexico, and every dollar spent there, but insures the acquisition of territory which must widen the ﬁeld of southern enterprise and power for the future. And the ﬁnal result will be to adjust the whole balance in the [US], so as to give us control over the operations of the Government in all time to come” ( Jay 1849, 182). Along his forceful way Polk alienated a number of factions in the northern wing of the Democratic Party who began to accuse the administration of a southern tilt. Polk promoted the annexation of Texas, precipitating war with Mexico, but when it came to the Oregon Territory he compromised with Great Britain on what is now the present boundary at 49 degrees of latitude, giving up what is now southwestern Canada. Since the United States couldn’t afford two major wars, by committing to war with Mexico, Polk made it impossible to pressure credibly the British in the present-day Northwest, which annoyed Democrats in the Midwest (what is called today the Midwest was in 1846 called the Northwest, e.g., Northwestern University in Chicago, but to reduce confusion I shall anachronistically label the area the Midwest) who wanted opportunities in the northwestern direction. A midwestern Democratic senator complained: Texas and Oregon were born in the same instant, nursed and cradled in the same cradle [the Democratic Party Convention] . . . There was not a moment’s hesitation, until Texas was admitted; but the moment she was admitted the peculiar [an allusion to the south’s “peculiar institution,” slavery] friends of Texas turned and were doing all they could to strangle Oregon. (quoted in Morrison 1967, 12)

When the Oregon treaty with Great Britain came to the Senate for ratiﬁcation (requiring a two-thirds vote), 13 out of 16 northern Democrats deserted Polk and voted against it. The treaty was saved by the unanimous vote of the Whigs in its favor, who supported it because they disfavored

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war and expansion, and by 15 out of 16 southern Democrats who wanted to secure the northern ﬂank so as to attack what was then upper Mexico to the south (Voteview, 29th Senate, Roll-Call #114, June 18, 1846). Since the southern slave interests also had annexationist designs on the remainder of Mexico, Central America, and the Caribbean, in contemporaries’ eyes the Mexican War had unknown implications for the future character of the republic. To further sweeten the British, Polk fought for and won lower tariffs on imported goods, a traditional Democratic goal, but one which endangered some northern Democrats from industrial areas, particularly Pennsylvania; and some northerners believed that Polk had obtained the acquiescence of the antislavery British to the annexation of Texas as a slave state by going easy in Oregon negotiations and by promising them to lower tariffs on British goods. Polk snubbed Van Buren on federal patronage appointments and also seemed otherwise to support the competing faction in Van Buren’s New York Democratic Party. Polk managed to make the Mexican War an accomplished fact, and New England Democrats resented having to vote for Polk’s war appropriations. The Whigs, who opposed the war on principle, also at times felt compelled to provide votes from their own ranks to pass war authorizations and appropriations (e.g., HR 145, to prosecute war against Mexico, passed 174 to 14 in the House, Voteview, 29th House, Roll-Call # 72, May 12, 1846; and passed 40 to 2 in the Senate, Voteview, 29th Senate, Roll-Call #218, May 13, 1846). This is not as peculiar as it seems on ﬁrst glance. Just as, for example, with the Vietnam War, antiwar legislators needed to support the valiant troops in the ﬁeld, which included Whig generals and the sons of leading Whig Congressmen. The Whigs’ forerunners, the Federalist Party, not only opposed but actively obstructed Madison’s prosecution of the War of 1812, and the popular contempt that followed was the ﬁnal death blow to the ailing Federalist coalition; a lesson the Whigs kept clearly in mind. Similarly, the Whigs wanted to avoid blame should the war they opposed end in defeat, as they initially expected it might. This is where Riker’s inference of SQ > WP went wrong; yes, the Whigs opposed the war, but no, they would not vote to end the war if their votes were decisive; they spoke of a right to oppose the President but a duty to support the country. Further, a bill to favor a popular midwestern cause by lowering the sale price of public lands was kept alive while Polk still needed the votes of midwestern Democrats to win his tariff reduction bill, but once Polk won the tariff reduction, he had the lands bill killed. Finally, the midwestern Democrats also would be the major beneﬁciaries of the usual rivers and harbors bill (aka “pork”) because improvements in public transportation

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249

increased their markets to the east, to the south, and thence overseas, but Polk successfully vetoed that measure. Riker accepts Polk’s own account of matters without comparing that to the accounts of other participants, which is not the way to do history. The point is not that Polk was right or wrong, but that Polk’s was one viewpoint among many. Yes, Polk thought that the ﬁgures on either side of the slavery agitation were insincere opportunists, but it is evident from his diary that Polk was richly endowed with that human propensity that sees one’s own actions as motivated by lofty principle and the actions of one’s opponents as motivated by mundane interests. For Polk, to oppose his views was to be insincere. Further, Polk’s biographer (Sellers 1966, 487) comments that for reasons of age and background he “was not remotely equipped to understand the emotions men brought to the emerging slavery controversy.” By the end of the Congressional session in August, 1846, Polk had pursued traditional party goals so effectively that those Democratic factions that needed partial or ineffective accomplishment of one or another of the party’s goals were damaged. A more incompetent president would have been less resented. Polk was not a likable man either. In the words of the strange yet perfectly accurate song, “James K. Polk,” by the rock-music group They Might be Giants, the Napoleon of the stump was “austere, severe, he held few people dear.” Polk’s biographer describes the sentiment in Congress as “a spreading feeling that the President was congenitally disingenuous and manipulative in his methods” (Sellers 1966, 478). Churchill Cambreleng, Polk’s former Congressional colleague, complained: Heaven forgive me for having any hand in laying the foundations of this blundering administration. Tyler was bad enough, but he had this advantage – there was no mock mystery nor genuine duplicity in his conduct – if he betrayed his friends he was an honest knave, without any hypocritical cant about the sabbath &c &c. (quoted in Sellers 1966, 478)

So it was not that Polk was the one honest man in a sea of manipulators, as in Riker’s account, but rather that all concerned acted from composite motivations of principle and interest. The two houses had resolved to adjourn the Congressional session on Monday, August 10 at noon. Polk had freshly betrayed his friends in the ﬁnal week of the session, and then he sprung a new surprise. One pretext for the war against Mexico was that it owed large debts to American interests that it was unable to repay. The prowar faction thought that the Mexicans could repay by ceding land. No Mexican government could cede land without the political support of its army though, and

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Polk wanted two million dollars to bribe the unpaid Mexican army as a down-payment on full settlement of the war on American terms. On August 4 he secretly asked this of the Senate, responsible for foreign affairs, which gave its approval, but Whigs in the Senate demanded that he also consult the House, responsible for appropriations. Polk wanted secrecy both to preserve his advantage with Mexico and to avoid public controversy at home since the request would involve the ﬁrst formal admission that territorial conquest rather than defense was the object of the war (informally that was plain, since Polk had already seized roughly what is now the southwestern United States – Colorado, New Mexico, Utah, Arizona, Nevada, and California – his main objective). On August 6 a bill to admit the Oregon Territory was in the House, and Thompson, a protariff Democrat from Pennsylvania, moved an amendment to prohibit slavery in the territory, using the identical language that founder and southern Democrat Thomas Jefferson had written to prohibit slavery in territories in the Ordinance of 1787. Thompson’s amendment passed resoundingly and even received a few southern votes (but was not acted upon by the Senate in that session). On Saturday, August 8, on a miserably hot Washington afternoon, a special message arrived in the House from the President. It was Polk’s request for two million dollars for extraordinary expenses relating to the Mexican War, and in his message Polk mentioned that the funds would be payment for concessions on “adjustment of a boundary between the two republics.” The cat was out of the bag. It quite naturally occurred to the disgruntled factions of northern Democrats that they could offer an antislavery amendment on Polk’s measure just as had been done with Oregon two days before, and thereby have their revenge on Polk. Wilmot had been an administration loyalist, but was sure to suffer at home for being the only Pennsylvanian to vote for Polk’s tariff reduction, with nothing in exchange for his loyalty. When the bill came to the ﬂoor that evening, in an atmosphere of heat, disorder, and drunkenness, the northern Whigs signaled the play to the northern Democrats. The northern Whigs said they could not support the appropriation unless the bill were amended to prohibit slavery in the acquired territory, and invited the Democrats to offer such an amendment. Wilmot offered his amendment, and it was passed by voice votes. Then the amended appropriation passed the House on several recorded votes, as we have already reviewed. The House bill was brought to the ﬂoor of the Senate on the morning of Monday, August 10 about 40 minutes before scheduled adjournment at noon. An amendment was moved to strike the Wilmot Proviso, which some say might have succeeded, and then the original Polk proposal could have been hurried back to the House for its concurrence. But Senator John Davis, Whig of Massachusetts, and

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one of the two senators who had voted against the ﬁrst bill to authorize the Mexican War, began an unhurried discussion of the issues. His plan may have been to delay the Senate to the last minute so that it would have no choice but to accept the House bill as is, with the Wilmot Proviso (several contemporaries believed that the Senate would have passed WP > SQ anyway), or his plan may have been the defeatist goal SQ (either way Davis was reviled by all responsible opinion). The clock in the Senate was eight minutes slower than the clock in the House, however, so when Davis would have been ready to yield the ﬂoor back for a vote in the Senate, the House had already adjourned, which technically ended the session for the Senate as well. The status quo, the least-favored alternative among Polk, the House, and the Senate, had prevailed. This was not the product of some profound political disequilibrium, however. It came about as a result of Polk’s deliberately befuddling last-minute tactics, antimajoritarian ﬁlibuster, and because of an exhausted blunder arising from unsynchronized timepieces. Alternative interpretation Now for an alternative interpretation of the voting on the Wilmot Proviso and Mexican War appropriations. We have four sets of data. First, OA > SQ, as shown by four votes at two different times. Votes to table OA failed on August 8, 1846 (Voteview Roll-Calls, 29th House, #450, #451, #452) showing that the House favored OA > SQ. Again on March 3, 1847 a vote was recorded on whether to adopt Polk’s three million dollar appropriation without the Wilmot Proviso and the motion passed (OA > SQ, Voteview, 29th House, Roll-Call #637). Second, WP > SQ, as shown by ﬁve votes at two different times. The vote on August 8, 1846 on whether to adopt the Wilmot-amended war appropriations passed (WP > SQ, Congressional Globe, 1st Session: 1217– 1218; Voteview, 29th House, Roll-Call #456, motion to table defeated with 79 yeas and 93 nays, also Roll-Calls #457 and #458). In the 2nd Session of the 29th Congress the whole issue replayed on February 15, 1847 and again Wilmot-amended war appropriations beat the status quo on two recorded votes (WP > SQ, Congressional Globe 425; Voteview 29th House, Roll-Calls #581 and #582). Third, WP > OA, as shown by three votes at two different times. The Wilmot amendment to Polk’s war appropriations was adopted by voice votes on August 8, 1846 (WP > OA, 92 yeas to 37 nays, and 83 yeas to 64 nays, Congressional Globe, 29th Congress, 1st Session: 1217). That was in the 1st Session, and in the 2nd Session replay on February 15, 1847 a roll-call vote on a Wilmot Proviso to Polk’s new request for war

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appropriations was recorded (WP > OA , Voteview, 29th House, Roll-Call #580, 115 yeas to 106 nays). Fourth, OA > WP, as shown only on the last vote. On March 3, 1847 a motion to adopt the Wilmot amendment to Polk’s war appropriations failed (OA > WP, Voteview, 29th House, Roll-Call #635). From the ﬁrst, second, and third sets of data it is apparent that the House of Representatives ranked the three alternatives WP > OA > SQ, and thus that there was no cycle. There is an explanation for the reversal in the fourth set of data, that we will get to shortly. Riker was able to obtain his cycle on the weakly warranted inference that SQ > WP. His argument was that because the northern Whigs opposed the war they would never support a war appropriation even with an antislavery amendment, but in fact they voted this way three times, once in August 1846 and twice in February 1847. There are sufﬁcient data to recover most legislators’ preference rankings. That would be like killing a mosquito with a ﬂame-thrower, however, and it is enough to look at the behavior of natural blocs of voters. There were more northerners than southerners in the House of Representatives, and more Democrats than Whigs. In the 29th Congress there were 87 northern Democrats, 63 southern Democrats, 59 northern Whigs, and 25 southern Whigs, according to Voteview. It is clear both from voting patterns and ideologies that the southern Democrats ranked OA > SQ > WP, and that the southern Whigs ranked SQ > OA > WP. We know from the ﬁrst and third collections of votes and from ideology that the northern Whigs ranked SQ > OA and WP > OA in both 1846 and 1847; and from the second collection of votes that they ranked WP > SQ in both 1846 and 1847; thus, they were WP > SQ > OA. The northern Democrats were split into three camps, presented in increasing order of their opposition to expansion of slavery into the new territories. The ﬁrst camp, about a dozen in number, were geographically proximate to the southern Democrats and had the same ranking as they, OA > SQ > WP, and hereinafter I shall exclude this camp from the northern Democrats and include them in the southern Democrats. The second, loyalist, camp were the prowar yet antislavery northern supporters of Polk, who ranked WP > OA > SQ, and made up the bulk of the northern Democrats. The third, antiwar and antislavery, camp, about a dozen in number, had the same ranking as the northern Whigs, WP > SQ > OA. The Whigs opposed the war, and voted against it whenever possible, but they were always careful not to obstruct the war, for the reasons mentioned above. Opposition to the war was a party position, and different factions had different reasons to oppose the war; the northern Whigs opposed it in large part because they opposed the expansion of slavery into

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new territories. Therefore, if the northern Whigs were to contribute to the decisive outcome, they would opt for WP > SQ because WP would thwart both the Democratic President and the southern slavery interests, but SQ would undesirably position them as defeatists. Their antislavery constituents understood their vote WP > OA, but demanded to know why they voted for the Wilmot-amended war appropriations, WP > SQ. A contemporary explained: It may however, be asked with what propriety they could vote for an appropriation even with the proviso, which they themselves contended was to be used for the purposes of bribery and corruption. To this question they gave a far more satisfactory answer, than they ever returned to the question why they [had earlier] voted for a war which they denounced as iniquitous. Mr. Stewart of Pennsylvania, thus ably vindicated the policy and duty of voting for the appropriation with the proviso: “As a friend of peace, present and prospective, I am in favor of this proviso. The object of this war being the acquisition of southern territory, as long as there is a hope of accomplishing this object, there will be no peace. Put an end to this hope; and you at once put an end to the war, by defeating its object. The moment the President ﬁnds this proviso accompanying this grant of money, he will be for making peace, and so will all the South. They want no restricted territory. If the restriction is imposed, and the territory acquired is to be free, from that moment the President would pay Mexico to keep her territory, rather than bring it in on such conditions . . . impose this restriction and the war will be promptly ended.” Jay (1849, 186)

Stewart was ungenerous about Polk’s motives, which were genuinely nationalistic rather than sectional, but Stewart reﬂected the beliefs at the time of intensely antislavery northerners about the purposes of the war. I hypothesize, therefore, that in August, 1846, the northern Democrats expected that the northern Whigs would support WP > SQ and also, of course, that the northern Whigs would vote WP > OA. The northern Democrats could also be sure that if the vote were between OA and SQ, then the northern and southern Democrats together could ensure OA > SQ against the Whigs. That put the northern Democrats in the pivotal position between WP and OA so that by voting their sincere position WP > OA, although they would repel southern Democrats, they would attract enough northern Whigs to carry the war appropriation they needed with the bonus of an antislavery amendment; they could win their ﬁrst-ranked alternative. There is no incentive to vote strategically in the last stage of an agenda sequence when an alternative faces the status quo (WP against Q, or OA against Q); therefore, all votes were sincere in August 1846 (and in the vote with identical issues and outcomes in February 1847). Davis had ﬁlibustered in the Senate reportedly on the belief that WP would not have passed there, but no less an authority than

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Lewis Cass (D-MI), chair of the Military Affairs Committee and leader of the prowar forces in the Senate, believed that WP might have passed if it had come to a vote in the Senate, and at that time said he was disappointed that he was denied the chance to vote in its favor (Morrison, 1967, 28). Wilmot also said that public opinion and informed judgment considered that WP would have passed in the Senate on August 10, 1846 (Congressional Globe, February 8, 1847: 352). Incidentally, this is contrary to Riker’s unwarranted assertion that the Senate must have top-ranked OA (in secret session on August 4 they had voted OA > SQ, but WP was not on the table then). Certainly OA and perhaps WP could have been enacted by both chambers, but thanks to the blunder of the clocks, things didn’t turn out exactly as planned. On two separate occasions the House adopted the Wilmot amendment (WP > OA), once by two voice votes on August 8, 1846 and again by recorded vote on February 15, 1847, 115 yeas to 106 nays. From the recorded vote it is apparent that both the antislavery northern Democrats (WP > OA > SQ) and the antislavery and antiwar northern Democrats (WP > SQ > OA) voted to adopt the Wilmot amendment (WP > OA ). But on March 3, 1847, the third occasion, the House defeated the Wilmot amendment (OA > WP), 97 yeas and 102 nays. This would only be possible due to strategic abstentions or to vote changes between February and March. We have a very clean comparison between the WP against OA votes on February 15, 1847 and on March 3, 1847. Contemporaries alleged strategic abstention in March, but analysis of the two votes shows nothing unusual about the patterns of those not voting: about ten voters who voted yes in February did not vote in March and about ten voters who voted no in February did not vote in March. We can identify exactly the seven legislators who changed their votes from yea in February to nay in March and who thereby changed the outcome (the March outcome was 97 < 102; if the seven had not changed from February it would have been 97 + 7 = 104 > 95 = 102 – 7). They were Edsall (NJ), Foster (PA), Garvin (PA), Henley (IN), Russell (NY), J. Thompson (PA), Woodworth (NY); all were northern Democrats of the type WP > OA > SQ. To explain the reversal we have to backtrack to the commencement of the 2nd Session of the 29th Congress in December, 1846.2 The more powerful incentives of intraparty unity suppressed the divisive sectional issue. Wilmot’s Proviso attracted almost no public attention upon its introduction and was ignored in the 1846 elections. Polk, a slave-owner but no slavery ideologue, thought that the Wilmot Proviso was unfair to the South and more practically that it would depress needed southern political support for annexations of the territory about to be gained. Although the administration’s newspaper seemed to acquiesce to the

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Wilmot Proviso at the end of the 1st Session, by the beginning of the 2nd Session Polk had decided not to seek the bribery appropriation unless he could attain it without the antislavery amendment. Polk called in Wilmot, persuaded Wilmot that Polk was sincere about not extending slavery, beseeched Wilmot not to offer his Proviso, and Wilmot agreed to introduce his measure as a joint resolution apart from the appropriations question. Wilmot later said that Polk had offered him an ambassadorship in exchange for his cooperation (Morrison 1967, 188). The President also called in Cass (the prowar leader who had indicated support and success in the Senate for the Proviso) and two other leading senators to seek their cooperation, but they were not encouraging, or perhaps Cass was playing hard to get. The more intensely antislavery northern Democrats, led by Preston King (D-NY), quietly sought to revive the issue in the new session, but their brethren, like their President, Polk, wanted to avoid exploitation by the Whigs, and preferred to accomplish annexation ﬁrst and antislavery second as separate issues. Root, a Whig from Ohio, asked whether the northern Democrats could trust Polk. They had trusted him on Oregon, but he betrayed them by making a deal with the British that limited northern expansion in order to enable southern expansion. Would they now trust him to forge a treaty with Mexico? Polk could write a treaty with the Mexicans that permitted slavery in the conquered territories, present it as an accomplished fact to the more compliant Senate (with sole power to ratify treaties), and the House would have nothing to say about the matter (Congressional Globe, December 26, 1846: 88). The Whig taunts lashed raw nerves among the northern Democrats. On January 4, 1847, Democrat King deﬁed the administration and sought to reintroduce the Wilmot Proviso (WP > SQ) from the ﬂoor of the House, but failed with 88 northern yeas and 89 southern nays (Congressional Globe, 105; Voteview, 29th House, #105, mislabeled in Voteview as a vote on “Expenses of China Relations”). King gave a speech on the ﬂoor the next day, which triggered an avalanche of controversy. Then the Oregon bill with its antislavery proviso came up again in the House, and intensely proslavery southerners sought to amend it to the effect of extending the line of the Missouri Compromise (36 degrees, 30 minutes) to the Paciﬁc. The southern maneuver was fresh evidence of southern intentions for the new territory and breached the understanding among Democrats that annexation would be undertaken prior to and separate from the slavery issue. Northerners in the House united to defeat the southern maneuver on Oregon. As the session proceeded Wilmot came to the conclusion that the Polk forces would prevent consideration of the promised joint resolution on slavery in the territories, so that he had no alternative but to propose a proviso again when Polk’s

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request for a bribery appropriation came to the ﬂoor. After a week of passionate and excited debate, on February 15, 1847 a Wilmot-amended appropriation passed the House despite all of Polk’s carrots and sticks. But Polk had more success in the Senate; the authoritative Cass converted to Polk’s position. Cass considered the expansion issue to be more important than the slavery issue, wanted to avoid division in the Democratic Party because of his presidential ambitions (he would be the Democratic nominee in 1848), and if Polk had offered neophyte Wilmot an ambassadorship who knows what he offered to the more prominent Cass. During Senate deliberations of Polk’s request on March 1, 1847, a northern Whig proposed the Wilmot Proviso (WP > OA; Voteview, 29th Senate, Roll-Call #356). All southern Whigs and all southern Democrats voted against the antislavery amendment; all but two northern Whigs voted for the antislavery amendment, but the northern Democrats divided seven to seven, and we can speculate that Polk must have provided powerful private inducements as well. Missouri is sometimes confusing as it was a minor slave state but is usually also counted as a northern state; its two senators voted against the Wilmot Proviso. The remaining ﬁve votes were from Cass of Michigan, one senator from Illinois, two from Indiana, and one from New York. Now the Senate measure immediately came to the House on March 3, the last day of the 29th Congress. It would be nine long months before the 30th Congress would meet and apparently Polk had provided secret information that the bribery appropriation was now urgently needed to attain peace, a goal no one could oppose. At this point the House’s ranking was WP > OA > SQ and the Senate’s expressed ranking was OA > WP > SQ. The House could either concur with the Senate’s OA and attain its second-ranked alternative or by refusing to concur it could choose its least desired alternative, SQ, by inaction. Polk was busy with “persuasion” in the House as well; an antislavery contemporary says that “the whole inﬂuence of the Government, and all the appliances of party discipline, were now put in place to induce the House to concur with the Senate” (Jay, 1849, 191). So on March 3, 1847, seven northern Democrats changed from yea to nay on the Wilmot Proviso and it was killed, and then the House concurred with the Senate and Polk’s appropriation was attained. Antislavery forces charged that the seven were compensated, and there is surely some truth to this, but we must also notice that, given the urgency of decision and the Senate’s insistence on OA, it would be rational for sufﬁcient Northern Democrats of the type WP > OA > SQ to vote strategically against WP in order that their second-ranked outcome, OA, should prevail rather than their last-ranked outcome, SQ. One of the seven, Wentworth of New York, printed an explanation in the record

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(Congressional Globe, 29th Congress, 2nd Session: Appendix, 438–439). He is explicit that his vote is strategic: “I have changed no principle but have embraced expediency.” He fears that: My motives in so doing will be misrepresented and my conduct denounced. My vote will be ascribed to corrupt considerations. Those who, in my place, would not have hesitated to ask payment in advance for their vote, will be the ﬁrst, and most eager to calumniate me . . . I neither seek, nor want, ofﬁce. I am no supplicant for Executive favors.

Wentworth’s explanation is eloquent and apparently sincere. He says he is motivated by a desire for a swift and successful end to the war, which has claimed several thousand American lives. He says that when he voted for the Wilmot Proviso two weeks previously he gave notice that he would support whatever measure came from the Senate. He says that in the future he will vote for proposals to prohibit slavery in the territories, but that in this instance he must vote strategically, and that he will succeed in defending his vote to his antislavery constituents. Riker’s ﬁrst story about arbitrary manipulation of a cycle initiating the events that led to the Civil War fails. His second story, about the election of Lincoln in 1860 is the subject of the next chapter.

12

Unmanipulating the manipulation: the election of Lincoln

1. Introduction

By way of background, Riker’s overarching hypothesis is that the slavery dimension of concern was suppressed by the Democratic Party manipulative elite with the Missouri Compromise of 1820. The main dimension of contention between the Democrats and the Whigs, both bisectional parties, was economic, broadly speaking the Democratic coalition was agrarian, and the Whig coalition was commercial in orientation. Another manipulative elite, the northern wing of the Whigs, the weaker party in this period, sought to ﬁnd an issue that would split the Democrats and thereby allow the northern Whigs to organize a newly dominant coalition. The Wilmot Proviso in 1846 was their ﬁrst effort to contrive a cycle, and the election of Lincoln in 1860 was their last and most successful effort at contriving a cycle. There is much that is wrong about this story, but that is for the next chapter. In this chapter we ﬁrst examine Riker’s analysis of the 1860 presidential election. Riker estimates the preferences among the population over the four candidates. These estimates show both that there was a cycle among the top three candidates and that different hypothetical voting rules would yield different outcomes. This is the perfect illustration of Riker’s contentions that democracy is meaningless and arbitrary and that manipulation is probable on grand issues. I relate the histories and the ideologies of the four parties in the runup to the 1860 election. The ideologies of the four parties suggest a unidimensional and noncyclical distribution of preferences, with the question of slavery in the territories being the primary dimension of dispute in the election. County-level, state-level, and region-level aggregates further support the hypothesis of noncyclicity. Riker’s demonstration of meaningless and arbitrary outcomes depends on an unwarranted estimate that Bell, the candidate of the Upper South who received 2 percent of the vote in the North, was ranked second by more than 63 percent of Lincoln voters. If, as was far more likely, Douglas, the candidate of the Lower North, was ranked 258

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second by more than 37 percent of Lincoln voters, then most voting methods considered yield the same ranking, and all yield the same winner: Douglas.

2. Riker’s analysis of the 1860 election

There were four major candidates in the American presidential election of 1860. They were Abraham Lincoln, the nominee of the six-year-old northern political alliance known as the Republican Party; Stephen A. Douglas, the candidate of the northern wing of the Democratic Party; John Bell, from the recently formed Constitutional Unionist Party, an attempt at a conservative centrist coalition with its base in the upper south; and John C. Breckinridge, Vice President in the outgoing Buchanan administration and candidate of the renegade southern wing of the Democratic Party. The election of Lincoln as President in 1860 was a replay of the disequilibrium of the Wilmot Proviso, says Riker (1982, 228). Lincoln won by a plurality of about 40 percent, he continues, and so one must suspect a cycle. Riker displays 15 of the possible 24 rankings possible for strong preferences over four candidates and then estimates the total number of voters across the nation for each of the 15 likely rankings (each ranking total is the sum of regional subtotals that he does not display). From the voting data we know only the ﬁrst-ranked choices of the voters, so, as Riker explains, his estimation of the rankings over the remaining three choices in each of the 15 cases is intended as an informed historical judgment (he calls them “guesses,” but presumably they are not arbitrary or he would not have bothered to present them). Fair enough. The estimation of full rankings then permits the calculation of hypothetical outcomes by alternative voting rules. The results seem to conﬁrm Riker’s thesis that democracy is arbitrary and meaningless. Different voting rules lead to different outcomes, and pairwise comparison (the Condorcet criterion) discloses the presence of a cycle. Here are Riker’s results: r Plurality: Lincoln > Douglas > Breckinridge > Bell r Pairwise Comparison: (Douglas > Lincoln > Bell > Douglas) > Breckinridge r Borda Count: Douglas > Bell > Lincoln > Breckinridge r Approval Voting (two votes): Bell > Lincoln > Douglas > Breckinridge r Approval Voting (three votes): Douglas > Bell > Lincoln > Breckinridge. Riker concludes that with ﬁve methods of voting Douglas wins twice, Bell once, Lincoln once, and they are in a cycle and hence tie once. “Clearly,

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if my guesses are even roughly right, there was complete disequilibrium in 1860” (1982, 229). Riker’s demonstrations of disequilibria in the Wilmot Proviso and in the election of 1860 are the primary evidence for his inﬂuential theory of political disequilibrium and are widely accepted and repeated in the political science discipline today. We have seen that he was in error about the Wilmot Proviso and now we shall see that he was in error about the election of 1860 as well. His Display 9–2, “Possible Preference Orders in 1860, by Candidate of First Choice and by Region,” which lists his estimates of full preference rankings for the entire electorate, is daunting to the reader. Except for a few words about the regional breakdown of each ranking in the display itself, there is no textual justiﬁcation for the ranking estimates. They are presented as authoritative, and one could only check them by deep immersion in the history of the period. Fortunately, we need not sweat through all 15 rankings to detect the error, because it occurs in the ﬁrst 2 rankings he lists. These two categories are the estimated full rankings of all those whom we know ranked Lincoln ﬁrst. Moreover, the two rankings contain 40 percent of the voting population of the entire country, so if there is a major error among them then we need go no further. Riker’s ﬁrst group is 450,000 voters who prefer Lincoln > Douglas > Bell > Breckinridge and they are made up of onefourth of New England, mid-Atlantic, and midwest Lincoln voters; and all southern Lincoln voters. The second group is 1,414,000 voters who prefer Lincoln > Bell > Douglas > Breckinridge, and they are made up of three-fourths of New England, mid-Atlantic, and midwest Lincoln voters; and all border and western Lincoln voters. The problem is with these two estimates. The large majority of Lincoln voters did not rank Bell second, as Riker claims; they ranked Douglas second, and once we understand this error Riker’s demonstration collapses. For ease of exposition, henceforth ignore Riker’s inclusion of southern, border, and western Lincoln voters in the two rankings under consideration, as they represent about 5 percent of his total in the two rankings and don’t change anything in either his analysis or mine. Reconstructing Riker’s data, he has it that about 1,794,000 voters in the free north (excluding the northern slave state Missouri, border states, and Oregon and California in the west) voted for Lincoln, and he is correct enough on that. His further claim is that of those, one-fourth or about 450,000 ranked Douglas second, and three-fourths or about 1,346,000 ranked Bell second. I claim that it is just the reverse, that most, let’s say threefourths or more, of Lincoln voters ranked Douglas second, and few, say one-fourth or less, rank Bell second.

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3. The four parties

Who were the four parties and what did they stand for? To understand, we need to go back to the Missouri Compromise of 1820 which admitted Missouri as a slave state but divided the remainder of the immense Louisiana Territory at parallel 36 degrees and 30 minutes, with slavery prohibited north of that boundary.1 The gaining of the huge Oregon and Mexican territories in the late 1840s reawakened dormant sectional tensions over the question of slavery in the new possessions. Controversy intensiﬁed over four years from the introduction of the Wilmot Proviso in 1846, which proposed to prohibit slavery in the new territories acquired from Mexico, to the adoption of the Compromise of 1850, which one historian (Potter 1976, 90) quipped would better be named the Armistice of 1850. Among other elements of the Compromise of 1850, a law was enacted to force northern governments to return runaway slaves to their owners in the south, California was admitted as a free state, the Wilmot Proviso was squelched, and in its place for the territories that are roughly now Nevada, Utah, Arizona, and New Mexico the so-called doctrine of popular sovereignty was enacted: states organized from those territories would be free or slave as their citizens might decide. The Missouri Compromise remained in force for the Louisiana Purchase. Then in 1854, for interesting reasons that can’t detain us here, leading northern Democratic Senator Douglas won from Congress the Kansas–Nebraska Act, which organized the Kansas and Nebraska territories on the principle of popular sovereignty thereby abrogating the Missouri Compromise. This ignited anger in the North and split the northern Democrats. Meanwhile, in 1848, the Whigs, who had been weakened by their opposition to the hugely successful Mexican War, selected war hero and slave-owner Zachary Taylor (who did not know he was a Whig until tapped) as their presidential candidate. At the same time, former President Van Buren left the Democratic Party to become the candidate of the new Free Soil Party, which opposed slavery in the territories, but did not support abolition of slavery where it was found in the slave states nor necessarily equal treatment for African–Americans. Taylor won the election, and the few Free Soil votes did not affect the outcome. Taylor was a nationalist, not a sectionalist, and he took New Yorker William H. Seward as a principal adviser, a powerful and talented man but a leading opponent of slavery. Taylor, who died in midterm (Vice President Millard Fillmore took his place), weakened the Whig Party in the South. Southern Whigs felt that he betrayed them on regional issues, for example, by admitting California as a free state; the southern Democrats proved more zealous than the southern Whigs in pursuit of sectional interests;

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and popular northern resistance to the new Fugitive Slave Law was an incentive for northern Whigs to become more vociferously antislavery in their outlook, offending their southern colleagues. The Whig convention of 1852 deadlocked along sectional lines, and ﬁnally selected the northerners’ choice, Winﬁeld Scott, like Taylor a southerner and a war hero. The southern Whigs suspected that, like Taylor, Scott would betray them; Scott lost in the south, some southern Whigs migrated to the Democrats, and the Whig Party became all but dead in the South. The Democrats ran Franklin Pierce, a northerner who endorsed the Compromise of 1850 and denounced the abolitionists who opposed that compromise. As a result of Whig weakness in the south, Democrats were victorious in the Presidential and Congressional elections of 1852. The northern population grew rapidly between 1820 and 1860 due to high natural increase and to high immigration.2 New immigrants and their immediate descendants were 19 percent of the northern white male labor force in 1820 and 46 percent in 1860. The high rates of population growth meant that labor markets were frequently glutted. Immigration to the North exploded further after the Irish famine of 1845–1847 and the crushed revolutions of 1848 in Europe, and climaxed in 1854. Much of society beneﬁted from rapid economic growth, but native-born white artisans and their shopkeepers, about 25 percent of the northern population, experienced a “hidden depression”; from 1848 to 1855 they suffered a 25 percent to 50 percent decline in real wages. There was inﬂation in the same period, and a long northern recession from 1853 to 1855 as well. Due to urbanization and consequent epidemic disease, northern life expectancies from 1790 to 1850 declined by 50 percent. The new immigrants tended to be Catholic and vote Democratic against the Whig establishment. Natives of native-born parents were 62 percent of the northern Democratic vote in 1852, but 39 percent in 1860; naturalized males made up 10 percent of the northern presidential vote in 1840, 14 percent in 1852, and 25 percent in 1860. Native northern workers responded politically, but could ﬁnd no succor with the Northern Democrats, always the party of immigrants, nor with the Northern Whigs, the party of the bosses who got rich off immigrants. The nativists were without a political home. The 32nd Congress passed the Kansas–Nebraska Act abrogating the Missouri Compromise. In the same Congress, the Democrats, who had always favored a cheap land policy, abruptly turned against it, quite simply because southern Democrats realized that cheap land was increasing the population and prosperity of the north and west and thereby threatening traditional southern control over the federal government. The abolitionists had unsuccessfully alleged a Great Slave Conspiracy from around 1845, but the Democrats’ betrayal on Kansas–Nebraska and cheap land

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in 1854 suddenly made the charge plausible among northern workers, who now feared an invasion of the already distressed northern labor markets by slave labor. This set the stage for a nativist political upsurge, and the merger of nativist and antislavery concerns. In 1852 the southern wing of the Whig Party was decimated over the national party’s apparent betrayal of its interests; and in 1854 the northern wing of the Democratic Party began to bleed away. Northern Democrats suffered in the elections of 1854 after the treacheries of Kansas–Nebraska and defeated cheap land. Of the 91 incumbent free-state Democrats in the House of Representatives, 66 went down to defeat; of the 44 who had voted for Kansas–Nebraska only seven survived the election. The Democratic Party, already a bit tilted to the South, became even more southern as unhappy northerners exited. In the next Congress, southern Democrats outnumbered northern Democrats by two to one. The Kansas–Nebraska Act added bolting antislavery northern Democrats to the bubbling soup of factions adrift – abolitionists, Free Soilers, northern Whigs, nativists. In 1854 and 1855 the nativist American Party (aka the “Know-Nothings”) seemed to be the force that would replace the Whigs as the party opposing the Democrats. They swept local and state ofﬁces in Massachusetts in 1854. They were the dominant opposition in the key northern states; the Free Soilers were the lead opposition in only a few. All that changed in 1856. The Free Soilers succeeded in splitting the Americans into proslavery and antislavery wings, and harvested from the antislavery faction. At the same time immigration dropped by half from 1854 to 1856, inﬂation ended, and real wages increased. The various “anti-Nebraska” groupings slowly coalesced locally and nationally into the new Republican Party. After a protracted stalemate in 1856, the nascent Republican coalition elected a nativist the Speaker of the House on a plurality vote, and by 1860 the northern Americans were fully absorbed into the Republicans, who became the victorious opposition. Republican policy and practice made subterranean appeals against the twin despotisms of slavery and papery, but repudiated explicit nativist proposals (a party that proposes that a signiﬁcant portion of those who have the vote shall have it taken away cannot long be successful). Fogel (1992, 229–230) emphasizes that the salience of slavery over nativism in 1860 was quite contingent. If the Panic of 1857 had been extended, if immigration rates had returned to 1854 levels, the Republicans would have been unable to keep the lid on the two-ﬁfths of its membership who were former Americans, and by alienating the immigrant vote may not have been able to attain a majority in the electoral college in 1860. In 1856, the Republicans ran their ﬁrst presidential candidate, John C. Fremont, another politically inexperienced and rather frivolous war

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hero. He had a Catholic father and so was not tainted by vote-losing nativism and had no record in public life and so was not tainted by zealous denunciations of slavery as were the powers behind the scenes in the Republican Party. The Democratic convention, which required a two-thirds majority, was deadlocked until Douglas, still hot from Kansas–Nebraska, withdrew in favor of Buchanan, in expectation of consideration at the next opening for the presidency. Northern Whigs drifted to the Americans or the Republicans. The leftover southern Whigs rallied to the American Party in the south; the Southern Americans were proslavery and also appealed to southern interests by opposing the foreigners and cheap land that expanded northern population and power. They nominated Millard Fillmore, former Whig President and supporter of the Compromise of 1850. Fillmore’s practical hope would be to deny an electoral college majority to Buchanan, which would throw the decision to the House of Representatives where his centrist candidacy might naturally prevail. The race was between Buchanan and Fremont in the north, and between Buchanan and Fillmore in the south, and of course Buchanan beneﬁted from a split opposition. Also, those centrist voters in the north who feared disunion should Republican Fremont win voted for Buchanan from the only bisectional party. Buchanan won. Fremont, however, swept the upper north and did well although losing in the lower northern states of Illinois, Indiana, Pennsylvania, New Jersey, and also California. Fremont was a weak candidate, and Republicans were encouraged since all they would have to do is add Pennsylvania and either Illinois or Indiana with a stronger candidate and they might win in 1860. If a united Democratic Party carried the South, however, and Oregon and California, all it would need for victory is New York alone or Pennsylvania alone, or Indiana and Illinois together with one more state. The 1860 election would be won by whoever did better in the lower north. Two days after Buchanan was inaugurated in 1857 the Supreme Court issued its decision in the Dred Scott case, arguably the point at which the Civil War became inevitable. Dred Scott was a Missouri slave who sued for freedom on the grounds that his owners had for a time kept him in territories north of the boundary of the Missouri Compromise. Five of the judges were southern Democrats; two of the four northerners on the court were Democrats and one of those, Grier, was a champion of slavery who had southern relatives. Buchanan had secretly intervened with Grier to urge him to vote with the southern justices, and Buchanan blurted out a hint of his foreknowledge of the decision in his inaugural address. Chief Justice Taney for the majority denied citizenship to blacks including Dred Scott, found the Missouri Compromise of 1820 unconstitutional, and ruled that Congress lacked the authority to exclude slavery from the

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territories. In other words, the referee threw the game for the South. Republicans were apoplectic. Its nakedly partisan nature and the multiple and divided justice’s opinions accompanying the decision weakened its authority, however, and boosted the following of the Republican Party. Northerners implausibly but forcefully construed the portion of the decision relating to slavery in the territories as mere obiter dictum, a comment in passing without force, on the argument that since the court ruled that Scott was not a citizen the decision stopped at that point. The South, however, was now able to festoon its positions on slavery with all the ornaments of constitutionalism and legality; the Dred Scott case increased its sense of legitimacy and of grievance, and augmented its rhetorical bargaining power. The Supreme Court decision did not execute itself, and southerners began to agitate for a federal slave code that would enact the doctrines of the Dred Scott decision. The decision was intended to deny the newborn Republican Party its reason for being, but it also frayed the doctrine of popular sovereignty which was all that held the Democratic Party together. Taney’s opinion found that the territorial legislatures lacked the authority to prohibit slavery, and if effective would void popular sovereignty, but the opinions of other justices were silent on that question and thus perhaps it was mere dictum. If the issue arose directly to the Supreme Court, however, would the same justices who denied Congress the authority to regulate slavery in the territories then ﬁnd that the territorial legislatures had the authority to prohibit slavery? Douglas attempted to rescue popular sovereignty from Dred Scott with the argument that although slave-owners had a Constitutional right to their property in a territory, the territory need not protect that right with enforcement or legislation. Douglas’s construal riled southern Democrats and gave them more reason to demand a federal slave code to prevent such dodges. The doctrine of popular sovereignty also suffered in the controversies over the adoption of a state constitution in Kansas and its admission as a state to the union. Northern and southern immigrants to Kansas agitated at length and to the verge of civil war (200 died in guerilla skirmishes) on the slavery question resulting in two different conventions and constitutions for the state, one slave and one free. The free staters outnumbered the slave staters in Kansas by about two to one, but Buchanan demanded that Democrats in Congress support the slave Lecompton constitution. Douglas thought that to endorse the fraudulent slave constitution would damage the doctrine of popular sovereignty, kill him in his upcoming 1858 reelection bid for the Senate in Illinois and would destroy any chance of attracting northern votes to the Democratic Party in the 1860 Presidential election; and so he deﬁed the administration, but in the end Lecompton was accepted by the Senate.

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Even with all-out party pressure, however, Buchanan could not carry his Democratic majority in the House because of northern defections, and Kansas was not admitted. In 1858, more northern voters exited the Democratic Party over the spectacle of “bleeding Kansas.” The free state Democrats went from 53 souls in the House to 32, and 12 of those 32 survivors were those who voted against Buchanan on Lecompton. At this point the House Democrats consisted of 69 southerners, 19 northerners loyal to the administration, and the 12 northerners who voted against the south (called the Lecompton Democrats). The Congressional party was now by a small majority southern. The rules of the Democratic convention provided for representation from each state according to its electoral-college vote (each state gets to vote its number of representatives and senators), and since the north was more populated than the south, the convention party was by a small majority northern. Throughout his career Douglas, the leading political ﬁgure of the 1850s and a determined compromiser, had positioned himself at the center of the national party; geographically, the median voter would live in the Lower North (that is where Douglas did best in the 1860 election). He had stood aside for Buchanan in 1856, and in 1860 he was the heir presumptive. The convention met on April 23, 1860, unfortunately in Charleston, South Carolina (a state that yet today ﬂies the secessionist ﬂag over its state capitol), in the heart of plantation slavery. Douglas was the median candidate of the convention party, but also convention rules required a two-thirds majority vote for nomination. The majority of the Congressional party were southern, their position was endorsed by the Supreme Court, and by the Democratic President, and thus they felt entitled to having their views adopted. They wanted a federal slave code, which Douglas would not give them, because that would lose the election in the North, and hence in the country. The convention was chaotic and bitter. Douglas could not win two-thirds for the nomination, but he did win on the platform by majority vote. Winning on the platform meant that Douglas kept out the call for a federal slave code, the inclusion of which would ensure defeat everywhere in the North, but its exclusion caused Democrats from the Lower South to bolt the convention. Douglas may have welcomed their exit, betting that their temporary absence would allow him to attain two-thirds of the remaining delegates, but the convention chair, a southern sympathizer, unexpectedly ruled that two-thirds of all delegates, present and absent, would be required (Douglas might not have had two-thirds of the present delegates either). After ten days and 59 deadlocked ballots on the nomination, the convention adjourned for six weeks, to resume in Baltimore. The bolters determined to reconvene in Richmond, ﬁve weeks hence.

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The Constitutional Union Party convened on May 9. This group reunited the remainders of the Whig and American Parties in the Upper South – moderates from Maryland to Missouri – and also attracted some older Whig conservatives from the North uncomfortable with the Republicans. Its organizers were politicians of eminence and distinction, respected, intellectual, and moderate in conviction. This was the good-government party (superﬁcially resembling the Liberal Democrats in present-day United Kingdom) that would oppose the secessionists in the South, just as Douglas forces in the Democratic Party opposed the radical Republicans in the North. The organizers hoped to displace the Republican Party as the anti-Democratic Party, and originally believed that if they met ﬁrst in 1860 and nominated leading moderates the Republicans would be forced to ratify their ticket. Their more modest expectation was that the Republicans would nominate Seward, leaving the Lower North open to their moderate appeal. The party failed to attract more than symbolic support in the north, however, and its ambitions never came to fruit. They nominated John Bell of Tennessee, aged 64, and Edward Everett of Massachusetts, 67, respectable, but not charismatic, candidates. As in 1856, this faction’s most realistic hope was to deny any other candidate a majority in the electoral college and thus emerge as the brokered victors in a centrist compromise in the House of Representatives. The Republicans met next in Chicago on May 16. Seward was the dominant candidate going into the convention. Seward was talking moderate in 1860, but his record of vigorous denunciation of slavery was indelible. Party leaders feared he could not carry the Lower North, where the election of 1856 was lost, and which was now threatened both by Douglas and by the Constitutional Unionists. Lincoln was a barely noticed candidate going into the convention, but his managers cleverly worked to make him everyone’s second choice. Lincoln’s prior political career was one of well-planned moderation, and he was at the center of opinion in the party. The choice of Lincoln rather than Seward doomed Bell and would doom the Democrats unless they reunited. The Democrats reconvened in Baltimore on June 18. The southern delegates expected to control the convention and dump Douglas, but Douglas was the more clever politician. The disappointed southerners retired to their rump convention in Richmond, called for a federal slave code, and nominated John C. Breckinridge, the failed Buchanan’s Vice President. There seemed to be at least four schools of thought, not necessarily exclusive, among the bolting southerners. One was a myopic sectionalist passion that paid no heed to consequences. The second was to bully the tough Douglas into concessions, which failed. The third, among

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the more moderate bolters, was a rather muddled hope that the multiplication of candidates would deny Lincoln a majority in the electoral college, which would throw the election to the House of Representatives evenly split between parties under the requisite voting rule, and eventually the stalemate would go the Senate with a strong Democratic majority where the Republicans would lose. The fourth, among the more extreme bolters, was the frank desire for secession, which would have been much harder to justify if the candidate of a united Democratic Party were elected. Many of the leaders did expect that splitting the Democratic Party would elect Lincoln and hasten disunion. A contemporary journalist reported on the Charleston convention that, “the seceding States came to the convention with a deliberate purpose to break up the convention if they failed to get, as they knew they would fail to get, their extreme ultimatum, and their ultimate design is to break up the Union by breaking up the Democratic Party” (quoted in Nevins 1950, 227). Douglas was comfortable with popular sovereignty as a compromise because he expected that slavery would be impractical in the territories. As a practical politician, he would let nature rather than policy settle the issue. The southern demand for a federal slave code had little practical importance, and on the Senate ﬂoor Douglas complained: There is no necessity for legislation; no grievances to be remedied; no evil to be avoided; no action is necessary; and yet the peace of the country, the integrity of the Democratic party are to be threatened by abstract resolutions . . . The people will ask what all this is for; what it means; why is it so important to have a vote . . . Why? There must be some purpose. (quoted in Nevins 1950, 180–181)

After the Baltimore convention, when it appeared that Lincoln might win against the divided opposition, Jefferson Davis reportedly approached Douglas with a proposal to organize a fusion campaign against Lincoln, promising that Bell and Breckinridge would withdraw as candidates if Douglas would as well. Douglas reportedly replied that, “the election should never go the House, before it shall go into the House, I will throw it to Lincoln” (quoted in Nevins 1950, 285). It seems that Douglas feared disorder should the election go to the House. He reportedly believed that the leadership of the southern bolters, counting on either Lincoln to win or better for the election to go the House, had formulated a plan for a seizure of power in Washington in the weeks after the election. The Buchananites already held the federal ofﬁces in the capital. Breckinridge would carry the far south, and if he could win Virginia and Maryland, adjacent to the District of Columbia, military forces from those two states could back a Buchananite takeover (Nevins 1950, 295). Thus, Douglas campaigned hard in Virginia, Maryland, and North Carolina, not for

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himself, but for Bell and against disunion, so as to thwart a coup. Douglas declared forthrightly that the union should be maintained by military force. A month before the election, when it was plain to Douglas that Lincoln would win, even though quite ill, he bravely went into the Lower South and ﬁercely campaigned against disunion; he was in Mobile, Alabama on election day. Douglas died of illness in 1861 at the age of 48 while visiting his base in Chicago. The platforms of the four parties manifest a monotonic north to south gradation of position on the free soil question, the primary dimension of dispute in the election. Lincoln and the Republicans declared all territories closed to slavery; Douglas and the northern Democrats held to the doctrine of popular sovereignty; Bell and the Constitutional Unionists implicitly considered the territories open to slavery but a matter for political negotiation; and Breckinridge and the southern Democrats declared all territories open to slavery on implicit threat of secession.3 The Republican platform maintained inviolate the rights of the states, especially the right of each state to order and control its own domestic institutions; in other words, it guaranteed slavery in the slave states. The Republicans rejected the new dogma that the Constitution permits the extension of slavery into any and all territories as a dangerous political heresy; in other words, they held that the Dred Scott decision was limited in effect. They declared that the normal condition of all territory of the United States is freedom; slavery would be prohibited in all territories of the United States. They explicitly afﬁrmed that the union of the states must and shall be preserved, and denounced threats of disunion. They said that the controversies over the Lecompton constitution in Kansas revealed the Democratic doctrine of popular sovereignty to be a deception and a fraud. The Democratic Party (Douglas) afﬁrmed its Cincinnati platform of 1856, the doctrine of popular sovereignty. Popular sovereignty contained a useful ambiguity. For northerners it meant that a territorial legislature could prohibit slavery from the beginning, for the southerners it meant that the territory was open to slave-owners until it might apply to Congress for admission as a free or slave state (allowing slavery a toehold, as it would be expensive for a free state to compensate slave-owners for loss of property). The Douglas platform directly mentioned this difference of opinion, and pledged to abide by the decisions of the Supreme Court on the question. Douglas had earlier suggested that territorial governments might decline to protect slave property, but the platform again pledged faithful enforcement of whatever doctrine was decided by the Supreme Court. They also endorsed execution of the Fugitive Slave Law.

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The Constitutional Unionists said that platforms are misleading and divisive, and theirs was brief and basic. Their brief platform is a platitudinous appeal to “no political principle other than the Constitution of the Country, the Union of the States, and the Enforcement of the Laws” (emphasis omitted, Morison 1971, 1127). Because of this, and their poor showing in the election, many commentators neglect to locate them geographically and ideologically. Who they were and what they did not say is more important than the little they did say in the platform document.4 The convention did not seek to establish uniformity of opinion on the free soil question, leaving that to every individual’s judgment. The party would scrupulously avoid mention of the tiresome topic of slavery; although its state afﬁliates might take particular stands. Where Douglas sought an ambiguous formulation on the free soil question, the Constitutional Unionists sought none. Their platform pledged them, however, to “the just rights of the people and of the States reestablished, and the Government again placed in that condition of justice, fraternity, and equality which, under the example of the Constitution of our fathers, has solemnly bound every citizen of the United States” (emphasis added). Notice that the pledge of continued union is conditioned on the reestablishment of states’ rights and equality between the sections as found in the original constitutional compromise. It is the original constitutional compact that commands their loyalty, not present-day misinterpretations or usurpations. Outside the platform, the Constitutional Unionists denounced Douglas’s doctrine of popular sovereignty, and believed that Congress must protect the property rights of slave-owners in the territories. They also denounced the Breckinridge Democrats for threatening secession; but did not deny the right to secede should compromise fail. The practical difference between the two southern factions was that Breckinridge’s Democrats considered the election of a Republican president sufﬁcient to justify secession, while Bell’s Constitutional Unionists thought that resistance would only be justiﬁed by an overt act against southern interests by a northern administration. Presumably, Riker’s inference that Bell was the second choice of most Lincoln voters was based on the thought that the Constitutional Unionists contained many former Whigs, and that Whiggish Lincoln voters in the North would go for Whiggish Constitutional Unionists rather than for Douglas from their ancient enemy the Democratic Party. But most northern voters did not care to vote for the party of the Lower South: the Constitutional Unionists received 2 percent of the vote in the free states, 13 percent of their vote nationwide. Riker’s position that three-fourths of Lincoln voters in the North

The election of Lincoln

Lincoln U. North

271

Douglas L. North

Bell U. South

Breck L. South

Figure 12.1 Single-peakedness, 1860

ranked Bell second is not only undefended, it goes against the clear and convincing evidence. The breakaway Democrats (Breckinridge) declared that all territories are open to slavery, and that neither Congress nor a territorial legislature had constitutional authority to legislate otherwise. They said that the federal government had the duty to protect persons and property wherever they were threatened, that is, that the federal government should coercively suppress state, local, and territorial governments that legislate against slavery or fail to enforce a proposed federal slave code not directly mentioned in the platform. Territories that form a state constitution and petition for statehood ought to be admitted whether they propose to prohibit or permit slavery.

4. Unidimensional preferences in the 1860 election

I maintain that voter preferences in the 1860 election were for the most part single-peaked and unidimensional, as in Figure 12.1. Riker maintains that the preferences of Lincoln voters were not single-peaked because they ranked Bell second and Douglas third, as in Figure 12.2. Riker does not have direct data for his assertion that Lincoln voters ranked Bell second; it is an inference, and one not defended in his text. I have labored

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Lincoln

Douglas U. North

L. North

Bell U. South

Breck L. South

Figure 12.2 Riker’s cycle, 1860

in the preceding section to show that it is ideologically and geographically implausible that the majority of Lincoln voters ranked Bell second. Aggregate data will further support my position. Anyone can accuse an inference from an aggregate to its individual members of being an instance of the poorly named ecological fallacy. If the aggregate of ﬁrst-place votes shows A ﬁrst, B second, and C third, that does not necessarily mean that individuals who rank A ﬁrst rank B second. All A-voters could rank C second; from the aggregate data alone we are not entitled to a certain inference that A-voters rank B second. If, however, we have independent evidence that A-voters rank B second, then aggregate data bolster the conclusion that A-voters rank B second. The ecological fallacy is not a fallacy, but rather a logical possibility. It is a possibility and not an inevitability. The independent evidence I have just adduced on ideology supports my proposed inference from aggregate rankings to individual rankings. Why would a voter in the north choose Lincoln? High among the reasons must be Lincoln’s appeal to northern interests including his position on Free Soil; otherwise one of the other candidates would do. If such a voter were denied the choice of Lincoln, who would his second choice be? Why not Douglas, who is the next most adjacent on issues of northern interest? And if Douglas were not available where next would the typical northern voter turn? He would turn to Bell, the candidate of the Upper South, of course, not to Breckinridge the candidate of the Deep South. A zealous critic could claim that this is not enough; but please

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Table 12.1. State-level aggregation of ﬁrst-place winners, Upper North Upper North

L > D > Bl > Br expected

Connecticut Illinois Indiana Iowa Maine Massachusetts Michigan Minnesota New Hampshire New York Ohio Pennsylvania Rhode Island Vermont Wisconsin

L > D > Br > Bl L > D > Bl > Br L > D > Br > Bl L > D > Bl > Br L > D > Br > Bl L > Bl > D > Br L > D > Br > Bl L > D > Br > Bl L > D > Br > Bl L>D L > D > Bl > Br L > Br > D > Bl L>D L > D > Br > Bl L > D > Br > Bl

notice that my hypothesis – that Douglas the candidate of the Lower North ranked second among Lincoln voters in the North rather than Bell the candidate of the Upper South – is supported by some evidence, while Riker’s opposite hypothesis is supported by none. Riker is attempting to support his controversial and apparently counter-empirical doctrine of political disequilibrium; and the burden of proof is on one who would defend his extraordinary claim. A look at a map of the county-level winners in the 1860 presidential elections (McPherson 1993, 128) shows that latitude is attitude. The Upper North voted for Lincoln (more free soil), the Lower North voted for Douglas (less free soil), the Upper South voted for Bell (less slave soil), and the Lower South voted for Breckinridge (more slave soil). Nationally, Douglas and Bell did less well than Lincoln and Breckinridge and thus the east–west swathes of Douglas and Bell in the center are each thin and those of Lincoln and Breckinridge at the extremes are each thick. The strongly unidimensional (north to south) map of ﬁrst-place county winners supports the hypothesis that preferences were generally single-peaked. We can easily check whether aggregates at the state level show Douglas or Bell second in the North and whether aggregate preferences are generally single-peaked (see Table 12.1). Italics indicate an outcome contrary to the expectation of single-peakedness. Obviously, Douglas ﬁnished second everywhere in the North except for in Massachusetts and

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Democracy Defended

Table 12.2. State-level aggregation of ﬁrst-place winners, Middle America West

L > D > Bl > Br expected

California Oregon

L > D > Br > Bl L > Br > D > Bl

Lower North

D > L > Bl > Br expected

Missouri New Jersey

D > Bl > Br > L D>L

Upper South

Bl > Br > D > L expected

Delaware Kentucky Maryland Tennessee Virginia

Br > Bl > L > D Bl > Br > D > L Br > Bl > D > L Bl > Br > D Bl > Br > D > L

Pennsylvania. Bell ﬁnished second in Massachusetts, but that was because the Vice Presidential nominee on the Constitutional Union ticket was Edward Everett of Massachusetts who got a favorite-son vote in his home state. Incidentally, this suggests that to insist on the ecological fallacy is overly rigorous: in Massachusetts, Bell was second in terms of ﬁrst-place votes, and was probably second-ranked by Lincoln voters as well. In Pennsylvania, in a last-minute attempt to deny Lincoln a majority in the electoral college and salvage local campaigns, Douglas and Breckinridge forces formed an anti-Lincoln fusion candidacy with Breckinridge as the nominal candidate, and even then stubborn voters continued to vote for Douglas and for Bell. New York had a fusion of Douglas and Bell forces with electoral-college votes pledged two-thirds to Douglas and one-third to Bell. Rhode Island had a fusion ticket under Douglas. My ideological prediction that Bell would ﬁnish third is not supported: he ﬁnishes third in three states and fourth in eight states. This is the candidate that Riker would have us believe is ranked second by northern Lincoln voters. Breckinridge often did better than Bell because he enjoyed organizational support from the outgoing Buchanan machine, including many of the northern Democratic legislators and most of the local patronage appointees. In this region, 55 percent of voters favored Lincoln, 35 percent Douglas, 8 percent Breckinridge, and 2 percent Bell, L > D > Br > Bl. The two free western states should follow the northern pattern. Lincoln ﬁnishes ﬁrst in both. In California, Bell ﬁnishes fourth. In Oregon

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275

Table 12.3. State-level aggregation of ﬁrst-place winners, Lower South Lower South

Br > Bl > D > L expected

Alabama Arkansas Florida Georgia Louisiana Mississippi North Carolina South Carolina Texas

Br > Bl > D Br > Bl > D Br > Bl > D Br > Bl > D Br > Bl > D Br > Bl > D Br > Bl > D Br Br > Bl

Breckinridge ﬁnishes second, but this is because his Vice Presidential candidate, Lane, was a senator from Oregon. For the Lower North on ideological grounds I predict that voters would ﬁrst support Douglas, then Lincoln the other northern candidate, then Bell from the Upper South, then Breckinridge from the Lower South. Douglas is ﬁrst in Missouri, but against the schematic expectation Lincoln is last in this northern slave state. In New Jersey there was an anti-Lincoln fusion candidacy of Douglas, Bell, and Breckinridge, under the ﬂag of Douglas. Not showing at the state-level of aggregation, but connecting Missouri to New Jersey from west to east, are Douglas’s strengths in southern Illinois, southern Indiana, southern Ohio, and the fusion candidacy under Breckinridge’s name in Pennsylvania. In the Lower North region, limited to two states, Douglas obtained 42 percent of the vote, Lincoln 27 percent, Bell 21 percent, and Breckinridge 11 percent. For the Upper South the ideological prediction is that Bell would be ﬁrst, followed by the other southern candidate, Breckinridge, then Douglas, then Lincoln. Expectations for the Upper South are satisﬁed in Kentucky, Tennessee, and Virginia, and are imperfectly satisﬁed in the states of Delaware and Maryland. Overall in the upper south region, Bell received 45 percent of the vote, Breckinridge 43 percent, Douglas 11 percent, and Lincoln 2 percent. South Carolina, true to form, did not let its citizens vote for President, a choice reserved for the political elite. Texas had an anti-Breckinridge fusion slate under the banner of Bell. The Lower South satisﬁes expectations. Overall in the Lower South, Breckinridge got 55 percent of the vote, Bell 38 percent, Douglas 7 percent, and Lincoln was not on the ballot. The largest exception among all regions to the ideological singlepeakedness prediction places Bell fourth in the North rather than second where Riker needs him to be.

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Finally, let’s look at the section-level aggregate of votes. Riker does not provide a source for his election data, nor does he explain his calculations, nor is his arithmetic consistently reliable. Thus, it is not possible to infer what Riker’s source document was, and the numbers I use (derived from Burnham’s regional totals, 1955, 246–256) are quite close (1 or 2 percent) to what can be reconstructed from Riker but are not identical. There were about 3,450,000 voters in the North (excluding the western states California and Oregon but including the slave state Missouri). Of these, 53 percent voted for Republican Lincoln, 36 percent voted for northern Democrat Douglas, 8 percent voted for southern Democrat Breckinridge and 4 percent voted for Constitutional Unionist Bell: L > D > Br > Bl. After my ﬁrst analysis of the issue, Tabarrok and Spector (1999) appeared, an intriguing, useful, and a more technically sophisticated analysis of the 1860 election. Tabarrok and Spector had Riker’s rankings over the four candidates. They also queried 100 Civil War historians as to their views on the rankings, and 15 responded with opinions about the percentage of voters of various rankings over Lincoln, Douglas, Bell, and Breckinridge. For voters who ranked Lincoln ﬁrst, the historians’ median opinion was that 60 percent ranked Douglas second and 40 percent ranked Bell second. Of the 15 historian respondents, 12 had a view contrary to Riker’s; each of those 12 believed that 50 percent or less of Lincoln voters ranked Bell second. Two of the three respondents who seem to agree with Riker’s estimate (that Bell ranked second among more than 63 percent of Lincoln voters) are also those who make the most extreme estimate in either direction (90 percent and above for Bell). Tabarrok and Spector constructed a median historian’s proﬁle, and compared it to Riker’s. As I said, I believe that many commentators, a number of historians included, fail to locate the Constitutional Unionists ideologically and geographically, and my estimate of their support among Lincoln voters would not exceed 10 percent; however, nothing in the analysis here depends on my apparently extreme view on the question. The plane of possible outcomes in Tabarrok and Spector’s positional-vote space, using Riker’s proﬁle, is large, and permits a large variety of rankings by way of varying the weights of a positional voting rule – from plurality to Borda count to antiplurality and everything in between. The positional vote plane using the median historian’s proﬁle is small, and “Douglas wins . . . under any positional voting system which gives signiﬁcant weight to second- or second- and third-ranked preferences” (278); Lincoln wins by plurality count, which gives no weight to any preferences except for the ﬁrst-ranked. Condorcet pairwise comparison is cyclic with Riker’s proﬁle, but with the median historian’s proﬁle Douglas beats Bell by 15.1 percent, Bell beats Lincoln by 0.033 percent

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277

(three-hundredths of 1 percent), and Lincoln beats Breckinridge by 25.4 percent. The ideological data, aggregate data at the county, state, and sectional levels, and the opinion survey of antebellum historians, all support the hypotheses that Douglas and not Bell was second-ranked among Lincoln voters, and that preferences were for the most part single-peaked across the country. What does this revision do to Riker’s demonstration that democracy is arbitrary because different voting methods result in different outcomes and that democracy is meaningless because cycles will be contrived on major issues such as the future of slavery? The ﬁrst thing we must do is to correct Riker’s original claims. He claims that the Borda count ranks D > Bl > L > Br. This is not correct, the Borda count from his ﬁgures indicates D > L > Bl > Br. He also states that the “actual” method and outcome was the plurality ranking L > D > Br > Bl. That is not quite correct, as the actual outcome was determined by the electoral college where the ranking was L (majority) > Br > Bl > D. Customarily, the electors vote on the instructions of their states and if they deadlock, then the top three candidates in the electoral college go to the House of Representatives where each state delegation casts one vote, and if the House deadlocks then the top two Vice Presidential candidates go to the Senate where each senator has one vote. It is important to know that this arrangement, and not national-level plurality rule, was the voting scheme that motivated the candidates’ decisions. That gives us a corrected version of Riker’s ﬁndings: r Electoral College: Lincoln (majority) > Breckinridge > Bell > Douglas; r Plurality: Lincoln > Douglas > Breckinridge > Bell; r Pairwise comparison: (Douglas > Lincoln > Bell > Douglas) > Breckinridge; r Borda count: Douglas > Lincoln > Bell > Breckinridge; r Approval voting (two votes): Bell > Lincoln > Douglas > Breckinridge; r Approval voting (three votes): Douglas > Bell > Lincoln > Breckinridge. Riker has one-fourth of Lincoln voters ranking Douglas second and threefourths of Lincoln voters ranking Bell second. Bell got 2 percent of the vote in the states ranking Lincoln ﬁrst, but let’s be generous and adopt the median historian’s view that Bell was the second choice of 40 percent of Lincoln voters and that Douglas was the second choice of 60 percent of Lincoln voters. What happens then to the arbitrarily different outcomes and the meaningless cycle? They disappear! A pairwise-comparison matrix is displayed in Table 12.4. Riker’s ﬁgures are in roman type. The cells showing how many preferred Douglas to Bell, and how many preferred

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Table 12.4. Pairwise comparison matrix, 1860 election (thousands) L Lincoln Douglas

2516

Bell

2139

Breck

1713

D

Bl

Br

(Borda)

2165

2542 2265 –718 +1076 = 2623

2968 3658

(7675) (8439) (8797 )

3090

(7645) (7287 )

2416 +718 – 1076 = 2058 1023

1591

(4327)

Note: Riker’s estimates in Roman type, Mackie’s revision in italic type.

Bell to Douglas, are revised to reﬂect my proposed revision of the proportions of Lincoln voters second-ranking Douglas and Bell. My revised totals are in italic. The consequences are straightforward. By pairwise comparison, we have D > L, L > Bl, L > Br, D > Bl, D > Br, Bl > Br; and that reduces to D > L > Bl > Br, which is not a cycle. The Borda count is still D > L > Bl > Br. Approval voting with two votes changes from what it was to D > L > Bl > Br. Approval voting with three votes remains D > Bl > L > Br. Here is a summary of the ﬁnally corrected outcomes: r Pairwise comparison: Douglas > Lincoln > Bell > Breckinridge; r Borda count: Douglas > Lincoln > Bell > Breckinridge; r Approval voting (two votes): Douglas > Lincoln > Bell > Breckinridge; r Approval voting (three votes): Douglas > Bell > Lincoln > Breckinridge. With plurality runoff, Lincoln and Douglas would go to the runoff and Douglas would win (a runoff between ﬁrst-round losers Bell and Breckinridge has Bell as the winner, yielding the overall ranking D > L > Bl > Bk). All ﬁve of these voting methods select Douglas as the winner. Except for approval voting with three votes (in this example equivalent to antiplurality), the rules identify the same ranking D > L > Bl > Bk. That antiplurality is an exception is not a surprise, since antiplurality is an even more inaccurate voting rule than is the plurality rule. Antiplurality means that everyone votes against her least-favored candidate, and it is inaccurate because all other ranking information is ignored.

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279

It’s not perfectly proper for me to mix one ﬁnding from the median historian’s proﬁle, that Lincoln voters ranked Douglas second, with the remainder of Riker’s proﬁle. From the data in Tabarrok and Spector (1999), I have borrowed in most cases and calculated in a few cases, how the same voting rules would rank the entirety of the median historian’s proﬁle: r Pairwise comparison: Douglas > Bell > Lincoln > Breckinridge; r Borda count: Douglas > Bell > Lincoln > Breckinridge; r Approval voting (two votes): Douglas > Bell > Lincoln > Breckinridge; r Approval voting (three votes): Douglas > Bell > Lincoln > Breckinridge. Again, with plurality runoff, Lincoln and Douglas would go to the runoff and Douglas would win (a runoff between ﬁrst-round losers Bell and Breckinridge has Bell as the winner, yielding the overall ranking D > L > Bl > Bk). All ﬁve of these voting methods select Douglas as the winner. The median historian’s proﬁle yields rankings that are a bit more similar than from Riker’s proﬁle. The remaining big difference between the two proﬁles is that the median historian’s ranks Bell just barely above Lincoln. It is plausible that Bell as a more centrist candidate, attractive to the Lower South, the Upper South, and a bit in the Lower North, might do about as well as Lincoln as a less centrist candidate. The champion of Riker may still have doubts and, all evidence to the contrary, still insist that many Lincoln voters ranked Bell second. How sensitive is Riker’s assertion of a cycle? He says that 25 percent of Lincoln voters ranked Douglas second and 75 percent ranked Bell second. Riker’s cycle assertion is fragile: if merely 30 percent of Lincoln voters rank Douglas second and 70 percent Bell, then Riker’s cycle vanishes. How sensitive is the assertion of different outcomes from different voting rules? If the second ranking of Lincoln voters is 33 percent for Douglas and 67 percent for Bell, then that is enough for pairwise comparison, Borda count, approval voting with two votes, antiplurality, and plurality runoff to pick Douglas as the winner. If 37 percent of Lincoln voters ranked Douglas second and 63 percent ranked Bell second, then that is enough for pairwise comparison, Borda count, approval voting with two votes, and plurality runoff to converge on the same ranking: D > L > Bl > Br. So Riker’s case depends on the assertion that more than 63 percent of Lincoln voters in the north ranked Bell, the candidate who had obtained 2 percent of the votes in the North, second. That is too fragile to carry a case for pervasive political disequilibrium, a hypothesis which, as we have seen, is otherwise unsupported. Riker’s primary argument in Liberalism against Populism (1982) is the skeptical assertion that democracy is impossible because individual

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Democracy Defended

preferences are unknowable. Because preferences are unknowable we cannot ascertain whether or not outcomes of voting are accurate or fair; hence democracy is inaccurate. Further, because preferences are unknowable, there is a possibility of manipulation, and we cannot distinguish manipulated from unmanipulated outcomes; hence, democracy is meaningless. I criticized Riker’s basic argument pattern as self-contradictory in the second chapter. The unknowability of preferences also explains, in Riker’s scheme, why disequilibrium is pervasive yet difﬁcult to identify. In order to be persuaded to abandon the concept of the public good and the idea of democracy as in some sense the expression of the people’s will, most people would require that it be robustly demonstrated that manipulation of outcomes be frequent, harmful, and irremediable. There is no such demonstration. Because of his belief in the unknowability of preferences, Riker also believes that the relevance of political disequilibrium can only be demonstrated by means of artful anecdotes. We have examined the four major illustrations of disequilibrium in Liberalism against Populism and found each to be in error. All of his examples fail, and hence so does his overall case.

13

Antebellum politics concluded

Introduction Pairwise comparison, the Borda count, approval voting with two votes, negative plurality, and plurality runoff voting rules all choose Douglas as the most preferred candidate; and all but the negative plurality voting rule arrive at the same ranking: Douglas > Lincoln > Bell > Breckinridge. Yet Douglas was the last-ranked candidate in the electoral college (though second-ranked in the popular vote), and Lincoln won a majority in the electoral college (and was ﬁrst-ranked but with a 40 percent plurality in the popular tally). How is it that the actual election rule selected Lincoln rather than Douglas? Does the fact that Lincoln rather than Douglas was chosen support Riker’s claim that democracy is arbitrary because different voting rules result in different outcomes from the same proﬁle of preferences? Why was the 1860 election so peculiar? Lincoln beat Douglas because with plurality rule and four major candidates many voters’ preferences for Douglas over Lincoln were not counted by the voting rule and because Lincoln absorbed Douglas’s votes in the electoral college. Advocates of democracy have no obligation to defend the presidential election system, I argue, which was clumsily designed with antimajoritarian intent. Whether or not the election of Douglas, the median voters’ candidate, would have prevented secession and war is impossible to say; I suggest that the South may have seceded anyway. Pure plurality rule usually elicits no more than two major candidates, but the actual presidential election rule was more complex: ﬁrst, votes are aggregated by states, then, generally, states cast votes for single winners in the electoral college, and if the electoral college were to deadlock, its top three candidates would go to the House where the South had better strength, and if the House were to deadlock, then the Vice President becomes President if he had a majority in the electoral college, otherwise, the top two Vice Presidential votegetters in the electoral college would go to the Senate, controlled by the Democrats. The prospect of the election going to Congress elicited four major candidacies, rather than two 281

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as under pure plurality. I offer a novel hypothesis: that an unintended consequence of the misunderstood strategic situation with four major candidates was that sophisticated voting tragically made it appear that the population was more polarized than it was in reality. Then we undertake close examination of Riker’s theory of manipulation in multidimensional issue space, which he illustrates with the history of the slavery issue in American politics from 1800 to 1860. Riker rejects change in individual preferences, the standard hypothesis, as an explanation for change in collective choices. Change in collective choices is due to variations in the manipulative success of more potent actors in arbitrarily imposing an outcome on the chaos of multidimensional disequilibrium, he believes. The losing commercialist coalition repeatedly sought an issue that would divide the winning agrarian coalition. With the slavery issue they episodically came close to success in 1819 and 1846, and ﬁnally succeeded in 1860. An alternative hypothesis for the episodic nature of the issue of slavery in the territories, that it was related to the minority South maintaining its veto power in the US Senate, is more convincing. I ﬁnd errors in Riker’s historical narrative of the period. I present evidence in support of the standard hypothesis that changes in collective attitudes and actions on the slavery issue track changes in individual preferences, and argue that the standard hypothesis better ﬁts the evidence than Riker’s hypothesis of arbitrary manipulation. Why did Lincoln beat Douglas? Lincoln won an electoral college majority due to the distortions of two institutions. First, it is well known that it is possible for a two-tier system like the electoral college, in which a district casts a vote on behalf of the majority (or plurality) winner in the district, to have perverse outcomes. Suppose there are 100 districts and 100 voters in each district. Candidate Jerry Garcia wins 51 votes in each of 51 districts, but 0 votes in the remaining 49 districts. Garcia is the “majority” winner in the electoral college, even though he has received only 2,601 out of 10,000 popular votes. If rival candidate Leonard Cohen wins the remaining 49 votes in the 51 districts that each give Garcia 51 votes and Cohen wins all 100 votes in each of the remaining 49 districts, then Cohen with a total of 7,399 out of 10,000 popular votes loses to Garcia in the electoral college. The candidate with 2,601 votes beats the candidate with 7,399 votes. Second, we already know that plurality rule is potentially the least accurate of the commonly used voting rules. Suppose there are two factions in the population: those who favor electric blues and those who favor pop music. The electric blues voters are united on candidate Jerry Garcia,

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who polls 27 percent of the vote. The pop voters are divided, 26 percent ﬁrst-rank Britney Spears, 24 percent ﬁrst-rank Celine Dion, and 23 percent ﬁrst-rank Janet Jackson. The candidate of the electric-blues voters wins, even though he is not the ﬁrst choice of 73 percent of the population. Now combine the two institutions. In each of 51 districts Garcia obtains 27 votes and is the plurality winner, in the remaining 49 districts Garcia obtains no votes. Garcia wins the election with 1,377 out of 10,000 votes. The candidate ﬁrst-ranked by 14 percent of the voters is the victor. Majority rule over two candidates uses all information from voters and picks an obvious winner. Majority rule over more than two candidates does not use all information, does pick an obvious winner, but is often not decisive (e.g., when there are three candidates and none gets a majority). Plurality rule over several candidates throws away large amounts of ranking information. If there are four candidates and each voter has complete preferences over the four, then ranking information is potentially available for six pairwise comparisons (A:B, A:C, A:D, B:C, B:D, C:D), and for 24 relative-rankings among four alternatives, A, B, C, and D, but plurality rule gathers only each voter’s ﬁrst-ranking and throws away all other information. To illustrate, return to Garcia’s victory with 1,377 votes. It is logically possible that each of the remaining 8,623 voters ranks Garcia last out of the four candidates; the candidate last-ranked by 86 percent of the voters wins the election. We rarely observe such distortions, however, for two reasons. First, the examples provided are illustrative extremes, and for many distributions of preferences the distortion would not come about. For district voting, it is possible although unlikely that one candidate would have only 51 out of 100 votes in 51 out of 100 districts and 0 out of 100 votes in 49 out of 100 districts. For plurality voting, there is sometimes a clear majority winner even when there are multiple candidates. Second, and more important than the distribution of preferences, potential candidates strategically interact with the voting rules. For district voting, the party behind Leonard Cohen might choose a similar candidate, but one a bit less polarizing than Cohen, say that they choose Bob Dylan who is a lyricist like Cohen but a little more electric. Dylan will get fewer votes in the 49 districts that were 100 percent for Cohen, but more votes in the 51 districts that were 51 percent for Garcia. The Cohen–Dylan party only needs to pull four votes from the Garcia voters and it can afford to sacriﬁce 49 × 49 = 2,401 properly distributed votes in its quest. Alternatively, the Cohen party can stick with Cohen, but pull its electioneering resources away from the 49 districts where it is the sure winner and towards the 51 districts where it is the near winner. Anticipating the strategic response of the Cohen–Dylan party, the Garcia party, if it is motivated to win

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the election, would have to move far from Garcia and ﬁnd a candidate with appeal across more districts, in short, a candidate with majority appeal. For plurality voting in a single-member district, as we have seen, voters who do not want to waste their votes will vote for one among the two candidates they believe most likely to win, and weak candidates, anticipating those strategic votes, are deterred from entering. Thus, in the contest between electric blues and pop music, the pop voters will steer their resources and their votes probably to Britney Spears, the topranked among them, in order to defeat the icky Garcia. Those who back Celine Dion and Janet Jackson strategically vote for Spears in order to defeat Garcia. Only a few need to do so and, in the simple world we assume, anticipation of such strategic voting deters Dion and Jackson from entering the contest. Finally, if either voting by district aggregation or plurality voting are a problem, there are easy institutional remedies, for example, go from district voting to direct popular voting and go to assured plurality runoffs. The electoral college in particular was intended to be an antidemocratic institution, and democrats have no obligation to defend its outcomes. The electoral college ranking was Lincoln (majority) > Breckinridge > Bell > Douglas and the popular vote was Lincoln (plurality) > Douglas > Breckinridge > Bell. There are two questions to answer at the outset. First, why is Douglas out of order, why is he second in the popular vote and last in the electoral-college vote? Second, how does Lincoln move from a popular-vote plurality to an electoral-college majority? States tended to follow a winner-take-all tradition; a state would cast all of its electoral votes for the majority (or plurality) winner of popular votes in that state. Lincoln won majorities in 15 out of the 18 states contributing to his victory in the electoral college. The 15 states where Lincoln had a majority contained 80 percent of Douglas’s nationwide popular vote and 91 percent of Douglas’s free-state popular vote. The 18 states that gave Lincoln all of their electoral votes contained 84 percent of Douglas’s nationwide popular vote. Lincoln was boosted from a popular plurality to an electoral-college majority by absorbing the votes that went to Douglas in the free states. That is how Douglas, the candidate second-ranked in the popular vote ﬁnished last in the electoral college vote. Next, why did Lincoln win the plurality vote, when pairwise comparison, Borda count, and the others selected Douglas? We have a discrepancy between the plurality results – (Lincoln > Douglas) > (Breckinridge > Bell), and the results by most other reasonable voting rules – (Douglas > Lincoln) > (Bell > Breckinridge). For strategic reasons that I shall set forth shortly, the national four-party race for the most part collapsed into two sectional two-party races. In the North the two parties with most organizational

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force were Lincoln’s Republicans and the Douglas Democrats; northern voters tended not to waste their votes on Breckinridge or Bell. In the South the two parties with most organizational force were Bell’s Constitutional Unionists and the Breckinridge Democrats; southern voters tended not to waste their votes on Douglas, and Lincoln was not even on the ballot. Most southerners would prefer Douglas to Lincoln, but that is not the comparison they faced or reported preferences on. The information that southerners preferred Douglas to Lincoln was not counted under the plurality rule, which picked Lincoln over Douglas nationwide. The other voting rules would have counted that information about southern preferences, and thus would have picked Douglas over Lincoln nationwide. Most northerners would prefer Bell to Breckinridge, but that information was not counted under the plurality rule as well, which picked Breckinridge over Bell nationwide. The other voting rules would have counted that information about northern preferences and thus would have picked Bell over Breckinridge nationwide. Plurality rule tends to strategically elicit two major candidates between whom it can accurately choose; thus, we are not alert to its inaccuracy in deciding among four major candidates. We also must remember that candidates are not exogenous to the voting system. One voting system will encourage candidates A, B, C, D, E, and F to enter the contest; another voting system will instead encourage candidates C and D to enter, and another might inadvertently reward mostly candidates A and F . Although most of the time most reasonable voting rules will pick the same winner, sometimes they will not, and when they do not this is due either to candidates’ positions being very close to one another or is due to the interaction of potential candidates with the rules of the voting system. The voting system in place in 1860 elicited the candidacies of Lincoln, Douglas, Bell, and Breckinridge. A different voting system may have elicited a different set of candidates. The voting system that political actors faced in 1860 was not only a plurality race in each state and then each state casting its vote in the electoral college. There was also the provision that in event of no majority in the electoral college, the top three candidates would go to the House where each state would have one vote and if the House deadlocked that the top two Vice Presidential candidates would effectively go to the Senate for decision. Suppose that the system would have been different, that only a plurality would have been required in the electoral college and no election would be forwarded to the House. Then, speculatively, the smallest party, the Constitutional Unionists (roughly speaking, former southern Whigs and southern Americans) would not have formed or would have abandoned their candidacy since they would no longer have a hope of being the

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centrist brokers in a contest decided in the House. That would leave the Republicans (formerly the northern Whigs and northern Americans, among others), the northern Democrats (Douglas), and the southern Democrats (Breckinridge). Continuing the speculation, the Republicans would be motivated to pick a candidate at least as centrist as Lincoln so as to appeal not only to the Upper and Lower North, but also to their former Whig brethren the Constitutional Unionist voters in the Upper South. The southern Democrats would not be tempted by the fantasy of winning in the House or the Senate, and the Democrats further would be motivated to beat the Republicans to the center and choose a candidate like Douglas. The contest would then be fought over the center. The purpose is only to illustrate that candidates are endogenous to the voting system, not to argue that this would be the most probable outcome in that counterfactual world. The point is that if candidates are endogenous, then it may not be informative to observe that the hypothetical application of voting system B to the actual candidates and rankings endogenous to voting system A would result in a different winner. If the hypothetical voting system B had been in place, then also an array of candidates and rankings different from those endogenous to A would have emerged. Thus, to establish that democracy is arbitrary it would not be enough for Riker to show that Lincoln won the actual election and that with the candidates and rankings endogenous to the actual election that Douglas (or another) would have won one or another hypothetical election each with a different voting rule. Because of the possibility of endogenous differences in the candidate menus he would also have to establish that the voters’ underlying policy preferences that motivate them to choose among candidates aggregate to arbitrarily different policy outcomes from one reasonable voting rule to the next. This can be illustrated by explication of a problem with my speculative counterfactual, its unstated assumption that the Lower South did not want secession. It assumes that the voting rule requires winning only a plurality in the electoral college. In another counterfactual world if the leaders of the Lower South want secession then just as in the actual case they would be determined to split the Democratic Party. In the secessionist counterfactual world, if a center–south Democratic Party were to have won the election, then the leaders of the Lower South would have lacked the legitimacy to rally a critical mass to the cause of secession. Imagine yet a third voting rule in 1860, direct popular plurality election. Again, if there were secessionists they would be motivated to split the Democratic Party for the same reason, to prevent a centrist victory. The Democratic Party’s unfortunate two-thirds rule made it such that the secessionists could attain their aims regardless of Douglas’s response. If

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they had succeeded in driving Douglas from the ticket then their southern sectionalist minority platform would have lost the national election and the northern sectionalist election victory would have been a justiﬁcation for secession. If, as did happen, they failed to drive Douglas from the ticket, the most southern one-third of the party could claim the cloak of legitimacy in splitting the party, and by splitting the Democrats deliver the election to Lincoln again justifying secession. I think the main problem was that many leaders in the Lower South wanted secession in 1860 and probably would have had secession and war under most likely voting rules. After all, provinces or regions occasionally attempt secession from authoritarian regimes that lack any reasonable voting rules.1 With secession from nondemocratic regimes it is clearly not the voting rule but rather the desire to secede that is the main causal agent. In 1856 the southern Democrats favored Douglas at the convention and approved of the noninterventionist Cincinnati platform. In 1860 the same candidate and the same platform aroused their destructive wrath. At the conclusion of the Baltimore convention in 1860, Douglas warned, “Secession from the Democratic Party means secession from the federal Union” (Johanssen 1973, 772). He also said there that “There is a mature plan throughout the Southern States to break up the Union” (Johanssen 1973, 790).2 During the campaign Douglas told an audience in Virginia that in case of secession, “the President of the United States, whoever he may be, should treat all attempts to break up the Union, by resistance to its laws, as Old Hickory treated the Nulliﬁers in 1832 [i.e., credible military threat]” (Johannsen 1973, 789). What would have happened if Douglas had won (and had avoided death from illness in 1861)? It is impossible to say, of course. Perhaps he would have been less provocative to the South and more able to ﬁnd a workable compromise than Lincoln. As the leading northern Democrat in the Senate, Douglas feverishly sought peace, and he chastised both sections in that pursuit. He told a friend, however, “Better a million of men should fall on the battle ﬁeld than that this govt should lose one single State!” (Johannsen 1973, 813). After the fall of Fort Sumter to the South Carolinians, he said, “If I were President, I’d convert or hang them all within forty-eight hours,” and, “We must ﬁght for our country and forget all differences” (Johannsen 1973, 860). Secession and war may have followed even if Douglas had won. A number of historians have devoted their scholarly lives to the topic of the causation of the Civil War. I do not claim any original contribution to that effort. My purpose is to borrow from standard secondary sources in order to demonstrate the inaccuracies and implausibilities of Riker’s secondary account. As a student of politics who has an understanding of

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voting rules, however, I would like to offer a modest hypothesis for further investigation – not a strong theory – about the peculiar 1860 election. My hypothesis is consistent with the historical sensibility that appreciates that a concatenation of blunders, uncertainties, passions, and ambiguities can forge a causal path to a destination wanted by almost no one (I must add that because some social consequences are partly unintended does not mean that all social consequences are wholly unintended). Let’s begin by comparing the elections of 1856 and 1860. The South Americans and the remnants of the Whigs – much the same forces as those who would form the Constitutional Unionists (Bell) in 1860 – separately nominated Millard Fillmore as their candidate in 1856. In 1856, ﬁrst President Franklin Pierce and second Stephen Douglas as manager in Congress were favored by southerners at the Democratic convention because of their work to pass the Kansas–Nebraska Act in 1854, but were opposed by northerners for the same reason. On the seventeenth ballot, James Buchanan, conveniently absent as ambassador abroad during the Kansas–Nebraska deliberations, emerged as the compromise. The Democrat’s 1856 Cincinnati platform took the noninterventionist popular-sovereignty position on the question of slavery in the territories; Fillmore had a version of popular sovereignty as well. The Republicans and the North Americans nominated John C. Fremont; they were, of course, against slavery in the territories. Potter (1976, 259–265), whom I have been following, says that the three-way race reduced almost to two separate elections, one between Democrat Buchanan and Republican Fremont in the free states and another between Democrat Buchanan and South-American and southern-Whig Fillmore in the slave states. Potter observes that Buchanan might be expected to have suffered the disadvantage in that his positions had to span both sections while his opponents Fremont and Fillmore could appeal exclusively to northern or southern voters respectively. Nevertheless, Potter observes that Buchanan had the advantage because of what we would call in political science a classic case of strategic voting: “a great many northern citizens became convinced that the election of Fremont meant disunion, and that the candidate to vote for was the one who could beat Fremont. Since Buchanan appeared to have the better chance, this tactical factor, as much as anything else, brought about his victory and Fillmore’s ruin” (263). Buchanan won most of the slave states and some of the free states, the ﬁrst President not to win both sections since 1828. Much is made of the fact that Republican Lincoln received only 40 percent of the popular vote in 1860, but this is a hangover from southern propaganda, as Democrat Buchanan was also a plurality winner in 1856 with only 45 percent of the popular vote. The South controlled the country for most of the period

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from 1800 to 1860 in part because it was the majority faction in the majority party. Together, Fillmore, a prosouthern candidate, and Buchanan, a southern-leaning candidate, polled 67 percent of the vote in 1856. This was an era without opinion polls and without the communication and transportation connections we enjoy today. People of one section were able to generalize about people of the other section only on the basis of events so vivid as to merit national reportage. One of the most salient pieces of evidence for contemporaries concerning the attitudes both of one’s own and of other regions were the election returns, which possess the illusion of objective authority. Although there was an awareness of the phenomenon of strategic voting, I would venture that most did not consider how strategic voting, plurality rule, and the electoral college garbled the information to be found in election outcomes. The Democratic Party scored its biggest victory ever in 1852 after the collapse of the Whigs, Pierce gaining the presidency with the electoral college votes of 27 out of 31 states and Democrats taking 63 percent of the House. Pierce’s totals were bloated, however, by the defection of southern Whigs to the Democrats; and he did not attain a popular majority in the North. Perhaps imagining that their convincing victory was due to the popularity of their policies rather than to collapse of the Whigs and the vagaries of the electoral college, the Democrats mistakenly believed that they could abrogate the Compromise of 1850 in order to set up Kansas for admission as a slave state to balance California’s admission as a free state four years before, and were deeply surprised by the consequent northern uproar. After the Kansas–Nebraska Act in 1854 they suffered their worst defeat, falling to 18 percent of the House (Weingast 1998, 181). Duverger’s law is a probabilistic generalization that plurality elections in single-member districts tend to the production of a two-party system. As we have seen, this is due to strategic candidates anticipating strategic voters. The US presidency is superﬁcially a plurality election in a singlemember district, and this helps explain the tendency to two parties in American politics. The mechanism is at work in local and state elections as well, wherever there are plurality elections in single-member districts, such as for governorships, most Congressional races, and many state legislative races. Political forces in the US bifurcate at the local level, but then have incentives to federate in order to win statewide ofﬁces, and further incentives to federate nationally in order to win the presidency, helping perhaps to explain the crazy-quilt pattern within American political parties. Armed with Duverger’s “law” let’s reexamine the election of 1856. There were three parties. The theory proposes that voters will concentrate on the two parties believed most likely to win. Local and state elections motivate party organizations to the complementary labor

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of mobilizing for the party’s presidential candidate as well. In the south the two parties most likely to win in local and state races were the bisectional Democrats and the sectional ex-Whig Fillmorites. The Democrats had organizational force in more of the South than did the ex-Whigs, ex-Whigs won races where they were strong but overall Buchanan won the South. In the North the two parties most likely to win in local and state races were the bisectional Democrats and the sectional Republicans. Suppose a voter is a moderate motivated to support union and peace over disunion and war. If he is a voter in the South, he can vote for either Buchanan or Fillmore. If he is a voter in the North, he must vote for Buchanan even if he otherwise wants Fremont’s policies, because the election of Fremont might trigger southern secession. Enough voters in the North supported Buchanan to provide him an electoral-college majority in that section. When the southern-dominated Democratic Party took ofﬁce in 1857 it could imagine that its fortunes had recovered with the election of Buchanan, and southern forces could further imagine that the 67 percent of the vote for Buchanan and Fillmore indicated a reconsidered national inclination to conciliate southern interests. Just as they took ofﬁce, moreover, the Supreme Court with the Dred Scott decision declared that the southern position was constitutionally legitimate and thus that the Republican Party’s goals were politically impossible. In 1852 the Democratic Party, insensible to its true weakness, won with defecting southern Whigs; in 1856 weaker yet they won again with defecting northern Whigs. Consider the surprise of some then, at the election of Lincoln in 1860 – and the plausibility of conspiracy theories in either section. Look at the 1860 election with Duverger’s law in mind. Now there is no longer a bisectional Democratic Party and there are four parties in total. If Duverger’s law was at work at the national level with respect to the Presidential race then there should be only two parties. But the Presidential election is only superﬁcially a plurality contest in a single-member district. Remember, there is provision for the election go to the House if there is no majority in the electoral college. In the House each state gets one vote (more advantageous to the South than the electoral college), and an election there could go either way. There were 34 state delegations in the House, thus 18 states were needed for a majority. The Republicans controlled 15 of the state delegations; the Democrats controlled 14 and in each of 4 more states needed only to convert one South-Americanist Representative; Tennessee had a majority of Americans and was unlikely to support the Republicans. If the House deadlocked, the election would go to the Senate where the Democrats had 38 votes, the Republicans 26, and the Americans two (Fogel 1989, 382). The prospect of becoming centrist brokers in a House election is part of what motivated the Upper

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South candidacies of Fillmore in 1856 and Bell in 1860. In 1856 southern forces were split between Buchanan and Fillmore, yet Buchanan and his southern-leaning policies prevailed. What difference would it make in 1860 if a fourth party were added to the mix, some actors in the northern and southern wings of the Democratic Party may have reasoned. When there were four candidates in 1824, the election went to the House, and fourth-ranked Clay from the Upper South was pivotal to the House election. In 1836, the Democrats ran Martin Van Buren and Whig factions ran three candidates. The Whigs ﬁgured that their three candidates would appeal to three regions, and that they could decide on a winner in the House, but instead Van Buren won a majority in the electoral college. More parties make it more likely that there won’t be a majority in the electoral college; we’ll muddle through and work things out in the House, and with great luck we might even win in the Senate. The actors did not anticipate that adding a fourth party amidst expectations of an election possibly going to the House fundamentally altered the strategic situation. Four parties and Duverger’s law operating at the local and state level, as we have seen, turned the four-way race into two sectional two-way races. In the 1856 race in the North between Democrat Buchanan and Republican Fremont, a vote for Democrat Buchanan was a vote for moderation. It was entirely different in the four-way 1860 race. Extreme northern voters would vote for Lincoln and extreme southern voters would vote for Breckinridge. Here’s how a moderate northern voter might reason, however, to the extent he believed the electoral college would deadlock and the election go to the House: I prefer the moderate unionist policies such as those of Douglas, but if the southerners believe that we will support a moderate northern position then they will be motivated to support an extreme southern position so that the compromise in the House is drawn in their direction. Since the South would choose its more extreme candidate the North should choose its more extreme candidate so that in the House the compromise is nearer to our true position. The southern voter reasons reciprocally: I prefer the moderate unionist policies such as those of Bell, but if the northerners believe that we will support a moderate southern position they will be motivated to support an extreme northern position so that the compromise in the House is drawn in their direction. Since the North would choose its more extreme candidate the South should choose its more extreme candidate so that in the House the compromise is nearer our true position. I suggest that for some voters in each section the equilibrium was to vote for the more extreme candidate in order to accomplish moderate ends. The North always had more electoral votes than the South, but this had never made a difference before.

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The unintended effect of the strategic voting for the more extreme candidates contributed to Lincoln’s margin of victory in the crucial Lower North. The problem was exacerbated by the fact that plurality voting among four major candidates did not register the information that southerners preferred Douglas to Lincoln and that northerners preferred Bell to Breckinridge. Finally, the electoral college gave a majority to Lincoln with only a plurality of the popular vote. I do not claim that the collapsing-middle hypothesis is strongly supported, but if it did have any strength, consider the implications. I argued that people gathered information on the attitudes of others from vivid events such as the election returns. Suppose that a majority of people in each section are moderate unionists (The New York Times before the election said that the moderate position of popular sovereignty was supported by nine-tenths of the people, Morison 1971, 1117), but a majority of people in each section vote for the more extreme candidate for strategic reasons. A northerner reading the election returns is shocked – he is a moderate, but obviously the southerners are extremists; the southerner knows that he is a moderate but that the northerners are extremists. Moreover, the moderate comes to believe that the people in his own section are more extreme than they really are and that he is behind the times. We have surprise, suspicion, feelings of betrayal, and quickening polarization of attitudes, consistent with historical depictions of the outcome. The hypothesis is not inconsistent with the proposition that the leaders of the Lower South wanted secession. If the Democratic Party would have united on Douglas in 1860 there was a chance they could have reprised their Presidential victory of 1856. Some split the party because they wanted to rule or ruin, and some split the party because they expected to muddle through, and it was the latter who were betrayed by unintended effects. The election dynamic also might have made it easier for the rule-or-ruiners in the South to mobilize the undecided in their section. Riker’s theory of dimensional manipulation Riker (1982, 197) says that the Arrow theorem leads us to understand the hitherto impenetrable mystery, “the motive force for the perpetual ﬂux in politics.” Riker criticizes as reductionist theories that attempt to explain changes in preferences; it is the task of political science to explain political change as a function not of preference change but of institutions variably constraining pervasive disequilibrium. In multidimensional issue spaces there is almost always an alternative policy majority-preferred to any previous winner; hence there is continuing and intense dissatisfaction for a

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majority of political participants. The majority of dissatisﬁed losers has an incentive to introduce destabilizing new issues (Arrow) and new dimensions (McKelvey). Each voter sees politics in two or three dimensions, different voters see different dimensions so that in total there may be many dimensions, perhaps more dimensions than there are voters. Leaders competing for position create and advocate new dimensions. Just as Procter and Gamble offers new brands of soap on the consumer market, so does the politician offer new issues and dimensions to the citizenry. The economic and the political market each accepts or rejects the alternatives offered. Market needs are well deﬁned, however, and political needs are ill deﬁned. Therefore, politicians must try out alternatives “more or less randomly” (210). The political market is more like organic nature than it is like the economic market. “Thus, the rise and fall of issues is a process of natural selection, in which politicians, like genes, seek to survive and ﬂourish” (210). The mechanism of selection of political issues is apparently “institutions or constitutional structures” (211). Politics, like biological evolution, has no purpose. Riker’s account of the evolution of the slavery issue up to the Civil War is an illustration of his theory of manipulation and the natural selection of issues. The survey he hopes will establish the existence of manipulative agenda control on a grand scale. The political losers, he argues, successfully and luckily introduced a new issue or dimension so as to generate cycles or disequilibrium that they resolved with the Civil War thereby ﬁxing their coalition as supreme in American politics for several generations. I accept part of Riker’s story. From 1800 to 1860 there was an intersectional coalition of agrarian expansionists – Jeffersonian Republicanism and then Jacksonian Democracy – that frequently controlled the federal government. There was also a less successful commercial coalition, ﬁrst organized as the Federalists, later organized as the intersectional Whig Party, and ﬁnally organized as the Republicans, which constrained the agrarians but less frequently controlled the federal government. The commercial party desired high tariffs to protect industry, the agrarians low tariffs to obtain cheaper imports and promote exports; the commercial party wanted internal improvements such as canals and railroads, the agrarian party did not directly beneﬁt from commercial development; and so on. The multitude of issues imperfectly dividing the coalitions, and their evolution over time, are more intriguingly complex than this caricature, but we can’t afford to go into detail here (see Ashworth 1995, 366–492 for a thick discussion up to 1850). I also accept that from 1800 to 1860 politics was often organized along two dimensions, a usually stronger dimension of economic conﬂict and a usually uncorrelated and weaker dimension of sectional conﬂict.

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Riker’s argument is that the losing commercialists sought with one or another issue to split the winning agrarians. They tried the slavery issue several times and ﬁnally hit the jackpot with it in 1860. They used their victory in the Civil War to establish a new institutional equilibrium favorable to their coalition and unfavorable to the losers of that war. In Riker’s theory (1982, 200) it is the “skill, energy, and resources” of leaders, rather than the preferences of the population, that account for political change. For purposes of the theory it is as if the distribution of preferences were ﬁxed from 1800 to 1860; the engine of change is differences in politicians’ abilities to manipulate the agenda inside multidimensional issue space. Why does Riker assign causality to political leaders? Because of the episodic nature of the crises over slavery. Slavery existed for 200 years, and was settled by the constitutional convention for 30 years when the ﬁrst crisis, the Missouri controversy, arose in 1819. No economic factors account for the rise and fall of the slavery issue in the two years of the Missouri controversy, underlying sentiments were the same before and after, by elimination that leaves political leadership as the explanatory variable, according to Riker. The slavery issue subsided and lay quiescent until the controversy over the gag rule in the 1830s and then ripened into the episodic crises of the Wilmot Proviso in 1846, the Kansas–Nebraska Act of 1854, and the election of Lincoln in 1860. There is an alternative explanation, however. Weingast (1998), Riker’s quondam coauthor, explains that national crisis erupted whenever the sectional equilibrium in the Senate was threatened. For purposes of apportionment of representation in the House and the electoral college the South enjoyed a 35 vote for every slave owned, it had an effective sectional veto over selection of the President, it was the majority faction in the majority party, it was overrepresented on the Supreme Court, and it also enjoyed blocking power in the Senate. The US Senate is made up of two senators from every state, and from 1792 to 1858 the number of either free or slave states almost never exceeded one another by more than one; as the country expanded there was a deliberate effort especially by the South to maintain an equal sectional balance in the Senate (Weingast 1998, 154). Antislavery measures often passed the majoritarian House only to die at the hands of the southern veto in the antimajoritarian Senate (Weingast 1998, 168). In 1819 it was proposed to admit Missouri as a slave state, raising the question of whether the remainder of the vast but unsettled Louisiana Territory would be open to slavery. Northerners opposed admitting Missouri as a slave state for one reason because it was well north of the existing slave states; southerners opposed requiring Missouri to be a free state in part because it was settled by southerners. The eventual

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compromise, passed with many southern and fewer northern votes, was to admit slave Missouri as an exception above that latitude but otherwise close the remainder of the Louisiana Territory north of 36 degrees 30 minutes to slavery; also Maine was brought in as a free state to balance Missouri in the Senate. The next sectional crisis arose over the Wilmot Proviso starting in 1846, which emerged just as the United States was almost doubling its territory with the Mexican and Oregon acquisitions. California was admitted as a free state in 1850, giving the North an edge of one in the Senate, and under old expectations the South would be due the admission of a slave state. Blocked by the Missouri Compromise, the South had no practical opportunity for the organization of a new slave state, however. That is one reason why the Democrats at the height of their power in 1854 passed the Kansas–Nebraska Act. The plan was to encourage admission of Kansas as a slave state (and Nebraska as a free state many years later), but Kansas was north of 36 degrees 30 minutes and could not be organized as a slave state unless the Missouri Compromise was repealed; thus, another crisis. Minnesota and Oregon were admitted as free states in 1858 and 1859 respectively, making for an imbalance of 18 free states and 15 slave states in the Senate. By 1860 the South had lost not only the Senate, but the presidency, and then came the Civil War. Yes, there is a political explanation for the succession of episodic slavery crises, but it is the threat to sectional equilibrium in the Senate, not, as Riker would have, it the arbitrarily variable activation of dimensions by political operators. It is not exactly true that slavery and other sectional issues were quiescent except for periodic crises. Even in 1776 South Carolina threatened to secede over the question of federal taxation of slaves. Under the Articles of Confederation there was a controversy over navigation rights on the Mississippi that agitated the southerners; the Ordinance of 1787 forbade slavery in the Northwest Territory. In the Federal convention of 1787, delegates Gouverneur Morris and Rufus King excoriated slavery. At the ﬁrst Congress in 1790, Benjamin Franklin forwarded a Quaker petition beseeching federal action for the ultimate abolition of slavery (Stephens, in Hesseltine 1962, 124). In 1798 the Virginia and Kentucky Resolutions in response to the Alien and Sedition Acts were veiled threats of southern secession. In 1801 the Federalist Party was obsessed with the thought that Jefferson would not have won the presidency without the arrangement permitting the slave states 35 of a person’s worth of representation for every slave owned. In 1804 the House voted to ban slavery in the Orleans Territory (the measure lost in the Senate). Federalist leaders based mostly in the northeast threatened secession and a separate

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peace themselves during the War of 1812, destroying themselves as a party in the process. There were other political controversies over slavery in the west in 1784, 1785, 1789, 1802, 1804, and 1812. Then there was the Missouri controversy in 1819 and 1820. After the Missouri Compromise, “sectional hostility was not so much reduced as partly diverted into other channels, primarily of an economic nature. Meanwhile, the problem of slavery continued to be a troublesome element in American politics, always rumbling below the surface and sometimes erupting into controversy on the ﬂoors of Congress” (Fehrenbacher 1995, xiii). In 1832 South Carolina called a state convention and unilaterally nulliﬁed high federal tariffs, but President Jackson credibly threatened military action, and the crisis was defused by compromise (Divine et al. 1999, 304–306). Abolition became an organized and mobilized force in the 1830s. From 1836 to 1844 Congress enforced a gag rule to prevent the acceptance of citizens’ petitions against slavery. Northerners delayed admission of slave Texas for almost a decade (1836–1845). Then came the Wilmot Proviso and all that followed. (Except where noted otherwise, incidents are collated from Moore 1967, 1–32; Riker 1982, 215; Weingast 1998, 168). This is merely a panoramic sampling; close-ups would show frequent tensions over sectional issues including slavery. At the same time even in the feverish 1850s slavery was by no means the only political issue; people were concerned with other federal issues, and were much more concerned with state and local issues, and of course supremely concerned simply with leading their lives. The slavery conﬂict was always on a smolder though and would ﬂare, not arbitrarily, but when there was reason for it to ﬂare. Riker’s account of the Missouri controversy marshals support for his hypothesis of activation of dimensions by political leaders, but appears not to be completely supported by his sources. Consonant with his theme of arbitrary manipulation, Riker (1982, 217) tells us that: The immediate origin of the Missouri issue can fairly be attributed to the pettiest of politics. The motion to amend the Missouri bill was offered by James Tallmadge of New York. He was about to become a candidate for the state senate from New York City . . . [Democrat] Tallmadge had a special reason for raising the slavery issue . . . In New York City there were a signiﬁcant number of black voters, concentrated in marginal wards and typically Federalist in loyalty. Contemporary writers as well as recent historians have asserted that, as a result of his amendment, Tallmadge stood to gain black votes.

Riker cites Moore (1967, 36–37) in support of his fair attribution. The allegation is a routine one against politicians concerned with racial equality in the United States. During debate about the 17th Amendment in 1911

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southerners belligerently charged that northern senators concerned over negro voting rights in the South, and particularly New Yorker Depew, were motivated by greed for negro votes in their states; some senators were even known to have received negroes in their Senate ofﬁces, they charged. Gary Miller (1997, 182) notes that the same “insistent derogation of the motives of those who challenged the received racial pattern” was made against Rufus King during the Missouri controversy in 1820, and, “In mid-twentieth century America, white proponents of civil rights would be regularly accused of . . . taking the stands that they did in order to win ‘the Negro vote.’” It takes historical excavation even to determine that in 1818 Tallmadge was not a candidate to succeed himself in the US House of Representatives. Tallmadge was ill (Moore 1967, 40) and also his son had just died, and that may have been why he left the US Congress. In 1819 he was nominated by the Clinton faction of the Democrats for the New York State Senate. Moore (1967, 37) reports that it was believed his stand on Missouri would help him in the state Senate election, but Moore does not in any way suggest that this prospect is what motivated Tallmadge’s Missouri stand. In 1817, Tallmadge had worked for the ﬁnal emancipation act in New York State, to free all slaves ten years hence (Freehling 1990, 144). Moreover, Tallmadge lost the state senate election – and later abandoned the Clinton faction for the rival Tammany faction that had defeated him in 1819. Moore (1967, 36) tells us that Tallmadge was a man of great ability who did not rise as far as he could have because he was too much of an opportunist, changing sides too easily (that a politician would fail because he is too much the opportunist is an impossible thesis in Riker’s scheme). But does Moore (1967, 38–39), Riker’s source for the charge, believe that Tallmadge was an opportunist on the slavery question? Though more of a politician than a statesman, Tallmadge did have deep convictions and seems to have been motivated primarily by humanitarian and patriotic considerations in opposing the extension of slavery to new states. He retired from Congress soon after the long contest over Missouri began but continued to take a lively interest in it and wrote letters to his friend Congressman John W. Taylor, urging him to keep up the ﬁght. In his correspondence with Taylor he spoke of the contestants as being “cupidity” on one side and “principle” and “suffering human nature” on the other. While doubtful that his amendment to the Missouri bill would ever pass, he expressed a hope that it “may have produced moral effects which will eventually redeem our beloved country from Disgrace and Danger.” These sentiments were shared heartily by his family. His wife memorized portions of a speech on the subject, and his parents were proud of him – “Especily,” as his religious mother wrote, because they thought he was “on the Side of truth and justice.”

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Riker claims that Tallmadge was an opportunist on the slavery issue, but his sole citation is to a source which says he was not. Tallmadge’s failed quest in early 1819 was in later 1819 taken up by New Jersey Quakers and by philanthropists (the most entertainingly named of the reform groups, I think, was the New Jersey Society for the Suppression of Vice and Immorality and for the Encouragement of Virtue and Good Morals, Moore 1967, 70), especially one Elias Boudinot who also championed the Indians, and then was also taken up by prominent New Yorker and Federalist Rufus King, and by others, and eventually aroused the political North to public meetings, petitions, mandates – slavery in the territories became a major national issue. Now there is an odd turn in Riker’s argument. It was not Tallmadge’s allegedly opportunistic ploy, nor the organizational efforts of Boudinot, King, and their ilk, but rather “the interest of the large public” (Riker 1982, 217) that explains the event. He rejects a preference-change argument on the previous page (216): “no great change of the American heart occurred in 1819–1820.” But his argument about a large public interest must explain why the interest was dormant before 1819 and after 1820. What he means by the interest of a large public relates to the death of the Federalist Party by 1819. The Federalists were commercialist and also aristocratic; the electorate, expanded both by extension of the franchise and settlement of the frontier, tended to be agrarian and wanted agrarian policies from the national government; and the Federalist leaders had arguably committed treason with respect to the War of 1812. Although the Federalist Party was dead, its constituencies for high tariffs, internal improvements, and commercial development still remained, even if some of them had been forced to ﬁnd political refuge in an unnatural home, the Jeffersonian-Republicans. Thus, the commercialist losers were trying out a new issue, slavery, in the hope of splitting the winning agrarian coalition, “the motive for the agitation was to ﬁnd a new and disequilibrating program, a new agenda whereon dissident [Jeffersonian-] Republicans and old Federalists could combine to win” (Riker 1982, 218). They tried out slavery in 1820, they tried out anti-Masonic agitation after 1830, they tried out nativism after 1850, and they tried again with slavery after nativism failed, the story goes. “[T]he slavery issue was embraced with enthusiasm in 1819 and repeatedly thereafter until it generated cyclical majorities and civil war” (Riker 1982, 219). The commercialists failed the ﬁrst time they tried because the agrarian coalition squelched the slavery issue with the Missouri Compromise; the issue was buried for a time because the agrarians won and the commercialists lost. Riker’s argument is hard to grip. The motor force is at one point creation of new dimensions by the Yankee elite, at another point it is the activation of latent

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dimensions by the same elite, and at yet another it is already manifest political preferences among the masses. Conventional explanations, Riker says, for the rise of antislavery agitation in the 1830s include the political secularization of religious enthusiasm, an explosion of philanthropic associations and reform movements, antislavery among them. Among the various ﬂorid causes, only slavery became a national political issue, so the argument from moral zeal is without force, according to Riker. A second explanation is that slavery was in decline all over the world and would have arisen as an issue regardless of political institutions. A third explanation is that proﬁtable cotton plantationism expanded mightily in the 1830s and that the expanding territory, population, and wealth of the slave power increasingly threatened free labor in the North. Riker rejects the global-decline and the slave-power-expansion explanations as well because they do not account for the Missouri agitation of 1819–1820. His alternative theory is that in 1820 and in the mid-1830s the commercialist faction promoted slavery on the national agenda so as to try and split the agrarians. The commercialist elite avoided the issue from 1820 to 1829 because they were concentrated on the election and reelection of John Quincy Adams as President ( J.Q. Adams was Monroe’s Secretary of State, won the presidency in the House in 1824, and lost to Jackson in 1828). After that, the commercialists were distracted by the curious anti-Masonic political movement. The northern commercial elite was also drawn into the Whig coalition, a motley crew originally united only by its opposition to the policies of President Jackson, and including southern elites who opposed the economic policies, and crude populism and (white) majoritarianism of Jackson; the northern Whigs were restrained on slavery from the need to keep their southern allies in the coalition. Slavery was always an evil but only sometimes a political issue, says Riker. It appeared again on the national agenda around 1835 because it was in the interest of the commercial elite to put it on the agenda. They encouraged petitions from antislavery groups concerning the abolition of the slave trade or of slavery in the District of Columbia (one place where Congress had constitutional jurisdiction). Their motive, Riker says, was to obstruct Congressional business. The Democrats responded with a gag rule that effectively forbade the receipt of such petitions, in order to get on with business and also to please Southern Democrats who wanted to delegitimate antislavery sentiments. The leader against the gag rule was former President John Quincy Adams, who had taken up a career as a gadﬂy in the House of Representatives. J.Q. Adams, says Riker (1982, 222), was “the chief generator of the slavery issue that ultimately destroyed the Jacksonian coalition.” Thus, we are back to the familiar thesis of arbitrary

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manipulation of multidimensional issue space with victory to the forces possessing a superior will to power. When the Whigs won a majority in the House they attempted to continue the gag rule in order to mollify their southern wing, and moved to censure Adams. Adams’s powerful rhetoric forced a tabling of the motion to censure. Another northern antislavery Whig, Giddings, was censured as well, but resigned and was triumphantly reelected by his district. Then in 1844 the tiny antislavery Liberty third party ﬁelded a Presidential candidate, who may have cost the Whigs the election in New York by a few thousand votes (the Whigs won the Presidential contest in New York four years before and four years after), and thus for the presidency as well. Thereafter, northern politicians, Whig and Democratic, had to worry about the antislavery issue, says Riker. We are into extremely complicated territory here and in this space I can do no more than sketch some issues. Riker’s continual impugnment of the motives of politicians becomes offensive. In one moment he tells us that he does not mean to suggest that the great antislavery politicians J.Q. Adams and Joshua Giddings were insincere opportunists. In the next moment he states that Adams never mentioned slavery as President and that Giddings did not support black suffrage in Ohio in 1858, as if to take back what he said. Adams and Giddings were not abolitionist cranks grinding out fanatical pamphlets in some puritan village but were supremely practical politicians on the national stage. A similar tension is played out time and again in politics: a practical politician who must actually satisfy the many constraints on implementation will advocate the moderate version of a cause whose followers take more extreme postures because they lack the responsibility of governance. There is nothing insincere about pragmatic moderation. Riker reconciles the tension by saying that Adams and Giddings were Whigs ﬁrst and abolitionists second. This is inaccurate, as Adams, allegedly the mastermind of the commercialist coalition, was never fond of either party division or of the Whig Party; and Adams was never an abolitionist in the strict sense of the term. And Adams must have been quite the political genius in 1835 to foresee that, following his death in 1844, although the slavery issue would destroy his Whig Party in 1850 his Yankee grandsons would come roaring back with a sectional Republican victory 25 years later in 1860. The Whig coalition certainly never believed that Adams’s or Giddings’s agitations promoted the party’s political fortunes. And who initiated the gag rule controversy? Historian Lee Benson (in Stampp 1974, 21) argues that southern leaders cultivated the controversy in order to split the Whigs! James H. Hammond [of South Carolina] accidentally stumbled on the issue of trying to prevent Congress from receiving or routinely disposing of antislavery

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petitions. Accidentally discovered by Hammond . . . what came to be known as the “Gag Rule” issue was consciously used to heighten sectional antagonisms and Southern national consciousness. If a small group of Northern abolitionists had not existed, Southern nationalists, sectionalists and provincials would have to create them – as, in fact, they did.

Thus, if we did not have the luxury of reading history backwards, following the unsurpassed victories of the Democratic Party in the year 1852 we would have had to congratulate the southern agrarians for their brilliant success in splitting and mastering the Whig commercialist coalition. Also, I believe, Riker has his causation backwards. Did men such as Adams and Giddings instrumentally take up issues in order to advance the Whig coalition they belonged to, or did they instrumentally belong to the Whig coalition in order to advance the issues they believed in? Adams had aristocratic disdain for party spirit and had belonged to several. Giddings was motivated to enter politics from antislavery conviction, and I imagine that he would join whatever coalition would best advance his political goals including prominently antislavery. Giddings abandoned the Whigs for the Republicans. Further, I do not deny that politicians gleefully seek to divide the opposition and that this was an important part of antebellum politics. The disagreement is about the causality. For Riker political outcomes are a function of arbitrary manipulation in multidimensional issue space, no better than random. I think that, barring antidemocratic institutions, political outcomes are a function of the population’s preferences, and that collective change in a proper democracy tracks changes in the opinions and the wishes of the political public. Yes, political ﬁgures such as John Quincy Adams or Abraham Lincoln help form public opinion. But they operate against constraints; they must begin from unordered beliefs and desires in the population; they must craft a coherent, attractive, and useful vision; and the ultimate constraint on their ideological leadership is its popularity. Lincoln, for example, succeeded because he was luckily in the right places at the right times, because he was diligent, talented, and moderate, but also because of his gift for wise and apt argument. His argumentation helped people form their intellectual and emotional responses to difﬁcult problems better than did the argumentation of others. Riker’s story is that the commercialists kept at it with slavery until they succeeded at generating a cyclical majority. The most compelling and memorable part of his volume are the two case studies demonstrating cycles with the Wilmot Proviso in 1846 and the Lincoln election in 1860 resulting in Civil War. We have seen, however, that the case studies are mistaken. Without those two cases the multidimensional-disequilibrium argument is like a joke without a punch line. It doesn’t work. But there

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are a few issues left to examine. Concluding his vignette on the Wilmot Proviso, Riker (1982, 227) declares, “the issue of slavery, ﬁrst broached in 1819 as a means to break up the [agrarian] Jeffersonian intersectional coalition, actually did so in 1846.” He also explains why the commercialists ﬁrst succeeded in 1846. The northern Whig commercialists had often agitated on slavery but the northern Democrats who had resisted until that point succumbed in 1846 because they were newly afraid of losing elections on the slavery issue. Notice that Riker’s is inadvertently a preference-change argument here, not an argument from multidimensional disequilibrium. Weingast’s (1998) argument, that the sectional balance in the Senate was threatened by ambiguity in the status of the territories, is the more parsimonious explanation for the eruption of the issue in 1820, 1846, and 1854. Finally, the complete disequilibrium of 1860, explains Riker (1982, 229), “is how the slavery issue destroyed the Jeffersonian-Jacksonian coalition,” but we know now that his analysis of 1860 is wrong. Three elements of Riker’s doctrine are: that majorities are arbitrary and meaningless (1982), that the Civil War was brought on by the Yankee elite which had sought its opportunity for sixty years (1982, 213–232), and that the US Supreme Court should protect constitutionally guaranteed property rights threatened by the arbitrary and meaningless nature of majorities (Riker and Weingast 1988). These three elements happen to be echoed in Confederate ideology. Edward Pollard, one of the South’s leading apologists, wrote during the war in 1863 that it was a mistake for northerners to consider that the Constitution “resulted in the establishment of a grand consolidated government to be under the absolute control of the numerical majority” (Pollard, in Hesseltine, 1962, 44). Pollard said that the Missouri Compromise of 1820: afforded early and conclusive evidence of the secret disposition of all parties in the North . . .The issue of the controversy was not only important to the slave interest, but afforded a new development of the Northern political ideas of consolidation and the absolutism of numerical majorities. The North had acted on the Missouri matter as if the South had no rights guaranteed in the bond of the Union, and as though the question at issue was one merely of numerical strength . . .“The majority must govern” was the decantatum on the lips of every demagogue, and passed into a favorite phrase of Northern politics.

The Richmond, Virginia Semi-Weekly Examiner complained in 1860 that in “the Northern States the popular power has no check but the popular reason and will . . . There is but one defense . . . it is the ability and the will of the minority to resist the action of the ruling majority” (in Stampp 1974, 142–143). The writer explains that “the conservative inﬂuence of

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domestic slavery” and other class distinctions serve as a desirable check on the popular will in the South. Hesseltine (1962, 38) says that, “In the view of Alexander H. Stephens, Vice-President of the Confederacy, the Southerners were not only exercising their constitutional rights, but were defending the constitution of the Founding Fathers from the victorious conspirators who had seized the apparatus of the federal government.” Stephens (in Hesseltine 1962, 125) himself says that the usurpers had awaited their moment for sixty years: This Party, as we have seen, [in 1798] assumed the popular name of Federal, as it assumed the popular name of Republican in 1860. [The Alien and Sedition Acts] of 1798 came near stirring up a civil war, and would most probably have resulted in such a catastrophe if the Party so organized with such principles and objects had not been utterly overthrown and driven from power by the advocates of our true Federal system of Government, under the lead of Mr. Jefferson, in 1800. It was after this complete defeat on these other questions that the Centralists rallied upon this question of the status of the black race in the States, where it continued to exist, as the most promising one for them to agitate and unite the people of the Northern States upon, for the accomplishment of their sinister objects of National Centralization or Consolidation.

Finally, the Supreme Court’s disastrous Dred Scott decision interpreted the Constitution to read that the property right in slaves should be protected against the depredations of majorities. Riker and Weingast (1988, 373) call in the Virginia Law Review for a return to the jurisprudence of “the nineteenth and early twentieth century,” in which the Supreme Court would interpret the Constitution to read that property rights should be protected against the depredations of majorities. I am not suggesting that Riker and Weingast wish to reinstitute slavery. I am mischievously pointing out that they neglect to address an awkward implication of their argument. Preference developments from 1800 to 1860 The more conventional and the more parsimonious category of explanation for political changes in the period under study is developments in the population’s preferences. We have seen the evidence for the disequilibrium hypothesis. What is the evidence for the preference-development hypothesis? The slavery issue was plucked by a canny cabal from the chaos of multidimensional issue space in order to split and subordinate their enemies, the story goes. If the abolition of slavery is just a matter of arbitrary manipulation, however, then we should see among similar societies variations in

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the presence of the institution of slavery. In some democracies it happened that slavery was the issue used by one faction to subordinate another, but in other countries it happened that other issues served that purpose; such that in some countries slavery was abolished and in some countries it was not. My suggested prediction from Riker’s premises fails, however. Among the developed democracies slavery is extremely rare in practice and is universally and strictly prohibited by law. This suggests that there is something to the global-development hypothesis that Riker rejects. In 1820 all the Western Hemisphere but for Canada, the northern United States, Haiti, and the Dominican Republic was slave territory. Slavery was abolished in the four Central American countries and Chile in 1823, in Mexico in 1829, in all British possessions in 1834, in Paraguay in 1843, in all French possessions in 1848, in Bolivia in 1851, in Colombia in 1852, in Ecuador and Venezuela in 1854, in Peru in 1855. By the time of the US Civil War only Cuba, Puerto Rico, and Brazil continued to condone slavery. The day before Lincoln’s inauguration the Tsar of Russia freed the serfs (see Nevins 1950, 132–170 on the global decline of slavery). “While the struggle to end slavery was often associated with violence, it was only in the United States that slaveowners resorted to full-scale warfare to halt the abolitionist trend” (Fogel 1989, 205). The southern ideologists rejected the global-development hypothesis as well. In his bill of particulars against the North, apologist Pollard (in Hesseltine 1962, 55), discusses international opinion just after loss of sectional equilibrium in the Senate and unfair tariffs and before the horror of John Brown’s Harper’s Ferry raid: It was said that the South was an inferior part of the country; that she was a spotted and degraded section; that the national fame abroad was compromised by the association of the South in the Union; and that a New England traveler in Europe blushed to confess himself an American because half of the nation of that name were slaveholders.

The plaint of the wounded bully is ill concealed. Poole and Rosenthal (1997) set out to measure the dimensionality of all roll-call votes in the US Congress. As we have seen, they found that for all such votes, 83 percent are explained by one dimension and another 2 percent are explained by a second dimension. The ﬁrst dimension usually captures party loyalty and the second dimension usually differentiates the members by region within each party (46–51). Before the rise of the second, Democrat and Whig, party system in the mid-1830s the second dimension frequently involved public works. From 1837 through 1850 the second dimension frequently involved slavery or public lands. The Congress of 1851 and 1852, after the Compromise of 1850, is spatially

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chaotic, completely disorganized in dimensional terms. By the Congress of 1853 and 1854 slavery had become the ﬁrst dimension of politics and remained so into the Civil War. Furthermore, the major vehicle for realignment in the antebellum period was replacement of legislators, not changes in legislators’ positions (90), which I interpret to mean that the change was responsive to the electorate’s wishes. Independently from Poole and Rosenthal and their roll-call data, historian Fogel (1989, 321) identiﬁes the Congress of 1851–1852 as a period of transition. The political agenda of the prior decades was obsolete and a new agenda was yet to emerge. That Congress was split into a multiplicity of factional groupings who only occasionally coalesced – neither party nor section was inﬂuential. The primary political issues in 1851–1854 were local, responses to the turmoil of mass immigration, urbanization, and early industrialization in the North. Poole and Rosenthal also trace the history of roll-call votes on slavery issues (1997, 91–100). In the ﬁrst 14 Congresses there were only 43 roll-call votes on the issue and only weak party or sectional patterns. Almost three-fourths of the roll-call votes on slavery between 1817 and 1831 took place in the 15th (1817–1818) and 16th (1819–1820) Congresses. Historians call this the Era of Good Feelings; controversy over foreign wars had died away, the Jeffersonian-Republicans had adopted some of the Federalists’ economic policies, because of the demise of the Federalists there was no partisan divide, and President James Monroe was reelected in 1820 with only one symbolic vote opposed in the electoral college. The Missouri controversy played out in 1819 and 1820, and slavery votes ﬁt well into one dimension (indeed is the only issue with a high degree of ﬁt), but otherwise the spatial model is quite weak in this period, the 17th Congress (1821–1822) being the worst-ﬁtting to the model in American history. Poole and Rosenthal state that the collapse of the party system during the Era of Good Feelings “did not occur because slavery was the new, destabilizing dimension” (1997, 95). The collapse of the ﬁrst, Republican and Federalist, party system came about because the foreign-policy and economic issues that structured it were no longer of importance. Slavery rose as a Congressional issue with the Missouri controversy but fell with the Missouri Compromise. The second, Democrat and Whig, party system arose along an economic dimension but slavery never completely vanished as an issue, according to Poole and Rosenthal. The bulk of slavery votes came after 1835, they say, and slavery voting fell increasingly along a second dimension. “By 1853, this [ﬁrst] economic dimension collapsed and was replaced by the slavery dimension” (95). I suggest rather that after 1853 the slavery dimension merged with the economic dimension. What attraction did the

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Democratic Party hold for the northern agrarians? Originally, they were drawn to the Jacksonian coalition because it promised greater democratic equality and liberty (for white males) than did the aristocratic commercialists (see Fogel 1989, 316–319). Democrats advocated territorial expansion and the cheap sale of federal land to promote those values, and Whigs opposed territorial expansion and advocated that federal land be sold at high prices in order not to depress the price of the land they owned or inﬂate the price of the labor they employed. During the Congress of 1853–1854 the Democrats abandoned their deﬁning cheap-land policy because their southern wing had concluded that the policy politically advantaged the North. In the same Congress the Democrats abrogated the boundary of the Missouri Compromise, and thereafter slave settlers and free settlers clashed in the territory of Kansas. Meanwhile, over the objections of some of its formerly Whig members, the Republican Party took up the cause of cheap land. Northern agrarians were drawn to the new party that promoted their democratic equality and liberty, the Republicans. Poole and Rosenthal’s ﬁndings suggest that tensions over slavery increased over a long period, that the realignment within Congress was sudden, and the realignment was initiated well before the Republican Party became a force in politics (1997, 99). I interpret Poole and Rosenthal’s data to mean that there was not a common multidimensional issue space from 1800 to 1860 and thus that variations in political outcome from 1800 to 1860 were not due to the arbitrary manipulation of that space by political conspirators. Poole and Rosenthal show clearly that there was a strong party dimension and a weak sectional dimension and that by 1853 the sectional dimension became strong and in its wake restructured the parties along sectional lines. It was not, however, the Slave Power Conspiracy nor the Black Republicans (phrases of the respective sectional conspiracy theorists) who brought about the realignment, rather it was changes in the preferences of the political population. “By the 1850s, slavery was not a new issue but a very old one that had become more intense in both the North and the South” (emphasis added, 91). Weingast (1998, 163) too holds that northern opposition to slavery increased over the antebellum period. According to Potter (1976, 38–41), during the colonial period there was little difference between the sections concerning the morality of slavery, although slavery was far more prevalent in the South. The ideals of the Revolutionary War inspired both North and South to condemn slavery as evil; emancipation and colonization societies were as common in the Upper South as they were in the North. But as the proﬁtable cotton economy expanded and slavery with it, the economic and ideological center of the South shifted from Virginia to South Carolina. By 1832 the southern

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antislavery movement had vanished and an ideology of slavery as a positive good had arisen. Meanwhile, slavery had been gradually abolished in the North. Sectional opinion on slavery further polarized in the 1840s and 1850s. Weingast (1998) criticizes Riker’s model for failing to explain the stability of the second two-party system even with slavery always lurking in the background and for failing to explain why collapse came in the 1850s. The crisis of 1819–1820 and the crisis of 1846–1850 were each resolved, but the crisis of the 1850s was not. Weingast explains the change as a product of four factors. First, the slave states needed to expand in number in order to preserve sectional veto in the Senate but in the 1850s they ran into constraints; due to the increasing price of slaves expansion was not economically feasible in available new territories and politically slave settlers were hemmed in by the Missouri Compromise. Second, immigration to the North changed the size of the population and the nature of its economy and society. In 1800 the sections were roughly equal with two million souls each; in 1860 the North had a population of 20 million compared to 7 million whites and 4 million blacks in the South. It became more feasible to organize an all-northern party. Third, early in the period settlers in what we now call the Midwest were mostly self-sufﬁcient and what commerce there was went south along the Mississippi River. Later in the period, Midwest inhabitants produced more for the market and shipped their goods east by water or by rail. The second and third factors meant that the pivotal voter became more oriented to the North than to the South; I call this a matter of preference development. Fourth, Americans at the time did not fully understand the political implications of the second and third factors. We know now that political space had collapsed and that the Democrats were about to collapse with it, but in 1853 and 1854 the Democrats believed they were at their strongest. They passed the Kansas–Nebraska Act only to drive northerners out of the Democratic Party and into the anti-Nebraska groupings that became the Republican Party. Finally, Americans early on had dealt with slavery by means of geographical separation. There were free states and there were slave states, and most of life revolved around local or, at best, state concerns. The federalist institutions of the Constitution reinforced the separation. When the destabilizing issue of slavery in the territories arose, the natural solution was geographical separation as well. Slavery shall be allowed south of this line and shall be forbidden north of this line. Later on, increasing population, communication, and transportation brought the sections into increasing contact. Notice that trouble began when geographical separation failed. The Kansas–Nebraska Act violated the boundary of

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separation the northerners thought they had. The subsequent mixture of free settlers and slave settlers in Kansas resulting from the Democratic doctrine of popular sovereignty proved a political and a psychological nightmare – it drove John Brown mad. Most people are familiar with Seward’s (in Stampp 1974, 105) remark about “an irrepressible conﬂict,” but few know the ﬁne causal analysis that prefaces his remark: Hitherto, the two systems have existed in different States, but side by side in the American Union. This has happened because the Union is a confederation of States. But in another aspect the United States constitutes only one nation. Increase of population, which is ﬁlling the States out of their very borders, together with a new and expanded network of railroads and other avenues, and an internal commerce which daily becomes more intimate, is rapidly bringing the States into a higher and more perfect social unity or consolidation. Thus, these antagonistic systems are continually coming into closer contact, and collision results. Shall I tell you what this collision means? They who think it is accidental, unnecessary, the work of interested or fanatical agitators, and therefore ephemeral, mistake the case altogether. It is an irrepressible conﬂict between opposing and enduring forces, and it means that the United States must and will sooner or later become either entirely a slave-holding nation or entirely a free-labor nation.

The northern public wanted both to oppose slavery and support the Constitution and the Union, according to Potter (1976, 46–50), and they managed those contradictory goals by keeping them contextually separated. They accepted the constitutional obligation that left the question to each state and they abolished slavery in their own northern states. They had no personal responsibility for the actions of the southern states, and they believed that slavery would eventually die out. Anything that tended to expose the incompatibility of the values of antislavery and Union “by bringing them to the same level and forcing them to confront one another in the same context was . . . extremely threatening to the northern mind. This was why the abolitionists incurred so much hostility” (Potter 1976, 47). But where the abolitionists failed, the acquisition in 1846 of vast new territories subject to federal jurisdiction forced the values of antislavery and Union repeatedly into the same context, and the contradiction between them could no longer be managed by techniques of geographical or emotional compartmentalization. Riker promised to explain to us the perpetual ﬂux of politics, but his evidence was faulty. Nor can he explain to us stable continuity in politics – slavery was a tumultuous issue in the antebellum period, but after the Civil War slavery did not return as an institution nor has it returned to

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any country that has effectively abolished it. The great political and moral drama of the Civil War was not a consequence of arbitrary manipulation of the agenda in a multidimensional issue space. As Seward said, “They who think it is accidental, unnecessary, the work of interested or fanatical agitators, and therefore ephemeral, mistake the case altogether” (in Stampp 1974, 105).

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Introduction We shall return to the problem of manipulation by introduction of new issues and dimensions. Meanwhile, we shall examine the remaining published and developed anecdotes of cycling I have been able to ﬁnd in the political science literature, beginning with Riker’s in this chapter, followed by others’ claims in the next chapter. In the ﬁrst case, Riker detects a cycle in the deliberations of the Convention that crafted the US Constitution. The question was how best to select the executive of the new regime. Riker believes there was a cycle among three alternatives – for the national legislature to select the executive by joint ballot of the two chambers, the same but by separate ballot of the two chambers, and selection by electors in the states – and hence that the ﬁnal outcome was arbitrarily decided by the more intense will to win of the faction that favored selection by electors. I show that Riker’s purported cycle arises from a failure to distinguish among similar but not identical alternatives. I argue that it is a more plausible interpretation of the record to distinguish among similar alternatives, and if this is done, the reversal, tie, and cycle alleged by Riker vanish. The Convention, supposedly deadlocked in cyclic indeterminacy on the question of the selection of the executive, appointed a committee to resolve the question overwhelmingly dominated by supporters of selection by electors. Appointment of the committee is consistent with my equilibrium interpretation of events, but is an anomaly inconsistent with Riker’s disequilibrium interpretation. Riker’s ﬁrst published attempt to demonstrate an Arrovian cycle was in 1958, a study of a sequence of votes on agricultural appropriations in the US House of Representatives. Riker believes he has demonstrated a collective ranking intransitive in dollar appropriations (250 > 200 > 225 > 142 > 100) that indicates the presence of a cycle. Riker obtains his cycle, however, by counting 13 or more voters who voted strategically for 200 > 225 million dollars. Riker is explicit that the sincere ranking of these 13 or more voters was 225 > 200. If the sincere 310

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rankings of all voters are aggregated then the outcome is transitive (250 > 225 > 200 > 142 > 100) and there is no cycle. In the absence of strategic voting, the agenda sequence dictated by House rules would have prevented attainment of the collectively highest-ranked alternative of 250 million dollars; but with strategic voting, the House selected its highest-ranked alternative. Riker’s ﬁnding of a cycle is conceptually mistaken. Federal Convention, 1787 Riker (1984), in his presidential address to the American Political Science Association, believes he has found a cycle in the records of the Federal Convention of 1787. He provides much more detail on this case than is his wont; consequently, there is less need for me to add historical context. Also, I shall neglect many details of his essay and focus on his dramatic central claim of a cycle that changed the content of the US Constitution. One of the more difﬁcult issues at the Convention was the question of what method should be used to select presidents of the new republic. The Convention began its deliberations from the so-called Virginia plan, which among other things recommended the election of the President by the national legislature. Those behind the Virginia plan and ultimately the ﬁnal Constitution were nationalists who believed that the prior Confederation was an ineffectively loose alliance of states ruled by irresponsible state legislatures, a threat to commerce and property within, and endangered by foreign machinations without. Thus, the original proposal was that the executive be selected by the national legislature rather than by the states. This original proposal did not cohere, however, with another prominent opinion among the nationalists, that the powerful new government be self-constrained by checks and balances among its branches. If the President were selected by the national legislature, then he would not be independent, rather the President would be the creature of the legislature, and “intrigue” over appointment would be one of the undesirable consequences (see Madison, II 34).1 Those who were not so strongly nationalist wanted the states to have some role in the selection of the executive, and a minority perhaps of a more populist bent preferred that the President be elected by the people. Whether by the national legislature, by state governments, or by the people, there remained the controversy of how to weight the interests of the small states against the large states, and the free states against the slave states, in the selection of an executive. Just prior to ﬁrst serious consideration of the question of the executive the convention had reached the Great Compromise, providing for equal representation of states in the Senate and representation proportional to

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population in the House of Representatives. One issue was which agents should select the executive, a second was how to count the votes of those agents, and a third complication was the question of length of term for the executive and eligibility for reelection. There was a desire to reward Washington’s ability, but a fear of eventual monarchy or worse arising from the strong executive power. Finally, the three dimensions of concern were not independent of one another, an adjustment in one might require an adjustment in another. Election of the executive by the national legislature was initially a feature of both the Virginia (large states) plan and the New Jersey (small states) plan. That mode of selection was approved on ﬁrst test, June 2, eight votes to two, Pennsylvania and Maryland opposed (Roll Call #12, II 81). On July 17, a motion for election by the people failed, only Pennsylvania in the afﬁrmative (Roll Call #165, II 32); a motion for election by electors failed, only Maryland and Delaware in the afﬁrmative (Roll Call #166, II 32); and a motion for election by the national legislature passed unanimously (Roll Call #167, II 32). The ﬁrst contest of interest to our more formal analysis was a motion on Thursday, July 19 to strike that the President be selected by the national legislature and insert that he be selected by electors appointed by legislatures of the states, and that states less than 100,000 in population be allocated one elector, those between 100,000 and 300,000 two electors, and those above 300,000 three electors. The portion providing for electors (Roll Call #182, II, 50–59) passed with six votes for (CT, NJ, PA, DE, MD, VA), three votes against (NC, SC, GA), one state divided (MA), and two absences (NH and NY); note that Rhode Island did not participate at all in the convention. The portion providing that those electors be appointed by the state legislatures (Roll Call #183) passed with eight afﬁrmative votes, Virginia and South Carolina opposing. The portion allocating different numbers of electors to the states was agreed to the following day (Roll Call #191, II 60–70). Label the alternative of selection of the executive by electors appointed by the state legislatures on July 19 as B. Label selection of the executive by the national legislature, originally proposed by the Virginia Plan, as A. On July 19 the convention voted for B > A. A six-year term of ofﬁce was also agreed to, and a proposal to forbid reelection failed. On Monday, July 23, Houstoun (GA) moved and Spaight (NC) seconded to reconsider the question of the mode of appointment of the executive (Roll Call #208, II 95). Notice that Houstoun’s Georgia and Spaight’s North Carolina, along with South Carolina (Butler of SC complained about the distance to send electors on July 19, II 59), opposed election by electors on July 19: “Houston urged the extreme inconveniency & the considerable expense, of drawing together men from all the

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States for the single purpose of electing the Chief Magistrate” (II 95). At this point it was assumed that electors would meet in the national capital, and that the capital would be New York or Philadelphia (McDonald 1985, 245). Houstoun’s July 23 motion to reconsider passed with seven votes for (NH, MA, CT, DE, NC, SC, GA) and three votes against (PA, MD, VA). On the same day constitutional questions other than those pertaining to the executive were unanimously referred to a ﬁve-member Committee on Detail. On Tuesday, July 24 Houstoun moved to strike “by electors appointed for that purpose by the Legislatures of the States” and to insert “by the national Legislature” (Roll Call #215, II 98) and the motion succeeded, with seven votes for (NH, MA, NJ, DE, NC, SC, GA) and four votes against (CT, PA, MD, VA). It is not clear in the record, but it seems to me that Houstoun’s motion must have repealed by implication the scheme allocating different numbers of electors to different states; if there were no electors then the scheme of allocating electors would be nugatory. Houstoun “dwelt chieﬂy on the improbability, that capable men would undertake the service of Electors from the more distant States” and Spaight again seconded Houston’s motion (II, 99). Label the alternative of selection of the executive by electors appointed by the state legislatures on July 24 as B . On July 24, the convention voted for A > B . This was a reversal of the vote of July 19. Whose votes changed? New Hampshire was not yet at the Convention on July 19, but on July 24 voted for election of the President by the national legislature. Massachusetts was divided on July 19, but on July 24 voted for election by national legislature. The New Jersey and Delaware delegations changed from supporting election by electors on July 19 to supporting election by national legislature on July 24. Riker (1984, 10–11) “guesses” that New Jersey and Delaware were inconsistent due to shifting absences among the members of their delegations. We might also hypothesize that the delegates to the Convention were rational. If they were rational, then two further possibilities come to mind. First, that when they voted on July 19 many delegates failed to consider the question of the expense and difﬁculty of convening electors, but that by July 24 they realized that the expense and difﬁculty was too much. If B is cheap election by electors as mistakenly understood on July 19 and B is expensive election of electors as correctly understood on July 24, then delegates were consistent in preferring B > A > B . Second, New Jersey and Delaware were members of the small-state bloc. Excluding Virginia, the most populous state, and Delaware, the least, the large states (MA, PA, VA, NC, SC, GA) were on average only about 10 percent larger in population, but were much larger in territory and thus more likely to gain population, than the small states (NH, CT, NY, NJ, DE, MD)

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(McDonald 1985, 218). The distinction had little to do with population; rather, the large states had claim to western lands and the small states did not (Farrand 1913, 82). One might speculate that some members of the New Jersey and Delaware delegations (although their small-state allies Connecticut and Maryland favored election by electors both on July 19 and July 24) observed that Pennsylvania and Virginia, two of the largest states, strongly wanted election by electors, and that by holding out New Jersey and Delaware imagined that they might extract favorable concessions from Pennsylvania and Virginia on the allocation of electors among states. The two possibilities are not necessarily exclusive. I do not know of direct evidence for the second possibility in the record, but later I shall describe indications that some small states sometimes held out on voting for election by electors in order to extract concessions from the large states. With an executive elected by electors the delegates had approved of a six-year term open to reelection. After returning to election by national legislature, on July 26 they changed to a single seven-year term for the executive (Roll Call #224), so as to prevent intrigue in reappointment. Finally, the entire scheme for the executive including several elements not discussed here was approved on Thursday, July 26 by a vote of six for, three against, and one state divided (Roll Call #225, II 118); New Jersey remained in the afﬁrmative but Delaware went to the negative on the entire scheme. If we label the entire scheme as A , then the convention preference was A > B just as the convention preference merely for election by national legislature was A > B . For our purposes A , the entire executive scheme, is equivalent to A, the portion of the scheme directing that the executive be chosen by the national legislature, hence A ∼ A (one might argue that A > A, but neither of these inferences are essential to my interpretation). The convention then adjourned until Monday, August 6, so that the Committee on Detail could do its work. Although on July 26 the Convention returned to election of the executive by the national legislature, debate on the question raised problems with the national-legislature alternative and suggested solutions to those problems which inﬂuenced the ultimate outcome in the Convention. Madison’s objections to the national-legislature alternative were quite cogent, although his suggested alternative of election by the people was politically infeasible. McDonald (1985, 246) is of the opinion that one of Madison’s arguments, that the equivalent of selection of the executive by the national legislature in Germany and in Poland was much inﬂuenced by foreign interference (II 110), “affrighted a number of delegates into moving toward a decentralized election.” One problem with election by electors is that the delegates believed that electors would mostly

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vote for candidates from their own states, with divisive and unstable results. Williamson suggested that electors vote for three candidates, and G. Morris immediately suggested that they be required to vote for two, at least one not from their own state (II 113–114). This idea was used in the ﬁnal compromise. The next Convention debate on the question of the executive is a month later, on Friday, August 24. It was an inconclusive and confusing day; important motions on the topic failed, some on tie votes. Rutledge moved to amend election of the executive by the national legislature to require election by the joint ballot of the House and the Senate, and this succeeded seven to four, the larger states tending for and the smaller states tending against (Roll Call #356, II 399). If the two chambers balloted separately then that would increase the bargaining power of the small states because they would enjoy equal representation in the Senate; a joint ballot would decrease small-state bargaining power. It was not only an issue of large state against small state, however. The primary concern was to avoid the deadlock that might arise from separate balloting: New Hampshire voted against its small-state interest and for joint balloting for this explicit reason (II 402) and was joined by three other small states. Label A as amended by joint ballot as C; then C > A . Next, the small states moved that in the joint ballot each state be entitled to one vote; this failed with ﬁve afﬁrmative votes, four from small states, and six negative votes, ﬁve from large states (Roll Call #357, II 399). A motion to eliminate selection of the executive by the national legislature in favor of election by the people failed, with Pennsylvania and Delaware in the afﬁrmative, and the nine remaining states in the negative (NY was absent, Roll Call #355, II 399). The problem with direct election for the delegates is that it would favor large states over small states and free states over slave states; in contrast, a scheme of election by electors is amenable to allocating electors among states in some manner that balances the interests among the different states. Another motion to eliminate selection of the executive by the national legislature in favor of election by electors chosen by the people of the states failed with ﬁve votes in the afﬁrmative (CT, NJ, PA, DE, VA) and six votes in the negative (NH, MA, MD, NC, SC, GA; Roll Call #359, II 399). Note that New Jersey and Delaware are back in the election by electors camp. A motion to postpone consideration of mode of selection and term of ofﬁce of the executive failed on unrecorded vote, and a motion to send those issues to committee made up of one member from each state also failed on a tie vote (Roll Call #360). Finally, a motion was offered asking for support of election by electors “as an abstract question” (Roll Call #361, II 404), that is, some undetermined form of choice by electors as opposed to selection by national legislature.

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This motion failed on a tie vote with four states in the afﬁrmative (NJ, PA, DE, VA), four states in the negative (NH, NC, SC, GA), two states divided (CT, MD), and one absent (MA). We have already labeled national legislative election with joint ballot as C; now, label election by electors “in the abstract” as B . The Convention vote was tied and thus B ∼ C. Finally on August 24, the delegates decided to postpone further deliberation on questions of the executive. It is here that Riker detects his cycle. He labels national legislative election without joint ballot as A, election by electors as B, and legislative election with joint ballot as C. Reverting to my labeling, national legislative election (without joint ballot) beat election by electors in the states, A > B on July 24 and A > B on July 26. Election by electors in the states tied with national legislative election (with joint ballot) on August 24, B ∼ C. Earlier on August 24 national legislative election (with joint ballot) beat national legislative election (without joint ballot), C > A . By Riker’s labeling we have A > B ∼ C > A, a cycle. According to Riker, there was a “separationist” faction in the Convention, loosely led by G. Morris (“ever the opportunist and an exceptionally adroit parliament man,” Riker 1984, 12), which favored the separation of powers rather than a more uniﬁed form of government. Since there was a cycle, he argues, any result could have obtained in the abstract, and the outcome was decided by the superior will to power (“intense will to win,” Riker 1984, 14) of the leaders of the separationist faction. Morris masterfully exploited the cyclic deadlock in order to maneuver the question into a Committee on Remaining Matters (discussed below) dominated by separationists, Riker claims. “Had Rutledge not brought up the joint ballot [#356, C > A ], this cycle would not have been revealed – indeed it would not have existed. Legislative election would probably have survived . . . the signiﬁcance of the cycle that Morris revealed was that it gave him another chance in the committee [on Remaining Matters]” (Riker 1984, 13). In the absence of a cycle, or in the absence of Morris’s clever exploitation of the cycle, the ﬁnal Constitution would have had the executive selected by the national legislature, Riker claims. By my more strict labeling of the alternatives we have B ∼ C, C > A , and A > B , for a noncyclic or transitive ordering of B ∼ C > A > B . Is it reasonable to strictly distinguish alternatives? In order to generate his cycle Riker distinguishes between two similar but not identical alternatives, national legislative election with joint ballot (C) and national legislative election without joint ballot (A); thus, it must be legitimate to distinguish among similar but not identical alternatives. Riker (1984, 14) is aware that “all the continuing alternatives were changed in gross or subtle ways throughout the event.” Is my interpretation reasonable in

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substance? My proposed transitive ordering states that the convention was indifferent between election by electors in the abstract (with details of which agents select electors by what voting rules and how to pay for distant electors left undeﬁned) and national legislative election with joint ballot, that both those alternatives were preferred to national legislative election without joint ballot, and that national legislative election without joint ballot was preferred to the concrete scheme of election by electors appointed by the state legislatures. This is reasonable; someone might be indifferent between the prospect of a trip to an unnamed destination in France and a trip to London, prefer both to a trip to Oslo, and prefer Oslo to Rouen in France. The proposal to support election by electors in the abstract failed on a tie vote of four for, four against, two divided states, and one absent (Roll Call #361, II 399). The four states against were New Hampshire, North Carolina, South Carolina, and Georgia; and none of those four had ever supported anything other than selection of the executive by the national legislature (Roll Calls #12, #182, #215, #225, #359, #360, #361). The two divided states were Connecticut and Maryland, and this is signiﬁcant. Up until Roll Call #361, Connecticut had usually supported election by electors, whether appointed by state legislatures or elected by the people (Roll Calls #182, #215, #359 by electors; but #225 by national legislature). Maryland had always supported election by electors appointed by state legislatures but never election by electors elected by the people (Roll Calls #12, #182, #215, #225, #359). Connecticut and Maryland were also small states and earlier in the day had lost on a ﬁve to six vote the motion that each state would have a single vote if selection of the executive was by joint ballot in the national legislature. Three of the four supporters of selection by national legislature, New Hampshire, North Carolina, and South Carolina, had opposed the small-states’ motion. There was nothing that the supporters of selection by national legislature could offer Connecticut and Maryland, but the two states were obviously ripe for some kind of compromise with supporters of selection by electors. Michaelsen’s (1987, 65) monograph on the creation of the presidency states that for the proponents of election by electors, “The primary consideration was to enlist the backing of the smaller states which favored selection by the legislature as fairer to them than a popular election.” Massachusetts, a large state, had in the past voted thrice for election by national legislature (#11, #167, #215), was absent for one vote by national legislature (#225), voted against electors (#166, #359), was divided on electors (#182), and was absent on electors in the abstract (#361). This absence or abstention is peculiar, and suggests political motivation, since just minutes earlier Massachusetts voted

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against electors selected by the people (#359), and voted on all 11 of the remaining votes that day. On Friday, August 24 the Convention postponed questions on the executive to the following day, but the pace of closing deliberations on other matters kept it off the agenda. On Friday, August 31 the hurried delegates consigned all postponed issues (including questions on the executive) to a Committee on Remaining Matters (of eleven members, one from each participating state; II 481, not II 463 as incorrectly cited by Riker 1984, 13). The diligent Committee reported out some minor items on Saturday, but spent the rest of the weekend working out compromises. On Tuesday, September 4, the Committee reported their proposal on executive questions (II 493–504). As for selection of the executive they recommended that each state appoint in such manner as its legislature may direct a number of electors equal to the number of senators and representatives the state is entitled to, and that electors would meet in each state and forward their votes to the president of the Senate for counting, the person with the majority of votes would be declared the winner, and there were further provisions, among them mechanisms for dealing with plurality outcomes and tie votes. This settled the vexing question of whether electors should be selected by the people, by the state legislature, or by the state executive, through leaving it to each state to decide the issue in its own way. The exasperating controversy over allocating electors among small states and large states was settled by adaptation of the scheme already devised in the Great Compromise, cutting the issue down the middle; and since representation in the House was apportioned according to the Compromise counting slaves as three-ﬁfths of a person the conﬂict between free and slave states was reconciled.2 The objection that had ﬁrst scuttled election by electors on July 24, the expense of sending electors to the capital, was settled by having the electors meet in their respective states. The device of having the electors meet in their respective states simultaneously resolved the problems of executive independence, avoidance of cabal and intrigue in the electoral college, and the high cost of travel, opening the door to a solution (Anderson 1993, 137). G. Morris details the rationale of the committee at II 500. Label the Committee on Remaining Matters’ September 4 alternative of an electoral college as B . On September 5, Rutledge (SC) moved that the Committee’s report be postponed so that the convention could adopt the earlier plan of selection of the executive by joint ballot of the national legislature, already labeled as C (Roll Call #445, II 511). The motion failed, supported only by North Carolina and South Carolina, thus B > C. To continue the former analogy, if the delegates were indifferent between a trip to an unnamed destination in France and a trip

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to London, they far preferred a trip to Paris over either. Notice that Connecticut and Maryland, each divided on August 24, had come back to the cause of election by electors, and Georgia for the ﬁrst time declined to vote against election by electors. A quite involved debate followed on issues pertaining to the executive that are not the focus of our study. The founders believed that the electoral college would nominate presidential candidates and that the House of Representatives, each state with one vote (the committee proposal was the Senate, but that was amended on the ﬂoor in order to reduce the power of the Senate), would select from the nominees. They believed that the large states would have an advantage in nomination and the small states an advantage in selection. The small states believed (as did their opponents) that they had obtained such an advantage by this arrangement that they made concessions elsewhere in the negotiations (Jillson 1979, 395). This supports my hypothesis that Connecticut and Maryland, each divided on election of electors in the abstract on August 24, were available for a compromise on selection of executive that would advance small state interests. The Committee’s report was completed on the morning of September 5. The remainder of September 5 and all of September 6 was devoted to debating and amending the Committee’s proposal on the executive, which was perfected by the close of business on the 6th. The full report of the Committee on Remaining Matters on all postponed issues, as amended in deliberations, was adopted on Saturday, September 8, and was sent to a Committee on Style. Except for a few details, the Constitution was ﬁnished. The small states and those who favored federal over national government exacted maximum concessions from large states and nationalists in the construction of the executive. Large states wanted an executive elected on the basis of population. What they got was an electoral college half-way between representation by population and representation by state; but ﬁnal decision would be by the House with each state assigned one vote (delegates believed that the electoral college would not produce majorities and that the election would always go to the House). The nationalists wanted an executive independent from the national legislature. What they got was nomination by an electoral college independent from the national legislature, but, selection (they believed) by one chamber of the national legislature. I learned about small-state inﬂuence from McDonald (1985, 252). The small states had agreed to the Great Compromise on representation, including that money measures would originate in the House where large states would be favored. On August 8, the small states (instigated by NJ, DE, MD) reneged on the Compromise, moved to strike the requirement that money measures originate in the House, and they won by a vote of 7 to 4, because not all large state

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delegates considered the money requirement expedient (Roll Call #254, II 215). Some large-state delegates were quite passionate about the requirement, however, and brought it up again on August 9, August 13, August 15, and August 21. The question was sent to the Committee on Remaining Matters. That Committee completed its report on September 5, and recommended a provision that money measures originate in the House but be amendable in the Senate (a similar measure had died by a vote of 4 to 7 on August 13, Roll Call #289, II 267). The ﬁrst recorded vote on September 5, just after the Committee had completed its report, was on Morris’s motion to postpone consideration of the provision that money measures originate in the House, and the postponement passed 9 to 2 (Roll Call #445, II 509–510). Morris said that there had been a deal, and that he did not want to vote for the money provision until he saw that the bargain had been consummated. Madison grumpily explained in a footnote to his ongoing record of the Convention (II 514) that Mason, Gerry, and some other large state delegates supported the electoral college with its tilt to the small states in exchange for enough small states’ support for the provision that money measures originate in the House. Sherman of Connecticut, advocate of small-state interests, emphasized in convention debate that the Committee’s proposal was a compromise between the large states and the small states, the large effectively nominating and the small effectively electing the executive (II 512–513). Indeed, the successes of the small states led three of the more ideological nationalists, Randolph, Mason, and Gerry, to decline signing on to the Constitution, and Madison was not happy with the outcome (McDonald 1985, 252). Jillson (1979) is another analysis of convention votes on the selection of the executive. Jillson collects all votes of any kind on the executive department into two batches; one from the beginning of the convention to before September 4, the other from September 4 forward. He then does factor analysis to support his claim that there were stable voting groups on the executive question. For the early and middle parts of the convention, there was a more cohesive peripheral coalition of ﬁve states, in the far north (NH, MA) and in the far south (NC, SC, GA), in favor of election by national legislature, and a coalition of six states in the center (CT, NJ, PA, DE, MD, VA) in favor of election by electors. The central coalition was less cohesive than the peripheral coalition and was divided up into a large state faction (PA, VA, weakly MA), a small-state faction (NJ, DE, MD), and Connecticut voting independently of the other small states. Jillson’s analysis suggests that distance to travel was a primary motivation behind opposition to election by electors. Further, recall that it was New Jersey and Delaware who ﬁrst supported and then

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opposed election by electors, and that I speculated that they did so out of a small-state concern; in Jillson’s data they show up as two of the three members of the small-state faction on the executive question. For the late part of the convention, Jillson claims that a coalition of mostly small (four) and mostly northern (ﬁve) states were at the heart of the successful compromise (NH, MA, CT, NJ, DE, GA). That coalition was opposed by three factions, the large states (PA, VA), two southern states (MD, SC), and North Carolina independent of the other southern states. Jillson provides useful context on the dynamics of the deliberations as well. Michaelsen (1987) provides background on prior state and confederation experiences with the executive, and this bit of refreshing historical detail is at least as illuminating as Riker’s formalisms. Riker’s cycle claim confronts an anomaly. Why did the convention, supposedly in cyclic deadlock over the issue, appoint a Committee on Remaining Matters so strongly disposed to election by electors, 7 to 10 out of the 11 by Riker’s count? In a footnote, Riker (1984, 13) speculates that the convention voted individually rather than by states in the appointment of committees so that the large delegation from Pennsylvania favoring election by electors determined the convention outcome. Why would a convention full of skilled and experienced politicians commit such a blunder, however? Further, the Convention had earlier voted for a committee of one member from each state, which forged the Great Compromise on representation, whereby the small states gained equal representation in the Senate against the interests of large-state Pennsylvania. Pennsylvania opposed establishment of that representation committee, which was supported by the ten other states (I 516). If Pennsylvania could stack such committees, why did it vote against establishment of the representation committee, and why didn’t it stack the committee and thereby defeat the small states on representation? The Brearley Committee on Remaining Matters was also made up of one member from each state (II 481). How can one claim that the Brearley Committee is stacked if its proposal on selection of the executive survives a challenge on the ﬂoor by a vote of 9 to 2? A simpler hypothesis is that “the composition of the Brearley Committee [on Remaining Matters] suggests that the decision to abandon legislative election had already been made” (Anderson 1993, 136). This simpler hypothesis coheres with the observation that Connecticut and Maryland, each divided on election by electors in the abstract, but having favored more concrete proposals for election by electors in the past, voted for the Committee on Remaining Matters’ compromise proposal containing a particular scheme of election by electors that satisﬁed small-state interests. Riker’s cycling hypothesis does not explain the voting behavior of Connecticut and Maryland.

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Riker also holds that it was the political genius of G. Morris and his separationist camp that defeated selection of the executive by the national legislature and enacted the method of selection ultimately adopted by the Convention. The claim is doubtful. One authority on the Convention writes, “In all these debates over the executive, while there was the greatest diversity of opinion, lines of division do not seem to have been clearly drawn. Members expressed simply their individual and personal points of view” (Farrand 1913, 118). Riker believes that G. Morris, McClurg, and Houston collaborated on July 17 (II 32–35) to stigmatize selection by national executive by moving and arguing that such an executive should serve during good behavior, that is, for life, in order to make him properly independent of legislative inﬂuence. One problem with Riker’s story is that it appears that G. Morris seemed to genuinely believe that lifetime tenure is best. In debate on the motion on July 17, Morris, “expressed great pleasure in hearing it. This was the way to get good Government . . . He was indifferent how the Executive should be chosen, provided he held his place by this tenure” (II 33). Is that stigmatization? G. Morris also advocated that senators be appointed for life, and by the executive, so that the Senate too would be independent from the popularly elected House and from the people, so as protect wealth and property from the masses (I 512–513). Morris advocated that judges be appointed by the executive, with the advice and consent of the Senate (II 44). He also called for a strong and energetic executive; if elected by the people rather than by the national legislature then for two-year terms but with perpetual re-eligibility, and he believed that long tenure was likely; he was also initially against a provision for impeachment of the executive (II 52–55). Delegate Luther Martin, reporting to the Maryland Legislature after the convention, complained that there was a party at the convention that wanted lifetime tenure for the executive, that given the powers of the ofﬁce re-eligibility amounts to lifetime tenure, and that the life-tenure party succeeded in the last days of the convention in winning re-eligibility for election; Martin seems to be speaking about G. Morris (III 216). Another problem is that it was Houston, on July 24 (II 99–101), who moved to scrap election by electors, because of difﬁculty of attendance by electors from distant states, and return to election by national legislature. That motion succeeded, thus Houston acted to defeat the position Riker claims he conspired to advance. Madison stated explicitly in his journal (II 33–34), in order to protect his friend and Virginia ally McClurg’s reputation against charges of supporting monarchy, that McClurg’s support for life-tenure was a strategic exercise, consistent with Riker’s claim, that is, assuming that Madison’s journal entry was itself sincere, rather than a politically motivated reinterpretation of the facts.

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Riker believes that the Brearley Committee and its proposed compromise on the executive was the creature of G. Morris. The motion to form the Brearley Committee was made by Sherman of Connecticut (II 481), however, an advocate of the small-state interest, who was also elected to serve on that Committee (recall my hypothesis that Connecticut and Maryland were holding out on the vote to support election by electors in the abstract). “We know nothing for certain about how this compromise was made, but I infer that G. Morris put it together” (1984, 14), says Riker. He cites indirect and speculative evidence for this view. There is, however, direct documentary evidence that Brearley Committee member Pierce Butler of South Carolina claimed to have devised the compromise on selection (III 302). Finally, if there were a separationist camp led by Morris at the Convention, it would seem not that they cleverly succeeded, as Riker would have it, but that they failed, in that many delegates believed that the mode adopted would have one chamber of the legislature selecting the President. Perhaps Morris was clever in correctly predicting that the adopted electoral college scheme would pick majority winners and thus avoid selection by the legislature, but many other delegates believed, wrongly as it turned out, that ﬁnal selection would be by the legislature (Mason, II 500; Pinckney, II 501; Rutledge, II 511; Sherman, II 512–13; Randolph, II 513; Wilson II 522; Williamson, II 524; Hamilton, II 525). By carefully distinguishing alternatives we can identify a noncyclic ordering throughout the event. On Riker’s account the convention voted for both B > A and A > B; on my account they voted for B > A > B . On Riker’s account there is a cycle among A, B, and C; on mine there is not. In total, my account identiﬁes the following decisions: B > A, A > B , A > B , C > A , B ∼ C, and B > C. I assume that A ∼ A. There is no direct vote between B and B , but B > C by eight votes to two although B ∼ C by four votes to four, thus I think it’s fair to say that B > B . That yields B > B ∼ C > A , and B > A ∼ A > B ; from that data I think it is plausible to assume that C > B; and ﬁnally, I propose the total transitive ordering of B > B ∼ C > B > A ∼ A > B . Alternative B is ﬁrst, tied for second, fourth, and seventh in the ranking. What Riker labels as C is just another version of election by national legislature (but with joint ballot); we could label it A , and if we did then alternative A would be tied for second and tied with itself for fourth in the ranking. If we neglect to distinguish among different versions of similar proposals, then we will ﬁnd that the convention ranked B > B ∼ A > B > A ∼ A > B, etc., and thus that politics is pervaded by gross irrationality. If we distinguish among alternatives as carefully as did those who proposed and voted on them, then we ﬁnd order and reason.

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Jon Elster suggests I am caught in a contradiction, but I believe he is mistaken. We have already labeled selection of the executive by electors appointed by state legislatures as B , selection by electors in the abstract as B , and selection of executive by joint ballot of the national legislature as C. Further, label selection of the executive by electors appointed by the people as D, and label other possible schemes of selecting electors as E, F, G, . . . , Roll Call #361 was a tie between election of the executive by the national legislature, and election of the executive by electors in the abstract: C ∼ B . Elster claims that B is equivalent to (B or D), and thus that #361 shows that C ∼ (B or D). My suggested ordering of B ∼ C > A > B implies C > B . Roll Call #359 showed that C > D. Next, according to Elster, C > B and C > D are equivalent to C > (B or D), contradicting the equivalence he proposes from Roll Call #361. Such a contradiction would be fatal to my hypothesis that there was a transitive ordering of B ∼ C > A > B . The ﬁrst problem is that C ∼ B is not equivalent to C ∼ (B or D). My claim is not one of pure logic. When G. Morris moved electors in the abstract against the status quo (B versus C), he and the delegates were aware that the convention had already expressed C > B (C > A , Roll Call # 356; A > B , Roll Call #215 and others), and C > D (Roll Call #359), so he and they could not have intended B to be equivalent to (B or D), we presume that he was not wasting his time by introducing alternatives that had been clearly defeated. What he must have intended was that B contain the most satisfactory compromise over (1) method of selection of electors and (2) method of allocating number of electors per state, and an already rejected requirement that electors must be chosen by state legislatures (B ) could not have been most satisfactory, nor an already defeated requirement that electors must be selected by the people (D). B does contain all remaining methods of selecting electors, E, F, G, . . . , In the end, the concrete proposal of the electoral college, B , included the provision that each state is free to decide how to choose electors: by the legislature, by the people, or by some other method. Logically, those who voted for B on this basis also should have voted for B , but psychologically the concrete proposal was more attractive than the abstract proposal that contained it as a possibility. Incidentally, the method of state option is not equivalent to (B or D), because B requires that electors must be exclusively chosen by state legislatures, D that electors must be exclusively chosen by the people, and state option permits any method to be chosen. The second problem is that C > B and C > D are not equivalent to (C > (B or D)). (C > B and C > D) do imply that (C > (B or D)), but not vice versa, because (C > B and D > C ) also imply that (C > (B or D)). Would it do to say that C > B and C > D

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imply that (C > (B and D))? No, that would not be right either, because although we know that C is preferred to B and C is preferred to D, we do not know anything about whether C is preferred to B and D together (B and D do seem to be mutually exclusive, however). It is better to say that ((C > B ) and (C > D)). Returning to the ﬁrst problem, my construal is that B did not contain B and did not contain D, and thus there can be no inference that (C ∼ B ) or that (C ∼ D). There is no contradiction between (C > B ) and (C > D) in the ﬁrst problem, and the absence of an indifference relationship between C, on the one hand, and B or D, on the other hand, in the second problem. My suggested ordering, B ∼ C > A > B , therefore stands. In Riker’s world it was not the arguments of Morris and the Committee on Remaining Matters (II 500) as to the reconciliation of interests most likely to promote the public good that persuaded the convention to adopt by an overwhelming majority the method for selecting the executive. Rather, it was “because of the separationists’ rhetorical and heresthetical skill and persistence, because of the cycle generated by Rutledge’s unwise motion, and because of the clever appeal to diverse interests put together in the proposal for an electoral college” (Riker 1984, 14). In Riker’s world, politicians act “cynically” rather than realistically, “slyly” rather than capably, “cleverly” rather than wisely; politicians make “maneuvers” rather than proposals, and they “manipulate” rather than arrange. Sherman “accepted the entire rhetorical stance of the separationists” (9), rather than was persuaded of the correctness of their views. This style of interpretation purports to be mere positive description and thus value-neutral, but it plainly contains a contestably misanthropic view of human motivation and interaction that drives the results. What does Riker mean when he calls Morris, the architect of election by electors, an “opportunist”? If Morris is an opportunist, does that mean that he places his own private good above everyone else’s, or merely the good of his delegation above that of the convention’s, and, if either, why would respectively the delegation or the convention entertain his counsel or respect his judgment? Would he cheat, steal, and murder if he could get away with it? Why not just call him effective? Is everyone an opportunist, or is it only politicians? Among politicians, is Roosevelt an opportunist of a same or of a different kind than Stalin? Are Hubert Humphrey and Joseph McCarthy both opportunists? In order to preserve the useful meanings of contrasts, such as those between opportunism and principle, rhetoric and argument, deception and sincerity, both poles of the contrast must apply in the world. It could not be that every actor is at all times cynical, sly, clever, maneuvering, manipulative, rhetorical, and deceptive; otherwise the labels are drained

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of content. At least one important exception must be the scholar who claims universal opportunism, for otherwise we should not believe him. My view is that since individuals vary in honesty, trustworthiness, and public spirit in the face of identical material incentives, individual character is at least as important as political institutions. An alternative view is that individuals are equally corrupt in the raw but variably ethical depending on the institutional constraints they face or depending on the sphere of activity in which they interact. Proponents of this alternative view might argue, for example, that we can rely on the claims of those operating within the institutions of scholarship, but not on the claims of those operating within the institutions of politics. Is it that somehow politics is uniquely repugnant among human activities? There is a fertile abundance of incident upon which the posture of world-weary pessimism concerning the ethics of democratic politicians can draw for inspiration. That these are so widely known to the public is simply because politics is the public’s business, however. I think it is an illusion that humans are more venal in politics than they are in scholarship, family, enterprise, or religion. Indeed, it has been my experience that even though politicians are as ethically variable as nonpoliticians, on average they are more ethical than the people they represent (which must almost necessarily be so, since an important criterion of electoral selection is faithful representation); corrupt politicians correlate with corrupt populations. Many of those who are so sure all politicians are dishonest are just imagining what their own performance would be if they were lucky enough to gain ofﬁce. The pessimistic view of politics is not only debatable as description, it is associated with the party of tradition inside the arena of politics, while the optimistic view is associated with the party of change. In the American context, hostility towards politics and politicians is a leading theme in the ideology of the right, with antecedents in the tensions over desegregation, the defeat of the South in the Civil War, and earlier still in the content of southern subcultures identiﬁed by Fischer (1989), shaped by place and time of emigration from Great Britain. There is not some extrapolitical “science” apart from ongoing political debate that settles the contest in favor of one partisan attitude or the other. There was plenty of hard politics at the convention, but alternatives were not cannily invented by clever conspirators as in Riker’s account. Going into the convention, eight states elected their governors in the legislatures (PA, NJ, VA, MD, DE, NC, SC, GA) and ﬁve states elected the governor by popular election (NH, MA, RI, CT, NY; Anderson 1993, 134); Massachusetts in the convention voted against popular election of an executive, and this was because its delegate Gerry had turned against that method because the people had not reelected his ally Governor Bowdoin

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after the governor had moved against the Shaysite rebels (Michaelsen 1987, 70). The thesis of Michaelsen’s (1987, 79) monograph is that the institution of the presidency came about as a “consequence of American experience at the State and Confederation levels, and through the work of hard-headed, practical, experienced politicians.” The delegates began from these experiences, and used their political skills to harmonize these contrasting experiences with the practical requirement of devising a weighting of state interests sufﬁcient to win ratiﬁcation of the proposed Constitution. Contrary to Riker, Rutledge was neither obtuse nor provincial on August 24 when he moved (Roll Call #356) that election of the executive in the national legislature be by joint ballot. With the exception of tiny Georgia, the seven remaining states that elected their governors in the legislature did so by joint ballot (even unicameral PA, which balloted jointly with its executive council, Anderson 1993, 134); and selection by joint ballot was in the early Pinckney draft of a constitution (Michaelsen 1987, 60). Separate ballot would give rise to dangerous deadlocks and intrigues among the two chambers and presidential hopefuls. Yes, joint ballot for President happened to favor the large states, and they voted for it, but two small states (NH, DE) joined them to make for the majority against separate ballot. Joint ballot was the best policy regardless of state interest, and the convention voted for the best policy. The next motion, by the small states to insert “each State having one vote,” failed on a ﬁve to six vote, and several following motions failed on close votes. Rather than forcing close votes, the delegates shortly appointed a committee to work out a compromise designed to enjoy broad support. The delegates brought with them not only their experiences in state and confederation governments, among the leading members some had drafted state constitutions, some had made a systematic comparative study of state constitutional conventions and documents, and some had studied the political theorists on choice of institutions. An independent executive and an electoral college seem to be an almost miraculously ingenious compromise among interests apparently impossible to reconcile. Yet the same ideas can be found nine years earlier. In 1778 a proposal for a Massachusetts state constitution failed; and twelve of the towns that voted against it issued a document called the “Essex Result,” which called explicitly for checks and balances among three branches of government, and for a single executive elected annually at county conventions by electors previously chosen by the people (Michaelsen 1987, 17). Only by ignoring historical context can we imagine that Riker’s “herestheticians” invent alternatives from thin air that bamboozle their opponents. I do not want to make too much of my claim that aggregate preferences were consistent over time on the question of selection of the executive.

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Many alternative modes of selection were discussed, but none won wide support, and delegates came to ﬁnd the subject confusing and tedious. Gerry said, “We seem to be entirely at a loss on this head,” and proposed to send the issue to committee, “Perhaps they will be able to hit on something that may unite the various opinions which have been thrown out” (II 103). Madison added that “There are objections agst. every mode that has been, or perhaps can be proposed” (II 109). The delegates were not merely aggregating preferences, they were mutually persuading, individually and collectively deliberating, forming and changing preferences apart and together in the course of the convention. If I had made only a preference-change argument, however, the reader would have suspected that I had nothing against the correctness of Riker’s cycling claim on its own terms. Preferences were formed in the course of the Convention; that was one of its purposes. Early in the deliberation, on July 20, with respect to impeachment of the executive, “Mr. Govr. Morris’s opinion had been changed by arguments used in the discussion” (II 68). Late in the deliberation, on September 4, with respect to appointment of the executive, Wilson said that the subject had greatly divided the convention, and that “He had never made up an opinion on it entirely to his own satisfaction” (II 501). Or, as Franklin commenced his closing speech at the Convention (II 641–642): I confess that there are several parts of this constitution which I do not at present approve, but I am not sure I shall never approve them: For having lived long, I have experienced many instances of being obliged by better information or fuller consideration, to change opinions even on important subjects, which I once thought right, but found to be otherwise. It is therefore that the older I grow, the more apt I am to doubt my own judgment, and to pay more respect to the judgment of others.

In such an atmosphere one should not expect individual or collective preferences to be consistent between, say, July 24 and August 24 as required for Riker’s mistaken cycle. To a lesser extent, preferences might be inconsistent at a ﬁxed time as well, simply because individuals and the collective body have not completed the task of consistently ordering desires and beliefs. The task of ordering is a major part of the content of the deliberation, and in this case was not complete until the constitutional draft was completed. If we criticized a scholar on the grounds that consecutive drafts of an article were inconsistent with one another and with the ﬁnal document, the argument would have no bite. It is to the ﬁnal version that we should look for internal consistency, and given the inevitable conﬂicts among goods, only to whether it is more coherent than feasible alternatives. “Thus I consent, Sir, to this Constitution,”

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Franklin continued (II 643), “because I expect no better, and because I am not sure, that it is not the best. The opinions I have had of its errors, I sacriﬁce to the public good.” Agricultural appropriations, 1958 Riker’s ﬁrst published attempt to demonstrate a cycle and thereby the relevance to politics of the Arrow theorem was in 1958, a study of a sequence of votes on agricultural appropriations on the ﬂoor of the House of Representatives in 1952. Riker does not repeat this story in Liberalism against Populism (1982) nor in The Art of Political Manipulation (1986). Although Riker dropped the agricultural appropriations story, his followers continue to repeat it, for example Strom (1990, 28–29) introduces cycling and its empirical relevance with a version of the story. A proposal from the Subcommittee on Agriculture of the Committee on Appropriations for the budget of the Soil Conservation Service came before the Committee of the Whole in the US House of Representatives. The subcommittee’s original proposal was for $250 million. From the record, the Korean War was on and there were calls for economy. The minority Republicans, as usual, were for economy, some for a smaller reduction in the appropriation and some for a larger reduction. The American Farm Bureau Federation, its members the supposed beneﬁciaries, opposed the large appropriation as wasteful and socialistic. Urban Democrats seemed to act as if they felt that rural Democrats were getting more than their due in appropriations. Jacob Javits (R-NY), not on the subcommittee, moved an amendment that as later corrected proposed reducing the appropriation to about $142 million (142 against 250). Next, H. Carl Andersen (R-MN), ranking minority member on the subcommittee, moved a substitute for the Javits amendment, of $200 million (200 against 142). Then Whitten (D-MS), chair of the subcommittee and thus advocate of the original proposal, moved to amend Andersen’s substitute to $225 million (225 against 200). Finally, O’Toole (D-NY) moved to amend Javits’s amendment to $100 million (100 against 142). This is the maximum number of alternatives permitted by House rules. According to House procedures, ﬁrst the O’Toole amendment to Javits’s amendment (100 against 142) would be voted on, then the Whitten amendment to the Andersen substitute (225 against 200). Then the perfected amendment goes against the perfected substitute. The O’Toole amendment to the Javits amendment was defeated by voice vote, thus Javits (142) > O’Toole (100). The Whitten amendment to the Andersen substitute lost on a division of 74 to 139, thus Andersen (200) > Whitten (225). Next, Javits, the perfected amendment, went against

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Andersen, the perfected substitute. Riker completely omits this fact: on ﬁrst count, Andersen beat Javits, on a division of 132 yeas and 131 nays, thus Andersen (200) > Javits (142). On second count, Andersen lost to Javits, on a teller vote of 126 yeas and 131 nays, thus Javits (142) > Andersen (200). That left the vote between the Javits amendment and the original subcommittee proposal, and the Javits amendment was defeated, 35 yeas and 220 nays, thus Original (250) > Javits (142). The votes we have are apparently consistent. Javits > O’Toole, Andersen > Whitten, Javits > Andersen, Original > Javits, reduces to Original > Javits > Andersen > Whitten > O’Toole. In million dollar terms, the collective preference was apparently the peculiar ranking 250 > 142 > 200 > 225 > 100, which is intransitive in dollar amount. According to Riker (1958, 358): From the fact that all amendments failed one might infer that a majority favored the original proposal. Nevertheless, one awkward fact casts doubt on this inference: although the largest amount stayed in the bill the third largest amount (Andersen) beat the second largest amount (Whitten). From this fact one may reasonably suspect an intransitivity here, for if the largest amount were really favored over all others, and the amount was the dominant criterion, then logically the second largest sum should have defeated the third largest.

Riker is not as surprised that $142 million, the fourth largest amount, beat the third largest amount and the second largest amount as well. He explains that “On the crucial vote, although the Andersen substitute was formally pitted against the Javits amendment, the members clearly assumed that the substitute lay against the original” (Riker 1958, 359). In other words, when voting on Andersen (200) against Javits (142), members who favored the Original (250) believed that if Javits (142) won, then on the next scheduled vote Javits (142) would lose to the Original (250). Hence, voters who favored the Original (250) voted strategically for Javits (142) over Andersen (200); but the sincere collective preference was Andersen (200) > Javits (142). Recognizing this instance of strategic voting revises the apparent collective preference to 250 > 200 > 225 > 142 > 100; the fourth largest amount is now in order, but still the third largest amount beats the second largest amount. We are entitled to ask, though, given the ﬁnal outcome in favor of the Original (250), whether some of those who voted for Andersen (200) against Whitten (225) were also strategic voters. Perhaps voters who most favored the Original (250) would sincerely prefer Whitten (225) to Andersen (200), but voted strategically against Whitten (225) on the expectation that the sequence of votes would lead to victory for the Original (250), as it did. If there were such strategic voters on Andersen (200) against Whitten (225), then the

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Table 14.1. Riker’s estimates, Agricultural Appropriations, 1958 Number

Faction Name

Preference Order

108 13 30 91 10 5

Original–Whitten Original–Andersen Javits Andersen Whitten O’Toole

250 > 225 > 200 > 142 > 100 250 > 200 > 225 > 142 > 100 142 > 100 > 200 > 225 > 250 200 > 225 > 250 > 142 > 100 225 > 250 > 200 > 142 > 100 100 > 142 > 200 > 225 > 250

sincere collective preference was Whitten (225) > Andersen (200). If we grant that strategic voting succeeded on both votes, then we obtain the sincere preference rankings of Javits > O’Toole, Whitten > Andersen, Andersen > Javits, Original > Javits, which reduces to Original > Whitten > Andersen > Javits > O’Toole. In million dollar terms this is 250 > 225 > 200 > 142 > 100, which is perfectly transitive if dollar amount is the standard of measure, and thus Riker’s alleged cycle vanishes. Why then does Riker believe there is a cycle? He estimates the numbers and preference orders of different factions by means of several plausible inferences that I shall not repeat here. I report his results (1958, 361), in Table 14.1. Each faction is named after its most favored alternative, and then Riker posits further rankings such that alternatives closer to the most favored alternative are more favored, except for the Original–Andersen faction whose ranking is jumbled in dollar amount. The O’Toole faction, for example, ranks the lowest appropriation ﬁrst, the second-lowest second, and so on, and the highest appropriation last. Riker divides the Original faction into two camps. The ﬁrst, Original–Whitten, or the Original faction proper, ranks the highest appropriation ﬁrst, the second-highest Whitten second, and so on, and the lowest appropriation last. Whence the second, Original–Andersen camp, who perversely rank the third-lowest amount Andersen above the second-lowest amount, the very paradox we are attempting to explain? According to Riker, these 13 or more voters sincerely rank the alternatives the same way as do the Original–Whitten voters, 250 > 225 > 200 > 142 > 100, but voted strategically for Andersen (200) and against Whitten (225) in the contest between the two. The Original–Andersen voters “followed a highly contrived strategy in voting . . . Assuming that the original paragraph [250] could defeat the Andersen substitute [200] but not the Whitten amendment [225], they voted ﬁrst against the latter and then, safely, for

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Table 14.2. Pairwise comparison matrix, Agricultural Appropriations, 1958 Original 250

Javits 142

Andersen 200

Whitten 225

O’Toole 100

(BC ∗)

222

131 35

136 35 139 − 13 = 126

222 252 222

(711) (357) (696)

222

(696)

Original Javits Andersen

35 126

222

Whitten

121

222

O’Toole

35

5

118 + 13 = 131 35

35

(110)

Notes: The winner of a pairwise comparison is indicated by italic. ∗ This is the Borda count for corrected estimates, that is, it excludes the strategic and includes the sincere preferences of the 13 Original–Andersen voters.

the former” (Riker 1958, 359). In order to determine collective rankings, however, we cannot mix sincere and strategic individual rankings. It is by counting the Original–Andersen voters’ strategic ranking rather than their sincere ranking that Riker generates his illusory cycle. His estimates of the numbers in factions and their preference rankings yields the ﬁrst-listed number in each cell of the pairwise-comparison matrix in Table 14.2. Using Riker’s estimates that mistakenly include the strategic rankings of the Original–Andersen faction does indeed yield the collective preference order of 250 > 200 > 225 > 142 > 100 that Riker suspects of intransitivity because it is not transitive in dollar amount of appropriation. It is a matter of taste whether or not we would call that a proper cycle, but there is no need to debate the question since Riker’s proposed collective preference order is mistaken. The collective ranking is of Andersen (200) over Whitten (225) according to Riker’s estimates that include the strategic ranking of the Original–Andersen faction. If we counted instead the Original–Andersen faction’s sincere ranking, then we would subtract 13 votes in the cell counting how many votes Andersen got over Whitten and we would add 13 votes in the cell counting how many votes Whitten got over Andersen. This reverses the outcome between the two alternatives, and now Whitten (225) has a majority over Andersen (200). With that reversal we obtain the pairs 250 > 142, 250 > 200, 250 > 225, 250 > 100, 142 > 100, 200 > 142, 200 > 100, 225 > 142, 225 > 200, 225 > 100, each of which ranks the larger amount over the smaller amount, and indeed the pairs reduce to the collective ranking of 250 > 225 > 200 > 142 > 100, which is transitive

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in dollar amount. Riker’s ﬁnding of a collective ranking that is intransitive in dollar amount is merely an artifact of improperly counting the strategic ranking of the 13 Original–Andersen voters rather than their sincere ranking. The Borda count for the corrected rankings, which by use of information about relative rankings will give us an approximation of voters’ intensity of preference, shows $250 million in ﬁrst place (711), followed closely by a tie between $225 million (696) and $200 million (696); then there is a huge gap to $142 million (357) and $100 million (110). There is a possible instance of strategic abstention and logrolling that Riker does not report. Recall that on ﬁrst count, Andersen (200) beat Javits (142) by 132 to 131, a vote that Riker fails to mention in his article, and that on second count, Andersen (200) lost to Javits (142) by 126 to 131. The number of no votes is the same, 131 on each vote, but the number of yea votes declined from 132 to 126. There may have been simply errors between the two counts, or shifting attendance, or perhaps six yea voters strategically abstained on the second count in exchange for consideration from the Democratic and agricultural coalition on other appropriations issues. If we redo the pairwise-comparison matrix and add the 6 voters in the appropriate cells (for the reader who wishes to check, this involves adding 6 voters to the 91 voters in the Andersen faction), then we obtain a consistent but peculiar ranking: 200 > 250 > 225 > 142 > 100. The third-place amount has jumped to ﬁrst. This is extremely weak, however, 200 > 250 by only one vote and 200 > 225 by only one vote, so not too much should be made about it. From the Borda count we know that the three top alternatives – 250, 225, 200 – are almost tied and that the presence or absence of a few members might change the outcome. Adding the six voters, the Borda count becomes even closer among the three top alternatives but $250 million is still in ﬁrst place: 250 (723), 225 (714), 200 (720), 142 (357), 100 (110). One hypothesis about logrolling is that it permits an outcome that incorporates the intensity of preference information that pairwise voting throws away. By pairwise voting, the ﬁrst count including the six voters has Andersen (200) as the winner, even though the Original (250) would be the Borda winner; then, perhaps there was logrolling, which had the result of selecting the Borda winner. This is too weak to be a demonstration of the logrolling hypothesis, but it is consistent with it. Since Riker’s initial premises are mistaken, there is no purpose in examining the entire remainder of his argument, but there are a few points of interest. Even with the beneﬁt of his initial error, he still must make several “more or less arbitrary assumptions” (Riker 1958, 362) to obtain his cycle. On the one hand, “it seems likely” that the House took

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collectively “irrational action” due to cycling to the tune of $25 million (1958, 358). On the other hand, there was “quite possibly” no cycle: yet, this detailed investigation was undertaken simply because there was reason to suspect an irrationality. For the sake, therefore, of reconstructing a possible intransitive ordering of preferences, we shall assume [the reading of preferences that results in a cycle]. (Riker 1958, 360)

Thus, in the further development of his argument, although there was no persuasive reading of legislators’ preferences, the reading that generated a cycle was arbitrarily selected for demonstration purposes. Finally, if Riker had succeeded in demonstrating a cycle in this case study, it would have been an insigniﬁcant ﬁnding. If the alleged cycle were among alternatives distant in Borda ranking, say among 250, 225, and 100, and 100 won, then we would have had cause for concern. The cycle that Riker alleged would have been among the three top alternatives (250, 225, 200), however, any one of which was preferred to the fourth (142) and ﬁfth (100) alternatives, and all such a cycle would indicate, as we saw in the discussions of the Borda count, is indifference or near indifference among neighboring alternatives. Riker (1958, 356) claims that collectively “irrational action” due to cycling “is probably fairly frequent.” This case study is “an example chosen almost at random” (Riker 1958, 357). If cycles are so frequent that one can ﬁnd them by grabbing the Congressional Record and picking a page at random, then, one must ask, why publish this case based on extraordinarily weak (not to mention mistaken) data? Why not instead choose “almost at random” cases that contain plentiful roll-call votes, ﬁnd the strongest ones of those, and then publish strong demonstrations based on strong data? Could it be that the reason is that cycles are rare and irrelevant to politics?

15

Other cycles debunked

Introduction In this chapter we review all remaining published and developed cycle claims that I could ﬁnd in the literature, as well as some undeveloped cycle claims. Blydenburgh (1971), inﬂuenced by Arrow and Riker, sought to demonstrate a cycle in deliberations on the Revenue Act of 1932 in the US House of Representatives. The vote was among a sales tax, an income tax, and an excise tax. Blydenburgh’s ﬁrst argument is that a majority was against each alternative. A majority voted for the excise tax, however; and Blydenburgh’s inference that a majority nevertheless had preferences against the excise tax is in error arising from confusion about which alternative is pitted against which. The second argument makes two assumptions in order to obtain complete inferred preferences from incomplete revealed preferences. The ﬁrst assumption is arbitrary and weakly warranted, however, and further, Blydenburgh, without explanation, inconsistently applies the second assumption; if the ﬁrst assumption is dropped, or if the second assumption is consistently applied, then he has no cycle. His third argument again errs due to confusion about which alternative is pitted against which; and ultimately reduces to the failed second argument. Blydenburgh’s erroneous analysis is frequently cited by partisans of the irrationalist doctrine. Bjurulf and Niemi (1978) explore Rikerian doctrine in the records of the Scandinavian parliaments. They claim to ﬁnd three cycles. The ﬁrst concerns the construction of a hospital. In order to show a cycle they must go beyond expressed votes and infer some of the individual preference rankings. They reject a more plausible inference about one group’s ranking (that makes for no cycle), on the basis that it has no support in the record, only to advance a less plausible inference that also has no support in the record (and makes for the cycle); if their less plausible inference is incorrect for any 2 of the 37 members of the group in question, then there is no cycle. Furthermore, about half the chamber was absent for these votes, making inference of the full chamber’s rankings quite 335

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speculative. The second concerns appropriations for Swedish telephone and telegraph during the Depression. There is a cycle if we assume that one of the factions was strategically irrational, but there is no evidence to warrant that assumption. In the absence of conﬂicting evidence, it is better to construe actors as rational, and if we do then there is no cycle. The third concerns appropriations for the riﬂe club. The Social Democrats did vote strategically so as to thwart the majority will; but the majority found a creative device to restore the most favored alternative. Bjurulf and Niemi (1978) generalize that manipulations are frequent in Scandinavian politics, but as these are presumably their best cases, the generalization is doubtful. Neufeld, Hausman, and Rapoport (1994) ﬁnd a cycle over three alternatives concerning Muscle Shoals in the US Senate in 1925, a project later realized by Franklin Roosevelt as the Tennessee Valley Authority. Their demonstration is unique, they say, because they rely solely on recorded votes, not on inferences. One inference that they, and we, are able to draw, however, is that a key group of actors was voting strategically. Once we recover the sincere preferences of those strategic voters and adjust chamber totals accordingly, we see that sincere preferences are in equilibrium, and that the Condorcet winner prevailed in the end. Shepsle and Bonchek (1997) conclude that there is no such thing as the public interest on the basis of Riker’s cycling examples and on two novel examples, one based on phantom evidence, and one a cycle that speculatively could have occurred in a possible world but did not occur in our actual world. There are credible claims of occasional cycles, and of nonpopular choices, in the Finnish electoral college (Lagerspetz 1993, 1997). I argue that this is an exceptional case: the institution is one peculiarly suited to antimajoritarian mischief, and the two strong cycle claims are from a time when Finland was a highly polarized society, during the Great Depression and within memory of civil war and terror. It is possible that there may have been cycles among the preferences of disciplined parties, but not among the preferences of the population they represent. There is also strong evidence of an apparent cycle among preferences of Iowa senators over anticorporate farming legislation (Gross 1979), but I suspect that a cycle is unlikely in sincere preferences. Kurrild-Klitgaard (2001a) ﬁnds a ﬂeeting cycle in one of many public opinion polls concerning persons who might ﬁll the unelected Danish prime minister post in 1994. The momentary cycle is due to the closeness of the election among the forces who would select the prime minister; in the end, the most favored person ﬁlled the post. I also review some what-if cycles, those based in part on observed votes and in part on frankly hypothetical preferences. And,

Other cycles debunked

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I dismiss coffee-break cycles: “my coauthor in Barcelona knows someone in Auckland whose student found a cycle in Nepal, or was it Manitoba?” I conclude that many of the erroneous cycle claims are due to confusion about sincere and strategic voting. 1932 Revenue Act Blydenburgh (1971) thinks he uncovers a cycle in the choice of type of tax by the US House of Representatives in the Revenue Act of 1932. Riker and Weingast (1988) cite the study and its conclusions with approval, as one of three examples offered in support of their disequilibrium hypothesis. Blydenburgh introduces the topics of Arrovian cycling and Rikerian manipulation, and presents the paper as a test of the hypothesis that the use of the closed rule on revenue bills in the House functioned to force an arbitrary equilibrium on a topic otherwise destined to disequilibrium because of redistributive heterogeneity. Blydenburgh searched revenue debates from 1932 to 1954, and found two cases where there was both an open rule and sufﬁcient roll-call votes to test for the existence of a Condorcet paradox. Generally, “it is probably not true that a paradox of voting would have occurred on all major revenue bills introduced under the closed rule” (Blydenburgh 1971, 71), and the second case of consideration under an open rule in 1938 only “came dangerously close to a cycle” on Blydenburgh’s analysis, which is to say, it was not a cycle. That leaves the ﬁrst case where Blydenburgh’s position is that “a cycle probably occurred.” It was 1932, a bill was needed to raise a billion new dollars for Hoover’s antidepression programs, and public opinion then believed that it was imperative to balance the budget. The Ways and Means Committee reported a bill to the House that contained a new manufacturers’ sales tax. First, on the House ﬂoor, a motion to delete the new sales tax passed by a roll-call vote of 236 to 160 (Q > S ). Second, a motion to impose an income tax failed by a roll-call vote of 178 to 211 (Q > I ). Third, a motion to impose an excise tax passed by a roll-call vote of 204 to 187 (E > Q). On ﬁnal passage the entire bill passed by a vote of 327 to 64. The three roll-call votes allow Blydenburgh to reconstruct a portion of legislators’ expressed preferences. The ﬁrst claim is that there is a negative majority against each alternative. Commenting on the second case, Blydenburgh (1971, 70) explains that, “A negative majority is a necessary but not sufﬁcient condition of a paradox of voting.” That would mean, of course, that demonstrating a negative majority would not demonstrate a cycle. I confess that I do not understand what Blydenburgh is up to with his negative-majority

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Table 15.1. Blydenburgh’s analysis, Revenue Act 1932 Group label

Number in group

Vote∗ S, I, E

Revealed preference

Inferred preference

Corrected inference

A B C D E F G H

85 77 38 30 9 7 69 71

NYY NYN NNY NNN YYY YYN YNY YNN

(I, E) > S I > (S, E) E > (I, S) Against all For all (I, S) > E (E, S) > I S > (E, I)

I>E>S I>E>S E>S>I Indifferent S>I>E S>I>E S>E>I S > (E, I)

I>E>S I>E>S E>S>I −Indifferent +Indifferent S>I>E S>E>I S>E>I

Note: ∗ Those who abstained on all votes are not counted. Additionally, those who partially abstained are as follows: 3 NNA, 1 NAN, 1 NAA, 2 NAY, 1 YAN, 2 YAA.

analysis, hence, to be safe, I shall quote his argument in full, and then try to puzzle it out. It can be seen from the total vote on the amendments that a majority of 236 opposed the sales tax, 211 opposed the income tax, but only 187 opposed the excise tax. Evidence was found in sources outside the voting record that at least seven congressmen in Group A can be identiﬁed with the [pro-income-tax] “soak the rich” coalition (one might thus characterize the whole voting group). Apparently income tax was the alternative these seven most preferred. Their complete preference ordering is I > E > S. Further investigation showed that ﬁve congressmen in Group G were members of the Ways and Means Committee and supporters of the bill. The sales tax was apparently the most preferred alternative of these ﬁve congressmen, and, thus, their complete preference ordering is S > E > I. Adding these twelve (seven from Group A and ﬁve from Group G) to the 187 against E on the third roll call produces a negative majority of 199. Therefore, there was a negative majority against each alternative and a paradox of voting among the three amendments. (65–66)

Blydenburgh said in discussion of the second case that a negative majority is necessary but not sufﬁcient for a paradox of voting. So why in the ﬁrst case does he say that a negative majority means a paradox of voting? Next, in analyzing the legislative cases in this volume I have found it essential constantly to be clear about which alternatives are being voted on. There are never votes on lone alternatives, votes are always on pairs of alternatives; when not explicit the vote is often against the status quo, Q. The three roll-call votes under consideration were not direct contests among S, I, and E. The ﬁrst vote was between the sales tax and the status quo, and Q > S. The second vote was between the income tax and the

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status quo, and Q > I. The third vote was between the excise tax and the status quo and E > Q. That gives us collective expressed preferences of Q > S, Q > I, and E > Q, which implies both E > Q > S and hence E > S, and E > Q > I and hence E > I. With these data we do not know the collective preference between the sales tax S and the income tax I, but we do know that the excise tax is preferred to both, E > (I, S ). What happens when E goes against Q? We have the recorded vote, E beats Q. What would happen if E went against I ? Group C and Group G voted for E over I, for a total of 107 votes. Group B and Group F voted for I over E, for a total of 84 votes. The members of Group D voted against all taxes; thus, in a contest between E and I they should abstain. The members of Group E voted for all taxes, so add nine votes to E and nine votes to I. On present assumptions we do not know how Group A and Group H ranked alternatives E and I, and together they make up 156 votes. That leaves 116 for E, 93 for I and 156 undetermined. In order to turn E from the winner against I to the loser against I, we would need to demonstrate that at least 90 of the 156 undetermined votes in Groups A and G were I > E (156 = 90 + 66; 93 + 90 = 183 > 182 = 116 + 66) yet Blydenburgh claims only 7 from Group A for I > E; 7 falls well short of 90. What would happen if E went against S ? Group A and Group C voted for E over S, for a total of 123 votes. Group F and Group H voted for S over E, for a total of 78 votes. The members of Group D voted against all taxes; thus, in a contest between E and S they should abstain. The members of Group E voted for all taxes, so add nine votes to E and nine votes to S. We do not know how Group B and Group G ranked S and E, and together they make up 146 votes. That leaves 132 for E, 87 for S, and 146 undetermined. In order to turn E from the winner against S to the loser against S, we would need to demonstrate that at least 96 of the 146 undetermined votes in Group B and Group G were for S > E (146 = 96 + 50; 87 + 96 = 183 > 182 = 132 + 50), yet Blydenburgh claims only 5 from Group G for S > E; 5 is well short of 96. To keep the exposition simple, I neglected to include the ten voters who abstained on one or two of the three votes in the calculations, but this does not affect the substance of my argument. Is it that the vote is supposed to be between alternative E and some alternative not-E ? Alternative E won by a vote of 204 to 187, so say that there were 204 votes for E and 187 votes for not-E. Blydenburgh has 7 voters from Group A who rank I > E > S and thus prefer I to E, so subtract 7 from the total of 204 for E and add 7 to the 187 who are not-E. Blydenburgh has ﬁve voters from Group G who rank S > (E ∼ I ) and thus prefer S to E, so subtract another ﬁve from the total for E and add ﬁve to the total for not-E. Complete the adding and subtracting and

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there are 192 total votes for E and 199 total votes for not-E, perhaps this is Blydenburgh’s “negative majority of 199.” There is no alternative not-E composed of alternatives I and S for voters to choose, however. This is pairwise voting. We are already sure that E beats Q. If there were such a composite alternative not-E, then notice that the preferences of the 12 voters have been fallaciously construed. True, the seven voters in Group A prefer I to E and thus not-E to E, but since they are I > E > S they also rank E over S and thus E over not-E. Their seven votes for E > not-E are necessarily cancelled by their seven votes for not-E > E. That gets us back to 199 for E, 192 for not-E, and no cycle. Further, those in Group G prefer S to E and thus not-E to E, but since they are S > (E ∼ I ) they might rank E over I and thus E over not-E. If so, their ﬁve votes for E > not-E would necessarily be cancelled by their ﬁve votes for not-E > E. Some such reasoning as this accounts, I think, for Blydenburgh’s rabbit out of a hat feat of turning a revealed majority for E into an inferred majority against E. Next, Blydenburgh introduces what he calls stronger assumptions in order to complete the inference of preference orders and alternatively demonstrate a cycle. The ﬁrst assumption, which we shall see has an odd consequence, is that in the sequence of voting voters would vote for their most-preferred alternative and if that failed then on the next vote vote their next most-preferred, and so on. The second assumption is that the excise tax is more like the sales tax than the income tax, so it is “unlikely that the income tax would come between the sales tax and the excise tax in individual preference orderings” (66). He claims that these assumptions yield the inferred preference orders in the column with that label in Table 15.1. Summing up pairwise contests given Blydenburgh’s inferred individual preference orders, the sales tax S defeats the income tax I by 194 to 162. The excise tax E beats the sales tax S by a vote of 200 to 156. We have E > S, and S > I, or E > S > I. The remaining question, according to Blydenburgh, is about the contest between the income tax I and the excise tax E. He has 396 voters in total. The 30 voters of Group D voted against all taxes and he calls them indifferent. Also, three of the voters abstained on both the income tax and the excise tax. Thus a majority for a vote between the excise tax and the income tax would be 182 > (3962–33 ) = 181.5. Summing from his inferred individual preference orders, there are 180 votes for the income tax, two short of the requisite majority of 182, and 112 votes for the excise tax (including, from the partially abstaining voters, two votes E > Q, two votes Q > E and three votes Q > I ). Then, he says we are unable to order the 71 voters in Group H whose revealed preferences are S > (E, I ). If only four of those in Group H

Other cycles debunked

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were indifferent between E and I then the income tax would have a majority with 180 votes (112 + 71 = 183 − 4 = 179 < 180), according to Blydenburgh. If all those in Group H strictly ranked the two alternatives, but merely 2 of the 71 preferred the income tax to the excise tax, then again the income tax would win (180 + 2 = 182 > 181 = 112 + 69), according to Blydenburgh. If the income tax beats the excise tax, I > E, then the individual preference conﬁguration gives rise to the cycle E > S > I > E, he concludes. Now we shall examine his inference of preference orders. First, the 30 in Group D who voted against all taxes he terms indifferent, but I would like to call them negatively indifferent. Next, I mentioned that the ﬁrst assumption had an odd consequence. I would call the nine voters in Group E who voted for all taxes positively indifferent, but Blydenburgh, applying his ﬁrst assumption, determines that their preference order is the same as the sequence of votes, S > I > E. Someone is asked in sequence whether she would buy vanilla, chocolate, or strawberry ice cream, she answers yes in each case, and the investigator concludes that she prefers vanilla to chocolate to strawberry. Can Blydenburgh’s ﬁrst assumption provide a correct inference? I think not. Further, his second assumption is inconsistently applied, with no explanation. The second assumption is that the income tax will not be between the sales tax and the excise tax in individual preference rankings. Notice immediately that this is contrary to his odd inference that the positively indifferent voters in Group E ranked S > I > E: I should not be between S and E. There are far bigger problems, however. The second assumption transforms Group A’s revealed preference of (I, E ) > S into an inferred preference of I > E > S. The assumption is also applied to the incomplete revealed preferences of Group B and Group C respectively in order to obtain complete inferred preferences. The revealed preference of Group H is S > (E, I ). Applying the second assumption would yield the complete inferred preference order of S > E > I. Blydenburgh says, however, with no explanation for the inconsistency, that we can’t completely order Group H, meaning that the second assumption applies except to Group H. Why? It happens that if we applied the second assumption to Group H there would be no cycle; recall, he needs a few in Group H to be indifferent or for a few to be S > I > E in order to get his cycle. He only needs a few votes though, the reader might say, but no. We do not know how the 85 voters in Group A ranked E and I; the second assumption infers that they ranked I over E, but some or many could have ranked E over I. If we consistently apply the second assumption to both Group A and Group H, then when Blydenburgh says that a few in Group H could have preferred I to E the proper reply is, yes, but a few

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Democracy Defended

Table 15.2. Pairwise-comparison matrix, Revenue Act 1932 I I E S Q

187 194 211

E

S

Q

178

171 209

178 204 160

156 187

236

in Group A could have preferred E to I; one arbitrary exception cancels out the other. If we correct the 9 voters of Group E from S > I > E to S ∼ I ∼ E, then for Blydenburgh to make his cycle he would need not 4 but rather 13 voters in Group H to be indifferent between I and E, or he would need not 2 but rather 11 voters in Group H to prefer I > E. Or, if we apply the second assumption consistently to both Group A and Group H, then individual preferences do not aggregate into a cycle (by two votes, to be sure). In both cases the collective ranking is E > S > I. If we make both corrections (I have ignored the partially abstaining voters for ease of exposition) then E > S, 209 votes to 156; S > I, 194 votes to 171; and E > I, 187 votes to 178. Again, E > S > I and there is more robustly no cycle. Part of the confusion is due to the fact that there were actually four alternatives, not three: the sales tax, the income tax, the excise tax, and the status quo of no tax. The pairwise-comparison matrix Table 15.2 contains my corrected inferences of the rankings among S, I, and E as well as the revealed votes between each of those and Q. The pairwise rankings are E > I, E > S, E > Q, S > I, Q > I, Q > S, and that reduces to E > Q > I > S, which is consistent with the commonsense narrative about this vote, that is, the excise tax beat the status quo and was adopted but the income tax and the sales tax were defeated. It’s like breathing fresh air again. If there were a cycle, then the last alternative voted on would have won arbitrarily, he says. The last alternative voted on was E, which won. Blydenburgh (1971, 67) proposes that, “If the excise tax – the amendment that actually was adopted – had been introduced ﬁrst, it would have been defeated by the 180 voters who preferred the income tax plus the 28 voters who were opposed to any tax. Had the sales tax been introduced last, it would have been adopted.” What if the excise tax had been introduced ﬁrst? Then the contest would be between E and Q, and we know E would win that. If the contest were between E and S, then E would win 200 to

Other cycles debunked

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156 on Blydenburgh’s inferred rankings. If the contest were between E and I, and if his inferred preferences are correct, then I would win, but I have argued that there is no cycle because on my corrections E > I, 187 to 178. If the contest were between E and the impossible composite not-E, then, we have seen, E would win. Now Blydenburgh makes a third argument: 182 votes are required for I to have a majority over E; I has 180 votes against E, to the 180 we add the 28 voters (Group D) who were against all taxes and obtain a majority for I over E. Actually, Group D possessed 30 voters who voted against all taxes, but this is a side issue. The members of Group D voted against all taxes, they voted against E and they voted against I; thus, if the contest were between E and I they should vote for neither and abstain. If the members of Group D abstain, then on the remainder of Blydenburgh’s count there are 180 voters for I > E, 112 votes for E > I, the ranking of the 71 voters in Group H is undetermined, and we are squarely back at the issues already encountered in discussion of his second argument. What would have happened if the sales tax were voted on last? If the vote were between S and E, then E would win by 200 votes to 156 on Blydenburgh’s inferred count. And we know that E would beat Q. If the vote were between S and I, then S would win 194 votes to 162 on Blydenburgh’s inferred rankings. But S must go against Q, and then Q wins. Next, Blydenburgh (1971, 67) says that if the income tax had been voted on last, it “probably could not have passed because of the opposition of Group H.” Because there is a cycle, the argument goes, any alternative voted on last will win. But if the income tax were voted on last, it would not win, he says. Does this mean that there is a cycle, but only between S and E ? How would that be? I do not understand his argument. Finally, Blydenburgh uses the same methodologies to examine votes on the Revenue Act of 1938. The tale always gets better in the telling, and Blydenburgh (1971) is sometimes cited as having demonstrated cycles in both 1932 and 1938 (e.g., Shepsle and Bonchek 1997, 61). Blydenburgh does not ﬁnd a cycle in 1938, and the reader may be relieved to learn that there is no need to reconstruct his second case. Anyone who would read Blydenburgh (1971) attentively, with pencil and paper at hand to work through the details of his argument, would quickly discover the heap of conceptual confusions I have related. Yet, so far as I know, there are no other reports that Blydenburgh’s cycle ﬁnding is erroneous. Rather, the ﬁnding is cited approvingly as central evidence for the claim that democracy is meaningless (Riker and Weingast 1988; Shepsle and Bonchek 1997). This raises an important problem about the Rochester approach. Riker (1965) promised us that mathematics would introduce precision and eliminate ambiguity from political science.

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Bueno de Mesquita (quoted in Cohn 1999) told us that the Rochester school is dominant because the clarity of its work attracts attention. What we have seen, however, over and over again, is obscurity, not clarity, and confusion, not insight; an obscurity and confusion, moreover, disguised from the eyes of the world by superﬁcially impressive formalisms. Stephen Walt reminds us of the costs of formalization, that precision comes at a price. He says there is a tendency for formal theorists to present their ideas in an overly complex and impenetrable manner, and he criticizes the style in which formal methods are deployed to lend a quasi-scientiﬁc patina to otherwise simple (and sometimes mistaken, I would add) ideas. According to Walt (1999, 21): the larger the audience that can understand and evaluate a theory, the more likely is it that errors will be exposed and corrected and the better a theory has to be in order to retain approval. By contrast, an incorrect theory that is presented in an opaque or impenetrable way may survive simply because potential critics cannot ﬁgure out what the argument is.

The same malady notoriously afﬂicts certain narrative theories; consider, for example, the work of Talcott Parsons. A roll-call analysis is a comparatively simple exercise. The one we have here was botched from inception in 1971, yet as of 1997 it still ranks high in the Rochester canon. If gross error in a simple paper high in the canon goes unnoticed for 26 years, then what are we to think about the more formal treatments of more complicated problems since in the same tradition? Bjurulf and Niemi on Scandinavian parliaments Bjurulf and Niemi (1978) intend their paper to be an empirical exploration of Rochester doctrine. A case is being made, they write four years before the publication of Liberalism against Populism by Riker, Niemi’s colleague at Rochester, that voting systems are manipulable by strategic voting, agenda setting, and vote trading, although there is little hard evidence on the extent of manipulation in actual settings, they continue. The lack of evidence is due largely to the fact, as we have heard before, that the usual voting rules typically do not record voters’ rankings over all alternatives. Another reason for the lack of evidence, they add, is that legislators naturally desire not to publicize that they have voted strategically or that they have attempted to control the agenda. In the cases I have analyzed in this volume, however, legislators are frequently at pains to publicize the fact that their votes are strategic. In the 1957 replay of the Powell amendment, one Democrat after another stood up to say that his vote

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was “strategic.” In debate on the 17th Amendment to the US Constitution, Bristow freely declared the strategic nature of his voting. In the ﬁnal defeat of the Wilmot Proviso, one of the seven who switched votes published an explanation to his constituents concerning his strategic response to the situation forced upon him. This unsystematic sample shows that legislators sometimes naturally desire to publicize the strategic nature of their votes, surely so that constituents can appreciate their true positions. To continue the exposition, Bjurulf and Niemi’s cases lead them to the conclusion that, at least in the Swedish context, manipulation occurs not by way of an agenda-controller’s ordering of consideration of alternatives, nor by introduction of confounding new issues or dimensions, but rather by way of strategic voting emerging in response to unmanipulated sequences of alternatives. They report on three cases, and also report more generally on strategic voting in Scandinavian legislatures. I was unable to inspect the parliamentary record they rely on, lacking both access to the documents and ability to read Swedish. The ﬁrst case took place in Chamber I of the Swedish Parliament in 1931. There were three alternatives under consideration: r Big: Build the Karolinska hospital as planned. r Small: Build the ﬁrst section of the hospital, but not additional sections. r Nothing: Do nothing, remain at the status quo. Big was the choice recommended to the chamber by the committee of jurisdiction. The ﬁrst chamber vote, according to Bjurulf and Niemi, was between Small and Nothing, and Nothing won the ﬁrst vote. The second vote was between Big and Nothing, and Big won the second vote and thus the whole contest. r Nothing > Small, 46–41, with 63 abstaining or absent. r Big > Nothing, 54–16, with 80 abstaining or absent. There was not a vote between Big and Small, but Bjurulf and Niemi infer the collective ranking Small > Big by 47 to 37 from reconstruction of the preference orderings of “legislators present and voting” (7). Combining the latter inference with the two recorded votes they obtain Big > Nothing > Small > Big, a cycle. Their reconstruction is as follows. First, 10 legislators voted Small > Nothing and Nothing > Big, and apparently these 10 ranked Small > Nothing > Big. This is a reasonable preference order, in my view; such voters are willing to pay for a small hospital, but would rather have nothing than pay for a big one. Next, 14 legislators voted Small > Nothing, but abstained on Big versus Nothing. Bjurulf and Niemi interpret the abstentions as indifference between Big and Nothing. Three legislators voted Nothing > Small but were absent for the vote between Big and Nothing. Next, 17 legislators voted Small > Nothing and for Big > Nothing.

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Bjurulf and Niemi present evidence from the debate that legislators of this type expressed a preference for Small > Big for an overall ranking of Small > Big > Nothing. Six legislators voted Nothing > Small and Nothing > Big. Bjurulf and Niemi infer that these six also rank Small > Big and thus that their overall ranking is Nothing > Small > Big: “Since these legislators favored no expenditure at all, we conclude that they preferred a smaller expenditure . . . to a larger one” (8). This is the natural presumption I believe, but it’s also logically possible that these six ranked Nothing > Big > Small. The latter ranking might make sense, say, if there were a large private hospital these legislators’ constituents used that would be destroyed by competition from any size of public hospital: they would prefer the status quo of a private hospital, but if a public hospital must be built then better make it a big one. Nothing > Big > Small is a plausible inference, but in the absence of evidence it is not as plausible as Bjurulf and Niemi’s inference, Nothing > Small > Big. Finally, 37 legislators voted both Big > Nothing and Nothing > Small, and Bjurulf and Niemi infer that they ranked Big > Nothing > Small. I believe that this inference is mistaken. As with the 6 legislators just discussed, in the absence of other evidence, it is more plausible that the 37 ranked Big > Small > Nothing and were voting strategically on the ﬁrst vote between Nothing and Small. They sincerely preferred Small to Nothing, but since they also preferred Big to Small, on the ﬁrst vote they strategically voted for Nothing over Small on the belief that on the second vote Big would more probably beat Nothing than would Big beat Small. It is less plausible that the 37 sincerely preferred Big > Nothing > Small. Bjurulf and Niemi acknowledge in a footnote that the 37 could have been voting strategically and if so that the demonstration of a cycle would fail. Their response is that there is no evidence in the record to support the inference that any of the 37 were voting strategically. But neither is there evidence in the record, else they would have reported it, for their less plausible inference of Big > Nothing > Small. For the 37 we have no direct voting evidence, rather we must infer whether they rank Big > Small or Small > Big. Why doesn’t the presumption that Bjurulf and Niemi applied to the 6 legislators, that the second-ranked alternative should be intermediate in quantity to the ﬁrstand third-ranked alternatives, apply to the 37 legislators? If the presumption is consistently applied then the 37 must have sincerely ranked Big > Nothing > Small, and must have been voting strategically. Summing up Bjurulf and Niemi’s reconstructions, a total of 43 legislators favored Small > Big and 41 favored Big > Small, and thus the collective preference would be Small > Big; this, together with the recorded votes of Big > Nothing and Nothing > Small, is the inference that gives

Other cycles debunked

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Bjurulf and Niemi their cycle. If, however, merely 2 out of the 37 whom they infer ranked Big > Nothing > Small were, as I argue, strategic voters who sincerely ranked Big > Small > Nothing, then the collective preference would be Big > Small which yields the noncyclical collective ranking Big > Nothing > Small. Notice a peculiarity about these votes: there were about as many abstentions and absences as there were recorded votes: on the ﬁrst pair 87 voted and 63 did not, and on the second pair 70 voted and 80 did not. I have a hunch that the actual collective ranking for all legislators including the abstainers was actually Big > Small > Nothing, but this cannot be shown. Depending on the context, either there was considerable indifference among the three alternatives, or the full-chamber outcome was so clearly for Big that many legislators did not bother to attend the ﬂoor and those who bothered to come and vote against Big wanted to take a position of favoring economy in government. Without an explanation for the large number of nonvoters, no inference from these data is strongly warranted (Bjurulf and Niemi’s remaining cases report comparatively few abstentions and absences). In their second case, Bjurulf and Niemi do not claim that there was a true cycle, but they do claim that one faction by strategic voting manipulated its favored outcome from second place unfairly to ﬁrst place. Strategic voting can be defeated by strategic voting, however; thus, as we saw with Riker’s accounts of the Powell amendment and of the 17th Amendment, either the claim is incorrect or we must explain why some voters were irrational and voted in a sincere and self-defeating fashion. The vote was in the Swedish Parliament, in 1934, over how much to expand the Swedish telephone and telegraph company. There were three alternatives: r Twelve: Spend 12.35 million Swedish crowns on expansion r Eleven: Spend 11.35 million Swedish crowns on expansion r Ten: Spend 10.35 million Swedish crowns on expansion. The Social Democrats, the minority government, had campaigned in 1932 on increased state expenditures. Their 11 members on the 24-member committee of jurisdiction in Chamber I favored alternative 12, and the Social Democrats must have ranked 12 > 11 > 10. The 7 Conservatives on the committee, whose party had campaigned in 1932 on small state expenditures, proposed 10, and they must have ranked 10 > 11 > 12. Those present of the 6 Farmers’ Party and Liberal Party members of the committee proposed alternative 11 as a compromise. Bjurulf and Niemi suggest that 11 must have been the median preference. They acknowledge that the Liberals’ and especially the Farmers’ preferences between 12 and 10 are uncertain, “in fact they themselves may have been unsure about their preference between these two alternatives since

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Democracy Defended

in voting they sometimes favored one and sometimes the other” (9, emphasis added). From Bjurulf and Niemi’s reportage I infer that, going from left to right in Chamber I there were 61 Social Democrats, 19 Farmers, 17 Liberals, and 46 Conservatives; presumably the center of the Farmers’ Party was the median position in Chamber I. In Chamber I, the ﬁrst vote was between 11 and 10. The Farmers and the Liberals voted for their compromise proposal 11, the Conservatives sincerely voted for 10, and most of the Social Democrats as well voted strategically for 10, and thus 10 beat 11. All the evidence supports the inference that the Social Democrats’ vote for 10 was strategic; we can surmise that they believed that it was more likely that Chamber I would vote for 12 > 10 than it would vote for 12 > 11. The next vote in Chamber I then was between 12 and 10, but 10 beat 12 by 58 votes to 56 votes; thus, the Social Democrats’ strategic vote had been a blunder. If they had voted sincerely they would have won their second-ranked alternative, 11, rather than their last-ranked alternative, 10. Meanwhile, in Chamber II alternative 10 beat 11 by a “rise vote” (the Social Democrats there also apparently voting strategically), and then 12 beat 10 by a rise vote. I calculate that Chamber II contained, from left to right, 5 Communists, 104 Social Democrats, 36 Farmers, 24 Liberals, and 58 Conservatives. The median voter was presumably in the far left of the Farmers’ Party. Chamber II was to the left of Chamber I. If the Communists and Social Democrats were united and disciplined on an issue (as they were on this one) they needed to pull only 5 votes from any of the 118 legislators in the remaining parties (and Bjurulf and Niemi note that the parties were not always cohesive, 21). In Chamber I alternative 10 had won and in Chamber II alternative 12 had won, and apparently the Swedish rule was that differences between Chambers were settled by a joint vote of both Chambers. The results of the joint vote were that 12 > 10 by 67 to 56 in Chamber I, by 117 to 71 in Chamber II, and by 184 to 127 in the decisive summed votes of both Chambers. Why the reversal in Chamber I? The bulk of the Farmers in Chamber I voted for 10 > 12 on the ﬁrst round but for 12 > 10 on the second round. The vote of the Farmers in Chamber II over 12 versus 10 when Chamber II voted alone is unrecorded, but on the later joint vote with Chamber I most of the Farmers in Chamber II voted for 12 > 10. The collective ranking in Chamber I when it voted alone might have been 11 > 10 > 12, because 11 might have been the position of the median voter and we know that 10 > 12 on the second vote of the ﬁrst round. After the curious switch of the Farmers on the later joint vote the collective ranking in Chamber I may or may not have become 11 > 12 > 10. In Chamber II we know that the collective rankings

Other cycles debunked

349

were 12 > 10 and 11 > 10, but we have no idea how Chamber II ranked 12 and 11; thus, the collective ranking in Chamber II was either 12 > 11 > 10 or 11 > 12 > 10. In both Chambers the Social Democrats voted strategically for 10 > 11. The Conservatives in both Chambers failed to vote strategically for 11 > 10 in response to the Social Democrats and, the argument goes, thereby ended up with their third-ranked alternative rather than their second-ranked alternative. Bjurulf and Niemi’s proposition that the Social Democrats’ manipulation succeeded assumes that the Conservatives were irrational. The Conservatives in Chamber I were clearly not irrational, however: by voting sincerely the Conservatives won their ﬁrst-ranked alternative in Chamber I, while the bungled strategic vote of the Social Democrats left the Social Democrats with their last-ranked alternative there. Thus, Bjurulf and Niemi must believe that it was the Conservatives in Chamber II who were irrational for failing to vote strategically for 11 > 10. If the Conservatives in Chamber II believed, however, that the sincere collective ranking in Chamber II was 12 > 11 > 10 then those Conservatives would have had no reason to vote strategically for 11 > 10, indeed they would have looked foolish for doing so. Only if those Conservatives believed that the Chamber II ranking was 11 > 12 > 10 would they have acted irrationally by voting sincerely. We don’t have enough data to know whether Chamber II ranked 12 > 11 > 10 or 11 > 12 > 10, and the presumption of rationality commands that in the absence of other information we accept that the Conservatives in Chamber II believed that the collective ranking there was 12 > 11 > 10. In support of the view that the Conservatives in Chamber II rationally believed that the collective ranking in Chamber II was 12 > 11, consider that in the second-round contest between 12 and 10 in Chamber II 24 Farmers and Liberals voted for alternative 12 and 23 Farmers and Liberals voted for alternative 10, and 13 Farmers and Liberals abstained or were absent; to win a collective vote for 12 > 11 the 104 united Communists and Social Democrats would have needed only 5 out of the 60 Farmer and Liberal votes. On another point, the Social Democrats were the largest (43 percent of Chamber I and 46 percent of Chamber II) and the governing party. There is no reason to believe that their proposal of 12.35 million Swedish crowns represented the median position of their party. It is more likely that they would offer a ﬁgure they believed to be of median appeal to the joint Chambers, attracting all Communists, all Social Democrats, and the requisite handful of votes from the Farmers and Liberals. Finally, the three alternatives may have been so close to one another as to have been a matter of some indifference to the participants. The Conservatives took the position of supporting a slightly smaller expansion, the Farmers and Liberals initially

350

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took an intermediate position that distinguished them from the Social Democrats on the left and the Conservatives on the right, but, as Bjurulf and Niemi observed, the same Farmers and Liberals sometimes voted for 12 and sometimes for 10. We are more likely to witness inconsistencies that suggest the possibilities of a cycle or a successful manipulation when alternatives are very close to one another (and the normative implications of instability are trivial) rather than when alternatives are far apart from one another. In conclusion, Bjurulf and Niemi fail to demonstrate a harmful manipulation by the Social Democrats in the vote over expansion of the Swedish telephone and telegraph company. Riker writes of strategic legislators as omniscient Machiavellian schemers. Green and Shapiro (1994, 111) remind us that they can be bumbling oafs as well, as the Social Democrats were on the telephone and telegraph vote in Chamber I above and on the riﬂeman’s vote below. The third case, again in the Swedish Parliament, concerns the 1927 appropriation for the voluntary riﬂeman’s association. The minority committee report from the Conservatives asked for 500,000 Swedish crowns in order to include riﬂemen, or rather boys, aged 12 to 15 in the activity, a novel proposal. The Liberal government and the relevant committee report recommended the conventional appropriation of 470,000 Swedish crowns. The Social Democrats offered a minority report sincerely recommending no appropriation for the riﬂeman’s association. Bjurulf and Niemi argue that that the collective preference of the joint chambers was 470,000 > 0 > 500,000, but that the last-ranked alternative, 500,000, perversely prevailed in the end. Social Democrats, knowing that the Liberals were uncomfortable with the Conservative’s 500,000 because the Liberals disapproved of involvement of boys in the association, strategically abstained on the ﬁrst vote, between 500,000 and 0, in Chamber I. If the Social Democrats had acted sincerely the outcome would have been 0, but just enough of them abstained so that 500,000 won by one vote. The next vote then, was between 500,000 and 470,000. The Social Democrats strategically abstained again, forcing the outcome to 500,000 (their sincere action would have been to vote for 470,000). In the absence of strategic abstention by the Social Democrats the outcome in Chamber I would have been 470,000. Apparently, the Social Democrats believed that if the choice were between 500,000 and 0 then most Liberals would vote for 0, assisting the Social Democrats to win their ﬁrst-ranked alternative. This was quite a blunder, as the Liberals ultimately responded in a fashion so as to attain the Liberals’ objective and thwart that of the Social Democrats. Meanwhile, in Chamber II the votes were 0 > 500,000 and then 0 > 470,000, apparently with no strategic voting by any agents. Again,

Other cycles debunked

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because the two Chambers disagreed, the issue went to a joint vote between 500,000 and 0. In the joint vote, however, most Liberals (f ) in Chamber I switched from voting 0 > 500,000 to voting 500,000 > 0. The Liberals (f ) in Chamber I were decisive: if in the joint vote they had voted as they had when the issue ﬁrst arose in Chamber I, then the joint collective outcome would have been collectively second-ranked 0 rather than collectively last-ranked 500,000. What was the true position of these Liberals and why did they switch? Bjurulf and Niemi (12) are conﬁdent, citing debate evidence, that these Liberals sincerely ranked 0 > 500,000. Further: The explanation for this switch is very probably some sort of deal made with the Conservatives and the Farmers prior to the joint vote. We base this conclusion on the fact that the next year, 1928, the sum appropriated for the voluntary riﬂeman’s association was 440,000 Swedish crowns, with no dissenting alternatives from the Conservatives. The [1928] appropriation contained nothing for riﬂemen between 12 and 15 years of age. Thus, the situation seems to be have been that the Liberals, faced with the alternative of no appropriations or one that included appropriation for the very young, would support the [1927] appropriation with the understanding that the Conservatives and Farmers would not bring up this proposal again the following year. (16)

The best way to make sense of these events is to recognize that a fourth alternative had been introduced: 500,000 this year (30,000 above the conventional appropriation) so that the Conservatives and Farmers would not disappoint their constituents and so that the Social Democrats would be punished for their chicanery, on the understanding that 440,000 would be offered in the following year (30,000 below the conventional appropriation), which I denote with a prime mark. True, the Liberals (f ) ranked 470,000 > 0 > 500,000, and the abstention of the Social Democrats denied the Liberals their ﬁrst-ranked choice in the short run. But the other parties countered the Social Democrats by crafting 500,000 , which won majority support in the joint vote. The Liberals (f ) must have ranked 470,000 > 500,000 > 0 > 500,000. Strategic action was countered by strategic action such that the ﬁnal outcome was what it would have been in the absence of strategic action; attempted manipulation was neither irremediable nor harmful. Bjurulf and Niemi report on a more general survey of Scandinavian parliaments. They looked primarily in years when there were minority governments, because majority governments would rarely generate a record of strategic voting among more than two alternatives. They uncovered further cases that resemble the three cases we have analyzed in detail, and suggest that if analyzed in detail the further cases would further demonstrate cycles, harmful manipulation, and so on. Since their

352

Democracy Defended

three cases, which it is fair to assume are their best examples, are weak, their generalization is weak. In Sweden, they say, strategic manipulation frequently resembled that in the second case: the Social Democrats vote strategically for the Conservative alternative in order to eliminate the centrist alternative offered by the Farmers and Liberals, according to Bjurulf and Niemi. In 1957–1958, the Social Democrats, who were larger than any combination of two of the three bourgeois parties, attempted this more often than not whenever there were more than two alternatives to vote on. Bjurulf and Niemi point out that nevertheless the Social Democratic alternative had to be centrist enough to defeat the Conservative alternative. There was reportedly much less strategic voting in the other Swedish period examined, 1925–1938. In Finland during periods of minority government, the situation was much the same as in Sweden. A variation in Finland was for the Agrarians and Finnish People’s Party to vote strategically for the Communist alternative so as to eliminate the more centrist Social Democratic alternative. Bjurulf and Niemi claim that there were true cycles in Finnish politics, but none that were taken advantage of strategically. Even in periods of minority government strategic voting was infrequent, in 90 percent or more of roll calls there were only two alternatives to vote on. There were almost no strategic votes in Norway and Denmark as these countries used the “successive” procedure in which alternatives are voted on one at a time until some alternative receives a majority vote. This procedure is especially vulnerable to unpredictable voting-order effects which motivates legislators, say Bjurulf and Niemi, to limit to two the alternatives brought to the ﬂoor. Does the analysis of Bjurulf and Niemi support the proposition that democracy is meaningless? Their ﬁrst case attempted to show a natural cycle, but relied on the assumption that 37 of the voters had an extraordinary preference ranking. I showed that if only 2 out of those 37 were voters with an ordinary preference ranking but voting strategically then there was no cycle. Their second case purported to show a case of harmful strategic voting, but violated the presumption of rationality: without evidence they assumed that the Conservatives in Chamber II had beliefs which made their actions irrational, when it was possible to assign an equally plausible alternative belief that preserved the rationality of those Conservatives. My interpretation of their second case illustrates bungled strategic voting. The third case is an instance of strategic voting being countered by creative strategic activity that restored the centrist outcome. My view is that we should see either no strategic voting, bungled strategic voting, or strategic voting successfully countered by strategic voting, in any case such that generally the centrist outcome prevails. Bjurulf and Niemi’s general survey shows that even with minority governments votes

Other cycles debunked

353

involving more than two alternatives and associated possibilities for strategic voting are rare. Furthermore, frequently harmful manipulation is not established because their general survey relies on methods and insights shown to be mistaken in their three fully worked out cases. In sum, I dispute Bjurulf and Niemi’s conclusion that (harmful?) manipulation is a frequent occurrence. Neufeld, Hausman, and Rapoport on Muscle Shoals Neufeld, Hausman, and Rapoport (1994) review and summarize the standard cycling story, citing Riker and his followers, among others. Cycles are difﬁcult to identify, again because it is rare for there to be recorded votes over all alternatives. Indeed, “the literature on cyclical majorities has failed to uncover a single clear example of cyclical voting” (427, emphasis added), even though Riker’s analyses of the Powell amendment and the 17th Amendment “appear to be consistent with the paradox” (426). Neufeld et al. are an example of how Riker’s already mistaken stories become even more garbled in transmission. They cite as primary evidence for a cycle in the Powell amendment votes the fact that in the following year an education bill without the Powell amendment passed, although alas the evidence is too weak for a certain judgment, they continue. Recall that I showed that the unamended education bill actually failed in the following year, and cited that as important evidence against Riker’s cycle argument! The 17th Amendment failed, they write, because although the proposal for the direct election of senators contained a provision prohibiting federal supervision of elections, an amendment by the House eliminated the prohibition. I showed that the 17th Amendment earlier would have failed in the Senate with or without the prohibition provision; and later it was the House that demanded the prohibition and the Senate which successfully resisted it. Enough of my points against Neufeld et al. Their complaint against Riker is that his cases depend not only on recorded votes but also on uncertain inferences. In contrast, they believe they have ﬁnally identiﬁed “a deﬁnitive and signiﬁcant example of cyclical voting” (423) based only on recorded votes. It had to do with Muscle Shoals, an obstacle to navigation on the Tennessee River in Alabama, one of the most important issues in the US Congress in the 1920s, and which eventually evolved into the Tennessee Valley Authority in 1933 under Roosevelt. The votes were in a major political body, the US Senate. And by luck there were three pairwise votes recording expressed preferences over three alternatives. Finally, one of the participants stated that the body was caught in a voting “circle” among the three alternatives. What more could one ask?

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Democracy Defended

If Muscle Shoals were tamed, an obstacle to navigation would be removed, huge amounts of hydroelectricity would be generated, and nitrates could be manufactured for agricultural and military uses. Among the questions were how to proceed, whether to use public enterprise or private enterprise, and if the latter then which private enterprise. Senator Underwood’s bill “was crafted in consultation with the Republican administration, and it appeared to have the solid backing of President Coolidge” (429), and would lease the facilities to private enterprise. Senator Norris (R-NE), a left-liberal insurgent Republican and advocate of publicly owned power utilities, denounced the Underwood plan as a giveaway to private interests, which would result in another scandal like Teapot Dome, already a huge embarrassment to the Coolidge administration. In response: Republican senators came from meetings with the President convinced that Underwood’s measure would not pass and that the best disposition of Muscle Shoals was for it to be sent to a commission that would make recommendations to Congress after a year’s study. (Neufeld et al. 1994, 430)

The administration’s senators crafted a proposal to create such a commission, introduced by Senator Jones. Thus matters stood as the Senate recessed for Christmas. The votes occurred over one week in January 1925. Norris’s proposal (N ) was ﬁrst. Underwood offered his proposal (U ) as a substitute, and the Senate voted for U > N, private development over public development, by 48 to 37 (the ﬁrst vote). Several days of debate followed. Then, according to Neufeld et al., the Senate voted for J > U, a study commission over private development, by 46 to 33 (the second vote). Norris then reintroduced his proposal (with a cosmetic change to dodge the Senate rule against reintroduction of proposals) again, and Norris beat Jones, public power beat a study commission, N > J by 40 to 39 (the third vote). Thus, U > N > J > U: what we seem to have here is an unequivocally demonstrated cycle. Underwood sought then to reintroduce his proposal, which Norris moved was out of order, declaring that “we are in a circle with three points in it,” such that one alternative would beat the next and we “would go around the circle again, and we would be just where we started” (431). Underwood’s proposal was reintroduced the next day and passed by a vote of 46 to 33 (U > N, the fourth vote). Then Jones’s proposal was reintroduced, but there was something new in the air, as Norris promised not to reintroduce his proposal if Jones’s won. Indeed, U beat J, 43 to 38 (the ﬁfth vote). Yesterday Norris beat Jones and Jones beat Underwood, but today the combined forces of Norris and Jones aren’t enough to beat Underwood. This should make us suspicious

Other cycles debunked

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Table 15.3. Neufeld et al.’s account of Muscle Shoals preferences Group number and label

Preferences

#

1. Anti-Ford Republicans 2. Jones group 3. Norris group 4. Southern Democrats 5. Underwood group 6. Southern Democrats

J>N>U J>U>N N>J>U N>U>J U>J>N U>N>J

3 13 24 4 17 9

about the purported cycle. Underwood went on to beat the status quo by a vote of 50 to 30 (the sixth vote). There was no natural cycle because, as Neufeld et al. themselves point out, many of those voting for Jones truly favored Underwood, but at the prompting of the Coolidge administration introduced and voted for the Jones compromise on the belief that Underwood could not win in the Senate. Voting then revealed that Underwood could indeed win, and those Jones voters then shifted to Underwood. “There is evidence that the shift came at the direction of the Coolidge White House. The Republican ﬂoor leader shortly before the ﬁfth vote [U > N, 46 to 33] met with the President who was, by this time, reported as favoring Underwood’s position” (433). Neufeld et al. do not distinguish between natural cycles and apparent cycles contrived by strategic voting, believing that for prior attempts to demonstrate empirical cycles, such as Riker’s, “it is the attempt at manipulation (sophisticated voting by individuals) that creates the effect of cyclical majorities” (426), which is an incorrect reading of Riker, who sometimes wrongly believes that he has uncovered a natural cycle. Muscle Shoals appeared to be a cycle, as so often in these case studies, only because of bungled strategic voting; sincere preferences were in equilibrium. Despite both apparent cycling and strategic voting the ﬁnal outcome of the Muscle Shoals votes was in the center of the Senate’s opinion. Neufeld et al. make no claim that harmful manipulation occurred. The apparent cycle is borderline as well, because if only one of the voters had switched from N to J the expressed collective ranking would have gone from the cyclical J > U > N > J to the noncyclical J > U > N. Neufeld et al. tally the preferences of the 71 senators who voted on each of the ﬁrst three votes, U against N, J against U, and N against J. They assign senators to the six groups displayed in Table 15.3. For interpretations of each of the groups, see the original article. Notice that the southern

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Democracy Defended

Table 15.4. Pairwise-comparison matrix, Neufeld et al.’s count J J N U

37 30

N

U

BC

33

40 31

73 68 69

39

Democrats in Groups 4 and 6 wanted private or public development of the Tennessee River and did not want the delayed action of a Jones commission. Perhaps the Republicans who devised the Jones compromise on the mistaken belief that Underwood couldn’t win underestimated the strength of Southern Democratic support for this huge project in southern territory. Neufeld et al. observe that it was a shift of voters from Group 2 to Group 5 that voided the cycle in the end. Prior to that shift, pairwise outcomes, and associated Borda counts, were as shown in Table 15.4. J > U by 40 to 30, U > N by 39 to 31, and N > J by 37 to 33, for the apparent cycle J > U > N > J. The cycle is weak even on its own terms. The Borda count gives us the ranking of J > U > N. The Young–Kemeny rule, which tells us to break the cycle at the weakest link, would strike N > J by 37 to 33, and thus would also provide the ranking J > U > N. Neufeld et al. do not do a precise count, but, as I shall show in detail below, when we substitute for the strategic preferences expressed in the tables above the sincere preferences revealed by the exodus from Group 2 to Group 5, the true collective ranking becomes U > J > N, and it was U that passed out of the Senate: no cycle, no harmful manipulation. Neufeld et al. rely only on the votes of the 71 senators who voted on all three pairwise comparisons on the ﬁrst, second, and third votes (U against N, J against U, N against J ). It is also possible to infer the preference orders of senators who voted in only two of those three votes. If a senator voted U > N in the ﬁrst vote, missed the second vote, and voted N > J, we can make the fallible inference that he ranked U > N > J. The fourth and ﬁfth votes, after many Group 2 voters migrated to Group 5, only record preferences expressed over U against N and J against U. Again, it is possible to infer preference orders. For senators who voted for only two out of the ﬁrst three votes, and for senators who voted on both the fourth and ﬁfth contests, my fallible inference rule permits the 1,2,3 inference to borrow from the 4,5 rankings, or the 4,5 inference to borrow from the 1,2,3 rankings. Then, we can compare preference orders during the ﬁrst, second, and third votes to preference orders during the fourth and ﬁfth votes, and identify senators whose preferences changed from one day

Other cycles debunked

357

to the next, and make further inferences about the changes. I report this exercise in Table 15.5. The column labeled 1,2,3 reports inferred rankings arising from the ﬁrst, second, and third votes. The column labeled 4,5 reports inferred rankings arising from the fourth and ﬁfth votes. The column labeled 6 reports the ﬁnal vote between Underwood and the status quo. The summary rule of inference is to use all pairwise comparisons to infer ranking of the three alternatives, unless there is a contradiction. An asterisk indicates that a ranking was borrowed from 1,2,3, by 4,5 or vice versa. A double asterisk means that a ranking was not borrowed from one column to another. If an entry is underlined in the column labeled 4,5 that means the senator’s ranking changed from that of 1,2,3, and the change from one ranking group to another is reported in the column labeled comments. An underlined entry in the column labeled 6 indicates a vote inconsistent with earlier expressed preferences. No inferences are possible about senators who missed four, ﬁve, or six out of the six votes, nor do I count Greene. The rankings from Table 15.5 are summarized in Table 15.6. The column labeled N, H & R reports Neufeld et al.’s rankings from actual votes 1, 2, and 3. The column labeled M 1,2,3 reports the actual votes and my inferences over votes 1, 2, and 3, and the column labeled 4,5 reports my inferences over votes 4 and 5. There were 96 senators, and 88 of them cast at least one vote out of the six. I obtain expressed or inferred preferences for 80 or 81 senators, as compared to the 71 that Neufeld et al. obtain by relying only on recorded votes. One of the senators, McKinley, expressed a cyclical preference in votes 1, 2, and 3. When the administration senators in the Jones group were voting strategically during votes 1, 2, and 3, my 80 senators made up a collective ranking of J > U > N ∼ J, a weak cycle. If we add the votes of cyclical McKinley, however, then we obtain the collective preference ranking J > U > N, which is not a cycle! The collective rankings are obtained from the pairwise-comparison matrix in Table 15.7. Between votes 1,2,3 and votes 4,5, 17 senators changed expressed preference rankings. The most important are the ten who changed from Group 2 to Group 5; these were mostly the administration Republicans who were freed to vote for their most preferred outcome, Underwood. Further, two senators switched from 1 to 2, and another two switched from 2 to 1, canceling each other out. The remainder are: one from 6 to 4, one (McKinley) from 7 to 5, and one from 4 to 3. That yields a pairwise-comparison matrix, shown in Table 15.7, for sincere preferences that again conﬁrms the complete absence of any cycle. The Condorcet, pairwise-comparison order is U > J > N, as is the Borda count. It was U that won in the Senate. Hence, Neufeld et al. have failed to demonstrate

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Table 15.5. Mackie’s inferred rankings, Muscle Shoals Votes Senators Ashurst Ball Bayard Bingham Borah Brookhart Broussard Bruce Bursum Butler Cameron Capper Carraway Copeland Couzens Cummins Curtis Dale Dial Dill Edge Edwards Elkins Ernst Fernald Ferris Fess Fletcher Frazier George Gerry Glass Gooding Greene Hale Harreld Harris Harrison Heﬂin Howell Johnson–CA Johnson-MN Jones-NM Jones-WA

1,2,3

4,5

6

NJU (3) JUN (2) UJN (5) JUN (2)∗ NJU (3) NJU (3)

NJU (3)∗ UJN (5)∗ UJN (5) UJN (5)∗ NJU (3) NJU (3)

QU UQ UQ UQ QU QU

UNJ (6) JUN (2) UJN (5) JUN (2) NJU (3)

UNJ (6) UJN (5)∗ UJN (5) UJN (5)∗ NJU (3)

UQ UQ UQ UQ QU

NJU (3) JNU (1) JNU (1) UJN (5) UJN (5) UNJ (6) NJU (3) UJN (5)

NJU (3) JNU (1) JUN (2)∗∗ UJN (5) UJN (5) UNJ (6) NJU (3) UJN (5)

ABSENT QU QU UQ UQ UQ QU UQ

Comments

2 TO 5 2 TO 5

5/6 ABSENT 2 TO 5 2 TO 5 5/6 ABSENT

JNU (1)∗∗ UJN (5) NJU (3) UJN (5) UNJ (6)

JUN (2)∗∗ UJN (5) NJU (3) UJN (5) NUJ (4)∗∗

UQ UQ QU UQ UQ

UNJ (6) UJN (5)

UNJ (6) UJN (5)

UQ UQ

NJU (3) UJ UJN (5) JNU (1) NUJ (4) UNJ (6) UNJ (6) NJU (3)∗ NJU (3)

NJU (3) UN, UJ UJN (5) JNU (1) NUJ (4) UNJ (6) UNJ (6) NJU (3)∗∗ NJU (3)

QU UQ UQ QU UQ UQ UQ QU QU

NJU (3)∗ JUN (2)

NJU (3) JNU (1)∗

QU QU

1 to 2

5/6 ABSENT 5/6 ABSENT 1 to 2

6 to 4 5/6 ABSENT

5/6 ABSENT Incomplete

6/6 ABSENT 2 to 1

Other cycles debunked

359

Table 15.5. (cont.) Votes Senators Kendrick Keyes King Ladd LaFollette Lenroot McCormick McKellar McKinley McLean McNary Mayﬁeld Means Metcalf Moses Neely Norbeck Norris Oddie Overman Owen Pepper Phipps Pittman Ralston Ransdell Reed-MO Reed-PA Robinson Sheppard Shields Shipstead Shortridge Simmons Smith Smoot Spencer Stanﬁeld Stanley Stephens Sterling Swanson Trammell Underwood

1,2,3

4,5

6

NUJ (4) UJN (5) UJN (5) UNJ (6) NJU (3)

NUJ (4) UJN (5) UJN (5) UNJ (6) NJU (3)

UQ UQ UQ∗ (A) UQ QU

JUN (2)∗∗ NJU (3) NUJN (cycle) UJN (5) NJU (3) NJU (3) JUN (2) UJN (5) JUN (2)∗ NJU (3)

UJN (5)∗ NJU (3) UJN (5)∗ ? UJN (5) NJU (3) NJU (3) UJN (5)∗ UJN (5) UJN (5)∗ NJU (3)

UQ QU UQ UQ QU QU UQ UQ UQ QU

NJU (3) JUN (2)∗ NJU (3) UNJ (6)∗ JUN (2) JUN (2) UNJ (6)∗ NJU (3)∗∗ NJU (3)

NJU (3) UJN (5)∗ NJU (3)∗ UNJ (6)∗ JUN (2) UJN (5)∗ UNJ (6)∗ NJU (3)∗∗ NJU (3)∗

QU UQ QU UQ UQ UQ UQ QU QU

JUN (2)

JUN (2)

UQ

NJU (3) UJN (5) NJU (3) JUN (2) NJU (3) NJU (3) JUN (2) UJN (5)∗

NJU (3) UJN (5) NJU (3) JUN (2) NJU (3) NJU (3) JNU (1)∗ UJN (5)∗

QU UQ QU UQ QU QU UQ UQ

UNJ (6)

UNJ (6)

UQ

JUN (2) NUJ (4) NUJ (4) UJN (5)

JUN (2) NUJ (4) NJU (3)∗ UJN (5)

UQ QU UQ UQ

Comments

6/6 ABSENT 2 to 5 ? to 5

2 to 5 2 to 5 4/6 ABSENT 2 to 5

2 to 5

6/6 ABSENT 5/6 ABSENT

2 to 1 6/6 ABSENT 6/6 ABSENT ? 4 to 3

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Democracy Defended

Table 15.5. (cont.) Votes Senators Wadsworth Walsh-MA Walsh-MT Warren Watson Weller Wheeler Willis

1,2,3

4,5

6

Comments

JUN (2) NJU (3) NJU (3) UJN (5) JUN (2)∗∗ JUN (2)∗

JUN (2) NJU (3) NJU (3) UJN (5) UJN (5)∗ JUN (2)∗

UQ QU QU UQ UQ UQ

UJN (5)

UJN (5)

UQ

2 to 5 6/6 ABSENT

Notes: Rules of inference: use all rankings, unless they are inconsistent. Allow changes between 1,2,3 and 4,5, otherwise assume same rankings among two. Italics in column 4,5 means inconsistent with 1,2,3, ∗ = ranking borrowed from 1,2,3, by 4,5 or vice versa ∗∗ = ranking not borrowed from other column

Table 15.6. Summary of Mackie’s rankings, Muscle Shoals Group number and label

Preferences

N,H & R

M 1,2,3

M 4,5

1. Anti-Ford Republicans 2. Jones group 3. Norris group 4. Southern Democrats 5. Underwood group 6. Southern Democrats 7. McKinley

J>N>U J>U>N N>J>U N>U>J U>J>N U>N>J N>U>J>N

3 13 24 4 17 9

4 18 26 4 18 10 1

4 8 27 4 29 9

Table 15.7. Pairwise comparison matrix, before vote switch J J N U

40 32 + 1

N

U

BC

40 +1

48 34 + 1

88 + 1 74 + 1 78 + 1

46

Other cycles debunked

361

Table 15.8. Pairwise-comparison matrix, after vote switch J J N U

40 42

N

U

BC

41

39 35

(80) (75) (86)

46

a deﬁnitive and signiﬁcant example of cyclical voting. What they have shown is another case of bungled strategic voting. Shepsle and Bonchek’s cycles The cycles mentioned by Shepsle and Bonchek (1997) do not satisfy my criteria of consideration, that the case both be published and developed. Their textbook deserves examination, however, since it is based on a Harvard core course in politics. Shepsle and Bonchek state that Riker is their “inspiration” (viii). The ﬁrst observation in their volume is about politicians: Their sins are routinely depicted; their persons are often held in contempt; and their actions are regularly alleged to border on the venal, the immoral, and the disgusting. In nearly every culture politicians are taken as scoundrels of one sort or another . . . necessary evils at best, but scoundrels nonetheless. (5)

Shepsle and Bonchek declare that the study of politics used to be based on description and judgment, but has moved on to explanation and analysis. In their hands it has become “scientiﬁc” (7). Part II of their volume, on group choice, is a repackaging of Riker’s doctrine of democratic irrationalism. One empirical example offered in support of the argument is Riker’s (1982) and Denzau, Riker, and Shepsle’s (1985) account of the Powell amendment, but students are not informed, even by citation, of Krehbiel and Rivers’s (1990) criticism of that account. Other examples offered in support of the hypothesis are Riker’s account of the slavery issue, and of the Magnuson amendment (which I debunk in an upcoming chapter), and generally the student is referred to Riker’s The Art of Political Manipulation (1986, also upcoming) which contains more popular expositions of his cycle claims. Three examples are offered to establish the existence and importance of cycles on redistributive questions (Shepsle and Bonchek 1997, 60– 62). One paragraph alleges that there was a cycle over a wealth tax, a land tax, and no tax in the 1861 US House of Representatives, which led

362

Democracy Defended

to adoption of an income tax which was preferred over the three cyclic alternatives. For details of the case we are referred to Alt (1983), but Alt (1983) contains no mention of the case, let alone of any details. A second paragraph tells us that scholars have identiﬁed majority preference cycles in Depression-era revenue bills. The “scholars,” we learn in the footnote, are Blydenburgh (1971), who thought he found one cycle, and, as we have just seen, examination of the Blydenburgh article would show that the one claim is confused and invalid. Blydenburgh looked for cycles on revenue bills brought to the ﬂoor under an open rule. Shepsle’s intellectual program is that the institutions of Congress function to overcome what would otherwise be pervasive disequilibrium; the open rule on the ﬂoor is in disequilibrium, but the closed rule (no ﬂoor amendments allowed) arbitrarily imposes an equilibrium by forcing an up or down vote on the committee’s proposal. Here he argues that Blydenburgh (1971) is evidence that members of Congress “agree in advance to impose institutional restrictions on one another’s legislative rights . . . in order to avoid preference cycles” (Shepsle and Bonchek 1997, 61, emphasis added). The argument is purely functionalist, however, as there is no evidence that anyone intentionally designed a Congressional institution for the purpose of avoiding preference cycles. A third paragraph argues that in the Tax Reform Act of 1986 it was possible for there to have been a third alternative that would have created a cycle, but such an alternative was not offered for consideration. Such is the state of the evidence. In conclusion, the student is told that “the literature on social choice is quite sophisticated and covers, in an entirely more analytical style, much of the same ground as the more qualitative work on democratic political philosophy” (Shepsle and Bonchek 1997, 80). The triﬂing evidence we have examined is offered in support of the “philosophical” conclusion that there is no such thing as the public interest: “A public has no identiﬁable interest if its preferences are either incoherent or overly idiosyncratic . . . the public interest is a normative ideal that cannot be given concreteness in most real settings” (193). Finnish electoral college Suppose that Fredonia chooses its prime minister by the following method. Each citizen writes down one name on a slip of paper, the papers are thrown into a hat, one is blindly drawn, and the person named on the slip is declared the winner. Just because the method was used somewhere does not mean that the democratic theorist is obliged to defend it. Although the Fredonian method is somehow fair, it is not popular, in that it does not pick the candidate most-favored, in some sense. As a

Other cycles debunked

363

democratic theorist I would recommend a method that is both fair and popular, among other desiderata. Earlier, I argued that the most popular candidate in the 1860 American presidential election was Douglas, and that the democratic theorist need not defend the clumsy and antimajoritarian American electoral college. From 1925 to 1988, Finland, a semipresidential regime, selected its president by means of a method which often resulted in mischief and occasionally in probably nonpopular outcomes. The faults are not due to a fatal problem in principle with democracy, but are due to the speciﬁc institutional design and perhaps due to the preference proﬁles, I submit. First, there are usually about six serious parties, and on the basis of proportional representation (d’Hondt), 300 electors from those parties are elected to an electoral college. Second, each party may or may not nominate a presidential candidate in advance of the election. Third, the election proceeds by modiﬁed plurality runoff: at least 151 votes at any stage wins the election, in the third stage the top two vote-getters from the second stage face one another; however, parties may withdraw or nominate new candidates on either the second stage or the ﬁrst stage of the sequence. Fourth, vote is by secret ballot, but individuals nevertheless are sanctioned to follow the party line, preventing counterstrategy during rollcall, and reducing the effective number of electors to a small number. Fifth, the electors have one month between their election by the people and the meeting of the electoral college to collect information and devise strategies, preference information is revealed in ﬁrst-stage and second-stage voting, and during the college there are negotiation breaks between stages, allowing for further information collection and strategy formulation. Sixth, the president leads on foreign policy, has the formal power to nominate the cabinet, and informal power to nominate individual ministers; thus, there may be bargaining over policy, and over party and individual portfolios, in the course of the election. Seventh, Finland had a civil war, red terror, and white terror in 1918 that killed 1 percent of the population, and this polarized politics in the 1920s and 30s; in addition to the socialist-nonsocialist cleavage, there was an uncorrelated cleavage on foreign policy towards the neighboring Soviet Union (500 times the population of Finland; Finland seceded from the Russian Empire in 1917), and cleavages between democrats and nondemocrats on right or left, between city and country, and between Finn and Swede. Eighth, if preferences aggregated by party are cyclical, it is possible for those same preferences to be noncyclical if aggregated by individual, the more accurate measure. Proportional representation of parties can amplify the differences between parties and mute cross-cutting

364

Democracy Defended

Table 15.9. Distribution of hypothetical PR voters # of Voters: Rank

7

5

2

1

1st 2nd 3rd

A B C

C A B

B C A

B A C

Table 15.10. Aggregation of preferences by individual not cyclical A A B C

3 7

B

C

(BC)

12

8 10

(20) (13) (12)

5

Table 15.11. Aggregation of preferences by parties cyclical A A B C

3 8

B

C

12

7 10

5

preferences of minority members within parties. Each party might pursue the preferences of its median voter, but not of its members not at the median. The process of aggregation by party discards information about citizens’ preferences, and generally the more information is discarded the more the chance of a nonpopular outcome. Suppose that there is a population divided into three parties, of A-voters, B-voters, and C-voters. Preferences are as in Table 15.9. This population clearly favors A > B > C, by both Condorcet and Borda count, as shown in the pairwise-comparison matrix in Table 15.10. Now suppose that each party acts on the preference of its median voter. In the example, there is unanimity in parties A and C. Party B decides by majority vote that its position shall be the 23 majority position of B > C > A. Although the population’s preferences are noncyclical, preferences aggregated at the party level are cyclical, A > B > C > A, as summarized in Table 15.11. Most of Lagerspetz’s estimates are based on the united

Other cycles debunked

365

preferences of disciplined parties, not on the actual preferences of the range of members of each party, and of course they are not based on the range of preferences in the population. As there is some evidence of cycles in the Finnish electoral college in 1931 and 1937, but weak or no evidence in settings elsewhere, I suggest that the Finnish electoral college is an institutional outlier. The presidential term of ofﬁce is six years, with exceptions in extraordinary circumstances. There were elections in 1925, 1931, 1937, 1950, 1956, 1962, 1968, 1978, 1982, and 1988; in 1994, a new election method was adopted, popular vote in a two-stage plurality runoff, the top two votegetters in the ﬁrst stage going to the second stage. Under the old method, there was a ﬁrst-stage majority winner in the electoral college in 1950, 1962, 1968, and 1978; and the second-stage winner was unambiguous in 1982 and 1988. There are problems alleged concerning the ﬁrst three elections, 1925, 1931, 1937, and the 1956 election. Lagerspetz (1997) claims that there were at least two and maybe three cycles in 1931, 1937, and 1956. I do not read Finnish and cannot access detailed Finnish political history. Lagerspetz (1993, 1997) cites plentiful source material on the controversial elections, and the two articles seem to be based on strong historical research and strategic insight. In 1925, the Condorcet and Borda ranking of the four leading candidates, working from Lagerspetz’s (1997) estimates of electors’ rankings, was Relander > Ryti > Suolahti > Tanner. Relander was the ﬁnal choice of the electoral college, but it took strategic voting to get him through the maze of the modiﬁed plurality runoff, according to Lagerspetz. In 1931 there were four major candidates: Kallio (KA), Stahlberg (ST), Svinhufvud (SV), and Tanner (TA). Lagerspetz (1997, 60) says that “this is the clearest example of cyclical preferences on an important political issue described in contemporary literature,” and if his preference estimates are right, then the claim is correct. From his estimate of preferences, I calculate that the Condorcet pairwise-majority ranking of candidates was (ST >167 KA >211 SV >151 ST) >210 TA. The Borda ranking was KA (554) > ST (526) > SV (450) > TA (270). Svinhufvud (SV), third-ranked by the Borda count, was selected by the electoral college, however. What happened? The Social Democratic candidate, Tanner, was certain to lose, and the Social Democrats, 90 of the 300 electors, decided to seek a victory for their second choice, Stahlberg, the candidate of the republican-liberal Progressive Party. They resolved to vote for Stahlberg on the second round, but also to allocate some votes to their third-ranked Kallio from the Agrarians, believing (correctly) that Stahlberg would do better against Kallio than against Svinhufvud. However, they made their plans public, and this invited a counterstrategy from

366

Democracy Defended

the Agrarians, and on the ﬁrst round some conservative Agrarians voted for their second-ranked Svinhufvud in order to avoid their third-ranked Stahlberg. The Social Democrats withdrew from their plan and in the second round cast no votes for Kallio, but some Agrarians did vote for Svinhufvud. That left Svinhufvud and Stahlberg in the third round, and the Agrarian Party exercised superior discipline over their ranks to elect Svinhufvud, according to Lagerspetz, by a vote of 151 to 149. It may be, however, that Svinhufvud was selected by the electors for reasons other than ordinary preference. The Whites whom Svinhufvud had led in the civil war were agitating for a rightist coup with someone like Svinhufvud as charismatic fascist leader. Their actual coup attempt failed in 1932 because of President Svinhufvud’s forthright opposition, and thus Finland remained democratic. Otherwise, the election of 1931 raises some normative concern, as two candidates were more favored than the candidate selected, but there is a remedy: avoid institutional designs such as the Finnish electoral college, as Finland eventually did. A minimal reform to the 1925–1988 scheme would be to ensure organizational and informational symmetry – if each party is equally well-informed or poorly informed, equally well-organized or unorganized, then strategic voting won’t succeed. Going to direct election in a two-stage runoff helps in that regard, and also avoids the party-aggregation effect. A more ambitious reform would be to go to direct election by single transferable vote. That would far reduce strategic errors, widen and deepen the consideration of preferences below the ﬁrst, and more likely yield centrist outcomes. The same candidates were in play in 1937. Party preferences are plain.1 The collective ranking was probably (KA >189 SV >162 ST >158 KA) >205 TA, a cycle. The Borda count is Kallio (536) > Stahlberg (501) > Svinhufvud (478) > Tanner (285). This time the Social Democrats were determined to prevent reelection of their last-ranked Svinhufvud, and resolved, informing only allies, to vote for their second-ranked Stahlberg on the ﬁrst round, and failing that, their third-ranked Kallio on the second round. They carried through and on the ﬁrst round, Stahlberg got 150 votes, one short of victory, and with votes from the Social Democrats Kallio won a majority against both Svinhufvud and Stahlberg in the second and ﬁnal round. If there were the same cycle in 1931 and 1937, but choice of different winners, then this would be a nice illustration of Riker’s hypothesis, although limited to the particular institutional setting. We can take some comfort from the fact that the Borda winner won the 1937 election, but that could have been an accident as the Borda winner did not win in 1931 or 1956. Agrarians were median on economic policy and at some point after World War II were median on foreign policy. This large centrist

Other cycles debunked

367

party was included in 54 out of 64 parliamentary coalitions through 1988, compared to 33 for the Social Democrats, and 26 for the Conservatives. In the 1937 presidential election Social Democrats cooperated in electing the Agrarians’ Kallio, initiating the most frequent coalition pattern, Red-Earth, over the following 60 years. In 1956, six parties were elected to the electoral college, each with a nominated candidate. Parties were allocated electors as follows – 7, 20, 56, 57, 72, and 88 – no party had a majority. The three main candidates were Tuomioja for the Conservatives (TU), Fagerholm for the Social Democrats (FA), and Kekkonen for the Agrarians (KE). From Lagerspetz’s estimates of party preferences, Tuomioja would be the bare Condorcet winner, TU >151 KE >151 > FA, the strong Borda winner, TU (364) > FA (226) > KE (207), and the standard plurality runoff winner against Kekkonen by a vote of 151 to 149; that’s including votes but ignoring candidates of the three smaller parties. After the ﬁrst ballot, candidates from the three smaller parties were dropped, and the incumbent but aged President Paasikivi (PA) substituted for Tuomioja. Paasikivi was a bit stronger, by Condorcet, PA >156 KE >151 > FA, by Borda PA (384) > KE (295) > FA (221), and by standard plurality runoff against Kekkonen by a vote of 156 to 144. Paasikivi was in ill health, however (he would die in 1956), otherwise he would have been a sure winner, according to Lagerspetz. Kekkonen, the candidate most likely to continue Paasikivi’s foreign policy, won the election. Kekkonen’s victory was probably due to informational and organizational asymmetry: the Communists voted strategically but the Social Democrats failed to countervote strategically. On the second ballot, the Communists split their vote between their most-favored candidate, Kekkonen, and their least-favored candidate, Fagerholm, so that on the third and ﬁnal ballot Kekkonen would face weaker Fagerholm rather than stronger Paasikivi. Kekkonen’s Agrarians carefully estimated all 300 votes, and proposed the maneuver to the Communists, who carried it out with discipline and secrecy, according to Lagerspetz. If the Social Democrats had countered with some votes away from their own Fagerholm to Paasikivi on the second round, then the AgrarianCommunist maneuver would have failed and Condorcet–Borda winner Paasikivi would have won. Lagerspetz suggests that the most likely explanation has to do with internal politics of the Social Democratic Party. The large Tanner faction in the party probably favored Paasikivi over Fagerholm and his faction. Another SDP leader, Penna Tervo, may have persuaded the party to precommit to backing Fagerholm to the end ostensibly as a matter of party unity or perhaps as a way of forcing other parties to coordinate on its candidate. Further, says Lagerspetz, Tervo

368

Democracy Defended

was on bad terms with both Tanner and Fagerholm, and may have favored Kekkonen over the candidates of his own party. Thus, it is believed that Tervo may have gotten his way by tricking his party to vote for its mostfavored candidate, resulting in the victory of its least-favored candidate! The contest between Paasikivi and Kekkonen was close, as was the contest between Kekkonen and Fagerholm. Lagerspetz estimates that the 72 Social Democratic electors ranked FA > PA > KE. Suppose that just seven of those Social Democrats instead favored Kekkonen from the centrist Agrarians over Paasikivi from the Conservatives. Then the Condorcet collective preference of the body would have been KE >151 PA >226 FA (it would take 45 such reversals to make Kekkonen the Borda winner, however). Another way of looking at the outcome is as a step towards consolidation of a Red-Earth coalition. If the Agrarians (Kekkonen) and the Social Democrats (Fagerholm, Tanner, Tervo) had enough in common to coordinate on domestic policies, then together they would outweigh the various conservatives backing Tuomioja or Paasikivi. Also, perhaps coordinating on the Agrarian candidate with his promise of continuing Paasikivi’s realistic attitude towards the Soviet Union fortuitously would be more attractive to other parties than coordinating on the candidate from the Social-Democratic Party which generally was hostile to the Soviet Union. Kekkonen was reelected four times and served 25 years as President, suggesting that somehow the policy choice was not an unstable one. In 1966 he allied his centrist Agrarians with an SDP which had become more moderate about the Soviet Union and with the Communists to form a center–left coalition that brought neocorporatist consensus to Finnish politics. At the same time social cleavages between working class and middle class, and Finn and Swede, became less salient, and the Communist vote slowly receded. Perhaps after its civil war and before World War II Finland was less stable, with each interest pulling as hard as it could in its own direction, and perhaps wartime solidarity and growing experience after World War II led to moderation and more stability – notice that in this account stability is a function of variable preferences rather than of the constant of the aggregation rule. Finnish democracy has a remarkable history. Over almost a century, a democracy of a few million people survived civil war and terror, a large Communist movement, Fascist agitation, the Depression, great-power pressures from the Nazis on one side and the Soviets on the other, years of ferocious warfare in the 1940s, and abandonment to the Soviet sphere of inﬂuence after the war, to become one of the most free and prosperous countries in the world. In foreign policy it managed to avoid being swallowed by giants, and in domestic policy it achieved a strong economy and

Other cycles debunked

369

Table 15.12. Iowa Senate preferences, anticorporate farming Number of legislators

Preference orders A>B>C>D

5 2 1 4 2 6 7

OCRN ∗ OCNR ∗ ORCN CORN ∗ CNOR RCNO NRCO

Note: ∗ = not single-peaked

welfare state. Could it be that these policies were not chosen, but rather happened by random spin of the wheel? Corn in Iowa Gross (1979) presents the best evidence for any cycle claim. He has from 27 senators their stated rankings over four alternatives, he has actual votes from the 27 over three of the possible six pairs, he has explanations from each strategic voter about why her vote differed from her stated preferences, and he shows a cycle. The Iowa House passed a bill banning corporate farming in the state and sent it to the Senate (O). The Senate Agricultural Committee weakened the bill by dropping the corporate farming prohibition but including a restriction of vertical integration in the livestock feedlot industry (C ). A coalition of senators who actually preferred no bill proposed an amendment to C which required only that corporate farms report annually (R ). Favoring no legislation on the topic is labeled N. The distribution of sincere preferences, as stated by senators, is displayed in Table 15.12. By pairwise majority voting this aggregates to C > N > O > R > C, a cycle. The Borda count yields 52 for C, 43 for R, 34 for O, and 33 for N. If voting had been sincere, then on the ﬁrst vote R > C, 14 to 13, on the second vote O > R, 14 to 13, and on the third vote, N > O, 15 to 12. The actual vote was R > C, 14 to 13, R > O, 14 to 13, and R > N, 23 to 4. There was strategic voting on the ﬁrst vote which did not change the outcome. There was strategic voting on the second vote which did change the outcome: the one N > R > C > O voter strategically cast a vote O > R, believing that if O won it would be defeated by his or her ﬁrst-ranked N,

370

Democracy Defended

and two of the C > O > R > N voters, future conference committee members, voted R > O, believing that otherwise N would lose to O and that Senate selection of R would result in a conference compromise near their most-favored C. R won the third vote and went to conference. Gross does not report further events. The issue runs along a single dimension, from stronger to weaker regulation of corporate farming: O > C > R > N. Thus, it is curious that collective preferences are cyclic under pairwise majority voting, and suggesting that the reportedly sincere preferences are actually a mixture of sincere and strategic preferences. Some of the individual rankings are not single-peaked. Two senators reported O > C > N > R. I can make sense of that ranking: perhaps they viewed alternative R as so insulting that they would rank it below no action, or perhaps they wanted to deny Ndominant senators the opportunity of passing a phony corporate-farming bill. Two senators reported C > N > O > R. Again R is out of place, and again the same two explanations might apply. One senator ranked O > R > C > N: strong regulation over merely symbolic regulation over weak regulation over no regulation. I can’t make sense of that ranking, although that could be because I lack enough imagination. If that senator’s ranking is straightened out, it becomes O > C > R > N, and then the collective cycle disappears. If all four non-single-peaked voters are made single-peaked by forcing R to where it would be on one dimension, then the collective ranking becomes C > R > N > O. Gross’s article is about how “anticipated conference committee action can affect voting during the initial stages of the legislative process” (1979, 79). It is possible, and I think likely, that some of the “sincere” preferences reported by the senators were sincere with respect to their own chamber, but strategic with respect to interaction with the House; and the House might have passed a more extreme measure than it actually favored, anticipating that a more conservative Senate would moderate the measure. Senators were also strategic with respect to action in a future legislative session with an altered conﬁguration of members. All seven of those who stated that they ranked N ﬁrst, for example, voted for R and against N on the last vote. Gross explains that “these seven votes can be seen as acceptance . . . of a minimal bill in order to avoid stronger legislation in the future” (1979, 92). I conclude that a cycle in sincere preferences is unlikely. Ghosts in Denmark The 1994 general election for the Danish Parliament was expected to be very close, among the ideological camps, and among the ﬁgures most likely to become prime minister, according to Kurrild-Klitgaard (2001a).

Other cycles debunked

371

Table 15.13. Cycle, Danish prime minister Hans Hans Uffe Poul

38 47

Uffe

Poul

(Borda)

39

42 47

(81) (85) (92)

45

Polls were regularly taken by the Danish polling company GfK, including how respondents ranked the likely prime ministerial contenders pairwise against one another. The poll of May 14, 1994 found that Hans Engel was favored over Uffe Ellemann-Jensen, 39 percent to 38 percent (23 percent don’t know); that Uffe Ellemann-Jensen was favored over Poul Nyrup Rasmussen, 47 percent to 45 percent (8 percent don’t know); and Poul Nyrup Rasmussen was favored over Hans Engell by 47 percent to 42 percent (11 percent don’t know). There is a cycle: Hans > Uffe > Poul > Hans. Of course the Condorcet order, but also the Borda count, remains the same if we were to exclude nonvoters and renormalize pairwise votes. There are several problems with the supposed cycle. First, the citizens of Denmark do not elect a prime minister, rather, they elect parties, which form coalitions, and the governing coalition selects the prime minister. There were no cycles over the nine parties in the 1994 election, according to the Danish National Election Survey (Kurrild-Klitgaard 2001a). Poul’s Social-Democratic Party was ranked ﬁrst, Uffe’s Liberal Party was ranked second, and Hans’s Conservative Party was ranked third in that survey. Second, a number of polls were taken throughout 1994 by the polling company GfK, and only the one we have under discussion showed a cycle. The cyclic poll was in May, the election was in September. Third, the cycle is statistically fragile, the comparison between Hans and Uffe is almost equal, as is that between Uffe and Poul. Kurrild-Klitgaard says consideration of sample error cuts both ways, as there were two other of the polls that would become cycles if we made small changes in the responses. Fourth, if this is a cycle it is a balanced one, and arises because the three candidates are almost tied four months before the election. Just as there is nothing normatively devastating about ties between two leading candidates, the same goes for a balanced cycle among three candidates. We would worry if there was an unbalanced cycle that made it possible for an unpopular candidate to win. Fifth, data from the Danish Election Survey for 1994 on evaluation of party leaders show a transitive ranking of nine party leaders, and the ﬁrst three are: Hans > Uffe > Poul (Kurrild-Klitgaard

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2001b). The source does not report when in 1994 the respondents were polled, but does mention that the race was quite close. Presumably, rankings were volatile in a close race over several months of polling. Sixth, the Borda count, which allows us to extract an approximation of intensities out of the May GfK information, would rank the candidates: Poul > Uffe > Hans. This is identical to the ranking of the parties of the three candidates in the Danish National Election Survey, the Social Democrats in ﬁrst place. Seventh, the Social Democratic Party led in the actual election and formed a minority government returning Poul the incumbent as prime minister. Eighth, in related work Kurrild-Klitgaard (2001b) shows an almost total absence of cycles in twenty years of Danish National Election Survey data. These data probably deserved publication, because even the echo of a rumor of a ghost of a cycle is rare. Evidence such as this is not sufﬁcient, however, to justify a ﬁnding that democracy is arbitrary and meaningless. What-if cycles and coffee-break cycles A number of cycle reports in the literature are what we might call “whatif ?” cycles. The researcher observes some preference rankings over several alternatives, and remarks that if unobserved rankings were in a certain pattern, then there would be a cycle. The point is to illustrate a possibility rather than make an empirical claim, but such articles are later cited incorrectly as empirical evidence of cycling. The earliest entry in this genre is Farquharson’s (1969, 52–53) account, in his Theory of Voting, of a 1955 US Senate vote. According to Farquharson, Senator Al Gore, Sr. presented a proposal for road funding, with a Davis–Bacon provision for protection of local wage standards, B. Gore’s side later moved to strip the wage-standards requirement, in order to draw more votes from southern Democrats, C, and this motion succeeded, C > B. Suppose that A is the status quo of no roads bill. A motion to kill Gore’s amended bill by sending it back to committee failed, 50 to 39 against, and thus C > A. Farquharson says that preference orders were, “plausibly”: northern Democrats – B > C > A, southern Democrats – C > A > B, Republicans – A > B > C, one of the two cyclical proﬁles. According to his suggested proﬁle, on the ﬁrst vote, C > B, because only the northern Democrats had an incentive to vote strategically, then C > A. Farquharson’s cycle requires that Republicans most favored no spending (A), next favored spending at high wage standards (B), and least favored spending with low unregulated wages (C). True, as mentioned in Farquharson’s account, Davis and Bacon who originally sponsored the wage-standards legislation in 1931 were

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Republicans, but that was at the onset of the Great Depression. In 1947, Republicans passed the antilabor Taft-Hartley Act over Truman’s veto, and in 1959 the antilabor Landrum-Grifﬁn Act. Thus, it is less plausible that in 1955 most Republicans’ preferences were antispending and prolabor A > B > C and more plausible that they were the antispending and antilabor A > C > B, and therefore that the collective ranking was the noncylical B > C > A. If so, then on the vote between B and C, the Republicans would be tempted to vote strategically for B in order to get their ﬁrst-ranked A, but would refrain, for if they did the northern Democrats would counter with a strategic vote for C which would avoid their last-ranked A and preserve their second-ranked C. One way to decide between Farquharson’s interpretation and mine is to examine the record. The minority Republican report from the subcommittee of jurisdiction opposed Democrat Gore’s measure and proposed a substitute that would accomplish Republican President Eisenhower’s road program. The minority report speciﬁcally objected to the Davis– Bacon provision, with about 1,200 words of argument against it (Congressional Record, May 20, 1955: 6724). Republicans Prescott Bush of Connecticut, Martin of Pennsylvania, and Cotton of New Hampshire signed the report, and sought to move their broad substitute, which was defeated. Thus, evidence from the record suggests that the Republicans ranked A > C > B, and therefore the conclusion that there was no cycle. Gaubatz (1995) claims that public opinion is indeterminate in recent US policy debates on military intervention overseas, and that this indeterminacy is due as much to intransitivities in collective preferences as to the technical difﬁculties of polling or the complexity of the issues. Citing Riker, he relates “that it is unlikely that aggregations of opinion will reﬂect a notion of democratic preference in any philosophically acceptable way” (540). According to Gaubatz, Hinckley proposed that public opinion on US foreign policy sorts into three dimensions, which results in six types of respondents: unilateralists who favor force (18 percent); unilateralists who oppose force (7 percent); multilateralists who favor force (26 percent); multilateralists who oppose force (19 percent); isolationists who favor force (13 percent); isolationists who oppose force (17 percent). Hinckley identiﬁes four possible courses of action – withdrawal or doing nothing (W), multilateral sanctions (S), unilateral military intervention (U), multilateral military intervention (M) – then proposes an ordering of the four actions for each of the six types. Pairwise majority aggregation of Gaubatz’s proposed orderings results in multiple cycles. Gaubatz’s proposed orderings are not based on any evidence about people’s actual preferences over foreign-policy choices, but rather entirely on his intuitions of plausibility. It is easy, however, to propose equally

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plausible orderings that do not result in any cycles. For example, one tiny change in his orderings eliminates all cycles, as he concedes (548). He claims that forceful isolationists would favor multilateral intervention over multilateral sanctions; but if they didn’t, then no cycles. Thus, his exercise must be seen as the illustration of a logical possibility, and not, as he claims, a demonstration “that these questions are not simply academic or restricted to highly artiﬁcial and constructed examples”(540). Incidentally, there are errors of exposition worth noting. His Table 4 (546) is a pairwise-comparison matrix, but inverted such that the winner is stated column against row rather than row against column, and thus may confuse readers accustomed to the row-against-column convention. Further, Table 4 says M > W, 51 > 49, but from his proposed rankings it should read W > M, 56 > 44. His Figure 1, illustrating intransitive policy paths, is mistaken. The ﬁgure repeats the error in Table 4, and is confusing in that an arrow pointing into an alternative indicates its superiority (his statement that removing sanctions from consideration would not eliminate the cycles is based on the incorrect ﬁgure; actually, removing S results in noncyclical W > U > M ). A corrected ﬁgure would show three cycles: S > W > M > S, M > S > U > M, and W > U > M > S > W. Note that M > S is involved in each cycle; reversing that to S > M eliminates all cycles and yields the Condorcet collective ranking S > W > U > M. The Borda collective ranking, both before and after reversing M > S, is S > W > M > U; Gaubatz objects that the absence of cycles depends on a shift in the relative preferences of 13 percent of the population over their two least favored options (549), but the Borda results allay such concerns. He also objects that if S were the Condorcet winner, still it would be the ﬁrst choice of only 19 percent of the population (548), but this is to enshrine the plurality rule as our standard of choice among many alternatives, which we have seen already is not well-advised. The puzzle Gaubatz seeks to explain is ﬁndings such as these: 70 percent of respondents agreed that the US “should take all necessary action, including the use of military force, to make sure Iraq withdraws its forces from Kuwait”; 45 percent that the US should “engage in combat if Iraq . . . refuses to leave Kuwait”; and 32 percent that the US should “increase the level of its troops to force Iraq to leave Kuwait” (542). The conventional explanation is that responses differ according to subtle differences in question wording. Note that the variation on the three questions is not along Hinckley’s three dimensions; they do not variably appeal to the six different types. Thus, Gaubatz’s alternative explanation seems to lack relevance, for the example he offers anyway. He would have been more persuasive had he offered an example of questions varying

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across Hinckley’s dimensions. A public opinion survey typically measures single attitudes, often measures the strength of those attitudes, and sums responses on single attitudes; and sometimes responses undergo various statistical treatments such as multiple regression or factor extraction. Pairwise majority voting ignores strength of individual attitudes, compares alternatives pair by pair, and chains the results. These are quite different exercises. Gaubatz urges public-opinion surveyors to move from measurement of lone attitudes with its attendant problem of implicit alternatives, variable across respondents but unmeasured, to explicit alternatives and measurement of attitudes relative to one another. If that were done, then an opinion surveyor could aggregate individual rankings into a collective ranking. Such an aggregation, if carried out by pairwise majority rule, could conceivably result in cycles. But why should the researcher limit herself only to pairwise alternatives and aggregation by pairwise majority voting? Why not use the Borda count, if the data are of only ordinal quality? There is no hazard of strategic voting. Or, if data can legitimately be construed as cardinal, and each respondent counted as one, then a cardinal summation of attitudes could be carried out. An agnostic researcher might report aggregation results by several methods (I believe the reasonable methods would tend to converge). It is only dogmatic insistence on the IIA(A) condition that limits one to pairwise majority voting, introduces the possibility of cycling, and leads to declarations that democracy is meaningless. Gaubatz goes further and recommends that institutions be crafted that would “allow elites to shape the agenda in ways that overcome or even exploit public intransitivities” (553). Arguably, democratic leaders should have some latitude in devising foreign policy, and might justiﬁably carry out policies that receive retrospective rather than prospective approval. But Gaubatz’s direct call for antidemocratic manipulation goes beyond such considerations. Such counsel is especially disturbing in that it ultimately relies on the normative claim that “the preference ranking of any two options should be independent of the inclusion or exclusion of any third option” (538). But that contraction consistency condition, IIA(R-M), leads to possibility, not to Arrow’s impossibility. It is IIA(A), that the preferences over two alternatives shouldn’t change if preferences over any third alternative change, that drives Arrow’s impossibility result. Rose-Ackerman (1995) scrupulously reiterates that hers is a hypothetical exercise. Thus, the article should not be faulted. She examines the 1993 International Olympic Committee vote on choice of location of games in 2000 (Sydney won). The IOC proceeds by alternative vote: on each round the location with the least votes is dropped. She has some rankings revealed by votes, and assumes others. Crucially, for the 32 of

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the 88 voters who voted for Beijing, she assumes that their further ranking was Manchester > Berlin > Sydney > Istanbul. If so, then by pairwise majority voting there are three cycles, including one among all locations except Istanbul. Beijing, not Sydney, would win by the Borda count, and by several other voting rules. I suggest, however, that the 32 voters who ranked Beijing ﬁrst, may have further ranked Sydney > Berlin > Manchester > Istanbul. Then there would be no cycles, Sydney would win by pairwise majority vote, and by Borda count, as it did actually by alternative vote. As I have explained my work to political scientists in recent years, I have encountered many of what we might call coffee-break cycles. I am told, for example, that departmental hiring decisions are collectively irrational, but interlocutors neglect alternative explanations, such as the use of nearunanimity rule in many places, and neglect to consider that full rankings typically are not known. I am told that researcher X found a cycle, but whenever I track down X I ﬁnd out that she supposed preferences were such and such in order to illustrate the concept of cycling to students, or was looking for a cycle and didn’t ﬁnd one, or that the story is utterly garbled. In Australia, a half-dozen people told me that researcher Y had discovered that the frustrating defeat of the republic referendum was due to cycling disclosed by survey research data. Wrong. Many people knew that Y looked at survey data on the question, few knew that her ﬁndings were negative (and thus unpublished), and one insisted that I must have misunderstood what she told me about her results. I have stopped pursuing coffee-break cycles. Conclusion Given the wide inﬂuence of Riker’s teachings, the vastness of the political universe, and the certainty of academic publication for the most trivial cycling claim, it is remarkable that there are few such claims in the literature. That the few are almost all wrong is astonishing. One explanation for the errors is that most cycle claims are from Riker and that he suffered from conﬁrmation bias: he was looking so hard for cycles that he noticed indications that would support the ﬁnding of a cycle but did not notice indications that would not support the ﬁnding. Riker’s ﬁnding of a cycle in the Wilmot Proviso is based on gross factual error and Blydenburgh’s ﬁnding of a cycle in tax legislation is based on gross conceptual errors. Riker’s ﬁnding of a cycle in the 1860 election is based on an unwarranted inference of voters’ rankings of the four candidates, and in the Constitutional Convention is based on misspeciﬁcation of the alternatives. Otherwise, the major source of error is confusion about sincere

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and strategic voting. Riker’s study of agricultural appropriations in the US House of Representatives, and Neufeld, Hausman, and Rapoport’s study of Muscle Shoals each ﬁnds a cycle in expressed preferences, each concedes that there was a bloc of strategic voters, for each we can easily conclude that sincere preferences were in equilibrium, and in each the Condorcet winner was selected. Some of Riker’s versions of the Powell amendment, his account of the Depew amendment, and Bjurulf and Niemi’s Swedish telephone and telegraph cycle each inadvertently assumes irrational voters who fail to vote strategically when they should. I suspect that most future cycle claims will arise from cases that involve confusion between sincere and strategic voting.

16

New dimensions

Introduction We have been through a lengthy odyssey, more than a dozen case studies, each an island of terrors and delights. Now as we approach Ithaca it is time to recall why we started our journey. The Arrow theorem disclosed the logical possibility of a majority cycle, of perpetual political instability. But we observe stability rather than instability in democratic politics. Riker (1958) initially responds that cycles are common but rarely detected. Simulations show and empirical studies corroborate, however, that cycling is an empirical improbability. Riker then concedes that uncontrived cycles are quite rare, but that on major issues actors will contrive cycles by introduction of new alternatives. Actors also engage in strategic voting, agenda control, and the introduction of new dimensions in order to contrive multidimensional disequilibrium, according to Riker. I object that he must show that manipulation is frequent, harmful, and irremediable. Riker’s position is that it is either theoretically impossible or empirically difﬁcult to detect such manipulation. He is able, however, to produce spectacular anecdotes that show harmful manipulation on major issues, including a demonstration that the biggest event in American history was the consequence of a contrived cycle. We have worked through each of his examples, only to ﬁnd that each is mistaken, and thus Riker’s case fails on its own terms. In summary, theoretical considerations about the distribution of preference orders suggest that cycles are most unlikely; empirical studies show that cycles are of no practical importance; ﬁnally, almost every developed and published example of a political cycle has now been refuted. Thus, after ﬁfty years of scholarship, from the ﬁrst publication of Arrow’s theorem, almost no one has satisfactorily demonstrated the existence of a normatively troubling cycle in the real world. Over time, Riker’s argument increasingly came to rely upon the notion of creating disequilibrium, and thereby turning losing alternatives into winning alternatives, by the introduction of new issues and dimensions. We have already examined his major empirical illustration of the notion 378

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in the history of the politics of the antebellum period. Now we try to understand exactly how this mechanism is supposed to work. Almost everyone in politics is a loser in some respect, so why don’t we observe millions of attempts to introduce new issues and dimensions? There must be constraints on such introductions. The constraint is that the speaker’s introduction of a new issue or dimension must be freely rejected or accepted by the listeners. Deliberation is not subject to disequilibrium, and can indicate central outcomes such as the intersection of medians in multidimensional issue space; disequilibrium is a consequence only of the unfair assumptions of the McKelvey voting model. Further, I remind that the Arrow theorem, spatial voting theory, and the McKelvey theorem are only models, useful but not true. When a model does not agree with observations, at some point it is the model that must go. I continue that democratic discussion is a complement of, not a substitute for, voting. I reiterate that if there were a problem with cycles, the problem would be in the preference proﬁle not in the aggregation function. If cycling were a problem, deliberation would usually increase the similarity among preference rankings on the individual level, and by appeal to external principles at the aggregate level could rank the alternatives in a cycle. It is at least as easy to subtract as to add dimensions in public discussion; I provide an illustration of how, by reﬁning predeliberative preferences, public discussion might eliminate a cycle. Discussion also permits the identiﬁcation of the center of opinion and the organization of strategic voting so as to defeat unfair agenda control.

Introduction of issues and dimensions Riker attempts to rescue the pervasive-disequilibrium hypothesis from the improbability objection with the notion that on major issues actors introduce new alternatives or dimensions in order to generate disequilibrium where there was perhaps an equilibrium before. He illustrates the new-dimensions mechanism with his story of the Depew amendment to the proposal for the direct election of senators. In one dimension there was an equilibrium for passage of the constitutional amendment. Depew supposedly introduced a new dimension of federal regulation of Congressional elections in order to split and defeat the supporters of direct election. The institution in place required a two-thirds vote for departure from the status quo of legislative selection of senators, the alternative that Depew favored, so that by contriving a cycle Depew thwarted the majority and determined the outcome arbitrarily in his favor. Riker presented erroneous estimates of cyclical preferences over three alternatives under

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consideration. I showed that there were no cyclical preferences and that the proposed constitutional amendment for direct election of senators rather failed for lack of sufﬁcient votes. Let us linger to consider just how this mechanism of introducing new dimensions is supposed to work. Alternative B, along a ﬁrst dimension, would win on a straight vote. A manipulator, Deborah, prefers alternative A along a ﬁrst dimension, which is not the median voter’s preference, and she introduces a new second dimension in order to contrive a cycle. If Deborah’s favored alternative A is the status quo and if the voting rule in place is the backward-moving agenda such that the status quo is voted on last, then A is selected and Deborah need do nothing further. For Deborah to succeed she needs to know that there are cyclical preferences in the two dimensions. Also she must somehow have the power to unite the two dimensions together into one decision and the majority she thwarts must somehow lack the power to divide the question in order to consider matters dimension by dimension. Her success is barely plausible in the real world. If A is not the status quo under a backward-moving agenda then Deborah must additionally have control over the sequence of the agenda in order to have A selected and additionally the majority in support of B must vote myopically against its own interests. This is even less plausible in the real world. We can imagine a minority actor getting away with chicanery on a single occasion, but could an actor get away with this again and again? Why would the thwarted majority let her get away with it? On any unidimensional issue there may be a minority that would prefer a different decision. Say that there are 100 voters as in the US Senate and a unidimensional issue with a minority of 40 voters. Each of those 40 then has an incentive to introduce second, third, and nth dimensions in order to generate disequilibrium and snatch victory from the jaws of defeat. If all it takes to turn a loss into a win is the introduction of a new dimension, then we should routinely observe the introduction of 40, 80, 120 new dimensions by potential losers on any issue. That is not what we observe, however. Therefore, there must be constraints on the introduction of new dimensions. What might those constraints be? The answer is not clear in Riker. In his general treatment of contrived cycles, just as the natural environment selects among genes, it is the environment of “institutions or constitutional structures” (1982, 211) that selects among the new alternatives or dimensions that politicians randomly introduce. Earlier, however, Riker (1982, 192) held that such institutions themselves are in disequilibrium and thus subject to overthrow by introduction of new alternatives or dimensions; it is unclear what force selects among institutions.

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Moving from the general treatment to the illustrative example of the commercialists in antebellum America succeeding in splitting the agrarians after forty years of effort, “this particular outcome was not due entirely to the wit and persistence of the losers” (emphasis added, 213). The outcome was conditioned not just by constitutional structure, but also by underlying values and the state of the technology and the economy, he says. These “external circumstances” as well as the constitutional structure select from among many attempted manipulations only a few as winners. Why did the commercialists ﬁnally succeed with the issue of slavery in the territories? “The issue matured when Whigs had sufﬁciently frightened Northern Democrats that they too became, defensively, enthusiastic Free-Soilers, as in the Wilmot Proviso episode, the Free Soil party, and ultimately the Republican party” (229). Let’s think about Riker’s explanation. It couldn’t have been the southern Whigs who had so frightened the northern Democrats, because the southern Whigs were not Free-Soilers. It must have been the northern Whigs then. How did the northern Whigs frighten the northern Democrats? By inducing irrational beliefs in them? Or were the northern Democrats rationally frightened? What would they be afraid of? They would be afraid of losing elections. And why would they lose an election? Because a candidate strong on containing slavery might beat a candidate weak on containing slavery. And why would one candidate beat another? Because the winning candidate would receive the votes of those who thought that containing slavery is important. And why didn’t free soil matter before this point? Because before the voters thought that other issues were more important. And did northern Democratic incumbents change positions to accommodate the changed preferences of their constituents? Not much, we know from Poole and Rosenthal (1997, 90) that the Congressional issue space in this period changed mostly due to the replacement of legislators, indicating that the preferences of the electorate were the main force of change. And what caused the changing preferences of the voters? Their replacement by birth, death, and immigration, and the development of their preferences in response to events and changing circumstances. Prospective losers attempt to add a dimension to the issue space, according to Riker (1990a, 51). Some seek to raise dimensions (the Magnuson example, discussed below), some seek to reinterpret old dimensions (the Whigs reinterpreted slavery to be a national issue rather than a local issue, he says), and some seek to dismiss dimensions (by claiming, “that’s not an issue”). The mechanism of manipulation is the “displaying of the relevance of a dimension, recalling it from latent storage to the center of psychic attention” (1990a, 51). Is it then that the dimensions are already there in the citizen’s mind and the politician like

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a pianist manipulates the keyboard and the pedals? Can anyone at anytime add or subtract any dimension? What is the constraint? The constraint is what Riker is concerned to deny – free public reason. Riker’s spatial metaphor is motivated by a doctrine of democratic irrationalism, and is a cumbersome and misleading translation of what we ordinarily understand as the public consideration of reasons for and against a proposed action. Although there is no widely accepted account of how persuasion and attitude change might work, we are able to sketch the preconditions of public deliberation, among them: the inclusion of everyone affected by a decision, substantial political equality including equal opportunities to participate in deliberation, equality in methods of decision making and in determining the agenda, the free and open exchange of information and reasons sufﬁcient to acquire an understanding of both the issue in question and the opinions of others. (Bohman 1996, 16)

As an aside, it is instructive to consider how J.Q. Adams, according to Riker the master manipulator in the Yankee cause, attacked the slavery issue. The fanatical abolitionists relied on moralistic aggression, attacking the very character of the slaveholder. Abolitionists were disliked in the North for their self-righteous extremism, and Adams made plain that he was no abolitionist. Adams rather, on a regular basis over nine years, attacked in the US House of Representatives the gag rule that prohibited not only discussion but receipt of petitions on the topic of slavery. The fully intended exclusion of an issue from consideration is a clear violation of the deliberative ideal. Northerners were eventually moved not so much by sympathy for slaves but by the fear that their own concerns could be excluded from parliamentary consideration. Adams also found a way to emphasize the exclusion of slaves from the democratic ideal of free and equal citizenship. He asked the Speaker of the House for a ruling on whether he could submit a petition, he said perhaps of doubtful authenticity, signed by 22 slaves. The southerners went berserk, and ranted and raved for a whole week over this evil suggestion. It was proposed to expel Adams; to take the petition outside the House and burn it; Adams’s request was denounced as “an outrage that has no parallel in parliamentary history” (Miller 1997, 230–236). Adams let the furor ripen for days. When he did ﬁnally rise to defend himself, he explained that he doubted the petition’s authenticity because the slave petitioners had begged for continuation of the institution of slavery (apparently concocted by an overzealous slaveholder). That occasioned a further four days of invective. The southerners defended their cause in the name of liberty and equality (for example, “the principle of slavery is a leveling principle; it is friendly to equality. Break down slavery and you would with the same

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blow break down the great democratic principle of equality among men,” Virginia Representative Wise, quoted in W. L. Miller 1997, 439). Finally, Adams was put on trial in the House in 1842 on a motion to censure, which was withdrawn after his defense evoked an outpouring of public support. Again, it was more the slaveholders’ threat to the principles of liberty and equality than the issue of slavery that rallied support to Adams. An important factor in the ending of slavery was the gradual developmental maturation of the deliberative ideal. To continue, participants in public deliberation must of course be free to accept or reject an argument on their own will. An agenda-controller with appropriate institutional power could theoretically force the joinder of two or more dimensions so as to create pairwise, ordinal, majority-rule voting disequilibrium and carry out Rikerian manipulation, assuming no germaneness rule, no strategic voting, and the other unfair requisites of the chaos model. Discourse, however, is somewhat different from voting in this respect. True, an unconstrained monopoly rhetor – as in a totalitarian regime – would have unfair inﬂuence on auditors. A rhetor can argue that a second or third orthogonal dimension is relevant to the topic of concern, but in a free and equal society the rhetor cannot force the auditor to accept her argument. The auditor, normatively and practically, must freely assent to the relevance asserted by the rhetor. That is one giant constraint on the introduction of new issues and dimensions. When an auditor does freely assent to the relevance of an orthogonal dimension, the auditor is not thereby set adrift in a sea of internal disequilibrium. If making up one’s mind does resemble the spatial model of voting, in that one locates one ideal point on one dimension and another ideal point on a second orthogonal dimension, and so on – a contentious proposition that I assume only to explore Riker’s argument – even then one does not make up one’s own mind on the basis of pairwise, ordinal, majority-rule voting. One’s position would be simply the multidimensional ideal point at the intersection of the ideal points from each dimension. Thus, no matter how many dimensions might be involved, the manipulator cannot generate disequilibrium within the individual. To repeat, the introduction of new alternatives and dimensions is constrained by the consent of the audience. Then, the manipulator can only succeed in the frictionless, unrealistic world of the McKelvey voting model, only when granted the openly unfair advantage of being an unconstrained monopoly agenda-setter among myopic voters. Riker (1990a, 53) later conceded that, “in the real world, agenda-setters ordinarily do not have control over all amendments [and] there are probably no direct real-world analogues of this theoretical possibility of manipulation.” In that same article he tries to shore up his hypothesis with other

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mechanisms: manipulation is possible if manipulators vote strategically and others do not (appealing to his mistaken analysis of the Powell amendment), or if the manipulator is informed about the distribution of preferences but other voters are not (appealing to his mistaken construction of the Plott and Levine experiment), or if voters are denied the motion to divide the question (no example). Notice, however, that for each of these mechanisms, unfair output depends on unfair input. To conclude, cycles are naturally rare, and politicians are constrained from arbitrarily introducing new alternatives or dimensions in order to generate disequilibrium where there was none before. Model or reality? The Arrow possibility theorem assumes among other things that individuals have complete preferences over all possible states of the world, that each individual’s rankings are transitive, that preferences must be aggregated in an ordinal pairwise fashion, and that there is no natural similarity among individuals’ preference rankings. This may be a useful approximation of reality – recall that Arrow intends his assumptions to be descriptive – but all the same it is a model and not a reality. The model implies that political decisions would be constantly unstable yet this is inconsistent with our observations of political life. The model implies that there is no public good, yet this is inconsistent with our moral intuitions. At this point we can either reject the model and its assumptions as insufﬁciently unrealistic, or we can attempt to account for the discrepant observations and intuitions. There are no knockdown arguments that determine either choice; it is a matter of judgment, but judgment is not arbitrary. Those who follow the path of Arrow and Riker attempt to explain observed stability as a consequence of structure-induced equilibria such as agenda control, but in my view the sand slips through their ﬁngers, the attempts are not persuasive (agenda control is countered by strategic voting, proposed structures are not realistic descriptions, and so forth). I say that it is the model that is wrong, that randomly ordered preferences are not descriptively realistic and that pairwise comparison is not normatively compelling. The irrationalists do not – because they cannot – say that our observations of stability are an illusion. They do say, however, claiming the mantle of scientiﬁc authority, that our intuition that there is a public good is an illusion. They do not realize that our moral intuitions are data of a sort that themselves we want to ﬁt into some coherent scheme, that are constrained by considerations of coherence. Thus they do not notice, that without an idea of the public good we become unable to say that one political institution is better than

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another – our moral world no longer makes any sense. To give up the idea of the public good leaves only nihilistic criteria such as superior force or blind tradition for the evaluation of political institutions. We can accept the nihilistic consequences, or we can challenge the realism of the model. To give up democracy, for example, in order to avoid violation of Arrow’s condition of the independence of irrelevant alternatives seems to me to be an absurd bargain. Much the same goes for the multidimensional spatial model of voting. The spatial model additionally assumes that the political preferences of individuals and publics can be represented such that an issue inhabits a line and that alternative preferences on the issue inhabit points on that line. Another issue inhabits a second line orthogonal to the ﬁrst and alternative preferences on the second issue inhabit points on the second line; a third issue inhabits a line orthogonal to the ﬁrst two, and so on. Within that multidimensional space an individual occupies an ideal point and points away from that ideal point are less preferred. The governing metaphor is inspired by money accounting; an issue is a category of expenditure, and a preference on that issue is the choice of one number out of some range of expenditure. Say that it is possible to spend from 0 to 100 units on the issue, then one person most wants to spend 22 units, another person most wants to spend 87 units, and so on; there is another category of expenditure with a range from 0 to 100 units and the ﬁrst person most wants 43 units of this issue and the second wants 88 (the model can be more general than this, I am talking about its inspiring metaphor). This way of thinking is probably a useful approximation of reality, a simple model that provides insights that otherwise would not be available. But again, it is a model, not a reality. For one thing, the frictionless McKelvey model tells us that anything might happen, but since chaos is not what we observe then we must suspect that anything might be wrong with the model, which motivates the search for amendments to the model such as permitting the agents to vote strategically which does indeed return outcomes to the center, and so on. For another thing, although a useful approximation, it is only proposed and not at all established that the political preferences of individuals and publics are veridically portrayed as ideal points and indifference contours within a multidimensional issue space. Psychologically and socially, is this really how people are oriented to action in the political world? I do not have a better model to offer, but I do sense that there is much about the development and expression of political preferences that is not captured by the model, and thus that it would be a mistake to believe that the model is true rather than just useful. If the model violates observations or intuitions, we must remember that it may be the model that is at fault.

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The concept of issue dimensions is somewhat obscure. It is plain as day when graphically portrayed by familiar Cartesian geometry. But when you try to grasp the concept it slips away. How do issues and alternatives along issues emerge? Does a public share a common deﬁnition of issues and alternatives so that they inhabit the same issue space? If they do, how did that happen? How do we know when something is an issue and when it is not? Why do alternatives inhabit one issue rather than another? Does every issue deserve its own dimension? How do you distinguish one issue from another? What distinguishes an issue from an alternative? If the distribution of the population’s preferences on dimension A predicts their preferences along dimension B, then are A and B the same dimension or are they different dimensions? Riker (1993, 4) came to concede that “issue spaces tend to be one dimensional over time.” This conforms to my intuitions about politics, but why things should be this way is not obvious to me. Is every point in multidimensional issue space feasible? I think not; issues are constrained by communication, by commitment, and by budget, according to the interesting work of Hinich and Munger (1997, 193–194) on ideology; for example, one can’t prefer that 100 percent of the budget be spent on tanks, another 100 percent on schools, and a third 100 percent on solar energy. Is it these ideological constraints that collapse the dimensions? Is it the party system? Are preferences rather already nearly unidimensional in voters’ minds prior to institutional constraints? The mathematics of the spatial model are nicely developed, but its interpretation is less developed. There is much yet to discover. The state of knowledge does not license a doctrine so radical as democratic irrationalism. Deliberation and disequilibrium Many people in political science accept some version of the Arrow and Riker story about the instability of democratic voting. A few might have hoped that democratic discussion would solve the formal problems of democratic voting: deliberation would be a normative substitute for aggregation. But, in the absence of unanimity, the formal problems of democratic voting remain when democratic discussion concludes. I do not think that anyone has pointed out that Riker’s theory concerning the rhetorical introduction of new issues and dimensions is in fact an (erroneous) theory of deliberative disequilibrium. The irrationalist hypothesis of pervasive political disequilibrium must be attacked at its source, I believe, not evaded by vague appeals to democratic discussion. It is better, I think, to conceive of deliberation and aggregation as complements. The preconditions of free and equal discussion are much the same as the

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preconditions of free and equal voting. On the one hand, when discussion ends without agreement, remaining issues are decided by a method of free and equal voting. On the other hand, problems of unfreedom and inequality in democratic voting are remedied by democratic discussion, I shall argue. Upon reﬂection, the Condorcet paradox is not so surprising: why would an aggregation function work to reduce widely distributed disagreements? Voting does not reduce disagreements, it can only register them. Discussion is what reduces (or, unfortunately, increases) disagreements between people. Why is the Condorcet paradox intuitively disturbing? Because for a social choice to cycle among A, B, and C seems simply arbitrary – meaningless, as Riker says. But the meaninglessness is prior to the social choice, it lies in the particular cyclical proﬁle of individual preferences; where A > B > C, and B > C > A, and C > A > B are together possible. There is a trivial class of cyclical proﬁles: when the population is nearly indifferent among alternatives. The few cycles found in the empirical studies were mostly of this trivial variety (alternatives adjacent by Borda count). Suppose a population involved in many issues, and one of those issues is the collective purchase of ice cream. If there happened to be a cyclical proﬁle on this issue – Vanilla > Chocolate > Strawberry; Strawberry > Vanilla > Chocolate; Chocolate > Strawberry Vanilla – we would not be too surprised. The choice is a matter of mere taste, and the choice among ﬂavors is a matter of near indifference compared to the choice between having ice cream or not. Considered collective indifference is as normatively insigniﬁcant as considered individual indifference among alternatives. Then there is a repugnant class of cyclical proﬁles. Pick any three dissimilar states of the world – I suggested previously personal prosperity, the torture of kittens, and suicidal nuclear war. One voter prefers Prosperity > Torture > Suicide, a second Suicide > Prosperity > Torture, a third Torture > Suicide > Prosperity. There is a cycle among the three alternatives and a Rikerian manipulator could arrange for his favored alternative, such as suicidal nuclear war, to win. I have just shown that majority-rule voting can destroy all life on earth. What is wrong with this picture is not majority-rule voting but the absurdly unstructured preference proﬁle. Choice over those three alternatives is not a matter of mere taste; there are a few freaks in the population, but the huge majority prefers personal prosperity and that is the choice among the alternatives – it is very easy to understand and explain the preference for personal prosperity. Imagine a place where the distribution of preferences over all possible states of the world is random. One couldn’t make sense of the people in such a place. One could not interact with such people for lack of an

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approximation of what other people want. Repugnant cyclical proﬁles might be possible in rare instances, but they could not be prevalent, else other minds would be unintelligible, the unintelligibility not following from aggregation mechanisms but rather from the obscurity of other minds’ desires. The cyclical order of preferences is arbitrary, individuals’ preferences are unstructured, not ordered by any external principles open to public discussion. If the ordering of individual preferences is unstructured and purely arbitrary, then the ordering of social preferences will be unstructured and purely arbitrary as well. Accepting the arbitrary ordering of individual preferences is a consequence of the doctrine of consumer sovereignty or subjective welfarism from welfare economics. Taking as given the self-regarding preferences of price-taking individuals and ﬁrms, a competitive equilibrium is Pareto optimal: laissez-faire leads to the common good; and, almost any Paretooptimal equilibrium can be attained with taxes and transfers on individuals and ﬁrms; but, there is no Arrow social-welfare function (Feldman 1991). Elster argues that social choice theory fails to capture the distinction between the isolated and private expression of preferences on the market from the open and public activity of politics: The notion of consumer sovereignty is acceptable because, and to the extent that, the consumer chooses between courses of action that differ only in the way they affect him. In political choice situations, however, the citizen is asked to express his preferences over states that also differ in the way in which they affect other people. This means that there is no similar justiﬁcation for the corresponding notion of the citizen’s sovereignty, since other people may legitimately object to social choice governed by preferences that are defective in some of the ways I have mentioned. (Elster 1986b, 111).

Elster (1986b) and Sunstein (1990, 1993) categorize various sources of defective individual preference formation.1 Rather than emphasize defective individual preference formation to be reformed in principled public justiﬁcation, I will emphasize the continuity between principles of individual ordering of preferences and principles of public ordering of preferences. A competent adult is almost always the best judge of choices that affect only her, on informational grounds alone, if not on larger normative grounds. From the variety of conﬂicting desires and beliefs, the individual strives to construct a consistent order of desires, and a consistent order of beliefs, each as consistent and complete as needed for the conduct of life. In experimental situations, individuals often make intransitive choices in single experiments, but in repeated trials their choices become steadily more consistent (Elster 1979, 154, citing Davidson).

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When individual inconsistencies are discovered, consistency is regained by individual deliberation with reference to substantive principles. If we ask someone why he prefers A > B > C > A, we are likely to get a correction. We understand immediately why someone likes winning a lottery ticket better than cleaning the barn better than death by ﬁring squad. If we ask someone in a harder case why he likes A > B > C, we will hear understandable (possibly mistaken) reasons; often the provision of more and more context provides sense to the ranking. Even in the case of mere tastes, the framing case for welfarism, there is an understandable and nonarbitrary reason: “it tastes better to me.” Notice that reasons of taste are completely convincing in justifying only a portion of private choice and are completely unconvincing in justifying most of public choice. Stepping from private life to public life, to choices that affect others, information on desires and beliefs goes from certain to less certain, the construction of possible alternatives and their consequences is less certain than in private life, and individual preferences over public states of affairs are initially incomplete and intransitive. In the process of public deliberation, from the local assembly to the larger public sphere, individuals gain evidence and principles by which to order their own conﬂicting desires and beliefs over public affairs. The public existence of evidence and of substantive principles of consistency induces some similarity in individual preference orderings over public affairs, because beliefs are internally related by correspondence to independent objects, and because principles for ordering desires, although diverse, are on net necessarily more similar than random. The skeptic tells us that nothing has changed. Before deliberation there is a set of individual preference orderings to which certain possibility theorems apply. After deliberation there is a new set of individual preference orderings to which the same theorems apply. But deliberation may contribute the minimal consistency in individual ordering probably sufﬁcient for consistent public ordering. Moreover, if public inconsistency remains, just as does the individual when discovering a private inconsistency, so does the public body turn to deliberation over substantive ordering principles to resolve the inconsistency, if it is an important one. If serious inconsistency remains, the polity is in trouble, but the source of the trouble is in individuals’ preferences not in the voting mechanism. The skeptic’s trick was to exclude principled consistency by axiom at the individual level, only to demand it by intuition at the aggregate level. The construction of alternatives and dimensions is subject to the principle of interpretive charity and its constraints of logical consistency and correspondence of beliefs, and of transitive consistency and similarity of desires. Following Hinich and Munger (1994, 1997), multiple

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dimensions collapse as one dimension depends on another; the entire multidimensional space is not feasible because of the constraints of communication, ideological coherence, and budget. Here is an example of how deliberation and the budget constraint might collapse dimensions. At one time in my political life I was much enlightened by a naively designed public-opinion poll on county services. A huge majority wanted less money spent on tax collection, a smaller majority wanted more money spent on parks, and an even smaller majority thought the amount spent on the county’s main business, public safety, was about right. Each individual might be perfectly consistent in expressing his or her prepolitical preferences, but taken together the preferences are incoherent: less money spent on tax collection would mean lower taxes, and thus lower services. Suppose there are three alternatives: r A = less tax collection r B = more parks r C = same public safety. Since there are more than two alternatives, and majorities support every alternative, there is the possibility of a majority-rule voting cycle. Suppose that a majority faction of 60 percent prefers more parks to the same public safety (B > C), but a minority faction of 40 percent prefers C > A > B and knows that the majority is evenly divided between A > B > C and B > C > A, so that the minority faction plans to use agenda control in order to gain a victory for A = lower taxes. The agenda-controlling minority faction would propose B against C, which B would win (if the minority faction proposes A against B ﬁrst, or A against C ﬁrst, it would end up with its last-ranked alternative B). The minority faction then would propose B against A. The minority faction of 40 percent prefers A over B, and half of the majority faction, another 30 percent prefers A over B, making a majority of 70 percent for A over B. The cycle and hence the manipulated outcome would collapse after public deliberation, however, because of the incoherence of predeliberative preferences. If the minority faction pressed ahead it would win its second-ranked A, lower taxes, but this would make impossible its ﬁrst-ranked preference, C, the same public safety. The minority’s inconsistency would not be accepted as a matter of preference sovereignty, but would be justly ridiculed in debate. If lower taxes result in less services, then there are only two possible preference rankings: lower taxes > same or more county services, and same or more county services > lower taxes. With preferences developed by deliberation there is no longer a cycle. The critic may object that all I’ve done is manufacture an example where three alternatives easily reduce to two. But my point is that it is just as easy rhetorically to subtract alternatives and dimensions as it is to add them, and that the subtraction here is not

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arbitrary, but due to a coherence constraint discovered in public debate. To go further, because of the communication, coherence, and budget constraints on issue space, it is probably easier to subtract dimensions than to add them. There is empirical evidence for the proposition that deliberation can add to stability. Let’s call a collection of individuals’ preference orders that are unrelated to one another, such as under the impartial-culture assumption, unstructured preferences. Call another collection where there is more resemblance among preference orders more structured. The more closely a collection of individual’s preference orders approximate a collection of single-peaked preference orders, the more likely is it that the paradoxes and instabilities of social choice would be avoided. McLean, List, Fishkin, and Luskin (2000; see further, List 2002) show that deliberation can add structure to unstructured preference orders: certain perspectives on the subject become more salient, and random and ill-formed opinions drop away. The deliberative opinion poll selects citizens at random, assembles them, provides neutral information, and encourages public deliberation over the issues at stake. Attitudes are measured before and after deliberation. Deliberation might improve structure in three ways: ﬁrst, it might increase the proportion of preference orderings that can be arranged single-peaked, second, it might reduce the proportion of preference orderings that do not conform to the largest single-peaked arrangement, and third, it might reduce indifferent or incomplete preferences among the population. Seven deliberative opinion polls commissioned by Texas utility regulators provide data that show deliberation delivering all three effects. There was not much structure to incoming preference orders in the Texas case. McLean et al. also examined a deliberative opinion poll concerning the Australian Republic Referendum. The voters of Australia were to decide among, (1) change to a republic with president directly elected, (2) change to a republic with a president appointed by 23 vote of the legislature; and (3) the status quo, subjects of Queen Elizabeth. There was much structure to incoming preference orders, so structure did not improve by deliberation. Instead, the outcome changed from a stable predeliberative social preference for alternative (1) to a stable postdeliberative social preference for alternative (2). Curiously, alternative (2) was sent to the people by the legislature, and it failed the popular vote, suggesting perhaps that popular deliberation over the measure was incomplete or defective. Here is another way that deliberation might tame majority-rule voting disequilibrium, if one considers it a realistic problem. Ordinal pairwise voting contains no information about the intensity of preferences, and that is how the possibility of cycles arises. Public deliberation provides

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information about the intensity of preferences, and information about intensity allows for knowledge of the likely center of opinion. It will be objected that anyone can assert any intensity claim they please in debate, but those who have worked on committees will understand that the member whose positions are increasingly fervent and urgent is increasingly ignored. One need not resort to a controversial cardinalist framework for this effect; the relative ranking of ordinal preferences as indicated by the Borda count is enough. As for multidimensional disequilibrium in the McKelvey model, again deliberation can disclose the location of the intersection of medians, among other things. That knowledge of the center of opinion would motivate majorities to resist, with strategic voting or otherwise, a manipulator aiming for an extremist outcome. Something like this can be seen when legislative deliberators warn that the pending amendment is a killer amendment and advise their allies to vote strategically in order to obtain the majority outcome. A deliberative assembly can also open for public discussion the unfairness of the institution of an unconstrained monopoly agenda-setter, or any other shenanigans that violate the principles of freedom and equality. Riker says there are many transient majorities. If he is right about that, then the members of those transient majorities all have one thing in common: the demand for fair treatment. Lincoln at Freeport After Liberalism against Populism in 1982 came Riker’s The Art of Political Manipulation in 1986, intended for a more popular audience. The text and its examples are used in undergraduate political science courses. The 1986 volume illustrates Riker’s doctrines by way of twelve simple case studies. Riker coined the term heresthetic, the art of manipulation, in contrast to rhetoric, the art of persuasion.2 Rhetoric succeeds by changing others’ preferences towards those of the rhetorician’s, heresthetic wins instead by setting up the situation so that others must support the preferences of the heresthetician. Heresthetic is managing, manipulating, and maneuvering to get the decisions one wants. We examine two chapters in depth. The ﬁrst is about the Freeport debate between Lincoln and Douglas. Riker believes that Lincoln’s rhetoric forced a dilemma upon Douglas in which Douglas was forced to choose between losing supporters in the North or supporters in the South. Riker relies on outmoded historical interpretations of the Freeport debate, however. Modern scholarship does not support these highly dramatized interpretations. Moving from the empirical to the theoretical, Douglas did indeed face a dilemma, but it was one that was forced upon him

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by the changing preferences of the northern and southern populations, not by Lincoln’s discourse. The second chapter is about Senator Warren Magnuson and a controversy over the shipment of nerve gas to the United States during the Vietnam War. Riker believes that with a rhetorical ﬂourish Magnuson added a dimension to the debate that forced certain senators to vote for an action they opposed and thereby engineered a roll-call victory for an action supported only by a minority of the Senate. Riker gets several details of the story wrong and he does not fully understand the parliamentary situation. The record shows that Magnuson’s bill would have passed without fuss, perhaps without even a roll-call vote; the debate was over a more radical version of Magnuson’s proposal offered by Gravel. Senators stated that they voted for the more radical version of the proposal in order to gain the attention of the White House, which had not been responsive on nerve-gas controversies across the United States, and that they would withdraw Gravel’s radical proposal in conference committee if the White House became more responsive on the issue. Later in fact the Gravel proposal was effectively withdrawn in conference and the Magnuson bill effectively retained. Riker’s story asserts that Magnuson’s rhetoric forced 13 senators to vote against their own beliefs. But 40 senators felt free to ignore Magnuson’s rhetoric and voted against the radical Gravel proposal. The ﬁrst chapter, meant to illustrate the theme of dividing the opposition with a new alternative, tells the story of a debate between Lincoln and Douglas at Freeport on August 27, 1858, during their race for US senator from Illinois. Lincoln asked Douglas: “Can the people of a United States Territory, in any lawful way, against the wish of any citizen of the United States, exclude slavery from its limits prior to the formation of a state constitution?” (Riker 1986, 1–2). Much of the story is a recapitulation of our earlier discussions of the antebellum period. The story continues that Douglas was running for Senate in 1858 needing to win Illinois but was planning to run for President in 1860 needing to win the nation. If Douglas answered yes, that the people of a territory can exclude slavery, then he would please northern Democrats in Illinois in 1858 but displease southern voters in the nation in 1860. If Douglas answered no, then he would displease northern Democrats in Illinois in 1858, repudiate his long-held popular-sovereignty position, but please southern voters in the nation in 1860. Douglas answered yes, and won the 1858 election in Illinois, but in 1860 split the Democratic convention and lost the election in the country. Lincoln’s great heresthetical maneuver was at a stroke to consign Douglas to political doom. Riker leans toward but does not commit to the position that Lincoln foresaw that he would run against Douglas for President in 1860. Lincoln’s question was the capstone of

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the Republican strategy of splitting the Democratic majority, however, and such was certainly Lincoln’s full intention, Riker says. His source for the ﬁnal assertion? A long folksy quotation from a historical novel about Lincoln published in 1901. The Freeport Question was once a standard story in American history, but its melodramatic version has since been dismissed by historians as folklore. Potter (1976), the author of the standard history of the decade prior to the Civil War, says that “the Freeport question was one of the great nonevents of American history” (338) and introduces the topic with sarcasm: “When folklore appropriates a scene . . . it begins at once, unfortunately, to improve upon history by adding certain characteristic ﬁctitious touches . . . it dramatizes an ordinary contest into an epic struggle . . . virtue invariably overcomes wickedness by some simple but supernaturally effective device – a silver bullet, a magic phrase, a sling for David against Goliath” (334). The folkloric version neglects context. There are several problems. Lincoln was not a national ﬁgure and could not have known that he would be the Republican candidate in 1860, and could not have been certain that Douglas would be a Democratic candidate. Next, Douglas had already addressed the question in a speech in Springﬁeld, Illinois, on June 12, 1857, 14 months prior to Freeport. He attempted to avoid the dilemma by afﬁrming that the people of a territory could decline to enact local legislation necessary to the support of the institution of slavery (they may or may not have the right to exclude slavery, but they do not have the duty to enact legislation supportive of slavery). Meanwhile, Douglas was occupied with the much greater controversy over the Lecompton constitution, the biggest issue in Congress that year. In Kansas, free-staters outnumbered slave-staters by two to one. A proslavery gerrymander, however, put the state’s constitutional convention in the hands of the slave-staters, and free-staters boycotted the election in order to deny it legitimacy. The slave-staters at the Lecompton convention practiced Rikerian agenda control in designing a referendum on the state constitution that forced voters to choose between approving either existing slavery or expanded slavery in Kansas. Illustrating that ordinal pairwise voting is not the motor force of history, the free-stater majority in Kansas boycotted the unfair referendum, and the constitution with expanded slavery was approved by the minority slave-state voters. Elections to the territorial legislature were more representative, and its free-stater majority referred three alternatives to the voters: the Lecompton constitution with existing slavery, Lecompton with expanded slavery, or rejection of Lecompton entirely. The slavestaters boycotted this election, and the majority free-staters voted almost

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unanimously to reject the Lecompton constitution. The conﬂict migrated to Washington, DC. Democratic President Buchanan made acceptance of the Lecompton constitution a question of party loyalty, but Douglas and many northern Democrats would not – could not – go along. Admission of Kansas with the slave Lecompton constitution passed the Senate but failed the House. Buchanan opted for Lecompton because of pressures of the southern majority of the Democratic Party on him. Douglas came out against Lecompton because its fraudulent birth made a mockery of the popular sovereignty principle that he both seemed sincerely to believe in and needed politically in order to maintain the Democrats as a bisectional party. If Douglas had not opposed Lecompton he would have been dead in Illinois in 1858 and dead in the North in 1860. For purposes of Presidential election, the Democratic Party at that point had the South but needed the North. Before Freeport, the question arose three times in campaign events in July 1858, and Douglas answered, “Slavery cannot exist a day in the midst of an unfriendly people with unfriendly laws” (337). Moreover, Lincoln in a private letter written on July 31 acknowledged that Douglas had dodged the question and expressed the opinion that anyway because of the Lecompton controversy, Douglas “cares nothing for the south; he knows he is already dead there” (337). Lincoln’s purpose in asking the Freeport question, says Potter, was to return attention to the already established fact that Douglas could only reconcile Dred Scott and popular sovereignty with the lame proposition that constitutionally guaranteed rights could legitimately go unenforced; I would add that Douglas’s answer reinforces the suspicion that he was too expedient a character. But Lincoln did not vigorously pursue the question in any of the ﬁve joint debates that followed. Lincoln, in fact, did not want to overemphasize the question of the best policy for containing slavery, according to Potter, because there was little difference between the practical outcomes of the candidates’ policy proposals. Lincoln attempted rather to shift the debate from the policy dimension to the moral dimension. Lincoln said that the contest was between the Republicans who considered slavery wrong, and Douglas and the Democrats who did not consider slavery a matter of right and wrong. Further, Lincoln did go after Douglas aggressively on another question more likely to rouse the audience, according to Potter (1976, 349–351). Lincoln warned that the next slavery decision from the Supreme Court would go beyond Dred Scott to declare that no state has the right to exclude slavery from its limits. Douglas used his strongest language in the debates denouncing this charge. Douglas’s dilemma was larger than the Freeport question, and it was not posed by Lincoln. His dilemma was posed by preferences of the

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people and by how those preferences developed in response to events. The Whig Party had already collapsed. The Democratic Party was held together by the doctrine of popular sovereignty. On March 6, 1857, the Dred Scott decision ruled that the US Congress lacked constitutional authority to prohibit slavery in the territories – and Chief Justice Taney, although not the Supreme Court, declared that territorial legislatures lacked authority to prohibit slavery which threatened to nullify the doctrine of popular sovereignty. In February and March of 1858 the southern wing of the Democratic Party further threatened the credibility of popular sovereignty by attempting to force admission of Kansas with a minority slave constitution. It was the widening gap between the two sections of the party that was Douglas’s problem, not Lincoln’s discourse. Nor was it the Republicans who split the Democrats. Proximately, it was the Democrats who split themselves at their 1860 Charleston Convention, and ultimately it was because of preference development – especially the determination of the ﬁre-eaters in the Lower South to secede. On December 29, 1858, one southern Democratic politician wrote to another urging that the slavery issue be kept alive. He wrote that such a policy might result in “a Southern party which would either succeed and thus govern the country or fail and thus form a compact Southern party ready for action [i.e., secession]” (Nevins 1950, 179). The gap between North and South was most widened by the Dred Scott decision, which emboldened the South to take its intransigent stand. There is a hidden functionalism in Riker’s argument. Did the Republicans beneﬁt from the split in the Democratic Party? Yes; indeed, how could they have thrived without it? Did the Republicans try to split the Democratic Party? Yes, just as Douglas tried to split the Republicans by adhering to popular sovereignty, and just as Calhoun tried to split the Whigs. Did the Republicans cause the split in the Democratic Party, however? That would have to be shown. Did Lincoln cause the preferences of the secessionist gentleman I quoted? Evidence that Republicans discursively encouraged a split is not sufﬁcient as, according to Riker’s story, the Yankees had tried that for at least forty years already without any success. Is it that they had ﬁnally found the “magic phrase,” or is it that preferences and constraints had changed over the forty-year period? Magnuson and nerve gas This story, say Riker and Weingast (1988, 391), involves a motion that likely would have failed if unadorned, but that passed triumphantly when a single legislator embellished it rhetorically with an interpretation that other legislators knew to be meretricious, and that a majority probably

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opposed. Thus a single person brought about what appears to be a majorityopposed outcome.

Riker’s earlier cycling stories seemed to recede as Riker developed his notion of heresthetic, which is exempliﬁed by the story of Magnuson and the nerve gas. Riker frequently retells the story, in Riker (1986), in Riker and Weingast (1988), and in Riker (1990a). We’ll focus on the lengthier 1986 version. In 1970, during the Vietnam War and when Republican Nixon was President, the US Department of Defense decided that it had to ship a large quantity of nerve gas from Okinawa in the Paciﬁc Ocean to the United States. It would be landed in Seattle, Washington and then be shipped by train to a military depot in the neighboring state of Oregon. This became the federal issue of supreme concern to the Paciﬁc Northwest of the United States in that period, as I can attest having lived there at the time. On May 29, 1970, Senator Warren Magnuson, Democrat from Washington State, offered an amendment to the Foreign Military Sales bill stating that “No funds authorized or appropriated pursuant to this Act or any other law may be used to transfer chemical munitions from Okinawa to the United States” (Riker 1986, 107). The amendment was cosponsored by Senator Henry Jackson, another Democrat from Washington, a war hawk and friend of the Pentagon, by the two Republican senators from Oregon, Mark Hatﬁeld, a dove on the war, and Bob Packwood, and by antiwar Senator Mike Gravel, Democrat from Alaska. Riker says that Magnuson as a Democrat was trying to discredit the Republican President. The amendment had been discussed on the ﬂoor but had not yet been voted on when the Defense Department announced that it would not ship the nerve gas to Oregon, but rather to the Kodiak Naval Station in Alaska. Senator Gravel of Alaska on June 29, 1970 moved another two-sentence amendment to the still-pending Foreign Military Sales bill. The ﬁrst sentence of Gravel’s amendment was identical to Magnuson’s amendment. The second sentence of Gravel’s amendment read: “Such funds as are necessary for the detoxiﬁcation or destruction of the above described chemical munitions are hereby authorized and shall be used for the detoxiﬁcation or destruction of chemical munitions outside the United States” (Riker 1986, 108). The intent of the motion was to force the containment and encourage the destruction of the nerve gas on Okinawa. Magnuson’s great heresthetical maneuver was in support of Gravel’s amendment, according to Riker. Riker relies in part on Redman (1973, 207), whose reportage he recognizes was quite inaccurate (Riker 1986, 113; for example, Redman wrongly believes that Senator

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Harry Byrd of Virginia is Senator Robert C. Byrd of West Virginia). Redman (1973, 206–207), Magnuson’s aide at the time, wrote: I prepared another memorandum cataloguing the arguments he had marshaled against the shipment and took it to him at his desk on the Senate Floor. He surveyed the memo cursorily, then handed it back with an annoyed “No, no, no!” Bewildered, I retreated to the staff couch and waited to hear what argument he intended to use instead of the familiar ones of possible sabotage, dangerous sections of track along the proposed route, and populations that would have to be evacuated as a precaution against leakage. When the time came, he took a wholly novel and ingenious approach. The issue, he told his colleagues, was not one of the people versus the Pentagon, as the news media seemed to assume. Instead it was another case of the President versus the Senate. The Senator from West Virginia (Robert C. Byrd) had recently offered a resolution, which the Senate had passed, stating that the Senate expected the President to keep it informed throughout the treaty negotiations with the Japanese government on the subject of Okinawa. The President’s sudden decision to move the nerve gas off Okinawa must reﬂect some aspect of those treaty negotiations, Magnuson insisted – and the Senate had not yet been informed of, much less consented to, any such agreement. To allow the nerve-gas shipment under these circumstances, he asserted, would be to abandon the Byrd Resolution and to abdicate the Senate’s rightful role in treaty-making generally. The President, Magnuson said, might get the idea that he could ignore the Senate and its constitutional prerogatives whenever he wished. Jolted by this reasoning, the Senator from West Virginia and his Southern colleagues – friends of the Pentagon almost to a man, but vigilant guardians of the Senate’s constitutional responsibilities – voted down the line with Magnuson. The amendment, which had been doomed a few minutes earlier, passed overwhelmingly.

A sling for David against Goliath? The Church–Cooper amendment to the same bill, with the purpose of forcing President Nixon to withdraw from his Cambodian incursion, was voted on the next day. For the Gravel nerve-gas amendment, Riker thinks that Magnuson already had the votes of nine regional senators from Hawaii, Alaska, Washington, Oregon, and Idaho, but not of Democratic hawk Jackson of Washington state. Jackson supported the original Magnuson amendment, but, once the danger to Washington state had passed, Riker believes, Jackson voted against the Gravel amendment. He also thinks that Magnuson had the votes of the anti-Nixon forces, those who voted both for the Gravel amendment and for the Cooper– Church amendment; there were 40 of these, including 7 of the 9 regional senators. That means 40 + (9 − 7) = 42 natural votes for the Gravel amendment, out of a Senate of 100 members voting by majority rule. There were 24 senators who voted against both the Gravel amendment and the Church–Cooper amendment. That leaves 33 senators, 26 of whom were present for the vote on the Gravel amendment. The 26

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divide into two groups, according to Riker. The ﬁrst group of 16 voted against Gravel and for Church–Cooper, “they were not impressed by Magnuson’s heresthetic.” The second group of 10 voted for Gravel but against Church–Cooper, they “were indeed moved by Magnuson’s heresthetic, even though they probably recognized it for what it was, namely a tactic to manipulate them” (1986, 112). The only warrant offered for these imputations is the two vote counts. In the end, Magnuson added 10 to his natural tally of 42 to obtain a victory with 52 yeas and 40 nays, the story goes. “This is heresthetic at its best” (1986, 112). “Magnuson did not persuade, I think, but maneuvered so that those who would have lost in one dimension won in two” (1986, 113). Alas, Riker detected some errors in Redman’s bewildered account but he did not detect them all. The story manifest in the Congressional Record and The New York Times is not the one that either Redman or Riker tells. Redman’s account is regrettably na¨ıve and starry-eyed according to Riker (1986, 108), and these traits do probably contribute to Redman’s errors. Riker’s account, however, is cynical and murky-eyed and these traits probably contribute to his. Let’s start all over again. The US was at war in Vietnam. In 1968 thousands of sheep died in Utah due to a military nerve-gas accident (Congressional Record, May 21, 1970: 16482). This was an unnerving incident, the eerie pictures of dead sheep were known and discussed quite widely in the West, more than many other political issues, I recall. The Pentagon announced controversial plans to ship deteriorating nerve-gas materials, 27,000 tons, from Colorado, Alabama, and Kentucky to a New Jersey port for burial at sea. Japan had been pressing for the return of the Ryukyu Islands, including Okinawa, controlled by the US but home to a million Japanese subjects (The New York Times Index, 1969, 1,279). There were mass demonstrations, electoral agitation, and minor riots in Japan and in Okinawa. One obstacle to returning control to Japan was the need to remove US nuclear weapons from Okinawa. In the midst of this tension came a news report that 25 American military personnel in Okinawa were hospitalized after accidental discharge of toxic gas. The presence of the nerve gas became a big political issue in Japan, and shortly the Defense Department announced that it would remove chemical weapons from Okinawa – 13,000 tons or ﬁve shiploads full. In November 1969 President Nixon announced unilateral abandonment of biological weapons and proposed negotiations on the matter of chemical weapons (The New York Times Index, 1970, 339–340). In March of 1970 the Democratic National Committee called on Nixon not to ship the gas to the United States. The Republican governors of Washington and Oregon ﬁled suit in April in US District Court seeking to enjoin the shipment. Magnuson, Hatﬁeld, and

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Packwood joined the cause. Gravel joined the cause; he and Magnuson introduced legislation to prevent shipment to the United States including Alaska. On May 24, three days after Magnuson introduced his amendment on the ﬂoor of the Senate, President Nixon phoned Senator Jackson to tell him the gas would not go through Washington to Oregon, but the White House was considering Kodiak Island in Alaska as an alternative storage site. The Army announced that no nerve gas would be moved while the amendment was pending. In June, the Pentagon announced that it was studying Johnston Island, a US possession uninhabited by civilians 700 miles southwest of Hawaii. Meanwhile, deteriorating nervegas weapons from Army depots in Alabama and Kentucky were shipped by rail to South Carolina for urgent burial at sea off Florida. On April 30 Nixon announced that he would send US combat troops into Cambodia, which lit a ﬁrestorm of protest (Congressional Quarterly Almanac, 1970, 930–931). There were demonstrations and riots across the United States. On May 4 four students were shot dead by the National Guard at Kent State University. On May 9, 60,000 to 100,000 students demonstrated in Washington, DC. The Congress erupted as well, meetings were held between relevant committees and the President, and numerous proposals arose to prohibit expanding the war to Cambodia. Nixon backpedaled. Senator Harry Byrd (D-VA), Senator Thurmond (R-SC), and Senator Hollings (D-SC) did fuss on the ﬂoor about President Nixon’s negotiations with Japan over the reversion of Okinawa to Japan (Congressional Record, April 7, 1970: 10470–10478). On November 5, 1969, Harry Byrd had offered a resolution that the administration should not conclude negotiations concerning change in the status of Okinawa without seeking the advice and consent of the Senate (under the Senate’s constitutional right to approve treaties), and that resolution had passed the Senate, 63 to 14 (reported in Congressional Record, April 7, 1970: 10474). The speaking senators’ concerns were threefold: to uphold the prerogatives of the Senate, to protect the military interests of the United States in Okinawa, and, explicitly (10470), to restrain Japanese textile imports. For these three senators represented states with a textile industry damaged by cheaper Japanese imports. Jumping forward, in May and June of 1971, some southern senators threatened to defeat any treaty brought to the Senate concerning the return of Okinawa to Japan unless Japan agreed to curb textile imports (The New York Times Index, 1971, 1,276). By September of 1971, the Japanese government, which much desired the reversion of Okinawa for domestic political reasons, agreed to reduce “voluntarily” textile exports to the US in exchange for Okinawa. The Senate then approved the Okinawa treaty in November by a vote of 84

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to 6 (Harry Byrd and Magnuson were among the few nay votes, I don’t know why). Magnuson introduced the Magnuson amendment to the Foreign Military Sales Act on May 21, 1970 (Congressional Record: 16481–16482). He made several arguments about the hazards of the proposed shipment. He also mentioned the treaty issue, stating that he was aware of no commitment to remove the nerve gas from Okinawa in the Nixon administration’s negotiations with Japan. He boasted of his staunch support for military appropriations, a true claim. He said that he thought chemical munitions should be destroyed but that the decision about maintaining or destroying the Okinawa arsenal was properly the Pentagon’s. He mentioned that a chemical and biological warfare treaty was on its way to the Senate. Magnuson was perplexed: “If anyone understands this movement, explain it . . . I have not found anyone who supports this movement except Pentagon ofﬁcials” (16481). Magnuson reported that Evans, the Republican governor of Washington, and McCall, the Republican governor of Oregon, were beseeching the administration on the issue, and quoted McCall’s call to the Republican Vice President: “For heaven’s sake Ted, give the feelings of Oregonians a little consideration and ease up on the bullheadedness that is forcing so many supporters of the administration to the wall in Oregon” (16482). Church, Democrat of Idaho, and a member of the committee with jurisdiction over the bill, stated his support for the Magnuson amendment. Gravel of Alaska added that he believed that the gas should remain on Okinawa or be detoxiﬁed or destroyed, that it should not go to Alaska, and stated that Magnuson’s amendment prohibited its shipment to Alaska. The introduction of the Magnuson amendment did not stop the Pentagon from studying Alaska as a potential storage site, however. Five weeks later, on June 29, 1970 (Congressional Record: 22016–22023) Gravel returned with a new amendment. The effect of the Gravel amendment was to prohibit removal of the nerve gas to any US state or possession and to permit funding for destruction of the materials. Gravel was fulminating about chemical weapons. In Rikerian terms, he was adding a dimension to the debate – Nixon’s delay in presenting the 1925 Geneva chemical and biological warfare treaty to the Senate – but in a manner that palpably would lose him rather than gain him votes. Church suggested that the language of Gravel’s amendment would not prohibit removal to US possessions Guam or Johnston Island, but Gravel insisted that it would. Jackson objected. Jackson, Church, and Fulbright from the committee of jurisdiction tried to narrow the amendment to the states of the United States, but Gravel stubbornly refused. Magnuson intervened to explain that he had a more broadly sponsored amendment already

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pending, now joined by a senator from New Jersey, that would prohibit shipment of the Okinawa gas to the United States. Jackson and Tower objected that the Gravel amendment would weaken the US position in negotiations with the Soviet Union on biological and chemical weapons. Tower further objected that the Gravel amendment tied the hands of the executive in negotiating with the Japanese (an evident Senatorial norm is to pressure but usually not to dictate to the executive on foreign policy). Gravel replied, “Obviously, if it does impair the secret negotiations with the Japanese, I am sure that the conferees can be so informed and could strike it from the conference report” (22021). In other words, pass the Gravel amendment as a statement, but recede from it in the House– Senate conference on the bill. Gravel stated that his larger purpose was to promote biological and chemical disarmament. Now Magnuson made his argument. He explained that his more narrowly drawn and more broadly supported amendment was still pending. He thought that the Senate should take some kind of position on the affair. His basic complaint was that: on all of these occasions when we were discussing Okinawa, nothing was done to inform us of administration plans. We passed a resolution saying, “Please, Mr. President, before you start doing all these things concerning Okinawa, come to the Senate and discuss some of them.” The President never did this. That is what we have been arguing about for 5 long weeks. That would have saved us a lot of trouble. It would have saved a lot of trouble for the Senators from Alaska and Washington and Oregon. (22022)

I infer that Magnuson and the regional senators had been bushwhacked by the nerve-gas controversy and were angry about being kept in the dark by the Pentagon. Further, the Pentagon had tricked Magnuson; they said they would not ship the nerve gas to the continental United States, which he accepted, but then they said that Alaska was not part of the continental United States. It was at that point, he explained, that he and the remaining Washington and Oregon senators had joined with Gravel to introduce the Magnuson amendment (22021; The New York Times Index, 1970, 340). He also mentioned the political problems that other senators in other regions had with nerve-gas storage and shipments that year (by implication Utah, Colorado, Alabama, Kentucky, New Jersey, South Carolina, Florida): “if we are going to have chemical and biological weapons, then I think that the Senate should know a little bit about what is done with them . . . it has been a constant problem” (22021). He also argued that Nixon had ignored the Harry Byrd resolution asking that the Senate be consulted on Okinawa negotiations (Riker is focused on this issue, the prerogative of the Senate, but is not

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aware that the phrase is code for restrictions on imports of Japanese textiles). On May 21, Magnuson said he was aware of no agreement with the Japanese on the nerve-gas subject, on June 29, he said, “in the meantime this agreement on nerve gas was made” (22021); on June 29, at one point Gravel referred to an agreement with Japan to remove the gas (22018) and at another point disclaimed awareness of such an agreement (22020). I speculate that the senators had received conﬁdential information about the Okinawa negotiations and that they had learned that a provisional agreement had been reached with Japan to remove the nerve gas. I speculate further that the senators now planned to take a strong stand in order to prevent further local political nightmares at the clumsy hands of the Army. Magnuson said that he had heard that the Pentagon would ship the nerve gas to Johnston Island, but had heard nothing formal about such a proposal – in other words, he had no commitment from the Army about its plans. It may very well be that US negotiators needed a domestic reaction to counterbalance the diplomatic demands arising from domestic reaction in Japan. Church, on behalf of the committee of jurisdiction, asked Gravel again to narrow his amendment so that the gas could be shipped to US possessions such as Guam or Johnston Island. The implication was that if Gravel did so the committee would consent to the amendment and it would pass without controversy, probably even without a roll-call vote. Gravel again refused. Gravel said that he wanted to make a statement about biological and chemical weapons, but was willing to have the prohibition of shipping to Johnston Island withdrawn in the conference committee if the administration came and said it would be a problem. A clear understanding was offered by Gravel. Church responded that he could not accept Gravel’s broad amendment on behalf of the committee, but did declare that he would vote for it himself. Church said, “The Nixon administration has played rather loose on this matter. This discussion and vote should bring them up abruptly. It will force them to come to the Senate and the conference and lay their cards on the table” (22022). Church accepted the understanding offered by Gravel. Magnuson added that in the event the Gravel amendment failed the upcoming vote, Magnuson would again offer the Magnuson amendment, which by implication would be accepted by the committee and passed without controversy. The effective choice was between the Magnuson amendment that would pass without controversy, and the more confrontational Gravel amendment that would require a roll-call vote. The Gravel amendment passed by a roll-call vote of 51 to 40. We must redo Riker’s analysis of the vote. It is not obvious that the vote

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on the Gravel amendment on nerve gas is related as Riker would like to the vote on the Church–Cooper amendment to prohibit expansion of the war into Cambodia; 66 senators voted or expressed positions either for both or against both measures, but 30 voted in a mixed fashion on them, a rather weak correlation. The vote on the Gravel amendment does not ﬁt Poole and Rosenthal’s (1997) usually predictive spatial model of ideology (the model’s predictions err on 22 out of 95 votes, the issue scores 0.488 in terms of their measure of proportional reduction of error, Voteview, 91st Senate, Roll-Call #414). The Church–Cooper amendment does adequately ﬁt the ideological model (9 errors out of 99 votes, 0.775 proportional reduction of error, Voteview, 91st Senate, Roll-Call #425). To continue, 38 senators voted for both Gravel and Church–Cooper, 39 if we count a pair from Nelson (not 40 as in Riker). There were 9 Senators in Hawaii, Alaska, Washington, Oregon, and Idaho voting for the Gravel amendment (Jackson was the exception). That means, continuing to correct the arithmetic, that there were 39 + (9 − 7) = 41 (not 42) natural votes for the Gravel amendment. There were 23 senators who voted against both Gravel and Church–Cooper, 27 if we count a pair from Long and announced nays from Miller, Mundt, Russell (not 24). That leaves 32 (not 33) senators, 30 (not 26) of whom were present for the vote on the Gravel amendment. The 30 divide into two groups. The ﬁrst group of 17 (not 16) voted against Gravel and for Church–Cooper, the ones Riker said were not impressed by Magnuson’s heresthetic. The second group of 13 (not 10) voted for Gravel but against Church–Cooper, the ones Riker said were manipulated by Magnuson. Riker claims to see patterns distinguishing the 17 from the 13, but all I see is noise. Except that there is one slight pattern not mentioned by Riker among the 13 who voted for Gravel but against Church–Cooper: of the ﬁve Democrats, three are from states with nerve-gas transportation controversy (Alabama and Kentucky). The eight Republicans are ideologically and geographically scattered; I speculate that they had personal ties with the two Republican senators from Oregon who voted for the Gravel amendment. There is one more interesting pattern. Riker confounded two of Magnuson’s appeals. Magnuson did complain to the Senate about nerve-gas controversies that year involving Hawaii, Alaska, Washington, Oregon, Idaho, Alabama, Kentucky, New Jersey, Florida, and other states, and of failure by the White House to respond straightforwardly to the problems. He also appealed to those associated with Harry F. Byrd who sought to get the Okinawa agreement into the Senate so they could extract textile concessions from Japan. Riker notices that Harry Byrd and Thurmond ignored Magnuson’s appeal, but Riker is not aware that their issue was textile imports. The appeal of Magnuson – a free-trader whose

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state exports military equipment, airplanes, grain, logs, and lumber – to the textile protectionists fell utterly ﬂat: not a single senator from Virginia, North Carolina, South Carolina, or Georgia voted as Magnuson asked for the Gravel amendment. The great heresthetical maneuver was a big ﬂop in this respect. Redman is also deluded, as the southerners did not vote “down the line” with Magnuson after hearing his honeyed tongue – they were more solidly against him than any other region. All the premises of Riker’s argument are mistaken. He believes the Gravel amendment passed only because of Magnuson’s speech, but we know from the record that the Magnuson amendment would have passed without controversy. Magnuson’s appeal to the textile interests failed completely. His other appeal was not so much to the formal prerogatives of the Senate, but was about mistreatment of supportive senators by the Pentagon, its trickery on Alaska, and unwanted nerve-gas controversies across the United States. Democrat Magnuson’s purpose was not to discredit Republican Nixon – Magnuson, the two Republican governors of Washington and Oregon, and the two Republican senators from Oregon were trying to save their skins with their home publics. Jackson did not bail out as soon as the state of Washington was spared – Jackson was a cosponsor of Magnuson’s amendment which explicitly included Alaska. Jackson was for the Magnuson amendment but against the Gravel amendment, no doubt because Jackson the hawk loathed Gravel’s aggressively dovish views. Absolutely no evidence is offered to support Riker’s imputation that the senators who voted as Magnuson asked did not believe in the sincerity of his appeal. In sum, one person’s rhetoric did not bring about a majority-opposed outcome. There is a saying about how to get the attention of a donkey. You hit it over the head with a two by four. That is what Magnuson did. Given their generous support for the military establishment, the two Democratic senators from Washington should have had upon request a quick commitment from the Pentagon not to ship the gas to the Paciﬁc Northwest (of course the military were busy ﬁghting a major war in Southeast Asia at the time). Then the Pentagon tricked Magnuson over Alaska with the phrase “continental United States,” and he got out the small board of the Magnuson amendment. That did not get results. So then he let wild man Gravel loose, and whacked the Pentagon over the head with a big board. That did get results. The Pentagon eventually committed to shipping the gas to Johnston Island. Apparently, the administration did approach the conference committee, because the conference report on the Foreign Military Sales Act added a third sentence to the Gravel amendment: “For purposes of this section, the term ‘United States’ means the several states and the District of Columbia” (Congressional Record, December 31,

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1970: 44305). Johnston Island was a possession, not part of any state. The understanding between Gravel and Church was carried out. Magnuson got what he wanted. Gravel got what he wanted (although, I think, not as a result of his effort): in August 1970 Nixon sent the Geneva protocol on bacteriological and chemical weapons to the Senate. The textile industry got what it wanted: restriction on Japanese textile imports. Here we encounter a new contradiction. Riker conceded that cycles are unlikely on routine issues, but here is a routine issue where a single speaker purportedly turned a minority into a majority by dimensional manipulation, and such dimensional complication looks to be easy for any issue no matter how small. Indeed, there were many “dimensions” involved in this small issue, among them: safety of storage and transport of biological and chemical weapons in the northwest; safety of storage and transport of biological and chemical weapons elsewhere in the country; the expectation of senators to be spared needless political embarrassments; the biological and chemical warfare treaty; Senate–President relations; US–Soviet relations; US–Japanese relations; US strategic military capacity; the Vietnam War; protection of the US textile industry; and party, sectional, and personal ties among senators. Was it a case of “anything can happen”? No, again because discourse is unlike agenda control. A rhetor cannot force a dimension on an auditor. Magnuson complained that the Pentagon tricked him on Alaska, that a number of senators across the country had gone to political hell on nerve gas, and that the military was still not forthcoming on the issue – he asked if that is how Senate–Executive relations should be in the future. In the absence of evidence to the contrary, the inference must be that the senators who voted with Magnuson accepted his argument. Riker and Weingast (1988, 392–393) believe that “this manipulation succeeded even though the senators inﬂuenced by it doubtless recognized that they were being manipulated, and probably resented it.” Ignoring the several important errors of interpretation, the original story depends on this curious and unwarranted inference. We are to believe that 13 seasoned senators – including tough Senator Barry Goldwater (R-AZ) – were forced to vote against their own position because of Magnuson’s clever rhetoric, when another 40 senators felt no hesitation whatsoever in ignoring Magnuson’s plea entirely. Why did the 13 succumb but the 40 resist? We are offered no explanation. I suggest that the 13 senators may have been concerned about either their colleagues on whom they depended to build coalitions or their own fortunes given a pattern of increasing executive neglect of senatorial relations. As for the many other dimensions, discussion is not voting. Discussing the issues does not create a majority-rule disequilibrium. That can only happen

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when it comes to voting and then only under the unrealistic and unfair conditions of the McKelvey model. The art of political manipulation There are twelve stories in Riker’s (1986) The Art of Political Manipulation. The point of diminishing returns has already been passed in discussing such stories; it is no longer fruitful for my purposes to subject each new one to a searching examination (students may wish to take on the remainder). I have not patiently examined Riker’s chapter on heresthetic in C.P. Snow’s (1951) novel The Masters, about the election of a master in a Cambridge college; the chapter on trading votes at the constitutional convention; and the chapter on Speakers of the House Reed and Cannon. The ﬁrst part of the chapter about the ﬂying club tells the story of how Plott and Levine hoodwinked Levine’s ﬂying club into buying the planes Levine wanted by unfairly manipulating the choice of voting rules. I ﬁnd the story distasteful in several ways, and have not examined it in detail. The second part of the chapter reports Plott and Levine’s experiment, the one I described as suggesting that agenda control is possible only if the agenda-setter has unconstrained power over the sequence of consideration and unconstrained power over the distribution of information of preferences; in other words, if one party is given an unfair advantage then the procedure has an unfair outcome. The chapter about camouﬂaging the gerrymander tells the story of a city manager covertly managing a gerrymander of city-council districts in order to keep her job; it is said to be real, but is undocumented. The chapter on Pliny the Younger and parliamentary law we have already encountered; it is an example of agenda control countered by strategic voting such that in the end there was no harmful manipulation. The chapter on how to win a roll-call vote by not voting reports an isolated instance of parliamentary chicanery. Five of the stories, all alleging cycling and instability in one way or another, we have already examined and found wanting: “Lincoln at Freeport,” “Chauncey Depew and the 17th Amendment,” “Gouverneur Morris in the Philadelphia Convention,” “Warren Magnuson and nerve gas,” and “exploiting the Powell amendment.” The story from Riker (1958) about a cycle in Congressional agricultural appropriations is not included in the volume, and the celebrated Civil War stories in Riker (1982) about the cycle in the Wilmot Proviso and the cycle in the election of Lincoln are curiously absent. In response to my volume, there may be a renaissance of cycling claims in the literature. But such claims would miss the point, in two ways. First, anecdotes are not sufﬁcient. The only persuasive evidence would

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be a showing of frequency from a properly drawn sample of some deﬁned universe of voting, together with a substantive analysis of whether each instance of cycling is harmful. Second, even if cycling were shown by that standard, in order to salvage the doctrine of democratic irrationalism it would have to be shown further that undemocratic outcomes are irremediable.

17

Plebiscitarianism against democracy

Introduction Riker summarizes his case against “populism” (democracy) and then offers his case for “liberalism.” Populism is arbitrary and meaningless, there is no identiﬁable will of the people nor public good, he says. His liberalism, in contrast, requires only that it be possible for citizens to reject ofﬁcials of whom they disapprove. Riker’s alternative of liberalism fails, I maintain, because it reduces to merely the random removal of ofﬁcials, and because its justiﬁcation unavoidably appeals to a will of the people or a public good that Riker is concerned to reject. If Riker’s larger argument were correct, then neither democracy nor Riker’s minimal liberalism would survive. The chapter concludes by tracing the provenance of the doctrine of democratic irrationalism through James Burnham to the elite theorists of the early twentieth century, particularly Pareto.

The summary case against populism Riker’s case against populism depends crucially at every point on what I have called his basic argument pattern concerning the obscurity of preferences. Most commentators fail to appreciate the centrality of this premise to his total argument. His closing brief also crucially relies for evidence on his erroneous case study of the 1860 American presidential election. First in his summary case is the claim that democracy is arbitrary. If there are more than two alternatives on an issue of political concern, then any one of a number of reasonable voting rules could be applied. Different rules lead to different outcomes from the same proﬁle of voters’ preferences, however, and none of the reasonable voting rules is normatively better than any of the others, on his account. He conjectures that there are few voters’ proﬁles such that different voting rules would report the same winner (we reviewed evidence showing that the conjecture fails). Furthermore, most of the voting rules in wide use do not collect information on ranking of all alternatives, so we are not aware of how different rules 409

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might yield same or different outcomes. “This means that, even if some method produces a reasonably justiﬁable amalgamation [e.g., a Condorcet winner], we do not know it” (emphasis in original, Riker 1982, 235). For example, his reconstruction of the election of 1860 shows, he believes, that different voting rules would have reported different outcomes, but we can not be certain about his or anyone’s reconstruction, he says, hence we can never be certain about how voting rules perform. Outcomes are the function of both the preference proﬁle and of a voting rule inherited from some prior constitutional arrangement, in other words, the method of counting partially determines the outcome of counting. How can we judge that an outcome is fair if we cannot know the preference proﬁle and thus the extent to which the outcome is a function of the voting rule rather than of the voters’ preferences? Outcomes might be accurate amalgamations and they might not be, but we seldom possess the information to judge which is which. The arbitrariness claim depends on his basic argument about the obscurity of preferences. Second in his summary case is the claim that democracy is meaningless. Suppose that a society has decided to use a particular method of voting and deﬁne as fair the outcomes of that method. But even with one method of voting the same proﬁle of preferences can yield different outcomes; this we know from the theorems of Arrow on cycling, Gibbard and Satterthwaite on strategic voting, and McKelvey and Schoﬁeld on chaos in multiple dimensions. “Every reasonably fair method of voting can be manipulated in several ways. Since we cannot know whether manipulation has occurred, the truth and meaning of all outcomes is thereby rendered dubious” (Riker 1982, 236). One way to manipulate is by strategic voting, which is probably commonplace, thus “all voting is rendered uninterpretable and meaningless” (237); manipulated outcomes are meaningless and we can’t tell whether or not outcomes are manipulated. Another way to manipulate is by agenda control, and we can be fairly certain that it is commonplace; but we can never be sure when and how it occurs or succeeds, thus again all outcomes are rendered uninterpretable and meaningless. One variety of agenda control is the introduction of new dimensions in order to introduce disequilibrium where there was none before. This is demonstrated by his analysis of the election of 1860, he says. “It is hard to say . . . that the most momentous election in American history was a fair or true amalgamation of individual values, mainly because the decision was thoroughly – and . . . deliberately – confused by the inclusion of several issues” (Riker 1982, 237). Because of the obscurity of preferences we can never know for certain whether any one outcome was manipulated or not, thus all outcomes are meaningless.

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Riker’s basic argument pattern is also the basis for his rejection of what he calls populism and what the rest of us call democracy. Riker (1982, 238) says that populism can be summarized in two propositions: ﬁrst, “what the people, as a corporate entity, want ought to be social policy,” and second, “the people are free when their wishes are law.” We do not and cannot know what the people want, according to Riker (1982, 291): Populism is supposed to reveal a substantive will, a proposition with content. Yet if voting can fail to reveal such propositions accurately and if we do not and cannot know in any particular instance whether failure has occurred, then none of the propositions supposedly revealed can be believed.

The ﬁrst proposition falls, says Riker, because we do not know the people’s wishes, and the second falls because if we do not know their wishes the people cannot be made free by enacting their wishes. Populism fails, he says, not because it is morally wrong, but because it is empty. Before the Reformation, he says, the pope’s decrees as to the will of God were authoritative, but the proliferation of such claims after the Reformation rendered the batch uninterpretable and meaningless – no one could be sure what God wanted even if all postulated such an entity. Similarly, he continues, the discoveries of modern political science will lead our next generation to reject the will of the people as the basis of government. There may be a people, but we cannot know them. It is important to realize that Riker’s case against democracy is not based on the claim that there are inevitable imperfections in social choice, that the variety of real decision procedures only imperfectly approximate one or another of a family of justiﬁable ideals. No, Riker’s case is based on the claim that the preferences of other people are unknowable. If, for one reason or another, one does believe that it is possible to infer the preferences of others, then one may reject his case against democracy without much ado. The defense of liberalism According to Riker (1982, 242), the essence of his liberal interpretation of voting is that “voting permits the rejection of candidates or ofﬁcials who have offended so many voters that they cannot win an election.” Voting does not provide a statement of the popular will; all it does is provide that an ofﬁcial is retained or rejected. Then follows a remarkable argument. We “begin by assuming the existence of what we already know does not exist – namely, a fair and accurate amalgamation of voters’ values” (242). This will not taint the analysis, he says, it is an initial standard, not an instrument of interpretation (I shall explicate this claim shortly). He then

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comments on four possibilities: (1) that a good ofﬁcial is retained; (2) that a good ofﬁcial is rejected; (3) that a bad ofﬁcial is rejected; and (4) that a bad ofﬁcial is retained. As to the ﬁrst, if a good ofﬁcial (one who has not “offended enough voters for them to reject him in a fair and true amalgamation of their values,” [242]; Riker does not explicitly use good or bad) is retained, then whatever voting method is in use is working, and there is no problem. Second, if a good candidate is rejected, for example, if she is the victim of a plurality voting rule, strategic voting, agenda control, dimensional manipulation, and so on, then there is no problem with the liberal interpretation of voting, according to Riker. How is that? The liberal interpretation “requires the rejection of the offending, not the retention of the unoffending.” If a decision procedure permits rejection of an alternative, there is no reason to require that the mechanism of rejection work perfectly, he says. Furthermore, the liberal interpretation does not require that ofﬁcials be agents of the voters’ will since there is no such will, according to Riker. This means that an ofﬁcial in the Rikerian regime would abandon any effort at reading the voters’ will, “not because the ofﬁcial is sophisticated enough to know that there is nothing there to read, but merely because he or she knows by experience that voters’ rejection may be random” (Riker 1982, 243). (An implication would be that politicians’ obsession with opinion polling is an extravagant illusion.) The liberal interpretation intends to prevent abuse of ofﬁce or authority on the part of ofﬁcials by threat of removal at election; the randomness of the threat does not matter, says Riker, in fact, it motivates ofﬁcials to try even harder to avoid offending the voters. The older Riker’s claim about random punishment is just plain wrong, however. The younger Riker (1953, 110) states the reason: The process of government can be controlled by citizens only when elections are a transmission belt of ideas and decisions from the voters to the rulers. If elections have no relevance to public policy, then the policy makers need not respect the electoral sanction.

True, if there is a random chance of getting a ticket for driving faster than the speed limit, then my speeding is constrained by the expected value of the penalty. But if there is a random chance of getting a ticket whether or not I am driving faster than the speed limit, then I will simply do as I please. If I drive 30 miles per hour there is a 10 percent chance of getting a $500 ticket, and if I drive 100 miles per hour there is a 10 percent chance of getting a $500 ticket. Under those circumstances why should I drive 30 miles per hour if I would rather drive at 100 miles per hour?

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The third possibility is that a bad ofﬁcial is rejected. If that happens, the voting method is working, and there is no problem. The fourth possibility is that a bad ofﬁcial is retained. Failure to reject a bad ofﬁcial does not violate the liberal interpretation of voting, Riker says. In discussion of the second possibility (rejection of a good ofﬁcial), Riker said that all his liberal interpretation requires is the rejection of bad ofﬁcials, not the retention of good ones. Now, in discussion of the fourth possibility, we learn that failure to reject bad ofﬁcials is not a problem. All that his liberal interpretation of voting requires is “that it be possible to reject a putatively offending ofﬁcial, not that the rejection actually occur” (emphasis in original, Riker 1982, 243). We know from the social choice results that good ofﬁcials can almost always be defeated because in multiple dimensions there are almost always win-sets demarcating policies preferred by different majorities over any given status quo; so there are always majorities who can defeat bad ofﬁcials too, he says. “And if success is even sometimes possible, then the liberal interpretation can be sustained” (243). In a footnote Riker (1982, 290) addresses the criticism that he accepts liberalism if it works occasionally (that is, randomly), but rejects populism if it fails at all. He admits that he imposes different standards. He maintains that populism requires knowledge of the people’s will. As we have just seen, his rejection of populism essentially depends on his basic argument pattern: any one instance of voting might be manipulated, we cannot know which, hence preferences are obscure in all instances of voting, therefore the people’s will is unknowable. He maintains that the random rejection of ofﬁcials is sufﬁcient for liberalism. To ﬁll in his argument, if liberal voting randomly rejects any candidate it succeeds, but if populism is anything less than perfectly correct in rejecting bad candidates it fails. Riker does not discuss tolerances, although he should: if there is a 5 percent chance that a candidate is randomly removed by voting, is that liberal voting device better than a hypothetical populist voting device that rejects lesser alternatives 85 percent of the time? I shall begin with an analogy. A “liberal” engineer is asked by a vending company to invent a device that will distinguish the American 25-cent piece known as a quarter from washers (the generic term for such fakes is slugs) that one can obtain at ten for a penny at a hardware store. The company wants the device to accept quarters and to reject slugs. The engineer collects his fee and returns with a prototype. The device randomly accepts or rejects inputs. When it randomly accepts quarters, the engineer claims that it is working correctly. When it randomly rejects quarters, the engineer claims that this does not matter, what should matter is that the device reject slugs. When the device randomly rejects slugs, the engineer claims that it is working correctly. When the device randomly accepts slugs, the

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engineer audaciously claims that when a user inserts a slug there is the possibility that it might be rejected. Those who would pass slugs would be deterred by the knowledge that slugs are sometimes rejected; these counterfeiters would be even more deterred by the knowledge that rejection of slugs is random, the engineer claims. The engineer concludes his presentation with the observation that although he assumed a distinction between quarters and slugs for purposes of discussion, in fact both are just meaningless pieces of metal, the ﬁrst possessing higher value only as a matter of social convention, and so it does not matter anyway which inputs are accepted and rejected, which is the true beauty of his random mechanism. Such is Riker’s argument. He asked us to assume at the outset the existence of something that he says does not exist, a collective judgment or will concerning the good or bad performance of an ofﬁcial. So drop the initial working assumption and replace it with the supposedly correct assumption that there really is no such judgment or will as to good or bad performance of an ofﬁcial. Now his claim for the adequacy of random rejection gains clarity: if there is no good or bad then it doesn’t matter who is retained and who is rejected and thus a random device is as good as any device. The random replacement of ofﬁcials is all we can hope for from Riker’s “liberalism.” It seems worthwhile to point out just how little is contained in the liberal interpretation of voting . . . Since social decisions are not, in liberal theory, required to mean anything, liberals can cheerfully acknowledge that elections do not necessarily or even usually reveal general will. All elections do or have to do is to permit people to get rid of rulers. (emphasis added, Riker 1982, 243–244)

Now suppose that the vending company hires a “populist” engineer. The populist offers several devices that implement various techniques to measure various characteristics of the input – its size, its weight, its shape, the notching on its edge, and so on – and variously aggregate the measurements into a ﬁnal accept-or-reject decision (just as there are different reasonable methods of decision for human collectivities). One device is extremely costly, but will avoid both false positives and false negatives 99.95 percent of the time. Another device is quite affordable, and avoids both false positives and false negatives 95 percent of the time. The vending company rejects the liberal’s device, rejects the populist’s costly device, and accepts the populist’s cheap device. The company knows expected failure rates from direct tests before implementation. In practical application, the company does not know in advance whether any one particular input will result in a false positive or a false negative, but this does not lead them to accept the liberal engineer’s fantastic advice that quarters are unknowable.

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Do not be confused by Riker’s claim that his liberal interpretation pertains to the rejection of candidates who have earned the disapproval of voters. For the purposes of the social choice theorems that Riker interprets as defeating “populism,” the rejection of candidates by disapprovers is formally identical to the acceptance of candidates by approvers. If a theorem holds for A > B > C then it holds for C < B < A. Further, say that there are three candidates in the cycle so central to the irrationalist vision: A > B > C > A. For each of the candidates we can say both that she is approved of by a majority of the voters and that she is disapproved of by the voters. Riker does not deny this; he emphasizes in his exercise that any candidate, good or bad, can be arbitrarily defeated. One ﬂaw of Riker’s demonstrative exercise worth noting is the assumption that candidates are good or bad on their own without reference to an alternative. We can call this the Nixon–Agnew problem. You may think that Nixon is bad, but you won’t want to get rid of him when the alternative is Agnew, who is even worse, a consideration that former President Nixon perhaps had in mind when choosing his mediocre sidekick. Correcting for the absence of comparisons gives us eight different possibilities: (1) A better incumbent could beat worse challengers, which is ﬁne. (2) A good incumbent could beat equally good challengers, which is ﬁne too. (3) A bad incumbent could beat equally bad challengers, which is arguably bad. (4) A worse incumbent could beat better challengers, which is bad. (5) A better incumbent could lose to a worse challenger, which is bad. (6) A good incumbent could lose to an equally good challenger, which is okay. (7) A bad incumbent could lose to an equally bad challenger, which is arguably bad. (8) A bad incumbent could lose to a good challenger, which is good. The important case that Riker neglects to consider is when voters are forced to accept a bad candidate because the alternative candidates are worse. The majority of voters indeed disapprove of the bad candidate but their disapproval does not remove him from ofﬁce. But all of this is irrelevant, because for Riker there is no good or bad, no better or worse, to the matter. He says that ofﬁcials who abuse ofﬁce and authority will be rejected, but he seems not to notice that there is no test for such abuse apart from the collective judgment or will of voters, which he has already dismissed as a fantasy. If ofﬁcials cannot further the public good because it does not exist then neither can they further a nonexistent public bad. If there is neither public good nor public bad, another problem arises. What justiﬁes the institution of the random rejection of rulers, or indeed any political institution? There is no public good for the inhabitants of the People’s Republic of China; hence in terms of aggregate subjective welfare there is no way to distinguish between the party dictatorship and some democratic alternative. There is no way to distinguish

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the governments of Serbia and Slovenia. The Italian government of 1930 is no different than the Italian government of 1990. And so on. Riker does concede the existence of one kind of common interest: “a common or public interest is held in common, so voting is unnecessary to reveal it: Any randomly chosen member of the society can articulate public interest was well as any other” (Riker 1982, 291). Presumably he has the Pareto criterion in mind. If everyone in Italy wanted to depose Mussolini with the exception of Mussolini himself, we could not on Riker’s deﬁnition say that Italy had a common interest in changing its leadership. If only one member of a society rejects the principle of elections for public ofﬁce, then elections would not be in the common interest as Riker deﬁnes it. Riker goes so far as to say that there may be an objectively right public interest for a society even when people do not agree. But in the absence of unanimity each interpretation of that objective public good is merely arbitrary, he says; leftist reformer or demagogue Ralph Nader might correctly state the public interest and rightist reformer or demagogue George Wallace might correctly state it, but voting short of unanimity provides no evidence as to which of the two best approximates the objective public good. I would add that even a unanimous vote might miss the public interest if not implausibly there were a universally held false belief among the voters; the proper question is whether there is a probabilistic connection between voting and the public interest. Further, note well the absence of public reason in Riker’s scheme. He seems not to realize that by his eschewal of public reason he has painted himself into a corner. The judgment inherent in his liberal interpretation of voting that the random rejection of ofﬁcials would be in the public interest, perhaps even objectively, is invalidated if only one member of the society disagrees with it, and surely one of the ofﬁcials to be rejected would disagree, otherwise there would be no need to force his removal. Riker continues that his liberal interpretation of voting satisﬁes three desiderata of democracy: participation, liberty, and equality. His argument is contradictory, however. He says that rejection is possibly random, which is consistent with his argument against populism, but he thereby implies that the rejection is possibly not random. If the rejection is not random then that implies a public will, but if there is a public will then we are back to the populism that Riker denounces. His liberalism satisﬁes a kind of participation, he says, because each voter enjoys the possibility of rejecting an ofﬁcial. “At best ofﬁcials are responsive to a (possibly random) threat of expulsion from ofﬁce. But this may lead them to avoid gross offense to groups of citizens who can eject them from ofﬁce” (emphasis in original, Riker 1982, 245). What is this may? If rejection is random then ofﬁcials are not constrained. If rejection is not random then there

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is a public will and we are back to populism. He also says that his liberal participation engenders self-direction and self-respect within individuals, but how can that be if there is a random, that is, no, relationship between individual action and collective result? In his ﬁrst chapter Riker defended his liberalism on the ground that it made ofﬁcials an approximate agent of the electorate and thus achieved democratic self-control. Now in his last chapter he implicitly repudiates that earlier characterization (242– 243), yet he continues to insist that a random relationship between the electorate and ofﬁcials would also achieve democratic self-control. The liberal veto also promotes a kind of liberty because it is a curb on tyranny, he says. The chance to express disapproval of an ofﬁcial and the chance that the disapproval might result in rejection of the ofﬁcial satisﬁes the ideal of negative liberty, of freedom as absence of restraint. There are two problems. First, in Riker’s scheme, absent unanimity of judgment or will there could be no such thing as tyranny; because if there is no public will then there is no public will concerning what is tyranny and what is not. Second, if the removal of tyrannical ofﬁcials were imperfect, then one’s liberty would suffer each time the voting rule failed; and worse, if, as it must be in order to avoid the supposed populist error, the removal of public ofﬁcials were random then again there is no connection between an individual’s action and the collective result. In the Soviet Union one had the opportunity to cast a vote against some ofﬁcials, and occasionally an unpopular ofﬁcial would be replaced by another nominee from the party, yet there was no relationship between citizens’ preferences and policy outcomes. The Soviet voting system satisﬁes the older Riker’s (1982) liberalist criterion of formally possible rejection, yet would he want to call Soviet voting democratic? Contemplate this objection from the younger Riker (1953, 91–92): Truly responsible government is only possible when elections are so conducted that a choice of men is a decision on policy, that a decision on policy is soon transformed into action, and that action taken is popularly supervised . . . Consider, for example, plebiscites in the Soviet Union . . . The popular will is not really consulted; and the people, however avidly they vote, indeed do not rule. Elections are a fa¸cade . . . because the structure of government does not permit elections to inﬂuence policy making.

Indeed, actual tyrants are inordinately fond of plebiscites, which if they were held on some regular basis would be democratic by the Riker criterion. Finally, the liberal veto promotes a kind of equality, according to Riker. Voters have an equal right to participate, but the claim for equality carries only if one accepts that Riker’s liberal participation – the formal possibility to reject an ofﬁcial – is adequate.

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Populism and democracy What does Riker mean by populism? In his theory, it is some version of the notion ﬁrst theoretically articulated by Rousseau, that the legitimacy of the state is founded in the will of the people (1982, 11). What the rest of the world calls democracy Riker calls populism; that way he can remain a democrat even though he rejects the idea that government should respond to what its citizens judge best. This is convenient for his case, as populism is a label whose connotations range from the weakly to the strongly pejorative. Riker’s liberalism, however, unwittingly resembles what is pejoratively called plebiscitarianism – possibly tyrannical rule justiﬁed by merely formal opportunities for electoral rejection. Thus, we can accept Riker’s contrast of liberalism (positive) against populism (negative), or we can substitute the contrast of plebiscitarianism (negative) against democracy (positive). Democracy, or what Riker calls populism, includes but is by no means limited to the simplistic implementation of the people’s will that declares the public good to be whatever a bare and direct majority chooses from moment to moment in ordinal pairwise majority voting. Even the demonized Rousseau avoided this error: for Rousseau, the will of all revealed by voting may imperfectly identify what would really be good for all, the general will. A democrat may quite consistently and defensibly recommend broadly accepted institutions that neutrally reﬁne and enlarge the will of the people. Raw political preferences may be poorly informed and may be contradictory even within individuals. Public deliberation within multiple overlapping arenas, outside and inside elections and the representative assembly, serves to inform and to order raw political preferences. A democrat may hold that the people (and he among them) can be seized by myopic and self-defeating passions, and thus that it is advisable that the legislative power be conﬁned to the promulgation of general laws and refrain from applying law to particular individuals, that it is advisable for legislation to be approved by two or more differently composed bodies (lower house, upper house, executive, constitutional review), or for certain types of legislation to require supermajorities or perhaps better approval by two succeeding assemblies, and so on. A democrat may believe that representative democracy rather than direct democracy is necessary for a group the size and the nature of the territorial state. Representatives may specialize in political information, and may professionalize and depersonalize political conﬂicts. A democrat may insist that there are essential preconditions to democracy, such as rights to life, liberty and personal property, regular elections, equal voting rights, freedom of association, and freedom of speech, such that violations of these preconditions by

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minorities or majorities should be constitutionally prohibited and that their violation would justify rebellion by aggrieved parties. A democrat may propose to free and equal citizens an independent standard of the public good based on generalized interests discovered by hypothetical choice behind some veil of ignorance that yields principles similar to Rawls’s equal basic liberties, fair equality of opportunity, and the difference principle; or an independent standard such as Benthamite summation of utilities, which yields similar practical results; or, more modestly an aggregate subjective standard such as in a multidimensional issue space the point that is the intersection of medians; and propose consent to constitutional arrangements including methods of collective deliberation and decision that would approximate to an independent standard. All of these proposals are debatable, but they are all democratic since each is based, one way or another, on the will of free and equal people. When Riker takes on “populism” he takes on all of these conceptions, not just the simplistic conception of democracy that has few serious advocates. Populism in the standard sense of the term refers to a collection of distinct political movements related by family resemblance: These people and movements, then, are populist, and have much in common: the Levellers; the Diggers; the Chartists (Moral and Physical Force); the Narodniki; the US populists; the [Russian] Socialist-Revolutionaries; [Mahatma] Gandhi; Sinn Fein; the Iron Guard; Social Credit in Alberta; Cardenas; Haya de la Torre; the CCF [Cooperative Commonwealth Federation] in Saskatchewan; Poujade; Belaunde, Nyerere. (Wiles 1969, 178)

An adequate but imperfect deﬁnition of populism’s central premise is: “virtue resides in the simple people, who are the overwhelming majority, and in their collective traditions” (Wiles 1969, 166)). The ﬁrst movement with the name, and still the exemplar, was the American populist movement of the later nineteenth century. The American populists were a mass movement of small vulnerable rural producers in the South and the West, with a hostility to all large-scale agencies contrary to the interests of the farmer, with a desire for perfected competitive capitalism rather than an economy dominated by monopolies and trusts, with allies among frontier miners on the basis of free-silver monetary policies, and with aspirations for alliance with workers in the cities (Worsley 1969, 220). The populist ideal was that the general interest should prevail over the special interests. Most populist demands were eventually enacted by the two major parties. The Narodniki were a movement of intellectuals in later nineteenth-century Russia who envisioned a society built on the traditional mir (collective peasant village), and who were revolutionary anticapitalists; their label is translated into English as populism. The

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Narodnya Volya (the People’s Will) was a terrorist organization which assassinated Tsar Alexander II in 1881 (Worsley 1969, 220). Lenin disdained the peasantist policies of the Narodniki and their successors the Socialist Revolutionaries. Another sort of populism was identiﬁed in postcolonial Asia and Africa, whereby the nation is opposed to the outside world including the ex-colonial powers, and the nation is represented by an authoritarian party–state regime (Worsley 1969, 229). Yet another use of the term populism is for the charismatic presidential authoritarians such as Vargas in Brazil and Peron in Argentina who promised the urban masses a redistribution of wealth from the compradors and their American imperialist masters to the people (Hennessey 1969, 30). The avowed traditionalist Shils (as related by Worsley 1969, 242–244) offers a general deﬁnition of populism, based, however, on the American variant, that exhibits a waspishness on the topic in American conservative discourse. For Shils, the two principles of populism are ﬁrst, “the supremacy of the people ‘over every other standard, over the standards of traditional institutions and over the will of other strata. Populism identiﬁes the will of the people with justice and morality’” (244). Second, a direct relationship between leaders and the people, unmediated by institutions, is desired. This seems to be a slam against Roosevelt and his New Deal. Nevertheless, there are many varieties of what I termed democracy that are not included within Shils’s contentious deﬁnition of populism. Populism is a theoretical category for Riker, but what does he think are its empirical referents? Populism in Riker’s pejorative sense perhaps originates with the experiences of the French Revolution, when Robespierre and his Committee of Public Safety in the name of people’s will instituted the Reign of Terror. Populism in this sense is any tyranny that claims to rule in the name of the people. Oddly enough such regimes often originate in or are periodically sustained by manipulated plebiscite, which by Riker’s theory would provide legitimacy so long as there is a regular but merely formal possibility for rejection of the regime. Since, for some reason, most modern states claim to embody the will of the people, the scope of Riker’s term populism is vast. Communists (Riker 1982, 245), such as the ghastly Khmer Rouge in Cambodia of the 1970s, were populists in his sense, since they claimed to rule on behalf of the people’s true interests. He does not mention the case, but the Iron Guard in Romania of the 1930s viciously oppressed and murdered Jews and other minorities on behalf of the ethnic majority. Vargas of Brazil, Indira Gandhi of India, Peron of Argentina – each an elected leader who resorted to demagogic authoritarianism – are quite deﬁnitely populists, according to Riker (1982, 245). Riker explicitly includes Latin American constitutional dictatorships in the category of actually existing populism

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(1982, 246). Furthermore, anyone who sees liberty as not only negative, as the absence of restraint, but also as positive, as the capacity to direct one’s own life, the distinction offered by Isaiah Berlin, is a populist who will end up with “rulers who can oppress both the minority and the very majority whose will they are supposed to work” (245). Who is the most populist philosopher? Not Rousseau, not Pol Pot, but Bentham and his fellow radicals are the worst intellectual offenders (Riker 1982, 257). Elsewhere, Rawls, and “contemporary social democrats,” are denounced as populist utilitarians who “have consistently subordinated humane values to some arbitrary and imposed virtues they prefer” (Riker 1980b, 42–43). Which is the most populist society? The reader will be surprised to learn that Great Britain is the politically worst of all nominally democratic societies. In a footnote, Riker (1982, 256–257) explains that what he calls liberalism and populism is called liberalism and radicalism by Beer (1960, 33) in his comparative analysis of the British and American polities. Quoting Beer (1960), radicals such as Bentham, “would make government the instrument of the ‘will of the people,’ a uniﬁed and authoritative force in which he found the only sovereign for the polity and for which the majority spoke.” Riker does not indicate the remainder of Beer’s thought, that the radicals contrasted the general interest to the various special interests (as did the American populists). The superﬁcial individualism of the radicals evolved into the collectivist notions of the Labour Party, Riker continues, precisely Berlin’s development of coercion out of positive liberty. (It may not matter for the argument, but we should note that Berlin did not consider the policies of the parliamentary Labour Party to be a threat to British liberty.) Beer’s analysis in no way resembles Riker’s, however. In fact, Beer (1960, 31) considers the British system to be quite practically successful in combining popular participation with effective and coherent governance. Remarkably, his major reservation is that the British parties so strongly inﬂuence public opinion as to render the electorate too homogeneous (52–53), that the system may not adequately respect the rawer form of the popular will. In Great Britain, Riker believes, the populist elimination of constitutional limitations threatens a “constitutional dictatorship” (Riker 1982, 248), “it seems unlikely that the liberal sanction [of elections] can survive populist institutions,” he predicts (249). Which is the most liberal, in Riker’s terms, of all societies? Regular elections are sufﬁcient for the existence of Riker’s (1982, 250) liberal democracy, but further institutions are required for its maintenance, he says. Those are the institutions found in the US Constitution, such as federalism, the legislative, executive, and judicial branches of government, and the separation of powers. One would be more comfortable if it were

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not an American informing us that America has the best political institutions in the world. The younger Riker (1953, 161, 164) was of a different mind: the separation of powers was designed to impede majority action. It is, as it was intended to be, the primary obstacle to those effective, legitimate majorities which . . . are an indispensable necessity for realizing the democratic ideal . . . although the separation of powers has been justiﬁed as a protection of minorities, it has in reality the opposite effect. Genuine protection for minority groups is the process of compromise inherent in democratic politics . . . Ambition must be made to counteract ambition, said Madison; but after 160 years of experience we say, ambition must be subordinated to majority will.

That the Constitution with its prohibition on the taking of property, part of its implicit endorsement of slavery; its Senate, presidency, and Supreme Court designed so as to oppress an African-American minority and to defy a European-American majority which opposed the evil institution of slavery; its stable but brittle adherence to any inherited minoritarian status quo no matter how unfree, unequal, unparticipatory, and undemocratic it was; its federalism that invited the secession of the southern states; that this Constitution had anything to do with the onset of the bloody Civil War is not a proposition within Riker’s ken. The Civil War came about because of a meaningless cycle according to Riker’s investigations, not from a tragic conﬂict between irreconcilable principles and interests exacerbated by defective antimajoritarian institutions.1 Now a new conﬂict threatens. “The present situation in the United States is . . . that, although the constitutional limitations remain, populists persistently seem to undermine them . . . our homegrown populists may well succeed. Populism puts democracy at risk” (Riker 1982, 252). The remedy, he says, is to defend the Constitution in the short run and to widely disseminate the discoveries of social choice theory in the long run. Riker’s a priori political theory approves of the presidential democracy originating in the US Constitution and disapproves of the parliamentary democracy originating in Great Britain and the continent of Europe. Presidential democracy protects liberty but parliamentary democracy threatens it. This is curious, as empirical political scientists ﬁnd that “presidentialism seems to involve greater risk for stable democratic politics than contemporary parliamentarism” (Linz 1994, 70): with the outstanding exception of the United States, most of the stable democracies of Europe and the Commonwealth have been parliamentary regimes and a few semipresidential and semiparliamentary, while most of the countries with presidential constitutions have been unstable democracies or authoritarian regimes. (Linz 1994, 4)

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Particularly, it is hypothesized that demagogic-authoritarian tendencies in some Latin American countries are attributable precisely to their presidential constitutions adopted as a result of “admiration for the great American democratic republic . . . all presidential democracies were inspired by the US model” (Linz 1994, 4–5). Following Stepan and Skach (1994, 128–129), under pure parliamentarism the institutional incentives for politicians are to seek single-party or coalitional majorities, minimize legislative impasses, inhibit the executive from ﬂouting the constitution, thereby discouraging support for military coups in political society. Under pure presidentialism, there is less incentive to form parliamentary majorities, this maximizes legislative impasses, executives are more tempted to ﬂout the constitution, and political society is more encouraged to call for military intervention to surmount impasse. Under presidentialism, the president and the parliament are separately elected, they can be of different parties yet each claim legitimacy, and they serve ﬁxed terms no matter how unpopular and illegitimate each may become. Under parliamentarism, a prime minister, or a majority coalition, are each terminated whenever they lose the conﬁdence of the public. There is evidence that parliamentary regimes are more long-lived (stably democratic) than are presidential regimes. The authoritarian menace that Riker strives to blame on the will of the people may rather originate in the “liberal” presidentialist constitutionalism that he recommends. Riker’s populism includes Communism and the popular fascisms, Her Majesty’s Government and Sinn Fein, Mahatma Gandhi and Indira Gandhi, Kim Il Sung and John Rawls, Theodore Roosevelt and Franklin Roosevelt, John Lennon and Vladimir Lenin, Switzerland and Tanzania, the younger Riker (1953), in short, every political theory, movement, and regime that claims legitimacy in the people’s will, rather than in God’s will, hereditary succession, tradition, or frank elitism. Riker’s liberalism includes the older Riker (1982), some but by no means all of Riker’s colleagues and students, the United States Constitution as the Supreme Court interpreted it in the Gilded Age (Riker and Weingast 1988), William Rusher, an editor at the American conservative activist journal the National Review (Riker 1982, 15), we may surmise others of the libertarian constitutional-traditionalist persuasion; but not Madison, a major architect of the US Constitution. The distinction between “Madisonian” and “populistic” democracy originates in Dahl’s (1956) A Preface to Economic Democracy, according to Riker (1982, 255), who comments that his own usages are quite different from Dahl’s. The Madisonian US Constitution is the exemplar of Riker’s (1982, 252–253) liberalism. Dahl (1956, 28) rejects Madisonian

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democracy, because, among other reasons, its zeal to avoid majority tyranny licenses minority tyranny: If the freedom of some majority is already curtailed in such a way that only positive governmental action will eliminate that deprivation, and if a minority with a veto dislikes the measures proposed to increase majority freedom, then by exercising its veto a minority can maintain deprivations of the freedom of a majority and hence can tyrannize over it.

Dahl has in mind social-democratic measures of the twentieth century, but something similar could be said about the abolition of the right to hold property in slaves in the nineteenth century. For Dahl, populistic democracy is a theory that would maximize political equality and popular sovereignty, but which fatally lacks empirical content. Dahl himself opts for a third alternative, polyarchal democracy, an operationalization of populistic democracy that is both measurable and more or less approximately attained in practice. Riker’s “liberal” Madisonianism is not Madison’s, because, unlike Riker, Madison was not a nihilist with respect to the public good. Riker admits that his “liberalism” would not satisfy Madison: random rejection would generate false negatives, and Madison “would have been troubled by this case” (242); random rejection would generate false positives, and “Madison would have believed this case impossible” (243). Elsewhere, Riker (9) claims that Madison was unconcerned by the quality of democratic decision, whether good or bad, but it is easy to show that Riker’s claim is false. Madison is concerned that transient majorities might damage both the rights of individuals and “the permanent and aggregate interests of the community” (The Federalist No. 10 by Madison, in Hamilton, Jay, and Madison n.d. (1937)/1787, 54). Madison repeatedly appeals to the public good in Federalist No. 10. Under inﬂuence of their passions, a majority may enact measures contrary to the permanent interests of the community including those of a majority faction. Under inﬂuence of their partial interests, a majority may enact measures that damage the common good of the community including that of a majority faction (e.g., by fomenting factional strife that makes all parties worse off). Indeed, even Madison would be an outright populist by Riker’s criteria: for Madison, the advantage of representative democracy is that the assembly would “reﬁne and enlarge the public views,” and the patriotism and love of justice of its members would best discern the “true interest” of the country, and not sacriﬁce that interest to temporary or partial considerations. Furthermore, according to Madison, the citizen of the larger republic would inhabit multiple majorities and minorities, and thus would be reluctant to permit majorities to invade the rights of minorities. Madison would limit

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majority rule so as to promote both the public good and private rights. Riker is plain – we are not reading it into him – that there is no public good. It is an implication of his views that there are no private rights in the absence of actual unanimity about their content. Thus, there is no yardstick of public good or private right by which to compare constitutional alternatives; thus, there is nothing for his liberalism to promote.

Riker, Burnham, and Pareto The themes of Riker’s Liberalism against Populism are often taught, in my experience anyway, as the scientiﬁc gospel on democracy. This unfortunate circumstance is somewhat due to the fact that many in the political science profession accept his interpretations of social choice theory, even as they repress his irrationalist conclusions. I have shown that one need not accept his irrationalist interpretation of social choice theory. Now I want to show that Riker’s irrationalist doctrine is an old vinegar poured into the bright new bottles of social choice theory. The major elements of that doctrine come straight from the musings of the early elite theorists, Mosca, Sorel, Michels, and especially Pareto, as transmitted by the selfdescribed “Machiavellian” James Burnham, a founder with William F. Buckley of the National Review. Riker seems to borrow many ideas, and even some phrases, from Pareto, but does not acknowledge or mention Pareto as an inﬂuence. The one major element of the irrationalist doctrine that is not immediately apparent in Pareto – the content of Riker’s contrast of liberalism to populism – looks like it comes straight from Burnham, again without acknowledgment. The overlapping doctrines of Pareto and Riker are of interest because of their potentially malign inﬂuence on practical politics. The (classical) liberal Pareto’s doctrine of the irrationality of democratic politics directly helped inspire Mussolini, and Pareto ended his life as a liberal fascist. The liberal Riker’s doctrine of the irrationality of democratic politics has been cited against the democratic struggle in China: political science shows that democracy is arbitrary and meaningless, so it is better to maintain paternalistic party rule, the argument goes. This twist of fate is not a complete surprise, since ex-Communist Burnham’s Machiavellian innovation was to adapt Leninist methods to the defense of American interests. Neither Pareto nor Riker intended the illiberal application of his doctrine, but ideas do have consequences.2 Liberal autocracy made an unmistakable appearance in Pinochet’s Chile, is a current of inﬂuence in China today, and may be what troubles some people about the antidemocratic excesses of international economic institutions.

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Since it is not the details of Pareto’s theory but the provenance of Riker’s that is my theme, I shall be brief about Pareto’s ideas. Pareto distinguishes logical conduct from nonlogical conduct (I am following Burnham 1943, 124–133 on Pareto, perhaps Riker’s source). Conduct is logical when: (1) it is motivated by a deliberate end; (2) when the end is possible; and (3) the means for reaching the end are appropriate. Logical conduct is common in arts, crafts, sciences, and economic activity. Conduct is not logical if any one of the three conditions of logicality is absent: if the end is not deliberate, if it is not possible, or if the means are not appropriate. Nonlogical conduct is common in the social and especially in the political arena. For Riker (1982, 210), there is a strong objective connection between needs and the consumer’s private choice, but only the weakest objective connection between needs and the voters’ public choice. Riker (1982, 200–206) further contrasts the economic context and the political context. In the economic context, there is a “Pareto optimal” competitive equilibrium; everybody is better off relative to where they started; and even if individuals are dissatisﬁed with their endowments, the market does not leave its participants worse off. Political or moral scarcity, however, when contradictory values (such as the dispute over slavery) are believed by some participants to be universal, differs from economic scarcity; in politics the choice is among mutually exclusive alternatives so that there are almost always losers and the losers are usually worse off relative to where they started. It may seem that Riker’s contrasts are only a weak parallel to Pareto’s, but permit the case to develop. Riker (1982, 205) continues that the most common kind of political scarcity has to do with manipulating markets and money: An assertion of the general virtue of rural life on the family farm justiﬁes farm subsidies. An assertion of the general moral value of the health of communities . . . justiﬁes tariffs, subsidies, and noneconomic government contracts. An assertion about the general moral value of helping the unfortunate justiﬁes a huge variety of welfare subsidies such as social security. An assertion about the general moral value of a “fair wage” justiﬁes excluding some laborers from the market in order to lessen competition for others. Assertions about the general justice of rewarding inventors, investors, or consumers justify monopolies (almost all of which are granted or maintained by governments and regulation). Assertions about the general moral value of labor peace and “fair” bargaining power justify the cartelization of labor in unions. Assertions about the moral repugnance of the spoils system justify grants of permanent tenure to civil servants. Etc.

Compare Pareto (Les Syst`emes socialistes, in Finer 1966, 139–140): The direct production of economic goods is often a very laborious process, whereas appropriating those goods produced by others is sometimes a very easy matter . . . some manufacturers produce merchandise of a certain type; through

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protective duties on the materials they use, they pay tribute which goes to other groups of manufacturers, to farmers, merchants, etc. Other tribute is exacted from them by the circulation of paper money or by government measures of monetary policy; they pay tribute money to politicians, laying out cash to maintain certain prejudices which they judge favourable to their interests. In compensation they receive tribute from consumers in the shape of protective duties on foreign products which might compete with theirs, and from the workers through the issuing of paper money or through measures taken by the government to prevent the workers from freely negotiating the sale of their labour . . . the most paltry reasons ﬁnd acceptance when they serve powerful interests or minister to ﬁxed inclinations . . . most men make convictions of their interests.

Economics is rational, politics is irrational; politics is how the parasites expropriate the producers; conviction is constructed from interest – on these points Riker and Pareto agree. The two major features of Pareto’s system of sociology are residue theory and elite theory. Each is found updated in Riker’s Liberalism against Populism. What is Pareto’s residue theory? For Pareto, derivations are the varying rationalizations and verbal associations connected to constant residues. Residue is a sociological concept not a psychological one, but residue can be thought of roughly as typical human sentiments. Derivations differ from country to country and from era to era, but the underlying residues remain the same (Burnham 1943, 134–145). Riker (1980a, 433, emphasis added) seems to be Paretian when he seeks to explain the appeal of the supposed illusion that democracy is a device to combine individual values into decisions of government: the contemporary force associating individual values and social outcomes is wholly secular, though probably derived . . . from Christian modes of thought. In the ideology of democracy, which may well be a kind of secularized Christian theology, that form of government is often, though I believe quite inaccurately, deﬁned as the rule of the people . . . this picture of democracy is internally inconsistent and cannot be sustained . . . Nevertheless inconsistencies and inaccuracies do not deter most ideologues.

To translate further the notions of residue and derivation – interests always determine principles, principles never determine interests; moral discourse, or appeals to the common good, ultimately reduce to selfserving cant if not hypocrisy, for both Pareto and Riker. Riker’s (1982, 224) cynical analysis of the American Civil War insinuates that both the supporters and the opponents of slavery were primarily motivated by political opportunism, for example. Pareto (Les Syst`emes socialistes, in Finer 1966, 137) conﬁrms generally that what historians depict as a battle for liberty is merely the clash of competing elites; historians “believe . . . that

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the elite which in reality is seeking to get hold of power to use it and misuse it in just the same way as the elite it is opposing is moved only by pure love of its fellow men.” Riker (1982, 221) acknowledges that moral concerns can coincide with political interests, Pareto (1963, 1,295, section 1859) that many adherents of the democratic religion are sincere, although for each such is merely the sincerity of the deluded.3 What is Pareto’s elite theory? All the apparent variety of political history reduces to the circulation of elites. History is not an unfolding advance of the democrats against the oligarchs, it is the perpetual struggle of one elite against another. Using Pareto’s (Les Syst`emes socialistes, in Finer 1966, 134) vocabulary, suppose that A is the elite in power, aspiring elite B competes with A for the loyalty of the masses C; once A is defeated and B is in power, then aspiring elite D arises, and so on. Riker’s political theory posits the identical image of an unstable equilibrium of institutions. For Riker, disequilibrium is the characteristic feature of politics, even for apparently stable institutions such as the American Constitution – the American Civil War came about because the political losers in the minority commercial faction of antebellum American politics sought for sixty years an issue that would split the majority agricultural faction, and found an adventitious one in slavery to generate the cycle they needed for ascendance, consolidated by force. True, Riker (1980a, 445) concedes, institutions might temporarily stabilize the chaos of aggregated tastes, but institutions are only congealed tastes subject themselves to instability. Compare Pareto (Treatise on General Sociology, in Finer 1966, 254): “Every individual . . . endeavours to obtain a maximum of individual utility . . . an inﬁnite number of positions of equilibrium with the requirements of individual maxima of utility becomes possible. Public authority intervenes to impose some and exclude others.” Because of political disequilibrium, political outcomes are not the will of the people, they are rather the will of the “smarter, bolder, more powerful, more creative, or luckier people,” says Riker (1982, 200). Pareto’s (Les Syst`emes socialistes, in Finer 1966, 134) aspiring elite is distinguished by “energy, character, intelligence.” The virtue of liberal constitutionalism, according to Riker (1982, 253) in the concluding paragraph of his volume, is that it “guarantees some circulation of leadership so that great power is usually ﬂeeting and no vested interest lasts forever.” Riker (1980a, 443) says that political institutions are established by force, not by the summation of wills. Pareto (Les Syst`emes socialistes, in Finer 1966, 136) says that “for right or law to have reality in a society, force is necessary.” Interests determine principles, institutions originate in force, political history is the circulation of elites – the echo of Pareto in Riker, not only in ideas, but in phrasing, is remarkable.

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Each proclaims his views in a relentlessly scientistic tone. Burnham (1943, 124) on Pareto: He is not offering any programme for social improvement nor expressing any ideal of what society and government ought to be. He is trying merely to describe what society is like, and to discover some of the general laws in terms of which society operates. What could or should be done with this knowledge, once obtained is a question he does not try to answer.

Such a judgment belies Pareto’s lifelong political agitation. Riker (1980a, 432) urges a “science of politics,” and “the essence of science is, of course, the accumulation of more or less valid generalizations” (1990b, 166). Riker (1980a, 446) states that his political theory appears “to be mathematically irrefutable.” Each is passionate and oddly bitter in his denunciation of the “democratic ideology” (Riker) or the “democratic religion” (Pareto).4 Another remarkable parallel is Riker’s duplication of one of Pareto’s lesser-known doctrines. Pareto distinguished the objective utility of a community, its survivability in terms of political and military power, from the subjective utility for a community, the individual welfares of the community’s members. Objective utility and subjective utility seldom coincide, says Pareto; for example, conducting war decreases the subjective utility of the community but increases its objective utility. Riker (1982, 291): the notion of a public interest, so cherished by populist [democratic] propagandists, is not, technically speaking, rendered meaningless simply because the populist interpretation of voting is meaningless. A public interest is an interest attached to the collective body of society; and as long as society exists, it has, presumably, some interests, which are its common or public interests . . . By definition, however, a common or public interest is held in common, so voting is unnecessary to reveal it . . . A public interest may even exist when people do not agree. There really may be an objectively right but not indisputably evident policy for the society . . . the public interest cannot be revealed by nonunanimous voting.

Unanimity is Pareto optimality (Riker 1982, 117); only unanimous government decisions but any voluntary market exchange satisfy the Pareto criterion. If voting is always irrational and public discussion is always opportunist then that leaves only unanimity or force as the means for deciding public policy; as Pareto (“A Few Points Concerning a Future Constitutional Reorganization,” in Bucolo 1980, 273) put it, “strength and consent . . . are the foundations of government,” note the absence of public reason in Pareto just as in Riker. Riker seeks to justify liberalism as a defense against the thoroughgoing irrationality of politics, but fails to realize that liberalism is not the unique conclusion from the irrationalist premise. The

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alternative conclusion is that if democracy is irrational and fraudulent, then those with energy, character, and intelligence should impose their interpretation of the objective public interest by force, and Pareto eventually shifted from the liberal conclusion to the alternative conclusion. Pareto, more than anyone, imported the concept of equilibrium into social theory, as an alternative to organicism. Riker accepts equilibrium in the economic sphere, and his advance on Pareto is a claim to demonstrate permanent disequilibrium in the political sphere, yet thereby vindicating the master’s judgment as to the irrationality of politics. Riker’s core distinction between liberalism and populism is not immediate in Pareto, but does appear in Burnham’s transmission of Pareto and the remaining “Machiavellian” elite theorists. Burnham (1943, 174–175, 180, 182): “Democracy” is usually deﬁned in some such terms as “self-government” or “government by the people.” Historical experience forces us to conclude that democracy, in this sense, is impossible. The Machiavellians have shown that the practical impossibility of democracy depends upon a variety of factors . . . The theory of democracy as self-government must, therefore, be understood as a myth, formula, or derivation. It does not correspond to any actual or possible social reality . . . The truth is, however, that there are other meanings commonly associated with the word “democracy,” which have nothing to do with “self-government” . . . “democracy” means a political system in which there exists “liberty” . . . The crucial difference that freedom makes to a society is found in the fact that the existence of a public opposition (or oppositions) is the only effective check on the power of the governing elite.

Compare Riker (1982, xviii, 242, 245): The populist interpretation of voting (i.e., that what the people, as a corporate entity, want ought to be public policy) cannot stand because it is inconsistent with social choice theory. If the outcomes of voting are, or may be, inaccurate or meaningless amalgamations, what the people want cannot be known. Hence the populist goal is unattainable . . . The essence of the liberal interpretation of voting is the notion that voting permits the rejection of candidates or ofﬁcials who have offended so many voters that they cannot win an election . . . the liberal veto generates freedom because of the very fact that it is a curb on tyranny.

Burnham (1943, 176) holds that the ﬂaw of populism is its degeneration from parliamentary democracy to Bonapartism: if it is the will of the people that justiﬁes the extension of suffrage and parliamentary supremacy, then that same will of the people can justify abandonment of the democratic institutions. For Riker (1982, 249), “with a populist interpretation of voting it is easy for rulers to believe their programs are the ‘true’ will of the people and hence more precious than the constitution and free elections.” Each is caught in a conundrum by his rejection of the rationality of public deliberation in attaining the public good. Burnham’s contribution

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to the war effort against Fascism was a celebration of the elite theorists whose doctrines contributed to the intellectual formation of the totalitarian ideologies; Burnham does not once mention that Mosca and Pareto, his “defenders of freedom,” welcomed Mussolini’s Fascism. It is downright strange to oppose Bonapartism by appeal to its most prominent apologists, and Burnham was too clever to have overlooked this paradox. There seems to be a hint of esoteric glee in Burnham’s construction.5 Neither does Riker acknowledge Pareto or Burnham as forebears. Pareto, Mosca, and Riker each have the best of liberal intentions. Pareto did value liberty and probably would not have remained loyal to the complete trajectory fascism followed after his death in 1923. But his love for liberty was blinded by a hatred for democracy. The Pareto (“A Few Points Concerning a Future Constitutional Reorganization,” in Bucolo 1980, 275) that Burnham recommends to us recommended to Mussolini that he preserve freedom of speech but merely the appearance of democracy: The only aim must be that of freeing oneself from the democratic ideologies of the sovereignty of the majority. Let this sovereignty retain its shadow – it ﬂatters powerful emotions – but let the substance pass to an elite for the objective good.

If he had lived, perhaps Pareto would have seconded Mosca’s (quoted in Albertoni 1987, 10, emphasis added) sentiments in a speech to the Italian Senate in 1925: “I who have always been sharply critical of parliamentary government must now almost regret its fall.” Or, who knows, if he had lived even longer, perhaps he would have applauded the antidemocratic views of the Chicago boys in Chile, for whom the virtue of authoritarianism was that it permitted the scientiﬁcally correct policy. Said one of them in defense of the military dictatorship: “A positive science with ideology ceases to be a positive science; ideology which is only positive science does not have an element of ideology” (Barahona, quoted in Barber 1995, 1946). Riker calls his enterprise “positive political theory” and those of his theoretical opponents “ideology.” I ﬁrmly believe that Riker’s intentions are wholly liberal. What I am saying is that one may innocently endorse a doctrine which unforeseeably necessitates consequences one would not endorse. Some fellow travelers, as Burnham and other anti-Communists pointed out repeatedly, irresponsibly endorsed doctrines of peace and freedom which had the unintended consequence of furthering violence and oppression. I suggest that the doctrine of democratic irrationalism may have illiberal consequences in the world that its liberal adherents do not intend.

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Introduction In this ﬁnal chapter, I recommend other scholars to those who want a more formal approach to these issues. Next, I show that all the instability and manipulation results for the polity have parallels for the economy, but that there is a double standard which endorses the results for the polity but rejects them for the economy. Finally, I return to the hall of quotations, with answers to the new academic attack on democracy. Those looking for a more formal approach can turn for complementary insights to Sen and his constructive social choice theory, beginning with his Nobel Lecture (1999). Sen reports that the ﬁrst response to Arrow’s theorem was, in politics pessimism about democratic decision making, and in economics despair about evaluating social welfare. The background to Arrow’s theorem was Robbins’s incredible claims that every mind is inscrutable to every other mind and that no common denominator of feelings is possible. Sen’s diagnosis, made in many rich formal contributions over several decades, is that the impossibility is due to unjustiﬁed informational restrictions: “It is not surprising that the rejection of interpersonal comparisons must cause difﬁculties for reasoned social decision, since the claims of different persons, who make up the society, have to be assessed against each other” (365). He also points out that Arrow’s original impossibility result should be no surprise, as in aiming to identify a unique rule one may undershoot and yield multiple possibilities, or one may, as did Arrow, overshoot and yield none. Saari, in advanced (2000a; 2000b) and in introductory (2001a; 2001b) texts, also provides comprehensive and innovative perspectives on the problems of aggregation. The current and forthcoming work of Christian List (e.g., Dryzek and List 2003, List 2001, 2002, 2003, List and Goodin 2001) also merits attention.

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Instability: neither everywhere nor nowhere Rowley (1993, xiii), in my hall of quotations, spoke most conﬁdently about how Arrow’s theorem provides incontrovertible support for market process and for the minimization of democratic government. W. Dean Burnham (1999, 2250), with less enthusiasm, concludes that, “In politics, unlike in economics . . . virtually no naturally occurring equilibria exist.” Kuttner (1996, 333–345), in his book on the virtues and limits of markets, says that such a view is widespread. In public choice theory, according to his muscular rhetoric: the demonized state makes an almost perfectly Manichaean mirror image of the idealized market. The sacred economy is at constant risk of being violated by a profane polity. The core claim is that systematic error and opportunism are as endemic and logically inevitable in the political enterprise as self-puriﬁcation is in the marketplace. That premise then gives Public Choice theorist an all-purpose trump to any demonstration of market failure: Yes, the market does perhaps fail from time to time, but political interference will only make it worse. Public Choice theorists, in their zeal to impeach economic intervention, go further and impeach democracy itself. (333)

He explains that these conclusions are deduced from axiom, logical inference, and extrapolation of the market model. The presumptions lead to a series of syllogisms that supposedly prove that politics leads to chaotic, rapacious, or perverse outcomes. The inevitable conclusion is that the political realm should be made as narrow as it can be. He says that Arrow’s impossibility theorem is the Rosetta stone of public choice and is cited as if to demonstrate once and for all the futility of political efforts at social betterment. The celebration of the market has become an insidious form of contempt for political democracy, he says, and public choice poses as an expert witness for the claim that political intervention in the economy should be minimized. The typical student of philosophy, politics, and economics these days would be taught, rightly on my view, the advantages of the market economy as compared to the command economy. In the worst case, the student would only be taught propaganda about the miracle of the market, but in the typical case she would be taught in a nuanced way about market successes and also about market failures: monopoly; undersupply of public goods; incomplete markets; externalities; information failures; business cycles, unemployment, inﬂation, and deﬂation. In the best case the student might debate some normative problems of the unmodiﬁed market economy, such as unjustiﬁed inequalities in social ofﬁces and product, unfair disparities in bargaining power, invasion of liberties by private corporations, displacement of family and friendship, expropriation of desires

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by advertising, and so on. One of the main points of the public choice movement is that welfare economics uncritically assumed that democratic government would unproblematically rectify market failures. They argue that government failure is as possible as market failure. This is a valuable point, but possibility does not mean necessity. The destructive response is to prohibit the democratic government from addressing market failures (actually, to prohibit it from correcting all market failures except for the protection of private property). The constructive response is to assess the actual likelihood of government failures and from theoretical and empirical considerations to devise institutions, beyond undiscerning inaction, that would minimize failures of both market and government. Although a successful democracy protects its citizens from military invasion, civil war, autocracy, market failures, poverty, criminality, and other injustice, these days one seldom hears anything about the miracle of good governance, despite the conspicuous variations in government performance across the world. The students in Harvard’s core course in politics are told that politicians are venal, immoral, disgusting scoundrels (Shepsle and Bonchek 1997, 5). If the market economy works better than the command economy, does democracy work better than autocracy? Not necessarily. Shepsle and Bonchek (67) continue that the choice is between incoherence and dictatorship: “There is, in social life, a tradeoff between social rationality and the concentration of power.” These are disturbing teachings. Would autocracy really be more socially rational than democracy? Just as it is an error to compare an actual market with an idealized government, so is it an error to compare an actual democracy with an idealized dictatorship. If egomaniacal redistributional instability is possible in a democracy, even contrary to its commitments to fairness, then instability is even more possible, and certainly more dangerous, in a dictatorship which lacks democratic commitments to fairness. Although under a dictatorship there is no longer any Condorcet-rule voting creating the potential for cycles, certainly there are many possible military coalitions who would want to depose the dictator and seize the social ofﬁces and product each for itself. If there are instabilities, they afﬂict not just democracy, but also dictatorship, and also the market. The student who is taught the doctrine of democratic irrationalism is not taught the parallel ﬁndings about the economy. The prejudice is pervasive. The third fundamental theorem of welfare economics, Arrow’s impossibility theorem, is stated pessimistically rather than optimistically: dictatorship is the only possible social-welfare function, and so forth, as we have seen in this volume. A more optimistic version of the third theorem would state that given individual orderings there are many

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possible social welfare functions that would yield a social ordering, and a few good ones. The optimistic version would go on immediately to state qualiﬁcations. It would say that if voters were wholly selﬁsh and lacked any preferences for fair outcomes, then redistributional instability would follow with Condorcet pairwise voting. It would go on to say if Condorcet voting were to be excluded for any reason, then any other social-welfare function for three or more alternatives would require more information than is available from pairwise comparisons. It would note in a jocular aside that if pairwise Condorcet voting were excluded, yet pairwise comparison insisted upon, then the only remaining voting rule would be the dictatorship of one. It would not write the Condorcet paradox of voting on the blackboard and declare democracy to be meaningless. The student is rarely taught that the Arrow impossibility theorem applies to the economy as well as to polity, although Riker and his students are aware of the point. Most strikingly, Riker and Ordeshook (1973) state that the market allocates resources in nontransitive ways (85), and continue that they are not worried by the Condorcet paradox of voting, because: People are not invariably disturbed by the inconsistencies and incoherencies of market outcomes – such as the oft-discovered fact that society spends more on liquor than education although surely a majority would wish otherwise. Markets have been churning out such inconsistencies for centuries without leading us to reject them as useful tools. (114)

Perhaps this passage is due to the inﬂuence of Riker’s coauthor, as the message of Riker’s later Liberalism against Populism (1982) is not so placid. Ordeshook (1982) contested Riker’s later hypotheses of the pervasive disequilibrium of politics. Ordeshook responded that “the presumed stability of markets resides principally in our abstract description of them and not necessarily in reality” (26) and that social-choice results do not prove “something unsavory or even disturbing about democratic processes in particular and political processes in general” (31). In the same volume, Fiorina and Shepsle (1982) suggest that the differing emphases on equilibrium in economics and on disequilibrium in political science are due to professional incentives. In economics, “only equilibrium-preserving extensions of models are of interest (i.e., publishable)” (60). Positive political theory, however, follows in the footsteps of Arrow’s impossibility theorem in emphasizing disequilibrium. Presumably, models showing political equilibrium and democratic possibilities are not as publishable as those proclaiming paradoxes and impossibilities. It could have been otherwise, they suggest: “Political theorists might have decided early on that

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unidimensionality was a basic assumption of all political models, akin to the regularity conditions imposed on consumption and production sets by economists” (Fiorina and Shepsle 1982, 60–61), and economists could have followed up on an early observation that “instability seems to be a universal phenomenon in competitive economies rather than an exceptional one.” Further, they insist, as I have, that “Equilibria and disequilibria are properties of models. It remains to be demonstrated whether they are descriptive of empirical phenomena” (62). In the same volume, Schoﬁeld (1982), in response to Riker’s observations about the possibilities of manipulation in the polity, reviews possibilities of manipulation in the price system, and explores further parallels between political and economic instability. I applaud all this good sense, but I am afraid that it is not often declared in the rhetoric and pedagogy of the doctrine of democratic irrationalism. In contrast to the pessimistic phrasing of the third fundamental theorem, the ﬁrst fundamental theorem of welfare economics is phrased optimistically, as a marvelous possibility: the economy is in competitive equilibrium and the equilibrium is Pareto optimal, or, “laissez faire leads to the common good” (Feldman 1991). Riker (1980, 434) celebrates the scientiﬁc and intellectual success of the price theorists; he says their discovery of the competitive equilibrium makes economics the most prestigious of the social sciences. The ﬁrst theorem is a formalization of Adam Smith’s invisible hand. In the equilibrium each consumer maximizes her utility given her budget constraint, each ﬁrm maximizes proﬁts given market prices, and the market for each good clears (there are no shortages or surpluses). Yes, the theorem is taught in a nuanced fashion; qualiﬁcations are immediately stated. The theorem holds only if each agent is selﬁsh, only if each agent is a price-taker rather than a price-maker, and only if each agent knows all prices for all goods. It is sometimes acknowledged that Pareto optimality is a troublesome welfare criterion: those who start off rich end up rich, those who start off poor end up poor, and nonexchange transfers from rich to poor are prohibited because it would make the rich worse off by the Pareto criterion. Why not phrase the theorem in a pessimistic fashion? We could observe that not all agents are price-takers, there are monopolists. We could observe that not all agents are selﬁsh, that some care about what happens to others, or observe that there are many other externalities. We could observe that it is the rule and not the exception for agents to have asymmetric information about goods and prices. We could observe any of these facts about the actual economy, and then go on to state that high economic theory proves that, given a number of innocuous conditions, there is no competitive equilibrium in the economy.

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Even small information costs can have large consequences and many of the standard results – including the welfare theorems – do not hold even when there are small imperfections of information . . . whenever information is imperfect or markets (including risk markets) are incomplete – that is, essentially almost always – competitive markets are not constrained Pareto efﬁcient. (Stiglitz 2000)1

The market is arbitrary and meaningless. The evidence is all around us, witness depressions, speculative bubbles, involuntary unemployment, useless consumerism, have we got some stories! Dot-com entrepreneurs who waste other people’s money are paid a thousand times what teachers or nurses are paid for taking care of human beings! Americans buy unsafe gas-guzzling SUVs that waste a nonrenewable resource, contribute to global warming, make them international pariahs, and involve them abroad with detestable autocracies! That would be an unhelpful interpretation of the ﬁrst theorem, but I make it to illustrate that there is a double standard: the market is presumed to be stable and good, and democratic governance is presumed to be unstable and bad. Similarly, elsewhere in public choice, markets are presumed to be efﬁcient, no matter how far-fetched or unempirical the explanation required to excuse monopolistic behavior or other economic ﬁasco, and democratic governance is presumed to be inefﬁcient, even if empirically vindicated (Hovenkamp 1990b; and see Wittman 1995). What else? The competitive equilibrium assumes that there is no force or fraud on the market. Homo economicus will haggle to death over price but will never take what he wants by force; he operates ruthlessly within a strictly deﬁned bubble of sainthood, according to Skaperdas (2002). If the constraints of peace and honesty are removed, then the pursuit of material self-interest degenerates into a political economy of lord and serf. One agent specializes in forceful expropriation, and gets more compensation, and the other agent specializes in production and gets less compensation, says Skaperdas. I add that force and fraud are potential threats on markets, but are generally low in incidence; similarly, unfairness is a threat in democratic voting, but is generally low in incidence; and presumably there are various moral and material incentives in each realm that constrain such threats. Nevertheless, it’s considered legitimate for the market model to assume the absence of force and fraud, but illegitimate for the democratic model to assume a minimal concern for fairness. The competitive equilibrium of the economy stated in the ﬁrst theorem is static, not dynamic. What students are usually not taught about the economy is that it is possible that there is no dynamic process that leads to the competitive equilibrium, or, worse, that it is possible that the competitive equilibrium is unstable in that the smallest perturbation leads the economy away from it and into a cycle of prices or into complete

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chaos. Our friend, the cycle, as a matter of logical possibility, afﬂicts the market as it afﬂicts voting. Scarf (1960) began from the standard setup – individuals with utility functions for the same commodities, who trade beginning from initial endowments of those commodities, and respond to the announcement of an initial vector of prices, and if that vector is the competitive equilibrium then all markets clear. The ﬁrst theorem says nothing about what happens if the initial vector of prices is not the competitive equilibrium. Scarf assumed three agents and three goods, and assumed utility functions obtained by cyclic permutation of the goods and the initial endowments. What happens is a process such that prices fall away from the unstable equilibrium and revolve in an endless cycle. We could apply ideas from the doctrine of democratic irrationalism and argue further that because such a cycle could happen in any one instance, it could happen in all instances, and thus that preferences on the market are unknowable, and hence that market outcomes are meaningless, etc. It is logically possible that the dynamic economy is in complete chaos, paralleling the McKelvey–Schoﬁeld model of voting chaos. The mathematician Donald Saari (1995b) says that standard price-adjustment models admit highly chaotic behavior: I have no idea whether Adam Smith’s invisible hand holds for the “real world,” but, then, no one else does either. This is because, even though this story is used to inﬂuence national policy, no mathematical theory exists to justify it. Quite to the contrary; what we do know indicates that even the simple models from introductory economics can exhibit dynamical behavior far more complex than anything found in classical physics and biology. (222)

Saari explains what is called the Sonnenschein, Mantel, and Debreu theorem in economics. If there are at least as many agents as commodities in the economy, then there exist endowments and individual preferences such that “anything can happen!” (224, emphasis added). Demand could go up and price would go down. Saari goes on to deny that this instability ﬁnding is due to implausible preferences or to an overly simplistic model. He does ﬁnd, in what he believes to be a more comprehensive model, that “while an unregulated free market might not work as widely advertised, if correct regulations are imposed, the market now might behave as desired” (227). To further the mischief, I would add that perhaps multidimensional instability is more tractable in democracy than in the market, because in a democratic setting any one person can move to divide the question and thus reduce to single dimensions the issues under consideration. The irrationalists’ main point is not the inconsistency of the polity, but its manipulability and consequent meaninglessness, it may be objected.

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Unlike democracy, the market is not susceptible to such manipulation. Wrong. First, just consider the process of buying a used car. Second, as an abstract possibility, the problem is general in the economy, but is claimed not to be of wide practical importance. The Gibbard–Satterthwaite theorem about manipulation by strategic misrepresentation of preferences does not directly apply to market mechanisms, because economists do not demand the universal domain condition for the economy. Satterthwaite (2001) argues nevertheless that, “no attractive social choice functions exist for markets that are both strategy-proof and efﬁcient.” Market theory disposes of the problem by assuming that all agents are price-takers and thus nonstrategic. He illustrates market manipulability with an example. The cost of a product is 0.55 for a seller, its value 0.8 for a buyer, and since value exceeds cost, efﬁciency demands trade. The Walrasian auctioneer announces a price of 0.5, the seller declines, and the buyer is still willing. The auctioneer announces 0.6, but the seller decides to hold out for 0.7, and the buyer is still willing. A price-taking seller would have stopped at 0.6. The auctioneer announces 0.7, and trade is consummated at that price. But what if the seller’s value had been 0.68? Then the buyer would not have been willing at 0.7, and there would have been no trade. There is both an incentive for misrepresentation and a potential for inefﬁciency. It is interesting how such a problem is addressed in the discipline of economics. Satterthwaite observes that “people often act as if markets were strategy-proof,” indicating the empirical implausibility of the manipulability result. He presents a model of a double auction as a Bayesian game, which shows that as the number of agents in the market increases, equilibrium strategic behavior decreases rapidly toward zero and full efﬁciency is rapidly approached. Numerical examples suggest that a market of size 8 or better would be approximately, not exactly, strategy-proof. Thus, he argues, price theory is justiﬁed to ignore the possibility of manipulation, and exact strategy-proofness is too strong a requirement. Scarf ’s exposition of the market cycle suggests as one interpretation that such cycles actually happen, but alternatively suggests that the model is not realistic, or that similarity of utility functions would avoid the result. In positive economic theory, theoretical bads are trumped by empirical goods, and empirical bads are trumped by theoretical goods. In positive political theory the obverse obtains. I like how Saari (2001b) narratively generalizes the aggregation problem. Such problems are everywhere: the market, voting, sports or scholarship or any kind of nonmarket and nonpolitical ranking, engineering decisions, individual choice among multiattribute alternatives, some

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statistical manipulations. With respect to engineering, for example, a complex project is analytically decomposed into a number of simpler tasks, and then the results of the simpler tasks reassembled. In the process of analysis and synthesis, however, crucial information can get lost, resulting in perverse syntheses. That is just what happens with Arrow’s independence condition: it requires social decisions to ignore the full information available from individual orderings, and from discussion, and insists on only the diminished pairwise information from them. The independence condition is like a reader who only counts letters, rather than considering their relationship to one another: 3-t, 3-a, 2-s, 1-h, 1-m, 1-i, 1-k, 1-e, 1-’.2 Yes, a well-informed person should be aware that poorly designed aggregation can yield perverse results, but she should also be aware that well-designed aggregation can yield useful results. Talking back in the hall of quotations Think back to the hall of quotations presented in Chapter 1. Among the voices, Wolff (1970) initially seems to be the most consistent. He says that the Condorcet paradox of voting infects all democratic social choice, and suggests that there is no alternative but to embrace the doctrine of anarchism. Rowley (1993), to avoid the sting of Arrow’s impossibility theorem, recommends a minimal state rather than no state, and a full market. Shepsle and Weingast (1984) argue that the cycling legislature cannot reliably correct market failures. Tribe (1988) recommends a fuller state, but suggests that because of the Arrow theorem, courts know better than legislatures. Tushnet (1988) corrects Tribe, noting that the Arrow theorem would apply to the courts as well. If judicial guardianship fails, that would seem to leave nothing but the market, but we have seen in this chapter that the market is tainted as well. Thus, even Wolff falls short. Perhaps the most consistent position would be to abolish both state and market? But that would violate Condition P (if everyone prefers Metallica to AC/DC, then society prefers Metallica to AC/DC). All social life is impossible, according to consistently extended irrationalism. Katznelson and Milner (2002) say that the fall of the Weimar Republic and other democracies, and the rise of Fascism and Bolshevism in the ﬁrst half of the twentieth century, were due to the democratic instability shown by Arrow. However, if democracy is inherently unstable, but dictatorship is not, then how is it that Fascism and Bolshevism are gone from the scene, but many democracies remain? W. Dean Burnham (1999) ascribes the rise of the Nazis and, in contrast to Katznelson and Milner, the fall of the Bolsheviks, to political disequilibrium. The Soviet regime lasted some 75 years, however, hardly unstable compared to typical regime durations.

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Observe that the disequilibrium hypothesis explains everything – and nothing. Runciman (1963) says that the intuitive criteria of the Arrow theorem show that strict democracy is impossible, Tuck (1993) that Arrow showed scientiﬁcally that the program of the citizens making social decisions does not make sense, Cain (2001) that all voting systems have some normative blemish, and Samuelson (1977) that an ideal voting scheme cannot possibly be found. There is no ideal voting system, in the same sense, however, that there is no ideal dinner, no ideal residence, and no ideal holiday, simply because there are always tradeoffs among desiderata. Even if one voting rule is close to ideal, anyone can propose a new desideratum that the scheme is bound to lack. Given a set of desiderata, we are able to say that some voting rules are better or at least as good as some others, and to say why. It is especially disappointing that economists would be surprised to ﬁnd tradeoffs in the choice of one voting rule over another in various circumstances, since emphasis on tradeoffs and constraints is a hallmark of that discipline. Riker and Weingast (1988) say that cycles are ubiquitous, Plott (1976) that cycles are the case not the exception, Sunstein (1988) that cycles make accurate aggregation highly unlikely, and Katznelson and Milner (2002) that instability is an immanent feature of liberal democracy. This volume studied simulations, actual preferences, and anecdotal allegations and found a nearly complete absence of cycles. Further, it offered theoretical explanations for the rarity of cycles, suggested that most cycles which might occur would be of trivial consequence, and that there exist defensible voting methods that avoid cycles. Hardin (1993) says that no government of a complex society is likely to be coherently democratic, Bell (1974) that public decisions have no rationality, Przeworski (1991) that voting results do not identify any unique social preference, and Shepsle and Bonchek (1997) that it’s nearly impossible to arrange for the making of fair and coherent group choices. Yet there are no systematic or casual observations of the radical instability predicted by irrationalist theory. Riker and Weingast (1988), Mashaw (1989), Sunstein (1988), and Cain (2001) warn of the ubiquity of strategic voting and agenda control, but we have seen that these are only of consequence when institutions unfairly grant some actors more formal power than others, directly contrary to the democratic ideal, and that such defects are remediable. Next, who knows how many boxes of chalk and barrels of ink have been expended on explications of McKelvey–Schoﬁeld multidimensional chaos (“from [1976] on, political science as a discipline faced no more pressing challenge than to interpret and incorporate these profound instability results,” G. Miller 1997, 1,185)? Yet the simple parliamentary rule

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allowing any one member to request division of the question disposes of the problem, as does strategic voting in many circumstances, constraints on leadership, or a switch from Condorcet voting to Borda or other methods. Nevertheless, Riker and Weingast (1988) say that there is a fundamental arbitrariness to social choice under majority rule, Mashaw (1989) maintains that literally anything can happen when votes are taken and that apparently democratic decisions are the artifact of decision processes controlled by manipulators, Cain (2001) that we cannot validly infer anything about the preferences of the society based on laws produced by a legislature, and Shaviro (2000) that legislative enactments are random and purposeless. This is a startling hypothesis and one is entitled to ask: Are there any demonstrations that actual democratic decisions from a proper sample are uncorrelated with the preferences of the voters making those decisions? There are not. Feldman (1980) doubts all assertions about a general will, a social good, or even a social beneﬁt; Plott (1976) says that the public good cannot, in principle, exist; Ordeshook (1986) that there is no public interest or community goals; and Riker and Weingast (1988) that the will of the people has no meaning. If so, then no one, including scholars of the irrationalist bent, would be justiﬁed in recommending to us social institutions or social policies of any kind. Katznelson and Milner (2002) insist on a tradeoff between stability and democracy, Arrow (1963/1951) claims that in the noncomparabilist framework dictatorship is the only satisfactory social-welfare function, and Shepsle and Bonchek (1997) suggest that only “permitting dictatorship” avoids social irrationality. Is Arrow’s independence condition, that all voting rules should proceed only by pairwise comparison of alternatives, more normatively compelling than the choice of democracy over dictatorship? Conclusion The old academic attack on democracy in the late nineteenth century and early twentieth century, especially by the elite theorists Mosca, Michels, and Pareto, contributed to the retreat of democracy and the rise of Fascism and Bolshevism. If democracy is impossible and fraudulent, then superior individuals should impose the objective good, is the conclusion that others drew from the elitists’ hard-headed theories. There is a limited range of reﬂexivity in social life, such that, for instance, a powerful belief that democracy is impossible and fraudulent creates the situation it deﬁnes. Elitism was eventually refuted, and democracy revived, by the fruits that each bore. The new academic attack on democracy

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resuscitates discredited elite theory with the formally authoritative tools of social choice theory. The new academic attack on democracy fails, theoretically and empirically. The irrationalist interpretation of the Arrow theorem and associated social choice results is one of the bigger intellectual errors of the second half of the twentieth century. Its long, dark shadow over democratic politics is now lifting. Democracy is on the march in the world today. The Chinese students constructed a goddess of democracy in the days before their blood stained the ﬂagstones.3 The statue shines bright in images of the demonstration. For all those who battle against tyranny and for democracy, know that in theory, too, democracy shines resplendent.

Endnotes

2.      1. “Rochester school” refers to an intellectual tendency, not a place. It should not be assumed that former or current students or faculty from the Rochester Department share all or any of Riker’s views. 2. Quoted from http://www.rochester.edu:8000/college/PSC/intro/history.php 3. Quoted from http://www.rochester.edu:8000/college/PSC/graduate/intro.php 4. For a rational-choice account of political leadership, particularly the chairing of a political science department, see Shepsle and Bonchek (1997, ch. 14). Compare to Jane Mansbridge’s (1994, 156) remarks on public-spiritedness and chairing of an academic department. 5. I belong to the Public Choice Society, which welcomes scholars of all varieties to its ranks. 6. See Brennan and Lomasky (1993) for a profound examination of the paradox of participation. 7. See Cox 1999 for an alternative defense of rational choice, and generally for examples of healthy rational-choice research. 8. The exemplar of constructive social choice theory is Amartya Sen. See his Nobel lecture (1999).

3.     1. See Grofman and Feld (1988) and Grofman and Owen’s (1986) symposium on information pooling. 2. See Levin and Nalebuff 1995 on further pragmatic criteria for selecting a voting rule. 3. See Grofman and Reynolds (2001) for a recent “inventory of main ﬁndings” on electoral systems. 4. There is an emerging public discourse in America on alternatives to plurality elections. See Hill (2002), and Center for Voting and Democracy (www.fairvote.org) for introductions. 5. My account is adapted from Farrell (2001, 150). 6. Bradley (1995); although there is small evidence of nonmonotonic results in a recent election, Gallagher (1999). 7. Disputed by Dummett (1997), who suggests, without argument, a conservative 2 percent incidence rather than Allard’s 0.28 percent. 444

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4.       1. Philosophy too has moved many decades beyond the logical positivism that originally justiﬁed the ordinalist revolution. See Grifﬁn (1986, esp. 106–126) for an example.

5.         1. Michael Munger gave me this story. 2. I am adapting from Collie’s (1988) useful summary. See Lutz and Williams (1976) for a decisive survey of empirical evidence against the minimumwinning coalition, and Hardin (1976) and Grofman (1984) for further objections. 3. Shepsle and Weingast (1981), Niou and Ordeshook (1985). 4. For legislative discourse see, for example, Fenno (1966) on appropriations, Wildavsky (1974) on the budget, and Conlan, Wrightson and Beam (1990) on taxation. Wildavsky (1974, 17) points out that legislative budgeters distinguish the base, from which annual considerations begin, from the fair share, what the budgeted item is due. 5. That some give some to an anonymous recipient indicates some altruism; and contributions triple when the recipient is truthfully identiﬁed as a reputable charity (the Red Cross, see Eckel and Grossman 1996). 6. According to http://www.theindependent.co.zw/news/2002/August/Friday16/ muckr.html, he made the statement to the Sunday Times (presumably of Africa). 7. If people rank fair distribution second, but use plurality rule, which only counts ﬁrst preferences, then the voting rule would force unfair outcomes from moderately fair voters. See Reilly (2001). 8. Lewin (1991) also ﬁnds that the public-choice hypotheses of politicians as vote-maximizers and bureaucrats as budget-maximizers are unsupported by the evidence. There is an important difference between exploring such assumptions on an “as-if ” model-building basis, and mistakenly believing them to be true.

6.            1. Keith Dowding, Christian List, and Bruno Verbeek saved me from many major and minor errors in an earlier draft of this chapter. They are not to blame for those that remain. 2. Arrow’s Condition I is the conjunction of two conditions that can be written separately: one requiring ordinal measurability and no interpersonal comparisons, and another purely the independence of irrelevant alternatives. 3. Arrow’s book was dated 1951, and he published a 1952 article summarizing its ﬁndings. The 1951 book was reprinted in 1963, containing an important addendum which updates and responds to critics.

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4. Sen (1970), Plott (1971), Hansson (1973), especially Ray (1973), McLean (1995), but for another view see Bordes and Tideman (1991). 5. My example is adapted from Goodman and Markowitz (1952). 6. Sen (e.g., 1982, 330) blames the exclusion of non-utility information and the exclusion of any utility information involving interpersonal comparisons for the impossibility result. Both Saari and Sen ﬁnger the exclusion of available information as the culprit. 7. Christian List (2003) argues that even within the veriﬁcationist framework, the empirical “meaninglessness” or underdetermination of interpersonal utility comparisons does not imply the impossibility of such comparisons. 8. A positive afﬁne transformation is f(x) = a + bx, where a and b are real numbers and b > 0. 9. Social choice rules such as – do whatever the Bible, or the leader, says to do – need not weight voters. 10. The ranking computation of the Borda count “is a purely formal operation on ordinal comparisons and should not be interpreted as a cardinal utility” (Kelly 1988, 71). 11. The Condorcet case, however, does not violate either of the independence conditions.

7.      1. Stratman 1997 is my main source for this section, although the controversial interpretations are mine. 2. Stratmann (1997, 330) claims that logrolling implies cycling, but among the references he cites is Bernholz (1975, 961) who is concerned to correct this very error: “it is easy to show that logrolling does not necessarily imply the paradox of voting, nor does the paradox of voting imply the existence of logrolling situations.” 3. Strom 1990, 183 attributes to Riker (1980a) the “conclusion that legislators have little incentive to grant agenda control to either individuals or groups.” A case might be made that this is an implication of Riker (1980a), but this is certainly not Riker’s published position. Riker (1980a) was recycled into Chapter 7 of Riker (1982) on agenda control, under examination here, which claims that agenda control is ubiquitous. Riker’s (1993, 1) introduction to his edited volume on “agenda formation,” continues the theme “that making agendas seems just about as signiﬁcant as actually passing legislation.”

8.   1. For example, Ordeshook (1986, 81): “Some interpret [McKelvey’s theorem] mistakenly to mean that ‘anything can happen’. . . . In his original essays, however, McKelvey is careful to limit the implications of his analysis.” 2. This and the next two paragraphs borrow from Strom (1990, 115–125). 3. Hume’s Enquiries was ﬁrst published in 1777.

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9.   :    1. Then and now, Alabama schools, contrary to the national pattern of local revenue support, rely on state and federal funds, more even than neighboring southern states (Thomas and Stewart 1988, 85; personal communication, 2002, Brad Moody, Auburn University). Thanks to its New Deal Democrats, Alabama was the most liberal state in the south in the early 1950s; and civil rights controversies affected state elections later in Alabama than in neighboring states (Barnard 1974, 4; personal communication, Moody). 2. For the record, those who voted nay on the passage of the School Construction Bill in 1956 (Congressional Record Roll-Call Vote No. 92, Congressional Quarterly Vote No.48) who also voted nay in 1957 on the motion to strike the enacting clause of the School Construction Assistance Act (Congressional Record Roll-Call Vote No. 154, Congressional Quarterly Vote No.56: Andrews (D-AL), Elliot (D-AL), Grant (D-AL), Huddleston (D-AL), Jones (D-AL), Rains (D-AL), Roberts (D-AL), Selden (D-AL), Hays (D-AR), Trimble (D-AR) Natcher (D-KY), Siler (R-KY) Ford (R-MI), Judd (R-MN), Jones (D-MO), F.P. Bolton (R-OH), Albert (D-OK), Steed (D-OK), Fenton (R-PA), Kearns (R-PA), McConnell (R-PA, not recorded vote for 1957), Reece (R-TN), Byrnes (R-WI), and Laird (R-WI). 3. For the record, those who voted aye on the passage of the School Construction bill in 1956 (Congressional Record Roll-Call Vote No. 92, Congressional Quarterly Vote No. 48) who also voted aye in 1957 on the motion to strike the enacting clause of the School Construction Assistance Act (Congressional Record Roll-Call Vote No. 154, Congressional Quarterly Vote No. 56, Hosmer (R-CA), Scudder (R-CA), Sadlak (R-CT), LeCompte (R-IA), Fallon (D-MD), O’Neill (D-MA), Meader (R-MI), Cannon (D-MO), Hull (D-MO), Becker (R-NY), Bosch (R-NY), Derounian (R-NY), Keating (R-NY), Ostertag (R-NY), Radwan (R-NY), Taylor (R-NY), Feighan (D-OH), Dogue (R-PA). 10.   :    1. Voteview is an indispensable computer program which contains all US Congressional Roll Call votes, and allows for location of Representatives and Senators in a two-dimensional space. See Poole, Rosenthal, and Shor (1999). 11.   :    1. My account relies mostly on Morrison (1967); somewhat on DeVoto (1957) and Sellers (1966); and on relevant portions of the congressional record cited in the text. 2. I rely on Morrison (1967, 21–37). 12.   :     1. Throughout this chapter I rely primarily on McPherson (1993), with much detail from Potter (1976) and some detail from Nevins (1950). These are standard texts on the history of the period prior to the Civil War.

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2. On immigration I rely on Fogel 1992. 3. The platforms are reprinted in Morison (1971, 1123–1127). 4. Here we turn to Dumond’s close study (1931, 92–96). 13.    1. The subﬁeld of international relations could suggest additional causal hypotheses relating to the outbreak of war in general and civil war in particular. 2. Although I differ in minor details of the analysis, I am persuaded by Jenkins and Morris (2002) that the new evidence they develop strongly supports the view that the Southern Democratic leaders behind Breckenridge wanted a Lincoln victory in order to better justify secession. 14.      1. The records of the Federal Convention are found in Farrand (1966). References to the volumes of Farrand (1966) are indicated by the speaker’s name and a Roman numeral followed by a page number, for example – Madison, II 500. References to Roll Calls – for example, #12 – are also to Farrand (1966). 2. At this time there was slavery in both the North and the South, but it was much more important in the South. 15.    1. In Lagerspetz (1997) there was doubt about the position of the SFP. Since then, Lagerspetz has done further research, and communicates to me that the ofﬁcial position of the 25 SFP members was SV > ST > KA > TA. 16.   1. See also Cowen (1993), Kavka (1991), compare Gillroy and Wade (1992). 2. I have grown to dislike the word heresthetic, and do not encourage its adoption; I use it only in order to expound Riker’s doctrine. 17.    1. After writing these passages I discovered that the younger Riker (1953, 158– 160) argued forcefully and at length that the Civil War was due to the antimajoritarian features of the constitution. 2. A thinker’s political allegiances are irrelevant to judging the quality of his or her argument. However, if a thinker makes normative political recommendations, and those recommendations fail to work as intended, then the fact of failure does reﬂect on the content of the argument. A thinker might make a brilliant argument that, if party members were well intentioned, a one-party state would have beneﬁcial consequences; but the consistent failure of such schemes relevantly undermines the claim. 3. Pareto’s Mind and Society (1963) was originally published in 1935.

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4. A sympathetic commentator notes “Pareto’s private prejudice against parliamentary democracy. He was always reiterating that he held no such prejudice, that his work was scientiﬁc, not subjective. This is absurdly false. In some cases he let his prejudices obtrude by slipping in implicit value-judgments, in others by using loaded terms, by sarcasms, abuse and imputations of baseness” (Finer 1966, 65). Compare Riker’s vituperation of ideologues, quoted above. 5. In the McCarthy years, the Leninist but anti-Stalinist Independent Socialist League (ISL) sought removal from the Attorney General’s list of subversive organizations. Anti-Communist Burnham was subpoenaed to be the main, but reluctant, witness against his former comrades in the ISL. The government’s case collapsed when Burnham testiﬁed under oath that he would lie under oath if he thought it his patriotic duty (Wald 1987, 277). This is both a double deception and a triple deception. 18.   1. See Bowles and Gintis (2000) for another sophisticated retrospective on the competitive-equilibrium model. 2. Or, “That’s a mistake.” 3. Given recent events, I must note that democracy is a matter for the people involved to develop, not a matter for outside powers to impose by deception of force.

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Index

Adams, John Quincy 1–4, 56, 299–300, 301, 382–383 Africa 1, 420 African–Americans, voting rights and the Depew amendment 218, 219, 223, 224 agenda control 5, 17, 35, 72, 158, 159, 160, 166–171, 384 and academic attacks on democracy 441 and the Depew amendment 219 frequency of 193 and majoritarian processes 10 and multidimensional disequilibrium 378 and multidimensional issue spaces 178, 196 and Riker Art of Political Manipulation 407 basic argument pattern 37 case against populism 410 defense of liberalism 412 and voting methods 9 see also new dimensions agenda-setting 15, 344, 383 agricultural appropriations (1958) 21, 310–311, 329–334, 377 and the Andersen amendment 330 and the Javits amendment 329, 330, 331 and the O’Toole amendment 329, 331 and the Whitten amendment 329, 330, 331–332 Alexander II, Tsar 420 Amadae, S.M. 24, 28 American Civil War 20, 191, 302, 309, 407 and the Depew amendment 223, 225 and Pareto 427 and Riker’s disequilibrium hypothesis 428

468

and Riker’s liberalism 422 and slavery 293, 294, 295 and the Wilmot Proviso 240, 243 American Political Science Review 23 American Psychological Association (APA), presidential elections 49, 86 anarchism 440 antidemocratic doctrines 3 antiplurality see negative plurality approval voting 44, 45, 48, 66 accuracy 64–65 and the APA presidential elections 49 and Arrow’s possibility theorem 89 and the Copeland method 50, 51 evaluation 70, 72 and the Lincoln election 260, 277, 278, 279, 281 Arab world 1 Argentina, populism in 420 Aristotle 10, 29 Arnold, Matthew 2 Arrow, Kenneth 4, 10, 15 condition of unrestricted domain (U) 17, 93–94, 95–122 and cyclebusting voting rules 113–122 and redistributional instability 99–108 and self-interest 108–113 and simulations of homogeneity 96–99 contraction-consistency independence condition (IIA (RM)) 124, 140, 146, 151, 375 and democratic instability 440 on dictatorship 442 impossibility theorem 3, 10, 15, 16, 17, 70, 72, 329, 375 and academic attacks on democracy 440, 441, 443 collective choice rule 80

Index Condition D (nondictatorship) 81, 93 Condition P (Pareto principle) 81, 92–93 and the Condorcet paradox 8, 78–79, 80, 82, 84, 85, 89 and cycling 83, 86–92, 410 and the economy 434–435 independence of irrelevant alternatives 81 justifying the theorem’s conditions 92–94 and the market 22, 30 and new dimensions 378, 379, 384 and the paradox of voting 5, 35 and positive political theory 435 and the Powell amendment 43 and public choice theory 433 and Sen’s constructive social choice theory 432 and social choice theory 70, 72, 76, 78, 85 and social states 79 and voter preferences 39 independence condition (IIA) 17, 56, 123–157, 440, 442 consequences of 146–150 and constitutional engineering 157 as defending the wrong principle 124–131 ﬂawed irrelevance justiﬁcation in 136–142 and independence 151–156 and justiﬁcation of voting rules 142–146 and the market model of democracy 28 and multidimensional issue spaces 192, 196 public choice theory 10–13 Riker’s attempt to demonstrate an Arrovian cycle 310–311 and Riker’s theory of dimensional manipulation 292–303 and the Rochester school 24 Social Choice and Individual Values 76, 83, 127, 143 and strategic voting 161 Asia, populism in postcolonial 420 Athens, elections in 29 Austen-Smith, David 24, 162, 215 Australian House of Representatives 65 axiomatic approach 16 balanced and unbalanced cycles 117–122 ballots, infeasible or irrelevant alternatives on 136

469 Banks, Jeffrey S. 24 Barker, Ernest 2 Baron, David P. 102 Barry, Brian 123, 143 Bayesian Nash equilibrium, and the Powell amendment 197, 207 Beer, Samuel H. 421 Bell, Daniel 441 Bell, John 20, 258, 259, 267, 268, 269, 270, 271–279, 285 Benson, Lee 300 Bentham, Jeremy 419, 421 Bentham voting method 52, 53, 54 Berlin, Isaiah 421 bipolar-culture assumption, and Condorcet efﬁciency 48 Bjurulf and Niemi, on Scandinavian parliaments 21, 335–336, 344–353, 377 Black’s rule 48 Blydenburgh, John C. 21, 362 and the Revenue Act (1932) 21, 335, 337–344, 376 Bohman, James 382 bolshevism 10, 440, 442 see also communism Bonapartism 430, 431 Bonchek, Mark S. 15, 29, 68–69, 336, 434, 441, 442 Borda count 5, 6, 7, 8, 9, 44, 45, 51, 55, 442 accuracy and fairness 64, 68, 70–71 and agenda control 167–168, 169–172 and agricultural appropriations (1958) 333, 334 and the APA presidential elections 49 and Arrow’s independence condition 123, 124, 125–126, 127, 128, 138, 141 consequences of 147, 150 and independence 151–153 justiﬁcation of 144–146 and manipulation 154–155, 156 and cardinality 78 and Condorcet efﬁciency 48 and the Copeland method 50, 51 and cyclebusting 114, 117, 118, 120, 121 and the Danish parliament election 371, 372 evaluation 55–56, 59, 61, 62, 63, 64, 67, 68 and the Finnish Electoral College 364, 365, 366 and impartial-culture assumptions 48, 54

470

Index

Borda count (cont.) and individual preferences 392 and the Iowa corn vote 369 and the Lincoln election 259, 273, 277, 279, 281 and multidimensional issue spaces 184, 191 and the Muscle Shoals vote 356, 357 and numbers of parties 66 and plurality grading 60–61 as positional voting method 46 and the Powell amendment 200 and public opinion on US military intervention overseas 374, 375 rankings 52, 53 Riker’s recommendation 70–71 and simulations of homogeneity 97 and social homogeneity 49 and strategic voting 65 winners 50 Boudinot, Elias 298 Brazil, populism in 420 Breckinridge, John C. 259, 260, 267, 268, 269, 270, 271, 272, 273, 274–276, 285 Brennan, G. 102, 136, 166 Britain elections 59, 87 Labour Party working party on electoral reform 69 as a populist society 421 Buchanan, James 28, 264, 266, 288–289, 290, 291, 395 Buckley, William F. 425 Budge, Ian 91 Bueno de Mesquita, Bruce 24, 26, 28, 344 Burnham, James 409, 425, 429, 430–431, 433, 440 Butler, Pierce 323 Cain, Michael J.G. 15, 441, 442 Californians for Electoral Reform 53 Calvert, Randall L. 215 Cambodia, Khmer Rouge 420 Cambreleng, Churchill 249 Carlyle, Thomas 2 Chamberlain, John R. 49, 86 chaos theorems see McKelvey and Schoﬁeld chaos theorems Chile 425, 431 presidential election (1970) 59 China and democratic irrationalism 425 student movement for democracy 2, 4, 443

Citrin, Jack 109 coffee-break cycles 337, 372–376 Cohen, Jerry L. 49, 86 Cohen, Leonard 443 Cohn, Jonathan 25, 28 Cold War 1 collective decision making, paradoxes of 15 Collective Rationality, and Arrow’s independence condition 127 communism 1, 420, 423 Condorcet criterion 55, 56, 61–62, 68 see also pairwise comparisons Condorcet voting method 5, 7–9, 28, 35, 44, 55, 387, 435, 440 and American presidential elections 88 as an ideal rule 68 and the APA presidential elections 49 and Arrow’s condition of unrestricted domain 99–100, 108 and Arrow’s independence condition 124, 128, 138–139 consequences of 147 and independence 151–153 justiﬁcation of 144–145, 146 and manipulation 154–155, 156 and Arrow’s theorem 8, 78–79, 80, 82, 84, 85, 89 Condorcet efﬁciency 47–48 and social homogeneity 49 Condorcet-consistent rules 56 and the Copeland method 50 and cyclebusting 114 and the Danish Parliament election 371 and the Depew amendment 219 and dictatorship 434, 435 evaluation 55, 58, 59 and the Finnish electoral college 364, 365 Jury Theorem 63 and logrolling 163 and multidimensional issue spaces 176, 184, 186, 187 pairwise ordering 49 rankings 52, 53 and the Revenue Act (1932) 337 and self-interest 113 switch to other methods 442 see also pairwise comparisons Condorcet winners 44–45, 46, 49, 50, 51, 70–71 and agenda control 169 and Arrow’s condition of unrestricted domain 99–100

Index and public opinion on US military intervention overseas 374 and simulations of homogeneity 96–99 and US Senate deliberations on Muscle Shoals 336 consumer economics, and Arrow’s independence condition 125 contraction consistency 126, 127 Coombs, Clyde H. 49, 86 Coombs voting method 48, 49, 65, 66 Cooter, Robert 75–76 Copeland voting method 48, 50, 51, 64, 154–155 cumulative voting method 52–59 cycling 11, 15, 35 and academic attacks on democracy 441 and agenda control 166, 167–168 and Arrow’s condition of unrestricted domain 17, 99 and Arrow’s impossibility theorem 17, 83, 86–92 balanced and unbalanced cycles 117–122 coffee-break cycles 337, 372–376 and the Condorcet voting method 5, 8 cyclebusting voting rules 113–122 and the Danish prime minister post 336 and democratic irrationalism 408 and the Depew amendment 197, 217, 218, 219–220, 233, 235–237 as an empirical improbability 378 and individual preferences 391 Iowa senators and anticorporate farming legislation 336, 369–370 and the Lincoln election 54, 258, 259, 279, 301, 376 and logrolling 164, 165 and market failures 440 mistaken claims of 20–21, 335 Danish Parliament election (1994) 336, 370–372 Finnish electoral college 336, 362–369 Muscle Shoals 21, 336, 353–361 Revenue Act (1932) 335 and Riker 376–377 Scandinavian parliaments 335–336 Shepsle and Bonchek’s cycles 336, 361–362 and multidimensional issue spaces 178, 196 structured preference orders 182

471 and the Powell amendment 20, 197, 198, 201, 353 in Riker’s Art of Political Manipulation 407 and Riker’s basic argument pattern 37, 178 Riker’s cycles 181, 310–334, 335, 353 and the agricultural appropriations vote (1958) 21, 310–311, 329– 334 and the slavery issue 293 and the US Federal Convention (1787) 21, 310, 316, 311–316, 321–328, 329, 376 and self-interest 113 and simulations of homogeneity 96–99 and stability 10 unimportance of 21 and the US Civil War 20 what-if cycles 336, 372–376 and the Wilmot Proviso 241, 243, 258, 301, 376 Czech Parliament 91 Dahl, Robert A. 2 A Preface to Democratic Theory 83–84 A Preface to Economic Democracy 423–424 Davidson, Donald 40 Davis, Jefferson 268 Davis, Senator John 250–251, 253 deadlock, and Arrow’s possibility theorem 84 democracy academic attack on and dictatorship 440, 442 and elite theory 427, 428, 442 literature on 9–16 Madisonian and populistic 423–424 parliamentary 422–423 and plebiscitarianism 409, 418 polyarchal 424 preconditions to 418 presidential 422–423 and the public good 36, 419, 424–425 revival of 443 Riker on populism and 418–425 democratic irrationalism 3–4, 16, 22, 23–43 academic opinion on 9–16, 426 and cycling 408 and democracy defended 27–31 doctrine of 361, 409, 425–431, 436, 438 and the economy 434–435

472

Index

democratic irrationalism (cont.) and the introduction of new dimensions 382, 384–385, 386 and knowledge of other minds 39–43 and multidimensional issue spaces 192 and rational choice theory 23 Riker on democracy as arbitrary 409–410 Riker, William on democracy as meaningless 410 and Riker’s basic argument pattern 16, 17, 37–39, 258 and Riker’s Liberalism against Populism 4, 23, 31–36 and strategic voting in Scandinavian parliaments 352–353 Democratic Party and the election 16, 290 and the Dred Scott decision 396 and the Kansas–Nebraska Act 307 and the Missouri Compromise 306 see also Lincoln election Denmark Danish national elections 52, 88–89 Danish prime minister post 336 general election for parliament (1994) 370–372 strategic manipulation in 352 Denzau, Arthur 204, 212 Depew amendment 20, 91, 193, 195, 217–240, 297, 407 alternative interpretation 231–240 and the Bristow amendment 223, 226, 228–230, 231, 234–235 and cycling 197, 217, 218, 219–220, 233, 235–237 and the “Force Bill” 224 historical background 221–231 and the Insurgent Republicans 231, 238 and irrational voters 220–221 and new dimensions 379 and the Oregon voting system 221–222 and the Rayner amendment 226–228 and the Sutherland amendment 218, 220, 228–231, 233, 234–235, 239 developing world, and democracy 1 Dewey, John 2 dictatorship and Arrow’s impossibility theorem and Arrow’s independence condition 141 and democracy 440, 442 and instability 434 and majoritarian processes 10

direct democracy 418 disequilibrium 21 and agenda control 169 and democracy 440, 441 and equilibrium in economics 435– 436 and the introduction of new dimensions 380, 383 and McKelvey and Schoﬁeld’s chaos theorems 17, 196 and multidimensional issue spaces 180–181 and positive political theory 435 and Riker’s case against populism 410 Riker’s hypothesis 9–16, 17, 20, 42, 192, 196, 240 and the Lincoln election 260, 280, 410 and new dimensions 378–379 and Ordeshook 435 and Pareto 428 and the Revenue Act (1932) 337 and slavery 293 and the Wilmot Proviso 241, 242, 246 and Shepsle and Bonchek’s cycles 362 Douglas, Stephen A. 20, 258, 259–260, 261, 268–269, 271–279, 363 and the election 16, 288–289 and the Baltimore Convention 267, 287 choice of Lincoln over 281–292 and the Congressional Party 266 debate with Lincoln at Freeport 22, 392, 393–396 and the Democratic Party 267, 269, 292 and the doctrine of popular sovereignty 193, 265, 269 and the Lecompton constitution 394–395 Downs, Anthony 189 Dred Scott decision (Supreme Court) 396 and the Lincoln election 264–265, 269, 290, 303 and Lincoln’s debate with Douglas at Freeport 395 and the Missouri Compromise 264 Dryzek, John 13, 15 Dutch parliamentary elections 88 Duvergerian equilibrium 66 Duverger’s Law 289–292 and the election 16, 289–290 and the election 16, 290–292

Index Eastern Europe, fall of communist regimes 1 economic libertarianism, democratic irrationalist justiﬁcation of 30 economics and Arrow’s impossibility theorem 434–435 competitive equilibrium in the economy 436–438 doctrine of noncomparable utility 17 economic instability 436 and market manipulation 439 material-welfare school 26 Post-Autistic Economics Movement 74–76 and social choice theory 72 see also markets Eisenhower, Dwight D. 198, 210, 211, 212, 213 electoral colleges and the Federal Convention (1787) 318–319 Finnish 336, 362–369 and the Lincoln election 282, 284, 292 electoral heart 188 elimination rules 56, 65–66 elite theory 442 in Pareto 427, 428 Ellis, Susan 238 Elster, Jon 27, 107, 323, 388 empirical failures, and multidimensional issue spaces 178–182 Enelow, James M. 92 equality, Riker on 32, 36, 416, 417 equilibrium Bayesian Nash 197, 207 competitive equilibrium in the economy 436–438 in economics 435–436 Kramer’s dynamical model of political equilibrium 185 and multidimensional issue spaces 175, 178, 181–182, 191 adding friction to 188 and disequilibrium 180–181 structure-induced 178 Pareto-optimal 388, 426–427, 436, 437 and Pareto’s social theory 430 in public choice 13, 14 see also disequilibrium Essex result 327 ethical voters 111 Europe, democracy in the interwar period 2 Everett, Edward 267

473 fact–value distinctions 74 Farquharson, Robin, Theory of Voting, on a US Senate vote 372–373 fascism 1, 10, 423, 431, 440, 442 Federal Convention (1787) 310, 311–329, 376 and the Brearley Committee 323 Committee on Remaining Matters 316, 318–319, 320, 321, 325 and electoral college 318–319 and the Essex result 327 and executive selection by electors 314, 315–316, 317–318, 320, 321, 324–325 by joint ballot 315, 316, 317, 324–325, 327 by national legislature 311, 314, 316, 317, 320 and the Great Compromise 311, 318, 319, 321 and Houston’s motion 312–313 and the New Jersey plan 312 and political opportunism 325–326 and presidential term of ofﬁce 314 and rational action 313 and the separation of powers movement 316 small and large states 313–314, 319–320 and the Virginia Plan 311, 312 Fehr, Ernst 104 Feld, Scott L. 50, 85, 87, 182, 183 Feldman, Allen M. 10, 442 Felsenthal, Dan S. 50, 51, 87 Fenno, Richard F. 215 Ferejohn, John A. 102 Fillmore, Millard 264, 288–289, 290, 291 Finland civil war in 363, 366 electoral college 336, 362–369 history of democracy in 368 strategic manipulation in 352 Fiorina, Morris P. 102, 180, 435 Fischbacher, Urs 104 Fischer, David Hackett 326 Fogel, Robert William 263, 305 Franklin, Benjamin 295, 328, 329 Fremont, John C. 263, 264, 290 French Revolution 420 Funk, C.L. 109 game theory 24, 27, 67 and universalism 102–104

474

Index

Gaubatz, Kurt Taylor, on public opinion on US military intervention overseas 373–375 Gehrlein, William V. 49, 98, 115 general will, in Rousseau 23, 33–34 Germany fall of the Weimar Republic 10, 440 Nazism 13 Gibbard, A. 155 Gibbard–Satterthwaite manipulation ﬁndings 22, 161, 410, 439 Giddings, Joshua 300, 301 Glazer, A. 102 global scale of democratization 1 Goldwater, Senator Barry 406 Goodin, Robert 24, 107–108 government failure and market failure 434 Green, Donald 27, 28, 29, 109, 178–179, 181, 194–195 Grofman, Bernard 50, 52, 85, 87, 89, 182, 183 Gross, Donald 369 Habermas, Jurgen ¨ 2 Hamlin, A. 136 Handbook of Political Science (Goodin and Klingemann) 24 Hansson, B. 148, 149 Hardin, Russell 11, 15, 123, 143, 441 Hare voting system 48, 56, 65, 66, 140 and the APA presidential elections 49 evaluation 59, 66 preference voting 53, 54 harmful manipulation 159, 160, 378 and agenda control 168 and the Depew amendment 239–240 frequency of 193–196 and logrolling 163 and the Powell amendment 197, 198, 201 in Scandinavian parliaments 353 and strategic voting 162 Hauptmann, Emily 28–29 Haynes, George H. 221–223 hegemony, and rational choice theory 26 Heseltine, William B. 303 Hinich, Melvin J. 188–189, 190 Hitler, Adolf 13 Holmes, Stephen 110, 113 Hume, David 110, 194, 195 ideological coherence, constraints of 196 impartial-culture assumption 48, 49, 54, 55, 88–89 and the Condorcet efﬁciency 47–48

and multidimensional issue spaces 182, 183 and simulations of homogeneity 96, 97 inaccuracy and the Condorcet voting method 9 democratic voting as inaccurate 44 and Riker’s basic argument pattern 37 Riker’s inaccuracy hypothesis 52 India, populism in 420 individual motivation, and preference rankings 192 Indonesia 1 International Olympic Committee vote 375–376 Iran 1 irrationalism see democratic irrationalism Israeli–Palestinian conﬂict 1 Jackson, Andrew 296, 299 Jackson, Senator Henry 397, 400, 405 Japan, and US nerve gas materials 399, 400–401, 403 Jefferson, Thomas 295 Jillson, Calvin C. 320 judicial review 12, 15 justice, Platonic and Marxist conceptions of 31 Kansas–Nebraska Act (1854) 288, 289, 294, 295, 307 Kasza, Gregory 26 Katznelson, Ira 440, 441, 442 Kiewiet, D. Roderick 108–109 Kinder, Donald R. 108–109 King, Ronald F. 238 Klingemann, Hans-Dieter 24 Koford, K.J. 165 Kramer, Gerald H. 185 Krehbiel, Keith 197–198, 206, 207–208, 211, 214–215, 361 Kuga, K. 97 Kuttner on the virtues and limits of markets 433 Kurrild-Klitgaard, Peter 52, 88–89, 336, 370–372 Lagerspetz, Eerik 21 Latin America 1, 420, 423 Lecky, William 2 Lecompton constitution 394–395 legislative power, and democracy 418 Lenin, V.I. 2, 420 Levin, Jonathan 50 Levine, Michael 169, 407 Lewin, Leif 109 liberal political theory 2

Index liberalism Riker’s case for 25, 409, 411–417 and the Nixon–Agnew problem 415 and random rejection of candidates 413–416 and the rejection of populism 413, 416 and the retention or rejection of ofﬁcials 411–413 liberalist democracy 3, 22 and the doctrine of democratic irrationalism 31 libertarianism 4 liberty, Riker on 32, 33, 36, 416, 417 Lincoln, Abraham 301, 392–396 debate with Douglas at Freeport 22, 392, 393–396, 407 Lincoln election 20, 54, 92, 258–280, 407 and antebellum politics 281 and the Baltimore Convention 267–268, 287 choice of Lincoln over Douglas 281–292 and the Civil War 287 and the Congressional Party 266 and the Constitutional Unionists 259–260, 267, 269–270, 285 and cycles 54, 258, 259, 279, 301, 376 and the Democrats 259, 265, 266, 267, 269, 271, 285, 286, 289, 292 and Duverger’s Law 290 northern 261, 262, 263, 269, 286 southern 262, 269, 286 and the doctrine of popular sovereignty 265, 269, 270 and Duverger’s Law 289–292 and immigration to the north 262 and the Lower South and secession 286–287 and the nativist American Party 263 and the Republicans 263, 264–265, 269, 285, 286, 290 Riker on the 20, 54, 92, 240, 259, 258–260, 280, 281–282, 376, 409, 410 and the case against populism 202, 409, 410 and the slavery issue 294 and the Supreme Court Dred Scott decision 264–265, 269, 290, 303 voter preferences 271–280, 281 voting system and candidacies 285–286 and the Whigs 261–262, 263, 264 Lindsay, Alexander Dunlop 2

475 Lippmann, Walter 2 Little, I.M.D. 76 logical positivism, and Arrow’s independence condition 143 logrolling (vote trading) 17, 159, 160, 163–166, 171 and agricultural appropriations (1958) 333 as welfare-enhancing or welfare-reducing 163–164, 171 Lomasky, L. 102, 166 McDonald, Forrest 314, 319 McGovern, Senator 213 Machover, Moshe 51, 88 McKelvey, Richard D. 22, 102, 179 McKelvey and Schoﬁeld chaos theorems 17, 22, 30, 170, 184, 185, 196, 410 and academic attacks on democracy 441 and the Depew amendment 217 and the economy 438 and new dimensions 379, 385 Riker’s interpretation of 17, 173–176, 186–190, 196 McKelvey voting model 383, 392, 407 Mackie theorem 171 McMillan, H. 102 “Machiavellian” elite theories 430 Madison, James 22, 35, 314, 320, 322, 328 Madisonian democracy 423–424 Magnuson amendment and nerve gas 22, 361, 381, 393, 396–407 and the Church–Cooper amendment 398–399, 401, 403, 404 and the Gravel amendment 393, 397, 398–399, 400, 401, 403–404, 405 and the Harry Byrd resolution 400, 402, 404 Maine, Sir Henry 2 majoritarian democracy, Riker on 23, 49–51, 159, 302 majoritarian processes, and dictatorship 10 majority cycling, and Arrow’s possibility theorem 71, 72, 85–86 majority voting 44, 107 cycles and individual preferences 390 and the Lincoln election 283 and plurality rule 5 and social choice 14, 15, 44, 55–56, 83 and stability 10 voting problems with 5

476

Index

Mandeville, Bernard 110 manipulation 17, 35, 161 and Arrow’s independence condition 154–156, 157 and Arrow’s possibility theorem 70, 72–94 economic 436, 438–440 and the introduction of new dimensions 381 and the Magnuson amendment 406 in politics 436 and Riker’s basic argument pattern 37, 38, 258, 280 and Riker’s case against populism 410 and Riker’s defense of liberalism 412, 413 Riker’s manipulation argument 160, 158–160, 162, 171, 194–196, 292–303, 344–353, 384 in Scandinavian parliaments 21, 336 see also agenda control; harmful manipulation; multidimensional issue spaces; strategic voting Maoz, Zeev 50, 87 markets arbitrary and meaningless nature of 437 and democracy 28 force and fraud in 437 and instability 433–434 manipulation of 438–440 market failure 30, 434, 440 and the Pareto-optimal competitive equilibrium 426–427 and politics 14, 15, 22 Martin, Luther 322 Marx, Karl 2, 31 Mashaw, Jerry L. 10, 441, 442 Massachusetts state constitution, and the Essex result 327 mean voter theorem 183 meaningless, democracy as see democratic irrationalism Merrill, Samuel 48, 49, 55 Mexico and the Missouri Compromise 261 and the Wilmot Proviso 241, 242, 248, 249, 250, 251 Michaelsen, William B. 317, 321, 327–333 Michels, Robert 2, 3, 442 Miller, D.T. 112–113 Miller, G.J. 103 Milner, Helen 440, 441, 442 Missouri Compromise and the Dred Scott case 264

and Kansas 306 and the Lincoln election 258, 261 and northern politics 302 and Riker on slavery 294, 295, 296, 297, 298, 307 and slavery votes in Congress 305 and the Wilmot Proviso 245, 255 Monroe, James 305 Moore, Glover 297 Morris, G., and the Federal Convention (1787) 316, 320, 322–323, 325–326, 328, 407 Mosca, Gaetano 2, 3, 431, 442 movement and action, and voter’s preferences 38 Mueller, Dennis C. 156 multidimensional chaos 173 multidimensional disequilibrium 378, 392 multidimensional issue spaces 21–22, 35, 72, 159, 170, 173–176, 310 adding back friction 185–191, 196 and democracy 419 experimental and empirical failures 178–182 and harmful manipulation 193–196 nominatively attractive point in 176–178 and Riker’s basic argument pattern 37, 178 and structured preference orders 182–185 and voter preferences 178 see also new dimensions Munger, Michael C. 188–189, 190 Murdoch, Iris 74 Muscle Shoals (Senate deliberation on) 21, 336, 353–361, 377 and the Coolidge administration 355 Jones proposal 354, 356 Norris proposal 354 and the Republicans 356, 357 and the southern Democrats 356 Underwood proposal 354–355, 356, 357 Mussolini, Benito 425, 431 Mustasa, Didymus 108 Nagatani, H. 97 Nalebuff, Barry 50 Nanson’s voting system 48 Nash voting method 52 negative majorities, and the Revenue Act (1932) 337–338 negative plurality 66 and the Lincoln election 278, 281

Index Neufeld, John L. 21 Neufeld, Hausman and Rapoport on Muscle Shoals 21, 336, 353–361, 377 new dimensions 378–408 deliberation and disequilibrium 386–392 introduction of issues and dimensions 379–384 models of 384 and Riker’s case against populism 410 see also multidimensional issue spaces New Republic 25 Niemi, Richard G. 21, 86, 182, 335–336 Nixon, Richard M. 212 and the Magnuson amendment and nerve gas 397, 398, 399–400, 401, 402, 405, 406 and the Nixon–Agnew problem 415 normative democratic theory 2 Northern Ireland 69 Norway, strategic manipulation in 352 Nurmi, Hannu 47, 49, 69 objective utility, Pareto on 429 Olson’s logic of collective action 111 opinion polls 412 Oppenheimer, J.A. 103 opportunity costs, of rational-choice scholarship 28 opposition to democracy 2 Ordeshook, Peter C. 11, 24, 179, 435, 442 Packwood, Bob 397 pairwise comparisons 54 and agenda control 167–168 and agricultural appropriations (1958) 333 and Arrow’s independence condition 137–139, 141 and the Depew amendment 236 and dictatorship 435 and the Lincoln election 259, 277, 278, 279, 281 and logrolling 163 and multidimensional issue spaces 192 and the Muscle Shoals vote 356–357 and the Revenue Act (1932) 342 Papua New Guinea 67, 68 paradox of voting 5 see also Condorcet voting method Pareto criterion 76, 416 Pareto, Vilfredo 2, 3, 22, 409, 425–431, 442 and elite theory 427, 428

477 on logical and nonlogical conduct 426 on objective and subjective utility 429 and residue theory 427–428 Pareto-optimal equilibrium 388, 426–427, 436, 437 parliamentary democracy 422–423, 430 Parsons, Talcott 344 participation, Riker on 23, 32, 36, 416–417 path dependence, and the Condorcet voting method 9 Pellikaan, Huib 111 “perestroika-glasnost” movement in American political science 26 Philippines 1 Pierce, Franklin 288, 289 Plato 2, 31 plebicites 417, 420 plebiscitarianism 409, 418 Pliny the Younger 43, 168, 407 Plott, Charles 11, 169, 180, 407, 441, 442 plurality grading 60–61 plurality runoff 44, 48, 56 and Arrow’s possibility theorem 84–86 and Condorcet efﬁciency 48, 49, 60 and elimination 65 evaluation 59, 52–59, 60, 70, 72 and the Finnish electoral college 363, 367 and the impartial-culture assumption 47 and the Lincoln election 278, 279, 281 and social homogeneity 49 and strategic voting 160 plurality voting 5–9, 44, 49, 51 accuracy 64 and the APA presidential elections 49 and Arrow’s independence condition 142, 157 and Arrow’s possibility theorem 84 and the Borda count 6 and the Copeland method 50, 51 and the Lincoln election 259, 277, 281, 282–284, 285, 292 with more than two parties 66–67 in Papua New Guinea 67 problems with 5–9 pure plurality 68 rankings 52, 53 and Riker’s defense of liberalism 412 and social homogeneity 49 political tactics, and social welfare 15 political/moral scarcity, and the Pareto-optimal competitive equilibrium 426

478

Index

politicians and opportunism, and the Federal Convention (1787) 325–326 Polk, James K. 246–247, 248–250, 254–256 Pollard, Edward 302 polyarchal democracy 424 Poole, Keith T. 90, 91, 102, 189–190, 191, 193, 304–306 populism American populist movement 419–420, 421 in Britain 421 Riker on populism and democracy 418–425 Riker’s case against 23, 31–37, 409–411 populist democracy 3, 13, 22, 23, 31 Portugal, democratization of 1 positional voting 46, 56 and the Lincoln election 276 positive political theory 3, 22, 24, 159, 181–182, 431 and disequilibrium 435 postmodernist hegemony, and rational choice theory 26 Potter, David M. 306, 308, 394, 395 Powell, Adam Clayton 198, 204, 205, 209, 213 Powell amendment 20, 43, 43, 91, 193, 197–216, 361, 407 and the Ayres amendment 214–215 and the Brown v. Board of Education Supreme Court decision 198, 205, 209, 210 and the Civil Rights Act (1956) 206 and cycling 20, 197, 198, 201, 353 Desegregationist Republicans 202, 204 and harmful manipulation 197, 198, 201 and the NAACP 204–209, 210–211 northern Democrats 207, 207–208, 209, 211, 212 Powellites 202, 204–205, 206, 207, 209 recorded votes 199–200 School-Aiders 202, 206, 207, 210 Segregationist Republicans 202–204, 206 southerners 202 and strategic voting 20, 197, 198, 204, 347–350, 384 and the Wainwright amendment 213–214, 215

power, social rationality and the concentration of 14–15 preference rankings 20, 21, 44 preference voting 53 preference-development hypothesis 303–309 presidential democracy 422–423 probabilistic voting 196 and Arrow’s independence condition 147–148, 150 proportional representation 66 and the Finnish electoral college 363, 386 Przeworski, Adam 13, 441 public choice theory 13, 27, 29, 30 and markets 433, 434, 437 and self-interest 111–112 and the Wilmot Proviso 246 public good and democracy 36, 419, 424–425, 430 and the general will 34 and Riker’s liberalism 35 public interest and Riker’s defense of liberalism 416 and Shepsle and Bonchek’s cycles 362 public opinion, on US military intervention overseas 373–375 pure plurality 68 Radcliff, Benjamin 88 radical interpretation, Davidson’s principles of charity in 40 Rapoport, Amnon 50, 87 see also Neufeld, Hausman and Rapoport Rappoport, Peter 75–76 Raskin, Marcus 36 rational actions, and self-interest 109–110, 113 rational choice theory 23, 28–29, 106, 194 critics of 25–26, 27 and the Depew amendment 220–221 and the Powell amendment 205 Rochester school of 13, 22 Ratner, R.K. 112–113 Rawls, John 2, 419, 421 reciprocal fairness in voting behaviour 104–106 Redman, Eric 397–398, 399 Regenwetter, Michel 51, 89 Reilly, Benjamin 67 repeated alternative-vote procedure 50 representative democracy 418 Republican Party and cheap land 306

Index and the Kansas–Nebraska Act 307 and the Lincoln election 263, 264–265, 269, 285, 286, 290 residue theory in Pareto 427–428 Revenue Act (1932) 21, 335, 337–344 Riker, William 4, 12–13, 15, 17, 22, 158, 441, 442 on agenda control 166, 168–171 on agenda setting 383 and the agricultural appropriations vote (1958) 310–311, 329–334, 377 on the American Civil War 20, 407 and Arrow condition of unrestricted domain 101 impossibility theorem 3, 83, 84, 89–90 independence condition 146–148 The Art of Political Manipulation 22, 329, 361, 392, 407–408 cycling stories in 407 and the axiomatic approach 16 basic argument pattern 16, 17, 37–39, 40, 46, 71, 72, 178, 409, 411 and contrived cycles 378–379 and democratic irrationalism 3, 20, 29, 30, 31, 409 and the Depew amendment 20, 91, 193, 195, 217–240 and disequilibrium 9–16, 17, 20, 42, 196, 240 and empirical cycles 355 inaccuracy hypothesis 52 liberal interpretation of voting 35 and liberalism 22, 25, 409, 411–417 Liberalism against Populism 4, 17, 23, 31–36, 91, 193, 196, 279–280, 329, 344, 392, 425, 435 Pareto’s theories in 427 and libertarianism 4 and the Lincoln election 20, 54, 92, 240, 258–280, 281–282, 376 and the case against populism 202, 409, 410 on logrolling 163 and McKelvey and Schoﬁeld’s chaos theorems 17, 173–176, 186–190, 196 and the Magnuson amendment 361 and majoritarian democracy 23, 49–51, 302 manipulation argument 160, 158–160, 162, 171, 194–196, 344–353, 384 theory of dimensional manipulation 292–303

479 on the market 435 and mistaken cycles 376–377 and multidimensional disequilibrium 378 on multidimensional issue spaces 175, 186, 191–193, 196 on new issues and dimensions 379–384, 386 and Pareto-optimal equilibrium 426–427, 436 on Pliny the Younger 43, 168, 407 and populism 23, 31–36, 409–411, 418–425 and positive political theory 3, 22, 24, 159, 181–182, 431, 435 and the Powell amendment 20, 43, 43, 91, 193, 197–216 and the Revenue Act (1932) 337, 343 and the Rochester school of rational choice theory 13, 15, 29 and Shepsle and Bonchek’s cycles 361 and skepticism 42 on the slavery issue 192, 282, 293–303, 304, 307–308, 361 and social choice theory 13–14 on strategic legislators 345–350 on transient majorities 392 and the US Federal Convention (1787) 21, 310, 316, 311–316, 321–328, 329 on the US Supreme Court and property rights 302, 303 and voting rules 44, 46, 54, 55 evaluating 56, 64, 68, 70–71 and the Wilmot Proviso 43, 240, 302, 376 Rivers, Douglas 197–198, 206, 207, 208, 211, 214–215 Robbins, Lionel 74, 74, 75 Robinson, Dave 53 Rochester school of rational choice theory 13, 23–26, 28, 29, 30, 37, 175 and the Revenue Act (1932) 343–344 Romanian Iron Guard 420 Roosevelt, Franklin 36, 197, 336, 420 Roosevelt, James 212 Rose-Ackerman, Susan, on the International Olympic Committee vote 375–376 Rosenthal, Howard 90, 91, 102, 189–190, 191, 193, 304–306 Rousseau, Jean-Jacques 32, 33–34, 107 Social Contract 33 and the will of the people 418

480

Index

Rowley, Charles K. 12, 15, 433, 440 Runciman, W.G. 11, 441 Rusher, William 36, 423 Ruskin, John 2 Russia Narodniki movement in 419 see also Soviet Union Saari, Donald G. 46, 54, 61, 117, 184, 432, 438, 439 Samuelson, Paul 10, 11, 144 Satterthwaite, M. 155, 439 Scandinavian parliaments 21, 335–336, 344–353 and the Swedish telephone and telegraph company expansion 347–350, 377 and the Swedish voluntary riﬂeman’s association 350–351 Scarf, Herbert 438 Schoﬁeld, Norman J. see McKelvey and Schoﬁeld chaos theorems Schumpeter, A. 28 Schwartz rule (method of transitive closure) 58, 64, 116–117 Scott, Winﬁeld 262 Sears, D.O. 109 secret ballot, and the Finnish Electoral College 363 self-interest, and voting behaviour 108–113 Sen, Amartya 75, 77, 80–81, 82, 99–107, 112, 144 and social choice theory 432 Senators, election of US see Depew amendment Seventeenth Amendment (to the US constitution) see Depew amendment Seward, William 267, 308, 309 Shapiro, Ian 27, 28, 29, 178–179, 181, 194–195 Shaviro, Daniel 15, 442 Shepsle, Kenneth A. 14, 15, 23, 24, 25, 29, 89, 204, 212, 336, 434, 440, 441, 442 Shepsle and Bonchek’s cycles 336, 361–362 Shils on the principles of populism 420 single transferable vote 49–51, 66, 69 and Arrow’s independence condition 157 and the Finnish electoral college 366 single-peakedness, and multidimensional issue spaces 182 Skach, Cindy 423 skepticism 42, 43

slavery issue 21, 282 abolition of 304 and the introduction of new dimensions 381, 382–383 and Lincoln’s debate with Douglas at Freeport 393–396 and the preference-development hypothesis 303–309 Riker on the 192, 282, 293–303, 304, 307–308, 361 rise of antislavery agitation 299 and the US constitution 223 see also Missouri Compromise; Wilmot Proviso Smith, Adam 110, 436, 438 Snow, C.P., The Masters 407 social choice theory 13–14, 15, 16, 23, 24, 432 and Arrow’s possibility theorem 70, 72, 76, 78, 85 constructivist 29 deﬁning 27 and democratic means 31 and individual preferences 388 irrationalist interpretations of 16, 52, 443 and majority voting 14, 15, 44, 55–56, 83 origins of 72–78 Riker’s interpretations of 425 and Shepsle and Bonchek’s cycles 362 and voting rules 61, 70–71, 77–78, 107 social dilemmas and individual cooperation 106 and logrolling 165 social homogeneity, and voting rules 49 social rationality, and the concentration of power 14–15 social welfare function (SWF) and Arrow’s condition of unrestricted domain 80–81, 82, 92 and Arrow’s independence condition 123, 129, 143, 149, 146–149, 150, 157 and dictatorship 434–435, 442 social-utility-efﬁciency of voting rules 48, 55 Sonnenschein, Mantel and Drebreu theorem in economics 438 sophisticated voting see strategic voting South Africa 1 Soviet Union fall of communism 1, 13, 440 voting system 417 Spain, democratization of 1

Index spatial voting 10, 116, 179, 181, 191, 196, 379 multidimensional 385–386 Spector, Lee 276, 279 stability and democracy 10 and Arrow’s condition of unrestricted domain 95 and deliberation 391 instability in markets and government 433–440 instability in Scandinavian parliaments 21 tradeoff between 442 Stepan, Alfred 423 Stephen, Sir Leslie 2 Stephens, Alexander H. 303 strategic voting 5, 17, 35, 71, 72, 158, 159, 160–162, 171, 344–345 and academic attacks on democracy 441, 442 and agenda control 166, 168 and agricultural appropriations (1958) 330–331 and Arrow’s possibility theorem 91 and the Condorcet method 9 and cycle claims 337, 377 and the Depew amendment 233, 236, 239 and elimination 66 and the Finnish Electoral College 367 frequency of 193 and the Iowa corn issue 369 and the Lincoln election 282, 289 and majoritarian processes 10 and multidimensional disequilibrium 378 and multidimensional issue spaces 196 and the Muscle Shoals issue 336, 355, 361 and new dimensions 384 and the Powell amendment 20, 197, 198, 204, 347–350, 384 and public choice theory 13 Riker on 37, 194 and Riker’s case against populism 410 and Riker’s defense of liberalism 412 in Scandinavian parliaments 345–353 and social choice 14 and voting methods 9, 65 and the Wilmot Proviso 257, 345–350 Stratmann, Thomas 102, 165 Strom, Gerald S. 170, 180, 181, 188, 329 strong positionalist independence (SPI), and Arrow’s independence condition 150

481 structure-induced equilibrium 178 subjective utility in Pareto 429 Sunstein, Cass R. 13, 441 Sweden, strategic manipulation in 352 Tabarrok, Alexander 276, 279 Tallmadge, James 297–298 Tangian, A.S. 55, 97 Tanguiane, A.S. 52 Taylor, Zachary 261 Teapot Dome scandal 354 Tennessee Valley Authority 197, 336 Tervo, Penna 367 Thatcher, Margaret 6 Tocqueville, Alexis de 112 Tovey, Craig A. 188 transitive closure (Schwartz’s method) 58, 64, 116–117 Tribe, Laurence 12, 15, 440 Truman, Harry S. 204 Tuck, Richard 11, 441 Tushnet, Mark 12, 15, 440 tyranny battle against 443 and Madisonian democracy 424 and Riker’s defense of liberalism 417 see also dictatorship United Nations 91 United States agenda control in the US Congress 170 agricultural appropriations votes in the House of Representatives 21, 310–311, 329–334 American populist movement 419–420, 421 American progressivism 36 Cambridge City Council elections 53–54 campaign ﬁnance problem 30 candidate elections 59 Civil Rights Act (1964) 195 and democracy 1, 2 Federal Convention (1787) 310, 311–329 House of Representatives 65 Iowa senators and anticorporate farming legislation 336, 369–370 and the Lecompton constitution 394–395 Muscle Shoals in the US Senate (1925) 21, 336, 353–361, 377 presidential elections 84, 86–87, 88, 106, 311 see also Lincoln election

482

Index

United States (cont.) Revenue Act (1932) 21, 335, 337–344, 376 and Riker’s hypothesis of preferences in disequilibrium 192 Riker’s liberalism and the US Constitution 421, 423, 428 roll-call votes in US Congress 304–305 Seventeenth Amendment to the US Constitution see Depew Amendment slavery 21, 192 strategic voting in primary elections 162 Tax Reform Act (1986) 362 see also American Civil War; Powell amendment; Wilmot Proviso universalism 103, 102–104 utilitarian voting methods, and Arrow’s independence condition 146–147, 148, 150 utilitarianism 72–73 utility, interpersonal comparisons of 142–146 Van Buren, Martin 246, 248, 291 Van Deemen, Adrian 88 van der Veen, Robert J. 111 Vergunst, Noel P. 88 Victorian England 2 Vietnam War 397 Virginia school 20 vote trading see logrolling voter information, and multidimensional issue spaces 188 voter preferences and academic attacks on democracy 442 and agenda control 167, 169 and Arrow’s condition of unrestricted domain 95, 108, 99–108 and Arrow’s independence condition 138–146, 147 and Arrow’s possibility theorem 79–82 choices and underlying preferences 38, 39, 40–42 and cyclebusting 114 and democracy 418 indirectly inferring 37 individual preferences 47 defective 388 structured and unstructured 391 in the Lincoln election (1860) 271–280, 281 and manipulation 160

and multidimensional issue spaces 173, 177, 182–184 preference rankings 20, 21, 44 proﬁle of individual preferences 387–391 and Riker’s case against populism 409–410 and self-interest 108–113 and simulations of homogeneity 96–99 unknowable nature of 23, 37, 38, 39, 70, 72, 178, 279 and Riker’s case against populism 411 and Riker’s defense of liberalism 412, 413 voter’s paradox, inconsistency of the 11 voting, Riker on liberalism and populism 22, 32, 34–36 voting rules 5–9, 31 accuracy in 64 and Arrow’s independence condition 124, 137–142 axiomatic approach to 16, 68–69, 71, 72 and convergence 54 cyclebusting 113–122 democratic voting as inaccurate 44 elimination rules 56, 65–66 evaluating 55 fair voting methods 44 and the Lincoln election 259 and rational choice theory 27 and Riker’s case against populism 409–410 and social choice theory 61, 70–71, 77–78, 107 in the Soviet Union 417 tradeoffs in choice of 441 Waldron, Jeremy 30 Walt, Stephen 28, 344 Washington, George 312 weakened independence conditions (PI), and Arrow’s independence condition 149–150 Weale, Albert 13, 15 Weingast, Barry R. 14, 15, 24, 103–104, 294, 302, 307, 440, 441, 442 model of universalism 102 and the Revenue Act (1932) 337 Wentworth, Senator, on the Wilmot Proviso 256–257 what-if cycles 336, 372–376 will of the people 418, 419, 420, 421, 430, 442

Index Wilmot Proviso 20, 43, 91, 193, 240, 241–257, 258, 294, 295, 296, 302, 407 alternative interpretation 251– 257 and cycles 241, 243, 258, 301, 376 Ingersoll substitute 245, 246 and the introduction of new dimensions 381 McHenry amendment 245 and the Missouri Compromise 245, 255 and northern Democrats 241, 247, 253, 254, 255 and the Oregon Territory 247, 248, 250, 255 and southern Democrats 248

483 and strategic voting 257, 345–350 Wick amendment 245 Wilson, James Q. 25 Wolff, Robert Paul 12, 15, 440 World War I 1 Wright, J.R. 86 Young–Kemeny voting rule 55–56, 58–59, 63–64, 70, 72–94 and agenda control 168 and Arrow’s independence condition 123, 150, 154–155 and cyclebusting 117, 118, 121 and the Muscle Shoals vote 356 and the Powell amendment 200 Zimbabwe 108 Zywicki, Todd J. 238