Decision Theory and Rationality

DECISION THEORY AND RATIONALIT Y

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Decision Theory and Rationality J O SÉ LU I S B E R MÚDE Z

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Great Clarendon Street, Oxford   Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York  José Luis Bermúdez 2009

The moral rights of the author have been asserted Database right Oxford University Press (maker) First published 2009 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose the same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data Bermúdez, José Luis. Decision theory and rationality / José Luis Bermúdez. p. cm. Includes bibliographical references and index. ISBN 978-0-19-954802-6 1. Decision making. 2. Practical reason. I. Title. BF448.B465 2009 153.8’3—dc22 2008039124 Typeset by Laserwords Private Limited, Chennai, India Printed in Great Britain on acid-free paper by Biddles Ltd., King’s Lynn, Norfolk ISBN 978–0–19–954802–6 1 3 5 7 9 10 8 6 4 2

Acknowledgments Chapter 4 draws on my ‘‘Pitfalls for realistic decision theory: An illustration from sequential choice’’, forthcoming in a special issue of Synthese on realistic standards for decision theory. I would like to thank the editor of the special issue, Paul Weirich, for his comments and for inviting me to the conference on Realistic Standards for Decisions at the University of Missouri, Columbia, in April 2008. This manuscript has been much improved by comments from Anna Alexandrova, Eric Wiland, John Brunero, and the anonymous readers for Oxford University Press. Finally, my thanks to Santiago Amaya for preparing the index, and to Peter Momtchiloff, Mikki Choman, Christine Ranft, and Georgia Berry at Oxford University Press for their patience and help.

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Contents Introduction

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1. Decision Theory and the Dimensions of Rationality

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2. The First Challenge: Making Sense of Utility and Preference

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3. The Second Challenge: Individuating Outcomes

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4. The Third Challenge: Rationality Over Time

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5. Rationality: Crossing the Fault Lines?

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Bibliography Index

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Introduction The concept of rationality is at the heart of many different disciplines, from economics to political science, from philosophy to psychology, and from management science to sociology. The apparent omnipresence of the word ‘‘rationality’’ in the social and human sciences raises an obvious question. Is the word being used in the same way in all these different contexts? Are economists, for example, talking about the same thing as psychologists? If a psychologist identifies what she takes to be omnipresent irrationality when people reason about probabilities, is she denying what an economist would maintain by saying that economic agents are rational agents? Similar questions can be raised for many pairs of disciplines. There are important issues at stake here for the possibility of meaningful discussion and engagement across the human and social sciences—issues with serious ramifications for how we think about the unity of science. It is striking, in the face of the enormous diversities in range and methodology across the human and social sciences, that a small number of concepts keep reappearing. The concept of rationality is clearly one of these, and it is natural to think that it might prove an Ariadne’s thread running through the different disciplines. Something like this idea has traditionally been used to distinguish the Geisteswissenschaften from the Naturwissenschaften. But this clearly depends upon there being a single notion of rationality at work in all the disciplines in which the word ‘‘rationality’’ features prominently. Many theorists have thought that there is such a unitary concept of rationality. It is a popular view that rationality is, at bottom, a mathematically tractable notion, which it is the province of statistics, decision theory, game theory, and so on, to develop, and which can then be applied in different ways and at different degrees of abstraction. The various forms of Bayesianism in epistemology and the philosophy of science offer a striking illustration of this belief in the fundamentally mathematical nature of rationality, as do the dominant paradigms

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in microeconomics. At the root of all these ways of thinking about rationality is the mathematical theory of choice—or, as it is standardly called, decision theory. Decision theory is a tool for assessing and comparing the expected utility of different courses of action in terms of the probabilities and utilities assigned to the different possible outcomes. This tool can be used to identify one or more courses of action that maximize expected utility. What gives mathematical traction to the notion of rationality is equating rational behavior with behavior that maximizes expected utility. That equation is the canonical feature of decision theory, as standardly developed by mathematicians, economists, and statisticians. On the other hand, there are equally powerful currents of thought that seek to draw a sharp line between decision theory and the theory of rationality. These typically find applications of the notion of rationality that cannot (it is argued) be derived from mathematical models at whose core are requirements of maximization and consistency. For some theorists the mathematical conception of rationality lacks the right kind of normative force. It is purely instrumental. Christine Korsgaard has argued this with considerable force (in her 1996 and 1997, for example). For Korsgaard the norms imposed by decision theory are simply norms of consistency. They tell the agent how to translate the reasons that she has into action. But they neither provide a normative benchmark against which those reasons can be assessed, nor explain why those reasons are reasons. And nor do they provide a way of bringing into play any of the potentially binding and prescriptive reasons that might not be reflected in her ‘‘subjective motivational set’’. Even worse, Korsgaard claims that the norms of consistency enshrined in decision theory threaten to be completely trivial. As will emerge in Chapter 2, there are ways of understanding the key notions of probability and utility on which a suitably consistent agent cannot but maximize expected utility—and so cannot but be rational in the instrumental sense central to the theory of choice. Understanding rationality in terms of maximizing expected utility is in danger of turning a normative notion into a target that automatically moves to wherever the arrow is aimed. For others what is missing from decision theory is the social dimension of reasons and reasoning. By treating agents as self-determining atoms decision theory neglects all the reasons for action that can only be understood through seeing how agents are embedded in their

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social and cultural contexts. Homo economicus and Homo sociologus are very different beasts.¹ As Martin Hollis puts it, ‘‘Whereas homo economicus is an abstract, individual, yet universal, homunculus, homo sociologus is a social being, essentially located in a scheme of positions and roles’’ (Hollis 1979, 29). These positions and roles bring with them social norms and institutional rules that need not fall within the purview of decision theory. The theory takes an agent’s utilities as given. But the agent’s social context provides constraints and controls on what those utilities ought to be. And it has an even greater role to play than that, because the social context can determine collective reasons for action that cannot be derived from individual reasons for action. Both of these lines of criticism stress the intimate relation between rationality and reasons for action. Both charge decision theory with blindness to anything other than the chooser’s actual reasons, as reflected in her utility function. They accuse it of having nothing to say about the wide range of reasons that a rational agent should take into account, even when they are absent from her utility function. And even when the reasons that the agent should take into account are ones that the theory bids her take into account (because they are reflected in her utility function), it is objected that decision theory has nothing to say about what makes them reasons—about why the agent should give them weight. Here, then, are two fundamentally different ways of thinking about how to understand the notion of rationality. One seeks to understand it through decision theory and the norms of consistency and maximization. The other holds that decision theory can only (and at best) be part of the story, because rationality is ultimately a matter of the agent’s answerability to reasons that may fall completely outside the theory’s scope. How might we investigate where on the spectrum between these two extremes the truth lies? One way would be through a detailed comparison of different ‘‘case studies’’ from different disciplines. One might compare a philosophical discussion of the norms of rationality with a psychological discussion of the strategies that people use for ¹ The essays in Hollis 1996 present a nuanced discussion of this basic contrast, which has its origins in Max Weber’s famous distinction between formal rationality (Zweckrationalität) and substantive rationality (Wertrationalität).

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solving particular types of problems—or set an economist’s analysis of how goods should rationally be distributed against a political scientist’s solution to the same problem. Comparisons of this type are often very useful and instructive. But there is only so much that we can learn from them. It is difficult to extrapolate from individual case studies to broader conclusions about the conceptual frameworks within which they are embedded. My strategy in this book is more abstract. Decision theory is first and foremost a mathematical theory and the problem here is in essence a problem about the applicability of mathematics to the ‘‘real’’ world. But whereas most discussions of the applicability of mathematics focus on the physical world, the issue here is how a mathematical theory might be applied to the social world. This is why issues of normativity and reasons loom large. What makes the problem so complicated is that there is no easily identifiable and clear-cut phenomenon in the social world that we can see decision theory as modeling, in the way that we might interpret, for example, geometry as modeling the different forms that space might take. The notion of rationality is far more nebulous. In order to understand it we need to think about the uses to which it is put and the work that it is called upon to do. I will be looking at the different explanatory tasks that the concept of rationality is called upon to play. It is an open question whether the demands imposed by these different explanatory projects are consistent with each other. The first extreme view in effect claims that these demands can all be met by the mathematical models produced by decision theorists, statisticians, and so forth. The second view, in contrast, claims that these mathematical models satisfy a set of demands fundamentally different from, and alien to, the normative and/or hermeneutic explanatory projects of, say, philosophers, sociologists, and political scientists. My focus will be on on the relation between rationality and decisionmaking. The notion of rationality is sometimes applied in a more epistemological sense, as when philosophers of science or sociologists talk about the rationality of scientific theories, but my concern is primarily the relation between rationality and action (bearing in mind that seeking more information or suspending inquiry counts as an action). The decision-making I discuss is individual rather than collective, on the assumption that solutions to problems of collective rationality (such as bargaining problems and noncooperative games) presuppose accounts of individual rationality.

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My starting-point is that within the general sphere of individual decision-making the concept of rationality is appealed to in the context of three different explanatory projects: • • •

The project of guiding action The project of normatively assessing action The project of explaining/predicting action

To each of these projects there corresponds what I term a different dimension of rationality. The principal question I am interested in is whether these very different explanatory projects can all be served by a single theory of rational choice—in particular, by some version or extension of decision theory, as developed by mathematicians and economists. We know that the concept of rationality is used in these three different ways. But can these different ways of thinking about rational choice and rational action be understood in terms of decision theory? The notion of rationality looks very different under each of these different headings. Each explanatory project makes different theoretical demands and imposes different theoretical constraints. The narrowest and most circumscribed dimension is the action-guiding dimension. Decision theory, as standardly developed, is a theory of how to choose rationally, and hence by extension of how to act rationally, in decisionsituations that take a particular prescribed form. In its action-guiding guise decision theory is a theory of deliberation. The theory’s overarching principle is the principle of maximizing expected utility. The role of the expected utility principle in deliberation is elegantly summarized (using slightly different terminology) in the first paragraph of a leading textbook, Richard Jeffrey’s The Logic of Decision. To deliberate is to evaluate lines of action in terms of their consequences, which may depend upon circumstances the agent can neither predict nor control. The name of the eighteenth century English clergyman Thomas Bayes has come to be associated with a particular framework for deliberation, in which the agent’s notions of the probabilities of the relevant circumstances and the desirabilities of the possible consequences are represented by numbers that collectively determine an estimate of desirability for each of the acts under consideration. The Bayesian principle, then, is to choose an act of maximum expected desirability. (An act rather than the act, since two or more of the possible acts may have the same, maximum estimated desirability.) The numerical probabilities and desirabilities are meant to be subjective in the sense that they reflect the agent’s actual beliefs and preferences, irrespective of factual or moral justification. ( Jeffrey 1983, 1)

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Introduction

Looked at in this way, decision theory is primarily first-personal. It is a theory that a decision-maker can consult to solve particular decision problems. The theory tells her how to choose, in the light of the probabilities that she assigns to the relevant circumstances and how desirable she finds the potential outcomes. In its action-guiding guise decision theory has normative force. It is a prescriptive theory. The expected utility principle tells the agent how she ought to choose, given what she believes about the world and what she desires to achieve. But this normative force is limited. As an action-guiding theory decision theory delivers judgments of hypothetical rationality—given that these are your probability and utility assignments, the rational thing for you to do is this. The concept of rationality is frequently appealed to in the context of a more comprehensive and all-embracing assessment of rationality, which we might term all-thingsconsidered or absolute rationality. We often describe an action or decision as rational tout court. Sometimes what we mean is that the agent has effectively maximized in the light of her probability and utility functions. But all-things-considered judgments of rationality can be more wide-ranging than this. We can, for example, evaluate an agent’s probability and utility functions—both in the conduct of her overall psychological life and in absolute terms. We can judge the (ir)rationality of the agent’s judgments of likelihood and desirability, as well as of how she defined the decision problem that she set out to solve. The perspective from which these questions are asked is what I call the normative assessment dimension of rationality. Both critiques of decision theory considered earlier are in essence claiming that decision theory cannot accommodate the normative assessment dimension. They say, in effect, that for rationality in this sense we need normative criteria that can be applied to evaluate and ground reasons deriving from an agent’s probability and utility functions. This cannot be done, they claim, by a mathematical theory of choice that sees rationality as answerable only to subjective probability and utility functions. And there certainly is a very real question here. Can decision theory be extended to make sense of the all-things-considered judgments that arise when decisions and actions are being normatively assessed from a perspective that allows for reasons not exhausted by the agent’s current probability and utility functions? While most decision theorists think of rationality primarily in terms of deliberation and choice and many philosophers think of rationality primarily in terms of normative assessment, most psychologists and

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economists (as well as many philosophers) think of the concept of rationality primarily as a tool of explaining and predicting behavior. We predict what people will do by working out what it would be rational for them to do, given the information that we take them to have at their disposal and the aims and goals that we attribute to them. Similarly, we explain why people behave as they do by assuming that they are rational choosers and then working backwards from the choices that they make to beliefs and desires that rationalize their choice. The same question arises: Can we understand this way of thinking about rationality through decision theory? One of the many questions that arises here is whether we can give a plausible psychological interpretation of utility and probability, the central notions of decision theory. Some philosophers have explicitly claimed that talking about an agent’s probability and utility functions is really just a regimentation of our ordinary talk of beliefs and desires. David Lewis, for example, has written that ‘‘Decision theory (at least if we omit the frills) is not esoteric science, however unfamiliar it may seem to an outsider. Rather it is a systematic exposition of the consequences of certain well-chosen platitudes about belief, desire, preference, and choice. It is the very core of our commonsense theory of persons, dissected out and elegantly systematized’’ (Lewis 1983, 114). This way of thinking about decision theory needs to come to terms with considerable psychological evidence that the theory’s basic assumptions are not reflected in everyday decision-making (Kahneman and Tversky 1979; Tversky and Kahneman 1986). It turns out that people’s preferences are often inconsistent in ways that the theory of choice cannot countenance or accommodate. But then how can it be true both that the theory of choice is a systematic exposition of commonsense or folk psychology (as Lewis suggests) and that folk psychology is a powerful predictive and explanatory theory that rests upon assumptions of rationality? In general economists have been less troubled about the prospects of decision theory in this domain. Although psychological studies of decision-making frequently develop more conceptual worries raised by economists such as Allais (1979) and Ellsberg (1961), many economists are unconcerned with matters of psychological realism. Milton Friedman claimed in his famous essay ‘‘The methodology of positive economics’’ that the rationality assumptions of economic theory need not be psychologically realistic. All that matters is that they should yield accurate predictions of economic behavior (Friedman 1953).

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Introduction

In any event, appealing to the notion of rationality to explain and predict behavior is a rather different project from the deliberative and normative assessment projects we have been considering. If decision theory is to serve as the core of a unified theory of rationality then it must be able to serve all three of these explanatory projects. Yet there are fundamental challenges that need to be met before decision theory can be taken in this way. These are not challenges for, or objections to, decision theory per se. They are challenges that emerge when we try to extend the mathematical theory beyond its core role as a theory of deliberation. The challenges arise because each explanatory project imposes its own constraints and pressures on the theory of choice and these constraints and pressures pull in different directions. This book explores three of these challenges, one in each of the three principal chapters. Each challenge derives from a different aspect of decision theory. The first challenge comes when we think about how to interpret the theory’s central notion of utility. Most economists and decision theorists understand utility as a measure of preference revealed by choice, and hence understand the expected utility principle as essentially a recipe for preserving a certain type of consistency in one’s choices. This has some plausibility when one is thinking about decision theory as a theory of deliberation, but much less so when we think about the theory as a tool of explanation and prediction. If numerical utilities and probabilities are to give us ways of making sense of our commonsense psychological notions of belief and desire, then they must be understood more robustly. As we see in Chapter 2, however, it is very difficult to develop a notion of utility that is sufficiently robust to do the job of explanation/prediction, while at the same time fulfilling the demands of the action-guiding and normative assessment projects. The second challenge has to do with how decision problems are understood within decision theory. It is here that the question of the theory’s descriptive adequacy comes most prominently to the fore. Psychologists have produced considerable evidence that the basic assumptions of decision theory are not reflected in everyday decisionmaking (Kahneman and Tversky 1979; Tversky and Kahneman 1986). People’s preferences are often inconsistent in ways that the theory cannot countenance or accommodate. This poses obvious problems for the project of treating decision theory as a tool of explanation and/or prediction. The basic problem is that decision theory is standardly taken to be extensional. It takes no account of the twin facts, first,

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that a particular outcome can be thought about in different ways and, second, that decision-makers frequently assign different utilities to the same outcome depending upon how they understand it. Yet it looks very much as if from the perspective of explanation and prediction we need a notion of rationality that is intensional and takes into account how agents and decision-makers conceptualize the situation that they confront. Chapter 3 explores the tensions that this creates between the projects of explanation/prediction, on the one hand, and normative assessment, on the other. The third challenge comes when we try to extend decision theory to accommodate choice over time. A theory of rationality needs to be dynamic rather than static, diachronic rather than synchronic. It needs to be able to make sense of how probability and utility assignments can rationally change over time. Can decision theory do this? Once again we find tensions between the three different dimensions. In its actionguiding guise the distinctive feature of decision theory is that what counts as a rational choice at a given time is solely a function of the agent’s utilities at that time (together with her probabilities). Yet, from the perspective both of normative assessment and of explanation/prediction, it seems essential to allow plans and commitments made at one time to have force at a later time, even if they are not reflected in the agent’s preferences at that later time. As emerges in Chapter 4, the phenomenon of sequential inconsistency (in essence, deciding upon a plan and then failing to carry it through) looks very different from the normative and action-guiding perspectives. There is a number of strategies for extending and modifying decision theory to resolve the tensions that this creates. None of them turns out to be satisfying. Each of these three challenges has been the subject of much debate. I claim, though, that their real import has been missed. Discussion has been framed in all-or-nothing terms, as if the issue were the validity in some absolute sense of decision theory as a theory of rationality. And, unsurprisingly, decision theorists and their opponents have reached little consensus on the force or otherwise of the challenges! My aim in this book is to cast a new light on these debates by interpreting them in a finer-grained way. Instead of thinking about, for example, the Allais paradox or the phenomenon of sequential inconsistency as challenges to decision theory per se, we should think about them as challenges to particular applications of the theory. What the challenges expose is that the decision theory has to be interpreted and developed in different ways depending upon which explanatory project is at stake.

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The conclusion that emerges from exploring these three challenges is that there is no prospect of taking decision theory to serve simultaneously as a theory of deliberation, a standard for the normative assessment of decision-making and action, and a tool for explaining and predicting behavior. By interpreting and extending decision theory in a way that allows it to serve one of these explanatory functions we effectively bar it from serving one or both of the other two functions. The required extensions and interpretations of decision theory are pairwise incompatible. But, as we see in the final chapter, the three different dimensions of rationality are not themselves inconsistent. Quite the contrary, in fact. I argue that they are interdependent. So we cannot have a theory of rationality that serves only one of the explanatory tasks. Any reasons that we might have for thinking that decision theory (or any other theory, for that matter) can give us a successful theory of deliberation will themselves be reasons for thinking that it serves the explanatory/predictive function. And there is no prospect of a theory of rationality that serves as a tool of normative assessment without at the same time serving as a theory of deliberation. It turns out, therefore, that the prospects for taking decision theory as the core of a theory of rationality are poor indeed.

1 Decision Theory and the Dimensions of Rationality The concept of rationality has (at least) three different dimensions. Most basic is the action-guiding dimension. We use the concept of rationality to identify a privileged subset of the set of possible ways of resolving a given decision problem, narrowing down the possible resolutions to those that are legitimate. We also use it for the purpose of normative assessment in a broader sense—a sense that does not simply take the decision problem as given, but extends to how that decision problem is configured. Finally, the concept of rationality is a tool for psychological explanation and prediction. The fundamental question for this book is whether decision theory can be interpreted and extended in a way that does justice to all three of these different dimensions of rationality. Can decision theory, as developed by economists and statisticians, yield a theory of rationality adequate to these three very different explanatory tasks? This introductory chapter sets out how I understand this question and how I propose to tackle it. I begin by explaining in more detail the different explanatory projects underlying the three dimensions of rationality. I introduce the basic elements of decision theory and show how it can serve as a theory of deliberation (as an action-guiding theory of rational decision-making). I then go on to explore how, at least on first appearances, decision theory might be deployed in the projects of normative assessment and explanation/prediction. In doing this I will identify three very basic challenges that decision theory must confront if it is to be taken as a theory of rationality. These three challenges will occupy us for the main part of this book. The present chapter allows them to come into view.

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T H E AC T I O N - G U I D I N G D I M E N S I O N Everyday life is made up of a constant series of decision problems of different degrees of seriousness and import. Choosing what to have for breakfast is a decision problem. So is choosing what college to attend or what career to follow. Many decision problems are resolved without much (and often indeed without any) explicit deliberation. But others provoke much soul-searching and deep thought. In the second case we might say that the decision problem is solved, as well as resolved. Any choice, random or thought-out, resolves a decision problem, but solving a decision problem involves reflection and deliberation. In its most basic sense, the concept of rationality applies to resolutions of decision problems. Some ways of resolving decision problems may be rational. Others not. In some cases there may be more than one rational resolution. And nor, at this stage, should we rule out the possibility that in some circumstances there may not be any. In what I will call the action-guiding sense of rationality, the job of the theory of rationality is to identify a privileged subset of the options available in a decision problem. These are the rational resolutions of the decision problem. What exactly is a decision problem? A decision problem arises when an agent believes herself to have a number of distinct possible actions open to her. She believes each action to have a range of possible outcomes. These outcomes may vary according to certain facts about the world that may or may not be within the agent’s control. Let us say, then, that a decision problem has three components. The first component is the acts that the agent believes to be available (jay-walking or waiting for the lights to change, for example). The second component is the outcomes that the agent believes might occur (arriving more quickly at her destination, say, as opposed to perishing in a traffic accident). The third component is given by the states of the world that will, together with the act performed, determine the outcome (in this case one might expect these to include the circumstance of my tripping as I cross the road, the circumstance of the car currently 100 yards away moving considerably above the speed limit, and so on). The decision problem is deciding which of the possible acts to perform in the light of the information available.

Dimensions of Rationality

Cdna

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Act1

Otca1

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Act2 ...

Otca2 ...

Otcb2 ...

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Figure 1.1 The abstract form of a decision problem, showing the relation between acts, conditions (Cdn), and outcomes (Otc). The subscripts index outcomes according to the acts and conditions that determine them.

In its action-guiding guise a theory of rationality aims to identify rational resolutions of decision problems that have this basic type. But a theory of rationality in the action-guiding sense needs to do more than this. As was remarked earlier, some decision problems are solved as well as resolved. An agent solves a decision problem when she reasons her way to identifying a privileged subset of the acts available in the decision problem. The solution is a rational one when the privileged subset the agent identifies either coincides with, or is a subset of, the one identified by the theory of rationality. A theory of rationality might reasonably be expected to give an agent tools for solving decision problems, so that she can herself identify the rational solutions to the decision problem. A theory of rationality in this sense would be a theory of deliberation. The raw materials for a theory of rationality in the action-guiding sense are the information that the agent has about the available acts and the relevant possible conditions of the world, together with her attitudes towards the possible outcomes. And the notion of rationality in play is at bottom an instrumental one. In very general terms, the rational resolutions of a decision problem are those that give the agent the best prospect of realizing her goals relative to the information that she has available to her. And so a theory of rationality in the action-guiding sense can be expected to provide the agent with tools for identifying how she can best realize her goals in the light of the information that she has. Such a theory will provide a blueprint for solving decision problems. To say that an agent has solved a problem in this sense is not necessarily to say that she thereby has compelling reason to act in

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the way that the solution prescribes. There may be moral reasons, for example, not to act rationally (at least if it turns out that morality is not ultimately grounded in a theory of rationality, in the manner proposed by Gauthier). And there may be reasons internal to the theory of rationality for not implementing the solution (in the cases, discussed further in the next section, where either an agent’s setting up of the decision problem or her practical deliberation is subject to charges of irrationality). More radically, as Niko Kolodny has recently argued, there may not be reason to follow the requirements of rationality (Kolodny 2005: See Broome 2007 and Kolodny 2007 for further discussion). The first and third cases are deep and important, but they fall outside the scope of this book. The theory of rationality cannot be expected to adjudicate on the relation between reasons and rationality (or rationality and morality, for that matter) and our primary concern is with the possibility of using decision theory as a theory of rationality. T H E N O R M AT I V E A S S E S S M E N T D I M E N S I O N A theory of rationality in the action-guiding sense is clearly normative. It privileges some actions over others. The rational actions are feasible options (acceptable alternatives). Those actions not in the privileged subset are neither feasible nor acceptable (from the perspective of rationality, at least). This is one way in which an action-guiding theory provides normative criteria for assessing how decision problems are resolved. But there are other ways, applying specifically when decision problems are resolved by being solved. To the extent that an action-guiding theory of rationality serves as a blueprint for practical decision-making, it gives normative criteria for assessing how an agent is deliberating about a particular decision problem in the light of the information available to him about available courses of action, relevant possible conditions of the world, and foreseeable outcomes. The agent might be failing to apply the blueprint correctly, for example. However, there are normative criteria for assessing choices in terms of their rationality over and above those derivable from the actionguiding dimension of rationality as so far discussed. In thinking about rational choices from the action-guiding perspective we hold fixed the agent’s goals and information. We take for granted her assessment of the available acts and the relevant possible conditions of the world, as well as her attitudes towards the possible outcomes. The agent’s

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assessment and attitudes set the parameters of the decision problem and an action-guiding theory of rationality can only be applied once those parameters are set. But we can ask about the rationality of how the parameters are set as well as about how a choice is made once the parameters have been set. For example, we might find irrationality in the attitudes that an agent takes to what he identifies as the possible outcomes. He might be in the grip of a ‘‘framing effect’’ that leads him to value what is essentially the same outcome in two different ways (suppose for example that he is prepared to shop at a store that offers a 5% discount for paying with cash as opposed to paying by check or credit card, but refuses to shop at a store that places a 5.2% surcharge on non-cash payments). Alternatively, an agent may display cyclicality in her preferences. She may prefer a over b, b over c, and c over a. The (ir)rationality of framing effects and cyclical preferences has been extensively discussed by philosophers, psychologists, economists, and decision theorists.¹ Both of these examples have to do ultimately with the consistency of the agent’s attitudes. Hume famously wrote in Book II section III of A Treatise of Human Nature that ‘‘ ’Tis not contrary to reason to prefer the destruction of the whole world to the scratching of my finger. ’Tis not contrary to reason for me to chuse my total ruin, to prevent the least uneasiness of an Indian or person wholly unknown to me.’’ If Hume is correct (and we take ‘‘contrary to reason’’ to be synonymous with ‘‘irrational’’), then being inconsistent is the only way in which an agent’s attitudes can be irrational. Hume’s view has been much criticized, particularly by philosophers.² At this point we need only observe that anyone who rejects the Humean view is thereby committed to the possibility of normatively assessing how the parameters of a decision problem are set. ¹ Framing effects will be discussed in detail in Chapter 2. The rationality or otherwise of cyclical preferences is often discussed in the context of so-called Dutch Book or money pump arguments, which set out to show that agents with cyclical preferences can be ‘‘pumped’’ of all their assets because the cyclicality of their preferences will lead them to pay to undo exchanges that they have paid to enter into. For an early version of the argument applied to cyclical preferences see Davidson, McKinsey, and Suppes 1955. For critical discussion see Schick 1986. Kaplan 1996 and Christensen 2004 discuss Dutch Book arguments in the context of epistemic rationality. ² Much of the discussion of Humean views of reasons in the philosophical literature is focused primarily on a separate but related claim associated with Hume to the effect that only desires and comparable mental states can be motivating. This is a claim about reasons and motivation, not about rationality. Influential discussions include Williams 1981, Smith 1994, and Blackburn 1998.

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There is also scope for normative assessment of the agent’s information-gathering. Even if one thinks that, outside the realm of games of chance and certain precisely defined physical situations, one is dealing with subjective rather than objective probabilities (with probability judgments that reflect subjective facts about one’s degrees of belief, as opposed to objective facts about frequencies or propensities), there are questions about how people arrive at their subjective probabilities. Agents sometimes fail to realize that the likelihood of a condition obtaining is affected by the action taken, as when my acting in a certain way makes it more likely that a particular condition obtains. Often what we need to take into account are probabilities conditional on one’s possible actions and agents tend not to be very good at assigning conditional probabilities of this type. And even when we are not dealing with conditional probabilities, agents are frequently poor at assessing likelihoods. It is easy to allow the salience of an outcome (a winning lottery ticket, for example) to color one’s assessment of its likelihood. Some of the different aspects of the normative assessment dimension of the concept of rationality are laid out in Figure 1.2. The first grouping has to do with the assessment of how agents resolve decision problems and how they implement their solutions. Here we are dealing with what may be thought of as the reciprocal of the action-guiding dimension. We are effectively considering the extent to which the action was appropriately guided. The second grouping moves beyond the actionguiding dimension. Whereas the first grouping assesses deliberation and action relative to the decision problem as conceived by the agent, the second grouping goes a step further back and considers how the agent defined the decision problem, evaluating such factors as the agent’s assiduity in gathering information and the internal consistency and general acceptability of their ranking of the outcomes.

T H E P R E D I C T I V E / E X P L A N ATO RY D I M E N S I O N According to influential philosophical models such as that in Davidson 1963, psychological explanation proceeds by working backwards from the action being explained to a psychological characterization of the agent. That characterization is correct just if the beliefs, desires, and other psychological states featuring in the psychological characterization

Normative dimension of concept of rationality

Immediately derivable from action-guiding dimension?

• How appropriately was the decision problem resolved? (relative to a particular formulation of the mathematical theory of choice)

NO • How effective was the agent’s information-gathering? (e.g. the appropriateness of judgments about the available acts, conditions, and outcomes) • How appropriate was the agent’s assessment of the relations between acts, outcomes, and decisions? (e.g. assessment of relative likelihoods)

• Is the agent’s ranking of the outcomes internally consistent? (e.g. transitivity of preferences, acyclicality etc.)

• How acceptable, from an external perspective, was the agent’s ranking of the outcomes?

Dimensions of Rationality

YES

• Was the action performed a rational solution to the decision problem?

Figure 1.2 Different aspects of the normative assessment dimension of the concept of rationality.

17

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Decision Theory and Rationality

are indeed the psychological states that gave rise to the action. In identifying those psychological states, however, the explainer is supposed to be guided by an assumption of rationality. The psychological states appealed to must be such that the action is rational in the light of the agent’s psychological profile. Rationality is a regulative constraint in psychological explanation. The same holds for psychological prediction. The aim of prediction is to work out, given one’s knowledge of the psychological profile of the agent, what that agent will do. In making predictions the predictor is guided by the regulative ideal of what it would be rational for that agent to do. Of course, it will not always be the case (either in explanation or prediction) that the rationality constraint secures a unique solution to the problem, but the claim is that satisfying the rationality constraint is a necessary condition of explanation or prediction even when it is not sufficient. The motivation for the rationality constraint is the same in the explanatory and predictive cases. It is the only way of bridging the gap between an agent’s psychological profile and his behavior. An action is compatible with indefinitely many psychological profiles and any psychological profile can be acted upon in indefinitely many ways. The rationality constraint cuts down the possible dimensions of variation. We assume, in working backwards from behavior to psychological profile, that the beliefs and desires we attribute must rationalize the behavior we are trying to explain. Without this assumption it is hard to know how we could even get started. The rationality constraint effectively imposes a tight connection between the action-guiding and the predictive/explanatory dimensions. If we are trying to predict someone’s behavior in a given situation then our prediction must be one of the actions that it would be rational, in the action-guiding sense, for the agent to perform. In fact, as proponents of the simulation approach to ‘‘theory of mind’’ have emphasized, one way of securing such a prediction is to think oneself into an approximation of the psychological profile of the person whose behavior one is trying to predict and then to ask oneself the action-guiding question from the first-person perspective (Gordon 1986; Heal 1986). The predictive/explanatory dimension can be understood, however, in a way that is neutral between particular models of how explanation and prediction are achieved. The force of the idea that the concept of rationality has an explanatory/predictive dimension depends upon how rationality is understood.

Dimensions of Rationality

19

Philosophers and economists tend to work with some version of decision theory. Scientific psychologists, in contrast, have typically approached the question from the opposite direction, taking it as given that a theory of rationality must provide a descriptively and predictively adequate account of decision-making and then working backwards from a descriptive model of choice to a theory of rationality. Kahneman and Tversky’s prospect theory is a case in point.³ Kahneman and Tversky themselves distinguish the explanatory/predictive project from the normative and action-guiding projects (Tversky and Kahneman 1986), arguing that no single theory can do all three jobs because the best normative theory is hopeless from a descriptive point of view. But other authors have tried to bring the normative and the descriptive into harmony. This is integral to the rational analysis approach to cognition (Chater and Oaksford 1999; Oaksford and Chater 1998). We will return in Chapter 5 to the question of whether the psychology of reasoning can be understood independently of the theory of deliberation.

T H E S T R AT E G Y In thinking about the consistency and the compatibility of the three dimensions of rationality we can take one of the dimensions as basic and then explore whether a theory of rationality that fulfils the requirements of that dimension can be extended and expanded to fulfil the requirements of the other two dimensions. There are two good reasons for starting with the action-guiding dimension. First, the domain of the action-guiding dimension is clearly circumscribed. There are fewer dimensions of variation. It is set by individual decision problems, on the assumption that the relevant parameters have all been set. A satisfactory account of rationality, from the actionguiding point of view, will be one that identifies either a single course of action within a decision problem as the one that it is rational for the agent to choose, or a subset of the possible courses of action as rationally admissible. In neither the normative assessment nor the ³ For a similar direction of explanation leading to a very different final theory see Weirich 2004. Weirich proposes to bridge the gap between the normative and descriptive by developing what in the title of his book he describes as ‘‘rules for nonideal agents in nonideal circumstances’’.

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explanatory-predictive dimension is the sphere of application so tidy. Factors that are taken as fixed from the action-guiding perspective are treated as parameters from the normative assessment dimensions—e.g. the agent’s attitudes to what she sees as the possible outcomes, not to mention the fact that these are the only possible outcomes that she sees. It is true that prediction often holds fixed the very same factors that are held fixed in practical deliberation. But an important part of the project of psychological explanation is working out how to regiment possible interpretations of the ‘‘springs of action’’ into the form of a decision problem. Suppose that we have such an account of action-guiding rationality. We can then ask whether that account, either as it stands or suitably extended, can serve the purposes of normative assessment and explanation/prediction. The viability of this strategy depends upon the plausibility of our account of action-guiding rationality. A second reason for beginning with the action-guiding sense is that we have very well-studied and elegant mathematical theories of which resolutions of decision problems count as rational in the action-guiding sense. From such theories we may derive, or so I argue, a core theory of minimal instrumental rationality in the action-guiding sense that we can take as our starting-point for thinking about the concept of rationality more broadly. This core theory is, in essence, decision theory. The next section briefly surveys the basic elements of decision theory, considered as an action-guiding theory of rational deliberation.

E L E M E N TS O F D E C I S I O N T H E O RY⁴ Many decision problems involve what is known as decision-making under certainty, where each action has only one possible outcome. Dining out can be modeled as a form of decision-making under certainty, since it is safe to assume that the food one orders will indeed appear (although ⁴ This section summarizes what I take to be the uncontroversial basic principles of decision theory. The details can be found in well-known textbooks, such as Jeffrey 1983, Resnik 1987 and chs. 2 and 13 of Luce and Raiffa 1957. Of course, as with any other theory, these basic principles have been criticized and modifications and replacements proposed. We will be considering some of these criticisms and replacements in Chapters 3 and 4 (particularly those that have to do with the somewhat contentious substitution axiom in axiomatizations of utility theory). Overviews of the full range of alternatives on offer can be found in Starmer 2000 and Sugden 2004.

Dimensions of Rationality

21

in cases where there is some uncertainty about how good the food will be, the problem can also be one of decision-making under risk—see below). Decision problems of this type have the following form: Act1 Act2 ··· Actn

Cdna Otca1 Otca2 ··· Otcan

Intuitively, all that the decision-maker need do is rank the relevant outcomes and then choose the action that leads to the outcome with the highest rank. What is it to rank a set of outcomes Otca1 , Otca2 , . . . Otcan so that this can be done? At a minimum it requires there to be some preference relation R such that, for any pair of outcomes a and b, either aRb or bRa or both. Alternatively, it is for there to be some relation R such that it is not the case that R fails to hold between any two outcomes. Any relation that has this property is said to be complete. We might plausibly take R to be is preferred or indifferent to (generally called the relation of weak preference), so that aRb holds just if the agent either prefers a to b or is indifferent between a and b. We can use relation R to define two further relations—a relation of strict preference and a relation of indifference. As one would expect, aPb (the agent strictly prefers a to b) holds just if aRb holds and bRa does not hold, while aIb (the agent is indifferent between a and b) holds just if aRb and bRa both hold. We obtain a suitable ranking of the outcomes if R is complete and has the further property of transitivity (that is, for any three outcomes between which R holds, if a bears R to b and b bears R to c, then a bears R to c). This allows us to organize all the outcomes into a linear ordering with the most favored at the top and the least favored at the bottom (assuming that there are only finitely many outcomes).⁵ We begin by grouping together all the outcomes between which the agent is indifferent (technically, these are the equivalence classes under the indifference relation). Then we order these groups of outcomes under the strict preference relation. The transitivity of the weak preference relation entails the transitivity of the strict preference ⁵ Technically it is not the outcomes that are being linearly ordered, but the equivalence classes of outcomes under the indifference relation.

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relation. It also rules out the possibility of the strict preference relation being cyclical (e.g. where an agent strictly prefers a to b, b to c and c to a).⁶ A transitive acyclical preference relation can be numerically represented by any set of numbers that preserves the ordering. Suppose, for example, that I am indifferent between a and b, but prefer them both to c and prefer c to d. Then I can assign numerical values in any way that respects those relations. I might, for example, assign 25 to a and b, 16 to c, and 9 to d. Let us call these numerical values utilities. We should not conclude that I would be indifferent between a, on the one hand, and c + d on the other, on the grounds that the utility of d is the difference between the utilities of a and c, since there are order-preserving transformations (such as taking square roots) that fail to preserve this property. To put it in the standard terminology, in thinking about decision-making in conditions of certainty we need appeal only to ordinal, rather than cardinal utilities. For decision-making under certainty decision theory tells us that a rational resolution of a decision problem is one that maximizes utility. If we are resolving the decision problem by solving it then we should choose the action whose outcome has the highest utility. For any agent with a transitive and complete preference ordering (over a finite set of outcomes) there will always be at least one such an action. If there is more than one, decision theory tells us not only that we must choose one of the tied actions, but also that there can be no rational grounds for choosing between them. If we need to break the deadlock then we will have to do so in an arbitrary manner, perhaps by tossing a coin. We move away from decision-making under certainty when there is more than one relevant possible state of the world. At one extreme we may assume that agents have a complete probability distribution for the different possible conditions. In some cases this might be a distribution of objective probabilities. In others it might be a complete subjective probability distribution over the relevant possible conditions, where a subjective probability distribution is an assignment of degrees of confidence, or degrees of belief, that respects the basic laws of the probability calculus (so that, if the relevant possible conditions are mutually exhaustive then the degrees of confidence I assign to them ⁶ Suppose that aPb, bPc, and cPa. By the definition of strict preference this gives aRb and bRc. Transitivity of weak preference gives aRc. But, again by the definition of strict preference, if cPa holds then aRc does not.

Dimensions of Rationality

23

must sum to 1; if I assign degree of confidence p to one of them, then I must assign degree of confidence 1 − p to its not occurring; and so on). This type of decision-making is often termed decision-making under risk. Suppose that the decision-maker has utilities corresponding to the different possible outcomes (as we will see, these cannot be the ordinal utilities that suffice for decision-making under certainty) and probabilities assigned to the different conditions. Then the decision problem looks like this:

Cdna

Cdnb

Cdni

pa

pb

...

pi

Act1

ua1

ub1

...

ui1

Act2

ua2

ub2

...

ui2

...

...

...

...

...

Actn

uan

ubn

...

uin

Figure 1.3 The abstract form of a decision problem under risk with probabilities assigned to conditions and utilities assigned to outcomes.

Standard models of decision-making under risk involve calculations of the expected utility of each available action. We start with each possible outcome, multiplying the utility of that outcome by the probability we have assigned to the condition of the world in which it will come about. Summing the values thus obtained for each of the possible outcomes of a given action gives the expected utility of that action. Standard models of decision-making under risk identify the rational resolutions of decision problems as those that maximize expected utility. These models take us beyond ordinal utilities. Suppose that you are choosing a ball from an urn with 20 white, 30 black, and 50 red balls. You will receive a prize depending on whether you have correctly predicted what color the ball turns out to be. As it happens you value the prize for the white ball over the prize for the black ball over the prize for the red ball. Since this ordering goes against the ordering of objective probabilities you will need to do an expected utility calculation. Suppose that we are dealing with ordinal utilities

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and we assign numbers that respect this ordering. We might obtain the following decision table

Predict White Predict Black Predict Red

Ball is White 0.2

Ball is Black 0.3

Ball is Red 0.5

25 0 0

0 16 0

0 0 9

Here EU(Predict White) = 0.2 × 25 = 5 > EU(Predict Black) = 0.3 × 16 = 4.8 > EU(Predict Red) = 0.5 × 9 = 4.5. So our decision rule tells us to Predict White. But the order-preserving operation of taking square roots reverses the ranking. Now we have EU(Predict Red) = 0.5 × 3 = 1.5) > EU(Predict Black) = 0.3 × 4 = 1.2 > EU(Predict White) = 0.2 × 5 = 1. Since we do not want the prescriptions of rationality to rest upon an arbitrary choice of numbers we need more constraints on how we assign numerical values to utilities in cases of decision-making under risk. We want a way of thinking numerically about the relative ‘‘distances’’ between valued outcomes that is independent of the particular scale used to measure those distances. Since it is the possibility of non-linear transformations (such as squaring, or taking the square root) that rules out using ordinal utilities for expected utility calculations, we can get rid of the anomalies these create by restricting the permissible transformations to positive linear transformations (where we can transform a set of numbers in a linear manner by adding or substracting a constant number to each of them, or by multiplying, or dividing, each of them by a given number).⁷ At the other extreme lie problems where the agent has no information at all about the probabilities (either subjective or objective) of the possible conditions. These are problems of decision-making under uncertainty. Plainly agents operating under uncertainty cannot employ the criterion of expected utility maximization, since expected utilities cannot be defined in the absence of numerical probabilities. Nor would it be wise to employ the criterion of straightforward utility maximization, since the outcome with the highest utility may in fact be so unlikely as to be irrelevant. ⁷ The numbers in the second case have to be positive, as multiplication by a negative number is order-reversing and multiplication by 0 is order-destroying.

Dimensions of Rationality

25

Decision theorists have proposed a number of decision rules for decision-making under uncertainty. Luce and Raiffa’s well-known textbook (Luce and Raiffa 1957) gives four such rules. •

•

•

Maximin. Choose the act whose minimum utility value is the highest among the available acts—colloquially, make the worstcase scenario as good as it can be. The decision-maker assigns to each act its lowest possible utility value (its security level) and then selects the act with the highest security level. Minimax regret criterion. This tells us to minimize the amount of ‘‘regret’’ that could result from our choice. If ua1 is the utility of performing act a in condition 1, then we define the regret index ra1 of a as the difference between ua1 and the maximum possible pay-off in condition 1. The regret level for a given action is the highest regret factor that it makes possible. Minimax regret tells decision-makers to minimize the maximum regret level. Hurwicz α-criterion. This works on the assumption that agents assign a certain weight to the occurrence of the worst-case scenario relative to the occurrence of the best-case scenario. Let the scale of possible weights be the interval between 0 and 1, and take α to be the pessimism index (i.e. the weight attached to the worst-case scenario), so that the weight attached to the best-case scenario is 1 − α.⁸ The Hurwicz α–criterion prescribes choosing the action An with the highest α–index, defined as follows (where mn is the worst-case and Mn the best-case scenario: α(An ) = mn (α) + Mn (1 − α)

⁸ Luce and Raiffa (1957, 283) suggest the following simple technique for calculating one’s pessimism index. Consider a simple decision problem under uncertainty in which there are two available actions with pay-offs as follow: Act1 Act2

Cdn1 0 x

Cdn2 1 x

The α–index of Act1 is α × 0 + (1 − α) × 1 = 1 − α, while the α–index of Act2 is α × x + (1 − α) × x = αx + x − αx = x. Suppose that we solve this decision problem for x —that is, that we find a value for x such that we are indifferent between Act1 and Act2 . Then we will have established a value of x such that 1 − α = x, which allows us to calculate a value for α. We can then take this value of α and apply it to other problems of decision-making under uncertainty.

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Decision Theory and Rationality •

Insufficient reason. This tells us, when we are confronted with a set of mutually exhaustive and exclusive states (i.e. such that we know that exactly one such state must hold) but are completely ignorant which state holds, that we should treat those states as equi-probable. So, if there are n such states we assign to each of them probability 1/n and then make a standard expected utility calculation with the aim of selecting the action that maximizes expected utility.

According to a certain type of Bayesianism in decision theory, we only ever need to take into account the idealized limit of decision-making under risk where agents have a complete probability distribution over possible conditions. Even when agents have no information, Insufficient Reason still yields a probability distribution. To propose any other decision rule is (it is said) to depart from orthodox Bayesianism. Nonetheless, one might reasonably think that much practical decision-making takes place in between these two idealized limits. In such cases agents fall short of the Bayesian ideal by having incomplete and indeterminate probability judgments. Bayesians think that such incomplete and indeterminate probability judgments reflect a certain type of ignorance—ignorance of one’s own numerically determinate probability judgments. But many authors have thought that there are cases where it is both reasonable and rational not to have determinate judgments of probability (Gärdenfors and Sahlin 1982; Levi 1974). One way to model these cases is to assume that agents have sets of probability distributions rather than single probability distributions. This assumption generates different decision rules. Here is one. •

Wald maximin (Levi 1986). This instructs us to work out the security level of each action by computing its expected value according to each distribution and then selecting the lowest. We then choose the action with the highest security level.

A different way of approaching decision-making between the two idealized limits is to represent judgments of probability in terms of intervals rather than points (Kyburg 1983). Again, this has been taken to lead to a variety of different decision principles. An example is •

Kyburg’s principle III. No action is permissible if its maximum expected utility (i.e. its expected utility calculated according to the upper bounds of the probability intervals) is exceeded by some

Dimensions of Rationality

27

other action’s minimum expected utility (calculated according to the lower bounds of the probability intervals). The vast majority of decision theorists are agreed on the principles of maximizing utility and maximizing expected utility for decision-making under certainty and decision-making under risk when the Bayesian condition is satisfied. Most of the disputes have to do with how to deal with situations where the Bayesian condition is not met. We will be able to steer clear of these debates most of the time. The tensions that exist between the different explanatory projects can be brought out in the context of decision problems for which the full Bayesian requirements are met. In sum, decision theory yields tools for solving decision problems with parameters set by the available courses of action; the outcomes of those actions; and the possible states of the world. It can satisfy the action-guiding constraint upon a theory of rationality. But what about the demands of the other two dimensions? If decision theory is to serve a normative role, it must be reflectively grounded in ways that are not required for it to serve an action-guiding role. As far as explanation and prediction are concerned, on the other hand, we need to occupy ourselves with epistemological questions in a way that is not required for either the action-guiding or the normative assessment dimensions.

D E C I S I O N T H E O RY A S A T H E O RY O F N O R M AT I V E A S S E S S M E N T In its action-guiding guise decision theory prescribes choosing according to certain basic principles—the principle of maximizing utility (for decision-making under certainty) and the principle of maximizing expected utility (for decision-making under risk). But does it have anything to say about why one ought to choose according to those principles? What would be wrong with failing to maximize (expected) utility? It turns out that decision theory can provide a powerful grounding for taking its basic decision rules as normatively binding. The grounding comes from the possibility of placing the theory on an axiomatic basis. We can see how this works by considering what decision theory says about an agent who fails to choose in a way that maximizes utility (in a case of decision-making under certainty). This might come about

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Decision Theory and Rationality

in one of two ways. The agent might have a transitive and complete (weak) preference ordering, but fail to choose the most preferred item. Alternatively, she might fail to have a transitive and complete weak preference ordering at all. The first case is not particularly interesting from a conceptual point of view. It is most likely to involve an error of memory or of basic self-knowledge, or simply weakness of will. More interesting are situations where an agent fails to have a transitive weak preference ordering. But why should this be subject to normative censure? What’s wrong with intransitive preferences? Money pump arguments provide one answer to this (see n. 1), but a more promising way of looking at the matter is through the relation between preference and choice. As we will see in Chapter 2, this relation is complex and has been understood in many different ways. For the moment, though, we need simply consider a case where an agent’s preferences are straightforwardly reflected in the choices that she makes. We can start with the choices and work backwards to the preferences. Suppose that the set X of possible outcomes has 3 members, so that X = {a, b, c}. We can represent choices through a choice function C over all the different possible combinations of members of X. Let us call these the feasible sets. To each feasible set the choice function assigns a non-empty subset (its choice set). Imagine that the choice function is as follows: C{a, c} = {a} C{a, b} = {a, b} C{b, c} = {c} C{a, b, c} = {a}⁹ In the case where C assigns more than one member of X to a choice set (as in the second case) this is to be read as saying that the agent has no grounds for choosing between them. These are cases where an agent would choose at random (rather than choosing both!). If, as we are assuming, the choice function is an accurate reflection of preference we can assign preferences as follows C{a, c} = {a} ⇒ a is strictly preferred to c (aPc) C{a, b} = {a, b} ⇒ a and b are indifferent (aIb) ⁹ Each single-membered subset of X is its own choice set, because choice sets have to be non-empty.

Dimensions of Rationality

29

C{b, c} = {c} ⇒ c is strictly preferred to b (cPb) C{a, b, c} = {a} ⇒ a is strictly preferred to b and a is strictly preferred to c (aPc & aPb) No ordering of these preferences can be transitive. Since the agent strictly prefers c to b, is indifferent between b and a, and strictly prefers a to c, this would entail that the agent strictly prefers c to c, which is impossible.¹⁰ Equally, an intransitive set of preferences such as this one can easily give rise to a choice function like that discussed. So, one way of thinking about what might be wrong with intransitive preferences would be by thinking about what’s wrong with this choice function. The choice function has a curious property. The choice set for {a, b} contains both a and b, thereby revealing that the agent does not either strictly prefer a to b or b to a. And yet when c is added to {a, b} the agent reveals a clear preference for a over b (because the choice set for {a, b, c} is {a}). This inconsistency breaches a form of what is known as Samuelson’s weak axiom of revealed preference (the idea behind the name being that my choices reveal certain facts about my preferences). The revealed preference axiom requires that, if one item is in the choice set for a feasible set that contains a second item, then the second item will not be in the choice set for a different feasible set that contains both items unless the first item is also in that choice set.¹¹ In the example we are considering the axiom is working in an ‘‘upwards’’ direction. That is to say, it is adding elements to {a, b} that results in a breach of the axiom. But the axiom can also be breached in a ‘‘downwards’’ direction, when the second choice set is a proper subset of the first. This would occur, for example, if we have C{a, b, c} = {a, b} and C{a, b} = a.¹² And there is no general requirement that one of the two sets be a subset of the other. The key point here is that it is provable that patterns of preferences are transitive if and only if the choices that they rationalize ¹⁰ The definition of strict preference entails its irreflexivity, since aPa would require aRa both to hold and not to hold. The argument in the text relies upon the property sometimes known as IP-transitivity—namely, that aPb, bIc, and cPd jointly entail aPd. This follows straightforwardly from the transitivity of weak preference. ¹¹ Let us say that a is revealed preferred to b if a is chosen when b is available. We write this aRC b. In some of these cases b will also be chosen. In others not. Where b is not chosen let us say that a is revealed strictly preferred to b. We write this aR∗C b. The weak axiom of revealed preference says that ∀x∀y ¬ (xR∗C y & yRC x). ¹² A downwards failure of the revealed preference axiom is often called a breach of the Chernoff condition (Chernoff 1954) or the α-condition (Sen 1993).

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satisfy the weak axiom of revealed preference.¹³ So, if the principle of utility maximization is justified in terms of the revealed preference axiom, then the choice theorist has a solid basis from which to censure failures to maximize utility that are due to lack of a transitive preference ordering. In grounding the theory’s normative force by arguing from what are taken to be simpler and more fundamental principles, the choice theorist is proceeding axiomatically, aiming to validate principles of choice by showing that they follow from intuitively compelling axioms. From a methodological point of view, moreover, the great advantage of the axiomatic method is that it makes clear the source of the (putative) normative force of decision-theoretic principles, thereby demarcating the argument-space for debate about whether and how those principles might be used for the purposes of normative assessment.¹⁴ The canonical application of the axiomatic method comes with decision-making under risk. The fundamental source for the normative force of expected utility theory lies in what are known as representation theorems showing that maximizing expected utility is equivalent to having preferences that satisfy certain basic consistency requirements, where those basic consistency requirements are the axioms of expected utility theory. The representation theorems show that, if an individual’s preferences satisfy the axioms then we can derive a probability function and a utility function such that those preferences come out as maximizing expected utility. ¹³ For the proof see Suzumura 1983 Theorem 2.2. The only condition required is that the choice function be defined over every finite subset of the relevant set X of outcomes. Suzumura also shows ( Theorem 2.3) that under this assumption the weak axiom of revealed preference is equivalent to a number of other intuitively plausible axioms, such as Arrow’s axiom. Arrow’s axiom requires that if we have S1 ⊂ S2 for two feasible sets, and if C(S1 ) ∩ C(S2 ) = Ø, then C(S1 ) = C(S2 ). In other words, if some elements chosen from S2 are also in S1 , then those are precisely the elements chosen from S1 . ¹⁴ Here ‘‘argument-space’’ is to be taken literally. There is extensive debate about how to axiomatize the theory of utility. This is an extensive debate about what constraints can plausibly be imposed upon rational choice. And some authors have objected to the entire enterprise. In a well-known article, for example, Robert Sugden argues that there are no self-evident and universally applicable constraints upon rational choice (Sugden 1985). His strategy is to provide apparent counter-examples to a very weak constraint, the principle of minimal consistency. According to minimal consistency, if C{x, y} = {x} (that is, if x is revealed strictly preferred over y in a pairwise comparison), then y cannot be in the choice set for any set that contains both x and y. This is a very weak condition indeed. It is not breached, for example, by the pattern of choices discussed in the text. For further discussion in this area see Anand 1993, which criticizes axiomatic defences of transitivity.

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There are many representation theorems in the decision theory literature.¹⁵ One relatively accessible example is the von NeumannMorgenstern representation theorem (although the axiomatic basis is somewhat different from that originally employed by von Neumann and Morgenstern in their 1944). We begin with the idea that actions can be represented as lotteries. If we assume, as von Neumann and Morgenstern do, that to each state of the world there is attached a definite numerical probability (which we can take to be an objective probability, of the sort that might correspond to a frequency), and that the probabilities sum to 1, then we can think of each action as a lottery over the different possible outcomes. We can distinguish simple lotteries, which are defined over outcomes that are not themselves lotteries, from compound lotteries, which can contain lotteries as possible outcomes. Parallel to the claim that for decision-making under certainty the agent has a complete and transitive weak preference ordering over outcomes, here we assume that the agent has a complete and transitive ordering over the relevant simple lotteries for the decision problem—in effect, that the agent has a complete and transitive weak preference ordering of actions. What is missing is the agent’s utility function defined over outcomes. This is what the representation theorem derives. The representation theorem shows how, starting from a complete and transitive weak preference ordering of actions satisfying basic consistency requirements, one can assign numbers to outcomes so that one action is preferred to another if and only if the expected utility of the first action is greater than the expected utility of the second action (where we calculate the expected utility of an action/lottery in the standard way by summing the utilities of the outcomes weighted by their probabilities). Since the force of the representation theorem is that it is a tautology that an agent satisfying the basic consistency requirements maximizes ¹⁵ The first representation theorem was suggested by Ramsey in his 1931 paper ‘‘Truth and probability’’. The von Neumann-Morgenstern representation theorem appeared in their 1944. Unlike Ramsey, von Neumann and Morgenstern assume objective probabilities. An accessible introduction can be found in Resnik 1987, ch. 4. The first mathematically rigorous representation theorem for deriving both a utility function and a subjective probability function was proved by Savage in his 1954. For the technically demanding details of Savage’s theorem see Fishburn 1970. A very different type of representation theorem was developed by Ethan Bolker for the version of decision theory developed by Richard Jeffrey. See ch. 9 of Jeffrey 1983 for an outline of the axioms used by Bolker, and Bolker 1967 for more details. The axioms used to axiomatize what is now known as Bolker-Jeffrey decision theory have little intuitive appeal, as Jeffrey freely admits.

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expected utility, the normative force of expected utility theory derives from the consistency requirements imposed by the axioms. One version (Resnik 1987) requires the following axioms. Rationality. The agent has a complete and transitive weak preference ordering over the available actions/lotteries. Reduction of compound lotteries. Compound lotteries can be reduced to simple lotteries and the agent is indifferent between the original compound lottery and the simple lottery to which it can be reduced. Continuity. For any three lotteries A, B, and C, if A > B > C, then there is some lottery L with A and C as prizes such that the agent is indifferent between L and B. Suppose that A is winning $1000 with certainty, B is losing $10 with certainty, and C is losing $500 with certainty (all of these are what are known as degenerate lotteries—i.e. lotteries in which there is only a single outcome). Then the Continuity Axiom holds that there is some probability α such that I am indifferent between {A, α; C, 1 − α} and B. That is, there must be some probability α such that I would be equally happy whether I had a certain loss of $10 or a gamble such that I win $1000 with probability α and lose $500 otherwise. Alternatively, there is a probability α such that I would pay $10 for the gamble that wins me $1000 with probability α and loses me $500 with probability (1 − α). Substitution. Imagine that I am confronting a decision problem with two available actions, a1 and a2 , of which I prefer a2 to a1 . The substitution axiom states that, if I embed a1 and a2 in comparable compound lotteries L1 and L2 , then I must prefer the lottery in which a2 is embedded to the lottery in which a1 is embedded. Since the substitution axiom is a biconditional it works in both directions and so I am also mandated, if I prefer L2 to L1 , to prefer a2 over a1 . Effectively, what the axiom is instructing the rational agent to do when comparing two lotteries is to ignore the value of outcomes for which each lottery has the same outcome. The expected utility theorem (the representation theorem) states that, given a complete and transitive weak preference ordering over simple lotteries satisfying the substitution and continuity axioms, we can define a utility function over outcomes in such a way that an agent prefers one lottery to another just if the expected utility of the first lottery

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exceeds the expected utility of the second lottery. This gives one way of grounding the normative force of the expected utility principle. We should maximize expected utility, it might be argued, because failing to do so entails having preferences that fail to satisfy the minimal consistency requirements.¹⁶ Of course, as was the case with axiomatic justifications of resolving decision problems under certainty by maximizing utility, the von Neumann-Morgenstern representation is intended primarily to illustrate a style of argument and a space for discussion, rather than to settle any issues conclusively. One way of thinking about the various representation theorems is a way of framing the issues about the normative validation of decision theory. The representation theorems allow us to reformulate questions about the normative validity of maximizing expected utility into much more tractable and focused questions about the normative force of different axioms.¹⁷ From the normative perspective, therefore, the representation theorems in the mathematical theory of choice yield two important conclusions. The first is that they reveal that there is really only one question where there earlier seemed to be two. In Figure 1.2 we distinguished the following two questions: (1) How appropriately was the decision problem resolved (relative to a particular formulation of decision theory)? (2) How internally consistent was the agent’s ranking of the outcomes/actions? ¹⁶ This way of thinking about representation theorems has been more prominent in discussions of the normative grounding of epistemic rather than practical rationality. See, for example, Kaplan 1996 and Christensen 2004. ¹⁷ As one might imagine, these questions have received considerable attention. Starmer 2000 and Sugden 2004 survey the range of alternative decision theories (and corresponding alternative axiomatic bases). From the decision-theoretic and mathematical perspective, the most discussed axiom has been the substitution axiom, which will be discussed in detail in later chapters. Philosophers have tended to focus more on the rationality and continuity axioms. There has been considerable discussion of the assumption of commensurability presupposed by the demands for continuity and completeness. See for example the essays collected in Chang 1997. The requirement of transitivity has been challenged by a number of authors, including Anand 1993 and Temkin 2001 (but see Arrhenius and Rabinowicz 2005). Challenges to transitivity from economists include Loomes and Sugden 1982. Many of these arguments are rehearsed in Hampton 1994 and 1998. For an argument that the transitivity and completeness requirements are inconsistent see Mandler 2001 and 2005. Mandler argues that each requirement is individually plausible, but only relative to a way of understanding the preference relation that does not apply to the other requirement. We will return to the question of how to understand the preference relation in Chapter 2.

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The existence of a representation theorem for a particular formulation of decision theory collapses these two questions into one. An agent resolves a decision problem appropriately if and only if she chooses in accordance with the principle of maximizing expected utility—and she chooses in accordance with the principle of maximizing expected utility if and only if her preferences are internally consistent. Secondly, to the extent that a particular formulation of decision theory can be axiomatized on the basis of normatively compelling axioms, it has built into it a partial answer to the question of whether resolving decision problems in the way that the theory prescribes does indeed give rational solutions to those problems. If one fails to resolve a decision problem in the manner prescribed by decision theory then one ipso facto contravenes some normatively compelling axiom. Nonetheless, the possibility of axiomatizing decision theory speaks only to some of the aspects of the normative assessment dimension identified earlier. All four of the external questions identified in Figure 1.2 can be asked of an agent whose preferences are internally consistent. In particular, it has seemed to many that there are situations where one might reasonably ask whether it is rational for an agent to act upon a consistent set of preferences. Suppose, for example, that I have made a commitment to act in a way that is incompatible with my maximizing expected utility on this particular occasion. There is an extensive debate about whether it is rational to honor the commitment or to maximize expected utility. As we have presented it decision theory is entirely synchronic. It deals only with single and clearly specified decision problems and has nothing to say about the relation between different decision problems over time. We will return to this in Chapter 4. There are also resolutions of decision problems that some authors have described as rational even though they manifestly involve failing to maximize expected utility (and hence involve breaching one or more of the axioms of consistent choice). It is not hard to see, for example, that decision theory requires a form of extensionality, so that a rational agent’s ranking of outcomes cannot be sensitive to how those outcomes are understood or conceptualized. There is no acceptable utility function that assigns a certain utility to an outcome under one description and a different utility to it under another description (where ‘acceptable’ means that an agent with that utility function is able to maximize expected utility). And yet some have argued that there are rational resolutions of decision problems that breach the extensionality principle. These will be discussed in more detail in Chapter 3.

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D E C I S I O N T H E O RY A S A N E X P L A N ATO RY / P R E D IC TI VE T H E O RY The enterprise of predicting what someone else will do is often very similar to working out what to do oneself. If one knows how an agent sees a decision situation and can attribute to them either a utility function (in cases of decision-making under certainty), or a utility function and a probability function (in cases of decision-making under risk), or a utility function and a decision rule (in cases of decision-making under uncertainty), then one can use decision theory for the purposes of prediction. There is considerable idealization here. It is implausible to require that a predictor be able to assign numerically determinate utilities. Decisionmaking under certainty and uncertainty are relatively unproblematic (since all that is required is an order-preserving assignment of numbers), but we need cardinal utilities for decision-making under risk and it is not often that a predictor finds himself in a position to assign utilities that are invariant up to positive linear transformation. The same holds for the assignment of probabilities. In the realm of urns and lotteries it is reasonable to assume, not only that the relevant states of the world have objective probabilities, but also that those probabilities are common knowledge. But in the real world, even when there are objective probabilities it is often not reasonable to assume that others know them (even if one knows them oneself) and, of course, decisionmaking often deals with issues for which it is inappropriate to think in terms of objective probabilities at all. In cases where one has sharply defined subjective probabilities it may be possible (after making suitable adjustments) to assign them to the agent whom one is trying to predict, but there are no doubt many situations where the predictor may not have numerically determinate probabilities, even of a subjective nature—and yet where it does not seem appropriate to treat the decision problem as a problem under uncertainty. There is a very general issue here concerning the line between decisionmaking under risk and decision-making under uncertainty. When one is dealing with decision problems that are (for the agent) straightforward examples of one or the other, prediction is not complicated. It is in fact simply a matter of identifying and then applying the relevant rule, which might be the principle of maximizing expected utility or

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whichever decision rule the agent is most likely to adopt in cases of decision-making under uncertainty (and this can often be worked out from what is known of the agent’s attitude to risk). But many decision problems do not fall neatly into one category or the other. I may have some idea of how the agent ranks the outcomes in ordinal terms, but not be in a position to assign cardinal utilities. Alternatively, I may have some idea of how the agent views the comparative probabilities of the different relevant states of the world (that the agent views the probability of rain as far higher than the probability of fine weather) without being in any position to identify a unique probability distribution over those states. In either case, and even more so when both hold, I am not in any position to deploy the principle of maximizing expected utility. There is insufficient information in place for the calculation to gain purchase. But nor, on the other hand, does it seem right to view this as a case of decision-making under uncertainty. It would be completely inappropriate to apply the Principle of Insufficient Reason on the agent’s behalf, for example. If I work on the assumption that the agent has no information at all, and so should rationally take the different states of the world to be equiprobable, then I am likely to generate highly inaccurate predictions, just as I am likely to do if I assume that the agent will apply minimax reasoning. The problem is not (purely) epistemological. It may sometimes be the case that, although you have a unique probability distribution, I am not able to work out what it is. But it is surely far more frequent that the reason I cannot attribute a unique probability distribution to you is that you do not have one. Even leaving aside problems about numerically indeterminate probabilities, the proposed application of decision theory creates an obvious hostage to fortune. As an action-guiding theory the theory answers the question: What is it rational to do here? It does not assume that the agent is rational. It merely tells the agent what counts as a rational resolution of the decision problem. In contrast, the rationality assumption is directly built into the use of decision theory as a predictive tool. If, as the theory maintains, acting rationally in situations of decision-making under risk is equivalent to maximizing expected utility, then the theory can only predict the behavior of rational agents. At a minimum, therefore, we have to assume that the agents whose behavior is being predicted meet certain minimal consistency requirements, such as having, for example, a transitive and complete weak preference ordering satisfying the continuity and substitution axioms. It is plain that this creates a hostage to

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fortune, although it is not yet clear what sort of fortune is at stake. It may be that the assumption is purely empirical, so that the applicability of decision theory as a predictive tool rests upon it simply being the case that a significant proportion of the population is minimally consistent in the appropriate manner. Or it may be, as Davidson has argued (in, for example, the essays collected in Davidson 2001), that the assumption is essentially regulative, serving as a framework principle for social understanding. According to Davidson, we cannot make sense of anyone’s behavior except on the assumption that they are minimally rational, where minimal rationality includes adherence (at least for the most part) to the axioms of decision theory.¹⁸ Whether the assumption turns out to be empirical or regulative, it is clear that it is equally presupposed by any extension of decision theory to the project of explanation. Once again one might think that, with the rationality assumption in place, the theory can easily be deployed in the service of explanation. Explanation is the process of working backwards from an action to the decision problem that the action is best seen as solving. The theory preserves the basic idea that explanation consists in identifying both the agent’s motives and the information in virtue of which he acted, but allows us to refine and regiment ordinary talk of beliefs and desires. In fact, it has two major theoretical advantages. Instead of thinking about single belief-desire pairs decision theory allows us to do justice to the twin thoughts, first, that agents act in virtue of patterns of preferences rather than single desires and, second, that agents act in virtue of a range of different information not just about how the world is but also about how it might be—information that sets the parameters of the decision problem. The first point develops the familiar idea that desires are dispositional states. To desire a certain item is to be disposed to choose it. But such choices are not made in a vacuum. We tend not to choose things simpliciter, but rather to choose certain items over other items. What matters in explaining my behavior is not my desire for a Coke, or even that desire combined with the belief that the best way to get a Coke is to go to the Coke machine. The important thing is that my desire for a Coke, discounted by the effort involved in walking to the Coke machine and the possibility that the machine might be empty, outweighs the ¹⁸ See Lepore and Ludwig 2005 for detailed discussion of the rationality assumption and how it fits into Davidson’s views on radical interpretation and the theory of meaning.

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value I attach to having fresh legs and a dollar bill in my pocket. The choices we make, and the dispositions we have, are fundamentally comparative, which decision theory recognizes and acknowledges by thinking in terms of orderings rather than isolated desires. Moving to the second point, we cannot think about actions in the abstract. We have to think about them in the context of specific decision problems. The information in virtue of which an agent acts, and hence the information that we are trying to identify when we set out to explain their action, is not just information about the specific action that they performed, but also information about the other available actions, the outcomes to which they might lead, the relevant states of the world, and the probabilities of those states holding. In short, we need to work backwards from the action performed to the decision problem to which it is a solution. The representation theorems of expected utility theory assure us that, when we are dealing with patterns of preferences that meet the minimal consistency requirements, it is at least in principle possible to work backwards from preferences over actions to unique probability and utility functions defined over states of the world and outcomes respectively. The von Neumann-Morgenstern expected utility theorem gives a highly abstract representation of how we might go about doing this. It involves finding for each available action a probabilistic mixture of the best and worst possible outcomes such that the agent is indifferent between the original action and that probabilistic mixture. But this requires us to take objective probabilities as given, which is not of much help in ordinary psychological explanation. We need a way of working backwards from preferences over actions to subjective probabilities (degree of belief ) as well as to subjective utilities. We can, following a method proposed by Frank Ramsey in 1931, show informally how this can be done.¹⁹ We can view Ramsey’s method as the idealized limit of psychological explanation—and, in particular, as an idealized limit that is a competitor to the idealized limit of finding a single belief-desire pair. Ramsey introduces the concept of an ethically neutral proposition, which is a proposition whose truth or falsity is of no concern to the decision-maker (such as the proposition that I have an even number of ¹⁹ The following informal and non-axiomatic presentation of Ramsey’s ideas follows Skyrms 1986, 202–4 and ch. 3 of Jeffrey 1983. A rigorous, axiomatic proof is mathematically demanding (see n. 3 for references).

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books in my library). The point of ethically neutral propositions is that they do not contribute any utility to the expected utility of gambles that depend upon them. All that they contribute is their probability. So, for example, if I am offered a gamble that will give me an ice cream if I have an even number of books in my library, and nothing otherwise, in working out what I would be prepared to pay for the gamble I need think only about the probability of having an even number of books in my library and the utility of receiving an ice cream. We assume that the agent has a best and a worst outcome—A and B respectively, to which we assign values 1 and 0 on the utility scale. We can find the mid-point of the utility scale if we can find an ethically neutral proposition h to which the agent attributes probability 0.5. We can do that by finding a proposition h such that the agent is indifferent between the gamble {A, h: B, ¬h} and the gamble {B, h; A, ¬h}, where the first of these is to be read ‘‘A if h holds and B if h does not hold’’.²⁰ Given that the agent prefers A to B, if she thinks that h is more likely than not (so that p(h) > p(¬h)) then she will prefer the first gamble to the second, while if she thinks that h is less likely than not (so that p(h) < p(¬h)) then she will prefer the second gamble to the first. We can be confident that there is always such an ethically neutral proposition h. Most people will both assign probability 0.5 to the proposition that a fair coin will come up heads and be indifferent to whether h turns out to be true or not. So, to find the mid-point of the scale we find an outcome C such that the agent is indifferent between C and {A, h: B, ¬h}. An ethically neutral proposition with probability 0.5 will always allow us to find the mid-point between any two points on the utility scale, and so this process can be repeated indefinitely many times to yield a cardinal utility scale as fine-grained as is required. Of course, the process just described depends upon there always being a C such that the agent is indifferent between C and the gamble {A, h: B, ¬h}, as well as the assumption that the agent is neither risk-loving nor risk-averse. But the basic idea should be clear enough. And once we have such a utility scale it is straightforward to derive the probabilities that the agent attaches to the relevant conditions. Let P and Q be outcomes and m an arbitrary condition (i.e. state of the world). There is no requirement that m be ethically neutral. We are trying to discover the probability p ²⁰ The gamble {A, h; B, ¬h} is equivalent to the lottery {A, p(h); B, 1 − p(h)}.

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of m. If e is the utility of the gamble {P, m; Q, ¬m}, then taking f and g to be the utilities of P and Q respectively yields e = p × f + (1 − p) × g = p f + g − pg So we have e − g = p(f − g). Dividing through allows us to derive p in virtue of p = (e − g)/(f − g). Of course, outside the laboratory or behavioral finance survey we are rarely in a position to elicit comprehensive information about how agents rank and compare lotteries and gambles, but nor on the other hand are we generally in the position of near-total ignorance from which the representation theorems assume that we start (recall that the starting assumptions are simply the minimal consistency requirements and the existence of a best and least-preferred outcome). We often have some knowledge of what an agent’s probability assessments are and can use those to triangulate on her utility function. In situations where, for example, the agent has more or less the same information about relevant states of the world as one has oneself, it seems reasonable to think that she will have a roughly comparable probability distribution. In game theory this assumption is formalized as the Common Prior Assumption, grounded in the so-called Harsanyi doctrine that all differences in probability assignments across individuals are derived from differences in information (Harsanyi 1967–8—see Myerson 2004 for a review and assessment of Harsanyi’s original three-part paper). There is no need for us to take a position on this controversial issue, but it is clearly often reasonable to transfer one’s own probability distribution over to another person in a comparable situation. And once we have probabilities we can solve for utilities, at least in a partial way. In other situations we have some grip on utilities, and can work backwards from these to probability assignments. Harsanyi suggests that it is frequently reasonable to assume similarities of utility function for specific groups of people: It is conceivable that in a given society with well-established cultural traditions people tend to enter bargaining situations with more or less consistent expectations about each other’s utility functions. It may happen that all members of a given society are expected to have essentially the same utility function. Or, more realistically, we may assume that at least persons of a given sex, age, social position, education etc, are expected to have similar utility functions of a specified sort. (Harsanyi 1962, 33)

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Once we have fine-tuned these stereotype utility functions to fit the individual by using some of the probabilities that can unproblematically be assigned, we can then solve for outstanding probabilities. Psychological explanation does not typically require us to generate a full reconstruction of the decision problem that the agent faced. We do not need to end up attributing to the agent a probability distribution that assigns a single and numerically determinate probability to each relevant state of the world. Nor do we need a comparably complete and precise utility function. Psychological explanation is fundamentally contrastive. We want to find out why an agent acted in this way rather than in some other way or ways. The contrast class (the set of possible actions such that we want to explain why the agent passed them over in favor of the action she actually did end up performing) is typically a proper subset of the set of available actions considered by the agent (which is itself a proper subset of the set of possible actions). There might in fact only be one or two actions that count as relevant alternatives in this sense. But this means that we can often be in the position of needing only relatively coarse-grained utility and probability functions. For practical purposes we rarely, if ever, need anything like the fine-grained utility and probability functions that the representation theorems show us how to derive. Decision theory can be used in much less complex ways to yield the desired result.

OV E RV I EW The concept of rationality has an action-guiding dimension. It serves a key role in the normative assessment of deliberation and action. And it is importantly implicated in explaining and predicting behavior. Decision theory satisfies the action-guiding requirements and seems at least prima facie to be extendable to the normative and explanatory/predictive dimensions. We can apply the theory to the dimension of normative assessment because decision theory can be placed on an axiomatic basis. The normative force of decision theory derives from the compellingness of the axioms from which it can be derived. Crucial here are the representation theorems of expected utility theory, which show that choices obeying certain fundamental axioms of rationality can always be interpreted as maximizing expected utility. The representation theorems also play an important role in underwriting the extension of decision

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theory to psychological explanation, because they ensure that it will always be possible to work backwards from suitably consistent sets of preferences over possible actions to utility and probability functions that can be viewed as regimentations of our standard, everyday psychological concepts of belief and desire. The proposed extension of decision theory from the action-guiding to the other two dimensions of the concept of rationality remains incomplete, however. There is a number of pertinent and germane normative questions that cannot be answered by the theory as so far developed. The theory takes the parameters of the decision problem as given, but there are important normative questions about how those parameters should be fixed. These questions are external to the framework within which decision theory is defined—a framework that assumes a decision problem already parsed into available actions, relevant possible states of the world, and anticipated outcomes. And even if we work within that framework, it is not clear that the action-guiding dimension is itself completely developed. Decision theory applies only to individual decision problems. The notion of rationality that it defines is purely synchronic. We do not have a diachronic conception of rationality that will allow us, for example, to make sense of binding commitments over time. Nor, finally, have we explored whether decision theory can be extended to meet the requirements of normative assessment and explanation/prediction simultaneously. In particular, we have not said anything about the two central notions of decision theory—the notions of utility and preference. How are these two notions to be understood? Can they be understood in the same way in each of the three different explanatory projects? Each of the three questions just identified poses a significant challenge for the idea that decision theory can be developed in a way that allows it to fulfil all three of the core explanatory projects to which the theory of rationality is relevant. These three challenges will occupy us for the remainder of the book. We begin in the next chapter with the challenge of clarifying the key notions of utility and preference.

2 The First Challenge: Making Sense of Utility and Preference Can we understand rationality through decision theory? Everything depends upon whether decision theory can carry out all three of the different explanatory tasks that the concept of rationality is called upon to perform. Decision theory needs to be an action-guiding theory of deliberation; a theory of normative assessment; and a tool for explaining and predicting action. As we saw at the end of the last chapter, there are several significant challenges that need to be met. The first of these is the challenge of explaining the notions of utility and preference that are at the heart of decision theory.

D I F F E R E N T WAY S O F U N D E R S TA N D I N G U T I L I T Y The concept of utility has a long and chequered history (see essay 2 in Broome 1999, Cooter and Rappoport 1984, and Ellsberg 1954 for historical surveys of shifts in meaning and usage). Used by Hume and others in the eighteenth century, it rose to prominence in the writings of the British utilitarians. Bentham’s definition of utility is frequently quoted. He begins An Introduction to the Principles of Morals and Legislation with the following definition: ‘‘By utility is meant that property in any object, whereby it tends to produce benefit, advantage, pleasure, good, or happiness, (all this in the present case comes to the same thing) or (what again comes to the same thing) to prevent the happening of mischief, pain, evil, or unhappiness to the party whose interest is being considered’’ (Bentham 1823, 12). One might reasonably think that Bentham is playing fast and loose by assimilating the concepts of benefit, advantage, and good, and as we shall see subsequent theorists made distinctions between the useful and the desirable that Bentham failed to see.

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Suppose that an object’s usefulness and/or desirability to the agent is a function solely of a single quantity to which it gives rise. This property might be pleasure, as in some forms of hedonistic utilitiarianism, or it might be good, as in the much more subtle form of utilitarianism developed in various writings by John Broome (1991, 1999). As far as the mathematics of decision theory is concerned the details of what exactly the quantity is do not matter. What matters is that it is a quantity that can be treated in the manner required by the theory. In fact, it does not even matter whether we take utility to be the disposition of an object or state of affairs to give rise to the quantity in question, or to be the quantity itself. We can only take utility to be a dispositional property of objects if we assume that the quantity to which it gives rise is measurable, because one state of affairs will have greater utility than another to the extent that it gives rise (or would give rise) to a greater amount of the relevant quantity. But then we could equally take utility in categorical terms, as being the quantity itself, rather than the disposition to give rise to it. So the distinction between taking utility to be a dispositional property and taking it to be the quantity generated by the dispositional property is not particularly significant. On both the categorical and dispositional ways of thinking about utility we are dealing with a cardinal rather than an ordinal notion. Unless utility is understood in cardinal terms the idea of maximizing expected utility fails to make sense (as explained in the previous chapter). In the early history of economics utility was also understood cardinally. A number of influential economists in the nineteenth century defined utility in a way that they took to reflect the usage of the British utilitarians. It is not always clear, however, that they were being as faithful to Bentham as they thought they were. In W. S. Jevons’s Theory of Political Economy, for example, the notion of utility is explicitly defined with reference to Bentham (Jevons 1871 cited in Broome 1999, 19). Nonetheless, at times it looks as if Jevons is taking a narrower view than Bentham. He writes, for example, that ‘‘the object of Economics is to maximize happiness by purchasing pleasure, as it were, at the lowest cost of pain’’ (quoted by Cooter and Rappoport at p. 510). Francis Edgeworth also seems to have had a fundamentally hedonic conception of utility, as evidenced by his proposal to measure utility in terms of just-noticeabledifferences (a concept more familiar from psychophysics) in the pleasure that an individual derives from a suitably gradated series of choices

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(Edgeworth 1881). It looks as if Edgeworth and Jevons are focusing on the ‘‘subjective’’ end of Bentham’s spectrum of purported explications of ‘‘utility’’. During the early part of the twentieth century economists such as Alfred Marshall, Arthur Pigou and Edwin Cannan adopted a somewhat different understanding of utility in terms of material well-being (Cooter and Rappoport 1984)—at the opposite end of Bentham’s spectrum. Material well-being is itself understood in terms of certain basic needs that must be satisfied for any individual to be physically fit and economically productive. This conception of material well-being had the advantage of being observable and measurable. It is rather different from any understanding of utility in terms of desirability. In fact, Pareto introduced a useful (but almost completely neglected) terminological distinction between utility (a property of things which are ‘‘conducive to the development and prosperity of an individual, a people, or the human race’’)¹ and ophelimity (which he understood in terms of a thing’s capacity to satisfy an individual’s desires). Bentham’s original characterization of utility as the property of producing ‘‘benefit, advantage, pleasure, good, or happiness’’ rides roughshod over Pareto’s useful distinction between two ways of understanding utility in cardinal terms—roughly speaking, between utility as usefulness and utility as desirability. The idea that utility could be understood cardinally went dramatically out of fashion during the so-called ordinalist revolution in the 1930s. The ordinalists proposed replacing utility functions (unique up to positive linear transformation) with (monotonic) scales of preferences, repudiating both the idea that utility could be measured and the assumption that it is possible to make comparisons of utility across persons (see e.g. Hicks and Allen 1934). The ordinalist rejection of cardinal utilities plainly extends both to utility-asdesirability (ophelimity) and utility-as-usefulness.² It is important to ¹ Quoted from Pareto’s Cours d’Économie Politique by Cooter and Rappoport (1984, 515). ² Both the Jevons-Edgeworth and Pigou-Marshall conceptions of utility are committed to the measurability of utility, and the project of welfare economics, as developed by Marshall and others, rests upon the possibility of interpersonal comparison of utility—although it is perfectly coherent to hold that utility is measurable but not something that can be compared across persons. In fact, this seems to have been Jevons’s own view. See Jevons 1871, 85. For more contemporary discussions of interpersonal comparisons of utility see the essays in Elster and Roemer 1993.

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recognize, though, that when the notion of cardinal utility was rehabilitated with the publication of von Neumann and Morgenstern’s Theory of Games (von Neumann and Morgenstern 1944) this was not necessarily a rehabilitation either of utility-as-desirability or utility-asusefulness. Many economists followed von Neumann and Morgenstern themselves in thinking that their fundamental representation theorem was a rehabilitation of the notion of cardinal utility. Cardinal utilities are measurable utilities and the representation theorem plainly offered a way of measuring utility. However, there are fundamental differences between von Neumann-Morgenstern cardinal utility, on the one hand, and both utility-as-desirability and utility-as-usefulness on the other (Ellsberg 1954). In the latter cases numerical measures of utility are tracking a quantity correlated with an object’s desirability/utility. On the von Neumann-Morgenstern conception, on the other hand, numerical utilities represent preferences. The idea that these numerical utilities might be tracking an independently specifiable quantity distinct from (and perhaps even underlying!) preferences is completely alien to the spirit of the theory. The aim of the theory is to provide a way of representing preferences that makes it easier to work out what preferences are consistent with one’s past preferences. The von Neumann-Morgenstern and other representation theorems do not have to be understood in this way. They are mathematical results about the numerical consequences of preference orderings that obey certain basic consistency requirements, and they have nothing to say about how those numerical consequences should be interpreted. The fact remains, however, that this is how von Neumann and Morgenstern understood the notion of utility that they developed through these results, and in this they have been followed by economists for whom, as Broome points out (1999, 28), the official meaning of ‘‘utility’’ is that which represents preference. The force of taking utility to be a representation of preference depends, of course, upon how preferences are understood. In economics and decision theory preferences are standardly understood operationally. Preference is defined in terms of choice behavior, so that there is no content to the notion of preference other than through its behavioral manifestations in actual choices or dispositions to choose. We find this view of preference taken as a ‘‘postulate’’ by Luce and Raiffa, who take it to be tautological that ‘‘of two alternatives which give rise to outcomes,

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a player will choose the one which yields the most preferred outcome’’ (Luce and Raiffa 1957, 50). This all suggests that we need to distinguish two ways of thinking about the central theoretical notion in decision theory. On the substantive understanding, utility is an independently specifiable quantity that is not simply a redescription of the agent’s preferences. To say that an agent maximizes expected utility is to say that the agent chooses the course of action that has the largest mathematical expectation of that quantity. As we have seen, there are different ways of thinking about what this quantity might be in terms of desirability and/or usefulness. Nonetheless, they all stand in sharp opposition to what I will call the operational understanding of utility, according to which utility is simply a representation of preference, which is itself to be understood in terms of choice. On the operational understanding, to say that an agent maximizes expected utility is effectively to say that they have revealed preferences over a set of actions that obey the basic axioms of expected utility theory. Some economists have treated substantive utility as if it were introspectively measurable. According to Jevons for example (as reported in Ellsberg 1954), we measure utility by measuring the different intensities of an agent’s likings for certain outcomes and then use the results of such measurement to predict what the agent’s preferences will be among lotteries defined over those outcomes. Such measurements are heavily dependent upon the agent’s introspective reports. We might, for example, ask an agent to rank a set of outcomes in order of preference and then ask her to compare the extent to which each outcome is more desirable than the next outcome in the ranking (if there is one). So, given an ordering A > B > C we might ask the agent to compare the extent to which she prefers A to B to the extent to which she prefers B over C. These introspective reports are thought to track the agent’s internal sense of satisfaction, pleasure, desirability, good, or whatever quantity is taken to constitute utility. Nonetheless, the substantive conception states merely that there is some quantity that is tracked by measurements of utility. It is not committed to holding that quantity to be introspectively accessible. This is important, because supporters of the operational conception sometimes argue for it indirectly by pointing out what they take to be the absurdity of the idea of an introspectively accessible utility function. This is a mistake.

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D E L I B E R AT I O N A N D T H E T WO I N T E R P R E TAT I O N S The distinction between substantive and operational conceptions of utility offers us two very different ways of understanding the action-guiding dimension of decision theory. These differences have significant implications for how we think about decision theory as a theory of deliberation. The substantive conception of utility sits very naturally with an intuitive understanding of the prescription to maximize expected utility. Here is a passage we have already encountered from Jeffrey’s The Logic of Decision: To deliberate is to evaluate available lines of action in terms of their consequences, which may depend upon circumstances the agent can neither predict nor control. The name of the 18th century English mathematician, Thomas Bayes, has come to be associated with a particular model of deliberation. In the Bayesian model the agent’s notions of the probabilities of the relevant circumstances and the desirabilities of the possible consequences are represented by sets of numbers combined to compute an expected desirability for each of the acts under consideration. The Bayesian principle for deliberation is then to perform an act which has maximum expected desirability. ( Jeffrey 1983, 1)

The assumption is that consequences/outcomes have numerically determinate utilities and probabilities. The aim of deliberation is to work out which available act yields the highest expectation of utility. This process of deliberation in turn rests upon utilities and probabilities being given independently of the choices in which deliberation results. When we think about deliberation on the substantive conception of utility, it is our utilities and probabilities that explain our choices, not vice versa. On the operational conception, in contrast, the utility values assigned to individual outcomes are derived from preferences over lotteries/actions, and so it is not open to the operational theorist to take the utilities of individual outcomes as basic. Instead, the weight of the theory is taken by the axioms that define a consistent preference ordering and the prescription to maximize utility becomes a prescription to act consistently. This comes across very clearly in the following passage from John Harsanyi. A Bayesian need not have any special desire to maximize his expected utility per se. Rather, he simply wants to act in accordance with a few very important

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rationality axioms; and he knows that this fact has the inevitable mathematical implication of making his behavior equivalent to expected-utility maximization. As long as he obeys these rationality axioms, he simply cannot help acting as if he assigned numerical utilities, at least implicitly, to alternative possible outcomes of his behavior, and assigned numerical probabilities, at least implicitly, to alternative contingencies that may arise, and as if he then tried to maximize his expected utility in terms of these utilities and probabilities chosen by him. (Harsanyi 1977, 381)

Luce and Raiffa explicitly describe the model of practical deliberation associated with the substantive understanding of utility as a fallacy. We may think of the theory as a guide to consistent action. Certain (simple) preferences come first and certain rules of consistency are accepted in order to reach decisions between more complicated choices. Given these, it turns out that it is possible to summarize both the preferences and the rules of consistency by means of utilities, and this makes it very easy to calculate what decisions to make when the alternatives are complex. The point is that there is no need to assume, or to philosophize about, the existence of an underlying subjective utility function, for we are not attempting to account for the preferences or the rules of consistency. We only wish to devise a convenient way to represent them. (Luce and Raiffa 1957, 32)

From the point of view of action-guidance, therefore, decision theory (interpreted operationally) is effectively telling agents to act in accordance with the basic axioms of consistency—that is, to have transitive and complete preferences over actions that respect the substitution and continuity axioms as well as the principle of reduction of compound lotteries.³ The operational understanding of utility limits the practical usefulness of decision theory. For one thing, a theory that restricts itself to prescribing consistency with past choices is of no use in situations where there are no past choices with which to be consistent. The best that decision theory can achieve from an action-guiding point of view is a form of boot-strapping from past preferences. Suitably consistent preferences over actions/lotteries set up a template that constrains future preferences over actions/lotteries involving the same outcomes. We might say that decision-making takes place within a consistency space determined by prior preferences. Where there are no relevant ³ This way of thinking about decision theory is obviously more appealing for some axiomatizations of utility theory than others. The axioms of Jeffrey-Bolker utility theory are not easy to understand, for example.

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past preferences the decision-problem is undefined. Things look rather different on the substantive understanding. If utility corresponds to a real quantity that is not solely determined by past preferences (although one would not expect it to be completely independent of past preferences) then it certainly makes sense to think about maximizing expected utility even in situations that are completely novel. Moreover, there are two ways in which a preference at one time might be inconsistent with earlier preferences. Most obviously, inconsistency could be the result of cognitive shortcomings in the agent, who might simply have forgotten his earlier choices and preferences, or failed to realize the implications of those choices and preferences (perhaps because he failed to see that two different decision problems actually involved the same outcome). It is easy to see why both operational and substantive utility theorists would count this sort of inconsistency as irrational. But one can also be inconsistent simply in virtue of having changed one’s mind about what is valuable. It may be that I take something to be more valuable than I previously did, which leads me to prefer A to B when formerly I preferred B to A.⁴ The operational conception cannot allow a rational preference that is inconsistent with past preferences in either of these two ways. Of course, nobody wants a theory that would prescribe the first type of inconsistency, but it seems undesirable to rule out the second type of inconsistency. From the perspective of the operational conception of utility, the type of change being envisaged (where, for example, I might reverse my earlier practice of attaching more importance to attending cultural events than to participating in sporting events) can only be completely arbitrary. If I then proceed to act consistently then the bootstrapping process can get started once again. But the actual moment of transition, and the choices that I make immediately following that transition, are totally opaque to decision theory, understood operationally. This is not the case, however, if utility is understood substantively. If utility corresponds to a real quantity over and above preferences, and if it is possible to measure that quantity, then it is perfectly possible for the theory to prescribe choices that are inconsistent in the second sense. If I come to derive more pleasure from attending cultural events than from participating in sporting events (continuing with our simplifying assumption) then decision theory will prescribe choices that are ⁴ See Chapter 4 for discussion of how preference change might be incorporated into decision theory.

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inconsistent with my earlier choices. And this, one might reasonably think, is as things should be. N O R M AT I V E A S S E S S M E N T A N D T H E T WO I N T E R P R E TAT I O NS The two limitations of the operational conception identified in the previous section carry across to the dimension of normative assessment. A normative theory ought to be able to assess the rationality of novel choices—as opposed to accepting whatever the decision-maker chooses to do in novel situations and then waiting to see whether subsequent preferences are consistent with the initial choice. This can be done on the substantive understanding of utility, but not on the operational understanding. Similarly, any theory of rationality suitable for normative assessment should allow for rational change of preference. There is an additional problem specific to the normative validity and force of decision theory. Considered as a tool for normative assessment, rather than simply as a tool for guiding decision-making, the theory’s basic prescriptions need to be reflectively grounded. As we saw in Chapter 1, this reflective grounding can be provided axiomatically, by showing how the decision principles proposed by decision theory are mandated by intuitively plausible axioms. The representation theorems of expected utility theory offer canonical examples of such grounding, by showing that any agent with a transitive and complete preference ordering over actions/lotteries satisfying the substitution and continuity axioms will prefer one lottery/action to another if and only if it has greater expected utility. But what grounds our confidence in the axioms? Utility theory is different from axiomatic theories such as Peano arithmetic in that we have no intuitive grasp of the intended model for the theories that we are axiomatizing. If we are not to be pure formalists, interested solely in the study of what theorems can be proved from particular sets of axioms and abstracting away completely from the question of which particular axiom system best characterizes a particular domain, then our axioms must in the last analysis be answerable to a domain of which we do have a clear, or at least a clearer, intuitive grip. We want to know what rationality prescribes in a particular situation and to be confident that our theory is giving us the right prescription we need to be confident that we have identified the correct set of axioms. But we do

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not have the sort of clear intuitive grip on what rationality demands that would bestow authority on axioms such as the substitution axiom in the way that our intuitive grip on the natural numbers bestows authority on the axioms of Peano arithmetic. So we need to hold the axioms to account and show that they can do work for us. Our best hope here is with the representation theorems. The representation theorems show that agents who follow the axioms are maximizers of expected utility. Plainly, then, to the extent that it is desirable to be a maximizer of expected utility this provides independent support for the axioms. In such a situation the reflective grounding works in both directions. The expected utility principle is reflectively grounded by the axioms, but so too are the axioms reflectively grounded by the expected utility principle. The substitution axiom is intuitively plausible, but this intuitive plausibility is reinforced by its role in providing an axiomatic basis for the expected utility principle. We can only argue in this way if we have a grip on the idea of maximizing expected utility that is independent of our understanding of what it is to act in ways consistent with the axioms of expected utility theory. This has implications for how we think about the concept of utility. If we understand utility operationally, then maximizing expected utility is analytically equivalent to choosing in accordance with the axioms of expected utility theory. This deprives us of the triangulation and independence required for the axioms and the expected utility principle to be mutually supporting. In contrast, the substantive understanding of utility does offer the required triangulation and independence, since it holds that measures of utility track an independently specifiable quantity that is independent of choice and action. P S YC H O LO G I C A L E X P L A N AT I O N / P R ED IC TI O N A N D T H E T WO I N T E R P R E TAT I O N S In thinking about decision theory as a tool for psychological explanation we are effectively taking probability assignments and utility assignments to be regimentations of our ordinary, commonsense notions of belief and desire. If I assign a probability p to the proposition that a particular state of affairs will occur then we might take this as an index of my believing to degree p that that state of affairs will occur. Similarly, the numerical values assigned by my utility function reflect the degree to which I find particular outcomes desirable—in effect, the strength of

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my desire. So, using decision theory to explain behavior can be viewed as a mathematically tractable and numerically precise way of applying ordinary commonsense psychological concepts. This way of thinking about decision theory has been proposed by a number of authors (see e.g. Rosenberg 1992, Lewis 1994 and Rey 1997—but see Gauker 2005 for an opposing view), who argue that the expected utility principle is really an idealization of the fundamental principle of folk psychology, which is, roughly speaking, that people do what they think will best satisfy their desires (the so-called belief-desire law). Admittedly, decision theory does not give us commonsense psychological explanation as many philosophers and psychologists understand it, because it does not involve any of the commonsense psychological generalizations, platitudes, and rules of thumb (apart from the belief-desire law, as codified in the expected utility principle) that are often taken to be indispensable elements in psychological explanation. But those theorists who think that the role of laws in psychological explanation is significantly over-stated will no doubt find this an advantage. The full force of thinking about decision theory as a regimentation of commonsense psychological explanation is only available on the substantive way of thinking about utility. If utility and probability assignments are to explain behavior in the way that attributions of beliefs and desires are thought to explain behavior then the utility and probability values must track psychologically real entities that are independent of the behavior being explained. There is relatively little explanatory power to be gained from explaining behavior in terms of probability and utility assignments if, as the operational theory holds, those assignments are simply redescriptions of the behavior being explained. The operational interpretation has some explanatory power, however. It shows how a particular choice/action fits into a consistent pattern of preferences, allowing us to explain why an agent behaved in a particular way on a particular occasion by pointing out that the action in question was appropriately consistent with his past choices. But it completely fails to accommodate the causal dimension of psychological explanation. If we want to know why someone behaved in a certain way it is not enough to be told that she is acting consistently. We want to know what caused her to act in that way—and why her behavior displays the patterns that it does. This plainly requires that numerical utility and probability values track independently existing quantities that can stand in causal relations to the behavior being explained.

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Here is an illustration. Suppose that we are trying to explain why the agent opted for a payment of $125 over a gamble with expected monetary value of $150 (a gamble, let us say, between a 50% chance of $200 and a 50% chance of $100). Intuitively, there is a number of different possible explanations for this preference. One obvious explanation is that the agent is risk-averse. Someone who dislikes risk is likely to attach a significant disutility to the fact of gambling, and correspondingly attach a greater utility to the certainty of $125 than to a 50% chance of $200 and a 50% chance of $100. But there are other possible explanations. It might be the case, for example, that there is something the agent urgently needs that costs exactly $125, while the next most expensive thing that the agent wants to buy costs far more than $200. Our agent might have a risk-averse temperament—sufficient, let us say, for him in normal circumstances to prefer a certain return of $125 over an expectation of $150. But in this situation this is not what drives his behavior. What drives his behavior is the perceived usefulness of receiving $125 for sure. The distinction between these two interpretations cannot be marked on the operational interpretation. From the operational perspective all we can do is note that the agent’s choices have a particular property (the property of tracing a concave utility curve). There is nothing to be said about the different reasons for which an agent’s utility curve might be concave. Since an agent’s utility curve is simply a representation of his preferences as revealed in choice behavior there is nothing more to be done than note the shape of the utility curve.⁵ The point is made very clearly by John Harsanyi, a prominent proponent of the operational interpretation. The decision maker’s ‘‘gambling temperament’’ has already been allowed for in defining his von Neumann-Morgenstern (vNM) utility function. Therefore, if the utilities of the various possible outcomes are measured in vNM utility units then the expected utility of a lottery ticket will already fully reflect the decision maker’s positive or negative (or neutral) attitude towards risk. (1977, 385)

The passage continues with Harsanyi objecting to any proposal to include additional considerations relating to the decision-maker’s attitude to risk in computing the agent’s utility curve. ⁵ The standard definition of the risk aversion coefficient (Arrow 1971) is the second derivative of the utility function, with sign reversed, divided by the first derivative. See Hansson 1988 for a lengthier discussion of risk aversion in the context of different interpretations of utility.

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If we now allowed for his gambling ‘‘temperament’’ for a second time, by introducing some measure of the risk involved into our computations at this point, then we would engage in unnecessary and impermissible double counting. Indeed, we should certainly violate at least one of the Bayesian rationality axioms: this would have to be the case since those axioms are known to logically entail equaling the utility of a lottery ticket with its expected utility. (idem)

Harsanyi’s point is sound. The whole point of the representation theorems is that they allow us to derive a utility curve solely on the basis of suitably consistent preferences. If we try to factor the agent’s attitude to risk into the utility then we will distort the basic relation between utility and consistency. But this does not really address the real concern from the point of view of psychological explanation, which has to do with how we explain the shape of the utility curve, not with how we construct it. According to the operational interpretation, we hit bedrock with the utility curve. There is nothing to be said about why it is has the shape that it does. And this, one might reasonably think, places an unacceptable restriction on psychological explanation. The situation is less bleak for the operational interpretation when it comes to prediction as opposed to explanation. Although learning that an agent’s behavior is consistent with his past preferences and behavior gives us only minimal explanatory power, learning what it would be consistent for an agent to do, given her past preferences and behavior, can provide considerable predictive leverage. The point about prediction, after all, is simply that it should work and both the operational interpretation and the substantive interpretation will work equally well, if the agent whose behavior is being predicted is indeed acting in accordance with the basic rationality axioms—while if the agent is not acting in accordance with the basic rationality axioms then neither the operational nor the substantive interpretation will generally have much predictive power. One class of situations where one might expect the two interpretations to diverge predictively comes with the two types of case we have already discussed—those involving novel situations and those where an agent is inconsistent because his valuations have changed. These are situations where the operational interpretation can gain no leverage, but where the substantive theory at least leaves open the possibility of successfully predicting what the agent might do (on the assumption, of course, that the predictor has a way of finding out what

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the agent’s utility function is that is independent of the agent’s past choices and preferences).⁶ The substantive interpretation also permits a more fine-grained approach to the prediction of behavior in the context of risk, because it allows us to make distinctions between different possible explanations for the concavity of the agent’s utility curve. If the reason is a general risk-averse temperament, then we can extrapolate from this and assume that the agent’s utility curve will continue to be concave. But if, on the other hand, the concavity arises for purely local reasons then such extrapolation may well be unwise. The operational interpretation allows us to identify patterns in a decision-maker’s preferences, and such patterns can be very useful in prediction. But we need to know how exactly to project the patterns, and this frequently requires more information about what lies behind those patterns than the operational interpretation is able to give.

T H E S TAT E O F P L AY There are two ways of thinking about the central concepts of preference and utility. The operational interpretation is characterized by two claims. (1) Utility is a representation of preference, so that what utility theory provides is a way of representing an agent’s preferences to make their structure perspicuous and mathematically tractable. (2) Agents’ preferences are revealed by, and exhausted in, the actual choices that they make. In contrast, the substantive interpretation holds that utility represents some quantity that is independent of the agent’s actual choices, but somehow reflected in those choices. If decision theory is interpreted operationally (as is standard in economics), it faces formidable problems in the second and third of the dimensions of rationality that we have been exploring. But what are the prospects for moving beyond the operational interpretation? ⁶ See, for example, the discussion of stereotypical utility functions at pp. 40–1 above. In many cases it is reasonable to work backwards from social and cultural background knowledge to a utility function (or at least the relevant fragment of a utility function).

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There are two ways of doing this. The first way retains the idea that utility is a representation of preference, while developing a notion of preference that is sufficiently robust to overcome the problems identified in the last section. The second way is to move away from the idea of preference in the manner suggested by the substantive conception. We explore both these options. A note on terminology. If we take ‘‘preference’’ to refer to the basic relation, whatever it is, that holds over actions/lotteries in a way that allows a utility function to be attributed, then any way of developing a substantive notion of utility is going to end up as a recasting of the notion of preference, because it is tautological in this sense that utility is a representation of preference. As I will be using the term henceforth, however, preferences are definitionally tied to choices, although not necessarily exhausted by them. Preferences may be understood in terms of actual choices, dispositions to choose, or choices that one might make in ideal circumstances, but there cannot be preferences that are not in some sense manifested, or at any rate manifestable, in choices. As we shall see, however, there are ways of understanding the basic relation in decision theory that do not meet this requirement. R E C O N S T RU I N G T H E N OT I O N O F P R E F E R E N C E According to the revealed preference account, an agent’s preferences are revealed in her choices, so that there is no scope for an agent to have preferences that are independent of, and potentially in conflict with, the choices that she makes. One obvious way of modifying this account is to place constraints upon the situations in which choice behavior can count as revealing preference. One commonly suggested modification of the revealed preference theory requires the relevant choices to be made under conditions of full information and unimpaired cognitive functioning. If we have any reason to think that the agent is operating with partial or misleading information; that they are choosing under compulsion or under the influence of drugs; or that they have not fully thought through the implications of the decision problem, then we should not take the choices that they make as revealing their ‘‘genuine preferences’’. Let us call this the ideal conditions theory. This is a perfectly sensible revision to the basic revealed preference theory, but it does not help with the basic difficulties for the operational interpretation of decision theory. The revision is intended to solve a

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different type of problem. The aim is to rule out as reflecting one’s preferences choices that are somehow made ‘‘inappropriately’’. The guiding thought is not to challenge the basic idea that choices reveal preferences, but rather to modify the simple view that all choices reveal preferences. We still end up with preferences that can be equated in toto and without remainder to actual choices. It is just that only a proper subset of the actual choices made are candidates for revealing preferences. There is still no clear blue water between the idea of preference and the idea of choice. All of the problems for the operational interpretation of decision theory remain in play. So, for example, even though the ideal conditions theory allows us to distinguish inconsistencies in choice behavior that can be taken to reveal changes in preference from those that should not be so taken (on the assumption that we can discount inconsistencies attributable to conditions that are suitably less than ideal), it has nothing to say about how or why some of the first group of inconsistencies could count as rational changes in preference. It is plain that the other difficulties with the operational interpretation remain in play. We must go further to rescue the idea that utility can be a measure of preference. At the very least we need, in addition to the distinction between choice and revealed preference, a further distinction between revealed preference and genuine preference, so that we can pose the question of whether a choice made in appropriately ideal conditions qualifies as a genuine preference. In Morals by Agreement David Gauthier develops a version of this distinction (Gauthier 1986). Unlike many who have challenged the way that economists and decision theorists standardly understand the notion of preference, Gauthier thinks that we should not completely abandon the idea that preferences can be revealed in choice behavior. He notes, however, that preferences are not simply revealed in choice behavior. They are also verbally expressed. Sometimes there is only one act that counts as simultaneously revealing and expressing a preference. If I am asked which item on a menu I prefer then the answer I give both reveals my preference and expresses it. But this type of case is the exception rather than the rule. There is generally considerable scope for divergence between revealed and expressed preference. We are often in situations where we can, and often do, speak in one way and act in another. Weakness of will is an obvious example. And the demands of politeness often require a disalignment of revealed and expressed preference. In many of these cases an agent will recognize the disalignment and will

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either restore consistency by repudiating an expressed preference (‘‘I was just being polite . . .’’) or will acknowledge, and perhaps try to explain away, a temporary attack of irrationality. Cases of the first type are not best viewed as genuine divergences between real and expressed preference.⁷ But in cases of the second type it is not clear that the agent has well-defined preferences at all, Saying, for example, that I found an extra glass of wine too tempting to resist goes some way to explaining what happened. But it leaves unanswered the question of what my ‘‘real’’ preferences were. Gauthier’s view, as a consequence, is that we should understand utility as a measure of what he terms considered preference, which is given by revealed and expressed preferences when they are in agreement (1986, 28).⁸ Since we are not always in a position either verbally to confirm the preferences revealed by our behavior, or behaviorally to confirm our expressed preferences, we must assume as a default position that an agent’s revealed and expressed preferences are in harmony. What the notion of a considered preference really provides is a negative criterion for eliminating non-genuine preferences, rather than a positive criterion for identifying genuine preference. Nonetheless, in a number of respects the considered preference account is a substantial advance over the ideal conditions account. It does, for example, provide a way of making sense of rational changes in preference. It is easy to see, for example, why a change from one considered preference to another might be viewed as a rational change in preference (as opposed, for example, to a change in revealed preference that is unaccompanied by a change in expressed preference). By the same token, it might frequently be the case that, even when an agent faces a novel choice in the behavioral sense (that is, a decision situation in which revealed preferences cannot be a guide), she can look for guidance to her expressed preferences. Moreover, it offers an independent fix on the idea of maximizing utility that restores content to the result that choosing in accordance with the axioms of expected utility has the inevitable consequence of maximizing expected utility. At the same time, the fact that the considered preference account remains grounded in revealed preference makes it straightforward to apply the formal machinery of decision theory to those revealed preferences that ⁷ One might define expressed preference in such cases counterfactually, as the preferences that one would express if unconstrained by social norms. ⁸ In fact, Gauthier reserves the term ‘‘utility’’ for behaviorally revealed preferences and prefers to talk about value as the measure of considered preference. But for our purposes it is easier to stick with ‘‘utility’’.

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are suitably in harmony with expressed preferences. Finally, in virtue of including expressions of preference the considered preference account introduces a cognitive dimension that is completely absent from the basic notion of revealed preference and that brings us closer to the idea that a utility function can be seen as a regimentation of the commonsense notion of desire—and hence closer to the idea that decision theory is psychologically explanatory. Nonetheless, there is something missing in the account so far. We cannot just take it as a brute fact that an agent’s revealed and expressed preferences are in harmony. What is ‘‘considered’’ about the fact of harmony? Harmony between revealed and expressed preferences could have any number of presumably undesirable causes. I might verbally endorse my actions, or bend my actions to my words, as a result of brain-washing, conditioning, social pressure, or, quite simply, lack of imagination and thought. It would be peculiar to describe any of these situations as ones where I have considered preferences. The problem is not merely terminological. Gauthier is addressing what he (rightly) sees as a shortcoming in equating preference with revealed preference. His principal objection to such an equation is that it does not allow for the possibility that an agent who is maximizing can nonetheless be acting irrationally. What he needs, then, is a distinction between what we might term revealed maximization and considered maximization, where an agent who is a considered maximizer is immune to criticisms that can be leveled at revealed maximizers. But on this understanding of what it is to be a considered maximizer, it is plain that we cannot count agents who have been brainwashed or pressured, or are totally lacking in reflection as considered maximizers, even though their revealed and expressed preferences are in harmony. Gauthier himself recognizes that harmony between revealed and expressed preference cannot be taken as a brute fact. He writes: ‘‘Preferences are considered if and only if there is no conflict between their behavioral and attitudinal dimensions and they are stable under experience and reflection’’ (1986, 32–3). Although he gives few details, Gauthier is naturally read as invoking a process of deliberation through which agents arrive at the preferences they express and resolve any conflicts between revealed and expressed preferences. Such preferences would quite literally be considered preferences. An explanation that appeals to this type of deliberation has the further advantage of actually explaining why considered preferences should have normative force. Their normative force is derived from the process of deliberation by

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which they are reflectively endorsed. In fact, we can view the harmony between expressed and revealed preferences as a form of reflective equilibrium secured by a process of deliberation. None of the situations envisaged earlier (the brainwashing case and so forth) would exemplify such a reflective equilibrium. Yet there is a basic and conclusive objection to any such model of considered preferences if it is put forward within the context of decision theory. A simple regress argument shows that any model of considered preferences along these lines is subject to exactly the same set of problems that led to the model in the first place. The first point to note is that any process of deliberation that could lead to the appropriate form of reflective equilibrium cannot be purely a matter of detecting inconsistencies (or, of course, of working out what would be consistent with past preferences, whether revealed or expressed). Where there is an inconsistency, deliberation must lead the agent either to modify behavior so that it is in harmony with expressed preferences, or to modify expressed preferences to bring them into line with behavior—or, in the worst case, to abandon both revealed and expressed preferences and start again. This means, of course, that the type of deliberation involved here cannot be simply a matter of logic. Logic can uncover inconsistencies, but it cannot help us to resolve them. So how is an agent to attain reflective equilibrium at the level of considered preference? In the simplest case the agent has two preferences that are out of kilter. Examining his behavior he realizes that he prefers A to B (to simplify I assume that the preference here is strict preference). We can write this A Pref R B. His behavior and his words do not match, however, because his stated preference is for B over A. We can write this B Pref V A. How is the agent supposed to bring these into reflective equilibrium? It is surely unreasonable to assume that stated preferences will always trump behavioral preferences (or vice versa). Sometimes they will, but sometimes they will not. The agent has to decide whether she identifies most closely with the stated preference or with the revealed preference. But this means, in effect, that the agent has to decide which she prefers of these two preferences. This is sometimes very easy (as when my expressed preference is dictated by social pressures). But often it is not, as in the more complicated cases of weakness of will, which is rarely as straightforward as being overwhelmed by the proximity of a drink or a cake. And when it is not easy, the agent confronts a decision problem over preferences. It is a decision problem under certainty. Each

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of the relevant outcomes is the agent having one of the set of possible preference orderings over which she is deliberating, and we can assume that if the agent decides to have a particular preference ordering then she will in fact have that preference ordering, so that there is only one state of the world to consider. Decision theory is very clear about how we should think about the family of decision problems of which this is a member. We solve decision problems in conditions of certainty by maximizing utility, where maximizing utility is a matter of choosing the highest ranked member of a transitive and complete preference ordering over the available outcomes. Adopting an obvious symbolism for higher-order preference, we are assuming that one of the following holds: (i) (A Pref R B) Pref (B Pref V A) (ii) (B Pref V A) Pref (A Pref R B) If (i) holds then the agent should stick with his revealed preference, while if (ii) holds then he should abide by his verbally expressed preference. But how are we to understand the preference relation in (i) and (ii)? As far as the agent’s behaviorally expressed preferences are concerned, the agent has already revealed a preference for (A Pref R B) over (B Pref V A). It seems tautological that when an agent behaves a certain way he reveals a second-order revealed preference for the preference that he has revealed. By choosing A over B he reveals his preference for acting on his revealed preference rather than his verbally expressed preference. This gives (i)∗

(A Pref R B) Pref R (B Pref V A)

But the same holds if we think about the preference relation in terms of verbally expressed preference. The fact that the agent has verbally expressed his preference for B over A manifests his (verbal) preference for (B Pref V A) over (A Pref R B). This gives (ii)∗

(B Pref V A) Pref V (A Pref R B)

But this leaves the agent in a higher-order version of the very problem with which he began. (i)∗ and (ii)∗ conflict, which means that he has to form a considered preference. At least one must be discarded. But this means that he needs to choose the one that he prefers most. And we are back where we started, because we can ask exactly the same questions about the type of preference that is in play.

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The problem generalizes as follows. An agent whose revealed and verbally expressed preferences diverge has to decide between them if he is to have a considered preference. Either this decision falls within the scope of decision theory, or it does not. If it does not, then it immediately follows that decision theory can play only a relatively minor role in a theory of rationality, since its most basic notion, the notion of preference, rests upon a type of deliberation that falls outside its scope. But the decision between revealed and verbally expressed preferences can only fall within the scope of decision theory if the agent has a second-order preference between their verbally expressed preference and their revealed preference. Ex hypothesi the agent has conflicting revealed and verbally expressed second-order preferences. But this conflict is structurally identical to the conflict that he is trying to resolve. So no progress has been made. Of course, if we assume that the agent has a considered preference for his verbally expressed preference over his revealed preference (or vice versa) then the problem disappears. But we have no indication of where this considered preference might come from. Is this fair to Gauthier? One of his examples of a revealed preference that fails to be a considered preference is a young lady who agrees to a proposal (no further details given) and then realizes her mistake. He writes of how she might come to form a considered preference: The young lady’s acceptance of the proposal is equally not a basis for determining her values. She may not lack the experience to form a considered preference. But she fails to reflect before accepting. When she does come to reflect she realizes that her firm preference is expressed by ‘‘No’’. Does she change her initial preference, or does she correct it? Neither alternative is acceptable; the first would imply that her successive preferences stand on an equal footing; the second would imply that initially she misstates her preferences. A better account is that without due consideration she forms a tentative preference revealed in her acceptance, which she then revises. Any choice reveals (behavioral) preference, but not all preferences are equal in status, so that the rejection of a firm or considered preference is not to be equated with the alteration of a firm or considered preference. (Gauthier 1986, 30)

It might initially appear that Gauthier’s young lady is not really solving a decision problem in the way I have suggested. Revising a preference is not, on the face of it, the same as choosing between two preferences. That may be. There are many ways of revising a preference. I might, as in another example Gauthier considers, revise my musical preferences because I become a more discriminating and educated listener. But

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considered preference involves the reflective revision of preferences, which in turn involves a process of deliberation and it is hard to see how one can deliberate on one’s preferences without choosing between two or more preferences. Suppose, for example, that I am deliberating on my revealed preference for A over B. If I am deliberating then I must at least take it as an open possibility that I not prefer A over B. At a minimum I need either to endorse my (revealed) preference or to reject it. And this in turn means that I must choose between preferring A to B and either preferring B to A or being indifferent between them. In fact, Gauthier’s own example fits this pattern rather neatly. The young lady who realizes that her firm preference is for ‘‘No’’ rather than ‘‘Yes’’ has effectively chosen a preference for ‘‘No’’ over ‘‘Yes’’ over a preference for ‘‘Yes’’ over ‘‘No’’ (and over indifference between ‘‘Yes’’ and ‘‘No’’). The problem generalizes to any account of considered preference that involves deliberation and reflection. Deliberating about one’s preferences is no different from deliberating about anything else. If such deliberation is to be modeled by decision theory then it rests upon preferences among preferences. These preferences cannot be assumed to be considered preferences, on pain of begging the question. But nor can they be assumed to be revealed preferences (or verbally expressed preferences), on pain of running into a higher-order version of the same problem. This renders deeply problematic the project of reconfiguring the notion of preference to avoid the problems identified with the operational understanding of utility. The regress argument just sketched out can be avoided by allowing for revisions of preference that do not involve reflection and deliberation. But what would then make the revised preferences more ‘‘real’’ than the unrevised preferences? Why might it be irrational to maximize on the basis of unrevised preferences, but not on the basis of revised preferences? If the revision is not to involve deliberation or reflection, then it can only be a function either of the information available to the decision-maker or of the decisionmaker’s state of mind. But this takes us back to the ideal conditions theory, which we have already seen not to address the real problems with the idea of preference being revealed by choice. As far as I can see, the ideal conditions and considered preference theories exhaust the possibilities for moving beyond the operational theory by developing a more nuanced notion of preference. We must turn, then, to the

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project of interpreting the basic relation in decision theory so that utility measures something other than preference.

S U B S TA N T I V E AC C O U N TS O F U T I L I T Y As John Broome has stressed on a number of occasions (see particularly his 1991 and the essays in pt. II of his 1999), decision theory, like any other formal theory, is no more than a collection of axioms and theorems, with the principal theorem being the representation theorem that we have discussed on a number of occasions. The axioms make reference to a particular relation that holds over actions/lotteries. Let us call this relation R. The content of the representation theorem is essentially that, if a relation R satisfying the rationality, continuity, and substitution axioms holds over a set of actions/lotteries, each of which is a set {a1 , a2 , . . . an } of possible outcomes, then it is possible to define a utility function U such that the value of U for each set of possible outcomes is the sum of the values of U for its constituent outcomes, each discounted by the probability that it will occur. From a mathematical point of view, the representation theorem states simply that real numbers can be assigned in a way that satisfies the equation. It says nothing about how R and U should be understood. It is standard among decision theorists and economists to take R to be the at least as preferred as relation, so that U(a1 , a2 , . . . , an ) ≥ U(b1 , b2 , . . . , bn ) just if the action/lottery whose outcomes are {a1 , a2 , . . . , an } is either preferred or judged indifferent to the action/lottery whose outcomes are {b1 , b2 , . . . , bn }. But of course R can be any relation that satisfies the axioms. Since the upshot of the previous section was very unpromising for any attempt to understand relation R as a preference relation it would be sensible to explore other ways of understanding it. We can begin by distinguishing two different approaches to the general strategy of reconstruing the R relation. On the internal approach the holding of relation R is cognitively accessible to the agent, where this means that the holding of relation R is available to be used in practical deliberation. An example here would be the at least as pleasant as relation, according to which the utility of an action is exhausted by the pleasure that the agent derives from it. If A is at least as pleasant as B then this fact is (at least in principle) cognitively accessible to the

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agent—although, of course, agents are not always very good judges of relative pleasurability. The perceived by the agent to be at least as good as relation is another candidate.⁹ In any event, I mention the internal approach to reconstruing relation R simply to put it to one side. The problem is that it falls prey to a dialectic very similar to the one that proved fatal to the preference-based approach. The crucial point here is that an internal construal of relation R must on occasion diverge from revealed preference. Part of the point of construing relation R internally is to give us a tool for describing as irrational an agent who appears to be maximizing expected utility (when preference is taken as revealed preference and understood purely in terms of choice). This was one of Gauthier’s original motivations for going beyond revealed preference, and one would expect it to be shared by any proposal for an internal construal of relation R. If there were no such potential for divergence then it is hard to see why we would not simply take relation R to be the revealed preference relation. But nor, on the other hand, should we assume that conflicts between relation R and revealed preference are always to be resolved in favor of whatever psychological quantity we are appealing to in our internal construal of relation R (pleasure, for example, or apparent good). Suppose that an agent (strictly) ranks α as more pleasurable than β, but nonetheless chooses β over α. The choice might be irrational, in virtue of breaching the R-ranking. But this will not always be the case. Sometimes a clash between R-ranking and revealed preference is a sign that the agent’s ⁹ There is an extensive debate among philosophers about how to understand reasons for action and it is frequently argued that reasons should be understood in terms of evaluative facts about what is good for the agent. This debate is in some sense orthogonal to what I am discussing here. For one thing, giving an account of reasons for action is not obviously the same project as giving an account of rationality. And even if the two projects are related, proponents of so-called value theories of practical reason are often explicitly opposed to consequentialist reasoning. Value pluralists such as Raz, for example, would reject the assumptions of completeness and commensurability that are at the heart of decision theory (Raz 1986). Nonetheless, we can take suitably formulated value theories of practical reason as illustrating possible ways of construing relation R. In the very general terms that I am using, these would be ways of construing relation R in terms of comparative goodness. Some construals might be internal (taking relation R in terms of what agents judge to be better for themselves). Others might be external, construing relation R in terms of objective facts about what is good for agents. Both ways of construing relation R will be discussed in the following. It will turn out that neither can do the job we need it to do in reconciling the demands of the different dimensions of rationality. But none of this, however, adds up to an argument that value theories of practical reason in any sense fail to solve the problems that they set out to solve. The claim is merely that they cannot be recruited to solve the problem that I am trying to solve.

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R-ranking needs to change. If I judge chocolate mousse to be more pleasant than crème caramel, but consistently choose crème caramel over chocolate mousse, then this could be a bizarre form of weakness of will (in which I act against my all-things-considered judgment of what is most pleasant), or it could be a sign that deep down I find crème caramel more pleasant than chocolate mousse. So, in cases such as these we need to ask how the agent is supposed to resolve a clash between R-ranking and revealed preference. The revealed preference ranking says one thing. The R-ranking says another. The agent confronts a decision problem between these two rankings. How is she to rank them? Suppose for simplicity that the R-ranking is a pleasantness ranking. The fact that she has made a choice that conflicts with pleasantness might be described as revealing a preference for revealed preference over pleasantness. But this is obviously not the last word. She may find it more pleasant to follow the pleasantness ranking over the revealed preference ranking. This puts her in a position very similar to that of the agent trying to decide whether to follow the revealed preference ranking or the expressed preference ranking. As we saw at the end of the previous section, every attempt to resolve this tension places the agent in a higher-order version of the decision-problem with which she began. This brings us to the external construal of relation R, according to which the holding of relation R is not in general cognitively accessible to the agent and available to be used in practical deliberation. The perceived by the agent to be at least as good as relation is, as mentioned earlier, a plausible candidate for relation R internally construed. We can derive an external construal of relation R simply by removing the cognitive accessibility that is built into that relation. This gives the at least as good as relation. Here we have a good candidate for a substantive notion of utility. The at least as good as relation removes us completely from the realm of preference-satisfaction, and there is certainly nothing tautological about being told that, provided the comparative goodness relation satisfies the basic axioms, the goodness of an action is equal to the sum of the goodnesses of the possible outcomes, appropriately discounted by their probabilities.¹⁰ Many theorists would say that it is plainly false, while those who think that it is true (such as John Broome) ¹⁰ For a clear statement of the difference between taking relation R to be the comparative goodness relation, on the one hand, and preference on the other, see Broome 2004, §5.1 and, more extensively, Broome 1991 (particularly ch. 2).

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present it as a substantial and controversial claim requiring considerable defence. At a very general level it seems clear that the betterness relation is ideally suited to the task of normative assessment. Since we are discussing the betterness relation construed externally, what is at stake is what is good for the person simpliciter, as opposed to what that person takes to be good for them. And what better perspective could there be for evaluating the decisions that an agent makes than the perspective of what is good for that person? When we turn to the specific problems that arose for using decision theory as a tool of normative assessment when utility is construed operationally, the advantages of the betterness relation are equally clear. The central problem has to do with the normative force of decision theory. We need a notion of utility on which it is informative to learn that agents satisfying the basic axioms are maximizers of expected utility. Indeed, we need a notion of utility that makes it perspicuous why it might be thought normatively censurable to fail to maximize expected utility. The betterness relation obviously fulfils both requirements. Some philosophers would reject the injunction to maximize expected goodness. Using the betterness relation to interpret the notion of utility makes sense only if we reject both the idea that some outcomes have such a low level of goodness that no action that might lead to them can be considered and the idea that some outcomes have such a high level of goodness that the agent has a duty to perform any action leading to them. Both of these ideas interfere with the basic tenet, fundamental both to the spirit and the mathematics of decision theory, that the goodness of any action is given by the sum of the goodnesses of its possible outcomes, each weighted by the probability of their occurrence. One might also be troubled (as Broome is—see Broome 1991, 124) by the fact that risk neutrality is built into decision theory construed as a theory of goodness. If we evaluate acts in terms of the goodness of their outcomes then it is irrational to prefer a certain outcome of n units of good to a 50:50 chance of 2n + ε units of good, no matter how small ε might be. On standard understandings of utility, an agent’s degree of risk aversion is reflected in their utility function (whether this is construed simply as a measure of preference or in a more substantive sense). But, one might think, outcomes have the same degree of goodness, irrespective of the agent’s degree of risk aversion. It is no solution to deny that goodness is expectational (that is, that the relative goodness relation has the expected utility property).

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The thesis that goodness is non-expectational cannot be combined with the thesis that there is a cardinal measure of goodness. If decision theory is interpreted in terms of the relative goodness relation then we must be dealing with a utility function that has the following property: U(a) ≥ U(b) if and only if a is at least as good as b. If the at least as good as relation satisfies the relevant axioms then it follows from the representation theorem that the utility function U has the expected utility property—that is, it is expectational. Plainly, therefore, the theorist who denies that goodness is expectational must deny that the at least as good as relation satisfies the axioms of expected utility theory. But that, in effect, is to deny that there is a cardinal measure of goodness. And we can see which axiom is likely to be rejected. The non-expectational theorist may well accept that the at least as good as relation is transitive and complete over a given set of lotteries. What he seems bound to reject, however, is the continuity axiom, according to which, for any three lotteries L1, L2, and L3, there are probabilities α and β such that L3 is equally good as α(L1) + β(L2). We need to find a way of thinking about goodness on which the claim that goodness is expectational does not seem so obviously counter-intuitive. Let us look again at the worry about risk aversion. What drives the worry is the thought that we can distinguish between the relative goodnesses of two lotteries (the degenerate lottery with a certain outcome of n units of goodness and the lottery with even chances of 2n + ε units of good or of nothing) and the decision-maker’s attitude to the two lotteries, in exactly the same way that we might distinguish between the expected monetary value of two parallel lotteries (where n and ε are sums of money) and the decision-maker’s attitude to them. In the monetary case we can define a risk-averse decision-maker as one who prefers a certain outcome of $n to an expectation of $n + ε for at least some positive values of ε; and a risk-loving decision-maker as one who prefers an expectation of $n − ε to a certain outcome of $n for some positive value of ε. Risk aversion is reflected in the shape of the utility curve that plots utility against monetary expectation. The worry about the risk neutrality of goodness depends upon assuming that something similar is possible in the case of goodness, so that to be risk-averse about goodness is to prefer a certain outcome of n units of goodness to an expectation of n + ε units of goodness for some positive value of ε. But this assumes that goodness is like

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monetary value, something that we can measure independently of its utility. Broome argues that we can take relation R to be the relative betterness relation without thinking about goodness in these terms. He suggests: ‘‘Utility embodies the results of weighing good across states of nature, and this weighing may well be what determines our quantitative notion of good’’ (1991, 146). Broome’s idea is that our utility/goodness function is derived from comparisons between differences of goodness in different states of the world. Suppose that we have two lotteries, each of which offers two sums of money with equal likelihood. The first lottery (L1 ) offers $100 if a fair coin lands heads and $200 if the coin lands tails, while the second (L2 ) offers $20 and $320 in the same circumstances. The comparison between these two lotteries rests upon the comparative goodness of what they yield in the two relevant states of nature (heads or tails). It is what would happen were the coin to land heads that makes L1 attractive, while the appeal of L2 lies in what would happen were the coin to land tails. If the coin lands heads then what is relevant is the difference in goodness between $100 (L1 ) and $20 (L2 ), while if the coin lands tails then what is relevant is the difference in goodness between $200 (L2 ) and $320 (L1 ). Broome’s idea is that we can take utility to be a measure of how these differences in good stack up against each other. If we let g (−) denote the goodness of whatever is named within the parentheses, then we have U (L1 ) > U (L2 ) ⇔ [g ($100) − g ($20)] > [g ($320) − g ($200)] If we take U to be a goodness function, then we have the result that the goodness of a lottery is derived from the differences in goodness across the relevant states of the world. There is no suggestion that a certain goodness attaches to, say, $100 independently of the fact that the difference in good between $100 and $20 outweighs the difference in good between $320 and $200. And, as Broome points out, the worry about enforced risk neutrality cannot get started, since there is no measure of good besides the weighing of relative goodnesses across states of the world. This paves the way for Broome’s argument that goodness is expectational, which is effectively that the betterness relation conforms to the basic axioms of utility theory. Broome’s proposal also blocks an obvious objection to understanding utility in terms of goodness. If we assume (as we must, if we are working

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within the framework of decision theory) that the goodness of an action is a function of its consequences, then we run into problems with the fact that the consequences of an act are frequently not known until long after the act has taken place (assuming, of course, that we are not engaged in decision-making under certainty). If the utility of an act is to be judged by the goodness of its consequences then there seems no hope for taking decision theory to be a theory of deliberation, since we cannot deliberate on the basis of information that is in principle unavailable to us. Nor does the explanatory/predictive dimension fare any better. Although, in certain cases, we as explainers might have access to the relevant information about goodness, we certainly cannot assume that this information is available to the agent whose behavior we are trying to explain. And as far as prediction is concerned, we are in exactly the same position as the person whom we are trying to predict. If the goodness of an action is the goodness of its actual consequences, then decision theory can only be a theory of normative assessment. The situation would be even more extreme than that which Sidgwick envisages for utilitarian consequentialism when he writes: ‘‘that Universal Happiness is the ultimate standard must not be taken to imply that Universal Benevolence is the only right motive for action . . . It is not necessary that the end which gives the criterion of rightness should always be the end at which we consciously aim’’ (Sidgwick, 1874/1907, 413). It is not obvious that we could ever consciously aim at maximizing goodness, if we can never be sure what would maximize goodness in a particular situation (of risk or uncertainty). The problem does not arise (at least not in the sharp form hinted at by the passage from Sidgwick) because Broome is proposing a probabilityrelative notion of goodness. The things that stand in the betterness relation are what we have been calling lotteries.¹¹ We are to assume that there is a betterness ordering of all available lotteries. This is primary. The goodness of specific outcomes is derivative—which of course is exactly what one would expect if the betterness relation is proposed as a way of interpreting relation R. If, as Broome argues to be the case, ¹¹ Actually, Broome’s framework is more general than the one we have been working with. He takes prospects as basic, where a prospect is a vector of outcomes. A prospect, in essence, is a lottery without the probabilities. He does this because he does not take objective probabilities for granted (in the way that they are taken for granted in the von Neumann-Morgenstern representation theorem). As a consequence goodness is assigned to prospects. This does not affect the general theoretical issues we are discussing, however.

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the betterness ordering conforms to analogs of the fundamental axioms of utility theory, then the mathematics of the representation theorem ensure that goodness is expectational (and hence that the goodness of each lottery is the sum of the goodnesses of its constituent outcomes, appropriately discounted by their probability). Taking lotteries to be the ‘‘vehicles’’ of goodness avoids the obvious practical problem canvassed in the previous paragraph. The goodness of different lotteries can be compared in advance. We do not need to wait until an act has been performed to evaluate how good it is. Rather, we view an act as a probability distribution over possible outcomes and consider that probability distribution as having a certain degree of goodness. Nonetheless, the difficulties have not been dispelled. They have merely been relocated. We need to ask what it is for a lottery to have a certain degree of goodness. It was argued earlier that no non-preferencebased interpretation of relation R can be construed internally, if the interpretation is to give us a genuine alternative to understanding utility in terms of preference. That means that the holding of relation R need not be cognitively accessible to the subject. Putting the point in terms of goodness/betterness, this means at a minimum that we need to distinguish between the betterness relation and the perceived-to-bebetter-than relation, since the latter is plainly internal. We certainly cannot assume that the goodness of a lottery is directly cognitively accessible to the decision-maker, even if we think that ‘‘goodness’’ means ‘‘goodness for the decision-maker’’. Admittedly, this does not rule out there being some cognitively accessible relation R∗ such that aR∗ b holds if and only if a is at least as good as b. Suppose it were the case, for example, that pleasure is the good, so that a is at least as good as b if and only if a is at least as pleasurable as b. Then, even though we are construing the betterness relation externally, we might reasonably assume that the fact that a is at least as good as b might be indirectly cognitively accessible to an agent who is a good judge of what is pleasurable. Of course though, pleasure is not the good and it is far from obvious what relation R∗ might be. This makes the deployment of decision theory for the purposes of action-guidance highly problematic. It is not very useful to be told to act in a way that maximizes goodness when one has no way of triangulating on what the good might be. Of course, it is easy enough to follow the prescription to maximize one’s perceived good, but this brings us back to the internal construal of the

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betterness relation and hence to the familiar problems of construing utility in terms of preference. Things only get worse from the perspective of explanation and prediction. It is highly implausible that an agent’s behavior is guided by what is good for them (although it may be, as some philosophers have argued, that one’s behavior is always guided by a conception of what is good for one). There is a dilemma here. If we suppose that agents are not good at tracking what is good for them then it seems clear that decision theory cannot be very useful for prediction and explanation. There is little point in making predictions about what people will do that are based on what is good for them if it turns out, as is surely the case, that people frequently fail to do what is good for them (even assuming that the predictor has reliable information about what is good for the person whom she is trying to predict). The same holds for explanation. A diehard goodness theorist (and we should note that Broome himself would not fall into this category, since his interest is primarily in the normative application of decision theory when it is interpreted as a theory of goodness) could argue that people are better at tracking what is good for them than is generally held. We might say that, while relation R is the at-least-as-good-as relation, relation R∗ is the perceived-to-beat-least-as-good-as relation. But this brings us to the second horn of the dilemma. Suppose that people actually are reliable trackers of what is good for them. This brings with it a coincidence between choice and goodness, so that by and large people choose what is good for them. This coincidence seems to lead us to what Broome terms the actual-preference-satisfaction theory of good, according to which, for two alternatives A and B, A is at least as good as B for a particular agent if and only if that agent either chooses A to B or is indifferent between A and B (Broome 1991, 132). As Broome notes, this theory can be interpreted in one of two ways. It can be interpreted constitutively, so that the good for a person is understood to consist in the satisfaction of his preferences. Or it can be interpreted instrumentally, so that the good is taken to be some quantity independent of the agent’s preferences but reliably correlated with them. Since the instrumental interpretation seems to be at the outer limits of empirical plausibility, it looks as if the only viable reading is the constitutive reading. But this, it should be noted, is effectively a version of the revealed preference theory, and hence is not a genuine alternative to the operational interpretation discussed earlier.

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ASSESSING THE FIRST CHALLENGE We are exploring the thesis that decision theory can explicate the concept of rationality as it is used in three very different explanatory projects: the project of guiding deliberation and action; the project of normatively assessing decisions and actions; and the project of explaining/predicting behavior. One basic challenge that emerges in thinking about the suitability of decision theory for these different projects is how to make sense of its fundamental theoretical notions of utility and preference. This chapter has shown how the different explanatory projects impose conflicting requirements and constraints upon the notions of utility and preference. Let me end by making explicit the resulting tensions. These tensions emerge when we review the different ways of interpreting the core notion of utility. Suppose to begin with that, with the vast majority of economists and many decision theorists, one chooses to interpret utility operationally. On the operational interpretation, utility is a measure of preference, so that an individual’s utility function provides a mathematically tractable way of describing his preferences. Those preferences themselves are standardly taken to be revealed in choice, so that there is no gap between what an individual prefers and his choice behavior. As emerged in the first part of the chapter, decision theory with preferences interpreted in the formal sense can indeed serve as a theory of deliberation and action guidance (at least in a restricted sense, where deliberation aims to secure consistency with past decisions and choices). However, the operational interpretation fails in one important dimension of the normative assessment project. It makes maximizing expected utility analytically equivalent to choosing in accordance with the axioms of decision theory. This blocks a powerful way of reflectively grounding the normative force of decision theory—namely by simultaneously using the intuitive appeal of the axioms to ground the expected utility principle, and the intuitive appeal of the expected utility principle to ground the axioms. Finally, the operational interpretation of decision theory permits only the most etiolated type of psychological explanation, one that plainly bars us from thinking of probability and utility functions as regimentations of our commonsense notions of belief and desire. And it can only serve a limited predictive function, if we assume, first that people act consistently with their past decisions and choices

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and, second, that there are past decisions and choices to take as benchmarks. There seem to be two possible ways of moving beyond the operational interpretation. The first is to reject the revealed preference principle by trying to develop a more robust notion of considered preference, while retaining the basic idea that utility is a measure of preference. This strategy faces a regress problem that is most acute for decision theory considered as a theory of deliberation and as a theory of normative assessment. Considered preferences are themselves the result of deliberation, and deliberating about one’s preferences is no different from deliberating about anything else. We have to have preferences about preferences in order to deliberate about them. Either those second-order preferences are considered preferences, or they are not. If they are not, then the problem we began with has not been solved. But if they are considered preferences then this can only be relative to some still higher-order preferences for which exactly the same question can be raised. A regress looms, then, for an agent who attempts to attain reflective equilibrium at the level of her considered preferences. Yet she has to establish what those considered preferences are if she is to deliberate according to decision theory, which makes the problem pressing from the action-guiding perspective no less than from the normative assessment perspective. Suppose finally that we try to move beyond the operational interpretation by rejecting preference as the central notion for decision theory. The most plausible version of this strategy takes the basic relation of decision theory to be the betterness relation rather than the preference relation. Taking relation R to be the at least as good as relation has a number of advantages as far as the normative assessment dimension is concerned, but runs into serious difficulties when it comes to the action-guiding and explanatory/predictive dimensions. Even if we develop a probability-relative conception of good, taking the betterness relation to be defined primarily over lotteries, the notion of goodness has to be external rather than internal, if this strategy is to be a genuine alternative to the preference-based conception of utility. Yet an external notion of goodness (i.e. one whose holding is not cognitively accessible to the decision-maker) cannot be deployed in practical reasoning—and hence cannot be the basis for a rationality principle guiding psychological explanation and prediction. Nor does there seem to be any prospect of finding a cognitively accessible relation that is a reliable index of goodness and so can stand proxy

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for it in deliberation. Here we see the sharpest divergence between decision theory in its action-guiding dimension and the other two dimensions. The conclusions of this chapter can be presented in tabular form. STRATEGY

Deliberation

Normative

Explan./Predict.

Utility and preference understood operationally Relation R as considered preference External construal of relation R

✓

✕

✕

✕

✕

✓

✕

✓

✕

The table represents the three strategies we have considered for explicating the basic theoretical notions of utility and preference. It shows that no strategy works for all three of the explanatory projects we have been considering. In fact, each of the three ways of thinking about utility and preference has serious shortcomings on at least two of the three dimensions. None of this is intended as an attack on decision theory. The point rather is that we need to think about the central notions of decision theory very differently depending upon the particular dimension of rationality that we want them to explicate. The different dimensions of rationality impose different ways of thinking about utility and preference. My claim at this stage is simply that these ways of thinking about utility and preference are incompatible. There is no unitary way of understanding the concepts of utility and preference that does justice to all three dimensions of rationality.

3 The Second Challenge: Individuating Outcomes The descriptive project of explanation/prediction is in prima facie tension with the prescriptive project of normative assessment. In explaining and predicting behavior we are interested in how things are. When engaged in normative assessment our interest is in how things ought to be. And so, one might think, the concept of rationality must appear in each project under a fundamentally different guise. When our concern is with explanation and prediction it is with facts about how people actually deliberate and make decisions, and the appeal to rationality as a background assumption should be read as a tacit reminder to respect the constraints imposed by what we know of the psychology of reasoning. When our concern is with normative assessment, on the other hand, we are thinking about rationality as a source of requirements, commitments, and prescriptions that can stand as correctives to people’s individual reasoning practices. This chapter explores the challenge that this general tension poses for the thesis that decision theory can be the core of a unified theory of rationality. In essence the problem is that the requirements of psychological explanation and prediction point us towards an intensional understanding of decision theory, while the requirements of normative assessment demand that the theory be understood in extensional terms. The tension manifests itself in two different approaches to individuating outcomes—that is, to individuating the items to which utilities are assigned. The normative dimension of rationality requires that we be able to take an external perspective on how agents parse decision problems. This requires in particular that we have a standpoint from which we are able to criticize how agents individuate outcomes. There are, for example, cases of paradigmatic irrationality where what has gone wrong is that the agent identifies two outcomes where there is really only one. In criticizing these cases we are applying the intuitively

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plausible principle of extensionality, which requires agents to value equally what are known to be different descriptions of the same outcome. Yet, as we see with particular reference to Frederic Schick’s proposal for an intensional decision theory, the demands of psychological explanation and prediction can push us away from the principle of extensionality. Explaining why people behave in certain ways (and predicting how they will behave) often seems to require taking into account not simply what they take to be the relevant outcomes, but also how they understand those outcomes. The same outcome can be valued differently depending upon how it is understood. This plainly contradicts the principle of extensionality, but must be accommodated in any predictively adequate and psychologically realistic theory of rationality. One solution to the tension between the demands of normative assessment and the demands of explanation/prediction would be to find a way of individuating outcomes that is sufficiently finegrained to be psychologically realistic while remaining extensional. We consider John Broome’s proposal to individuate outcomes in terms of what he calls justifiers. Roughly speaking, two outcomes fail to be equivalent just if it can be rational to have a preference between them. As we see, despite its usefulness in making sense of the puzzling patterns of choice frequently encountered in Allais-type situations, this proposal cannot resolve the tension between the normative and the explanatory/predictive dimensions of rationality.

N O R M AT I V E A S S E S S M E N T A N D T H E PA R S I N G O F D E C I S I O N P RO B L E M S Decision-making can be normatively assessed from either an internal or an external perspective. From an internal perspective one takes as given the way the agent parses the decision problem (what the agent takes to be the available actions and possible outcomes) and then, within that framework, assesses such factors as the internal consistency of the agent’s ranking of the outcomes (with respect, for example, to basic transitivity and completeness requirements) or the particular way in which the agent applied the decision principle determined by the core theory for problems of that type. It might turn out, for example, that the agent has cyclical preferences, or that she failed to choose the option that maximizes expected utility (perhaps simply due to an error of

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calculation). Alternatively, it might be that the agent’s decision-making was, so to speak, procedurally correct. From this internal perspective the normative and action-guiding dimensions of decision theory are very closely connected. But we can also step outside the framework within which the decision-maker is operating in order to ask, from an external perspective, about the cogency and validity of the framework itself. A decision might make perfectly good sense relative to a framework without that framework itself being rationally endorsable. Agents sometimes omit available actions and at other times they take actions to be feasible that are not really feasible. Likewise for outcomes. And when there are such failures it seems clear that agents should be held to account, even if they have applied decision theory impeccably to the decision problem that they have set themselves. It is obvious that agents frequently neglect to take relevant outcomes into consideration. Every time a natural disaster occurs it turns out that the total cost of rebuilding and reconstruction greatly exceeds the amount that insurance companies have to pay out, even in cases where almost all of the damage could in principle have been insured against. Some of those who face losses no doubt explicitly decided against taking out, for example, flood or earthquake insurance, and they may have done so in a manner that was entirely in line with decision theory, balancing their assessment of the risk of disaster against the certain loss of the insurance premium. Statistically, however, it seems that many people living in areas threatened by floods or earthquakes have in effect taken the ‘‘it will never happen to me’’ approach. They decline to see an earthquake or flood as a genuine possibility that they need to factor into their financial decision-making. A similar phenomenon can be seen among people who cycle without bicycle helmets. A small minority will no doubt have determined to their own satisfaction that (what they see as) the low probability of being involved in an accident is outweighed by the high probability of a modest amount of discomfort. It seems most likely, though, that the vast majority have failed to consider that being involved in an accident is a possible outcome at all. In both of these ‘‘it will never happen to me’’ cases it seems very plausible to think that there has been a breach of rationality. Agents in earthquake and flood zones (or who regularly travel by bicycle) have available to them, or at least know how to go about finding, information that should lead them to assign non-zero probabilities to the worst-case scenarios and hence to consider them as outcomes to be taken into account.

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There are more subtle and interesting ways in which agents can fail to make appropriate distinctions between possible outcomes in parsing a particular decision problem. One of the most basic ‘‘decisions’’ that an agent has to make in thinking about a decision problem is whether the problem is one of decision-making under certainty, under uncertainty, or under risk. There are possibilities here for misclassification, where the misclassification is a function of how outcomes are individuated. The most obvious case is where a decision problem is treated as a decision problem under certainty when it is best viewed as a decision problem under risk. Consider, for example, a wildlife manager considering the desirability of measures to stem the decline in the population of cougars in the Rocky Mountains. She might carry out a cost-benefit analysis on the assumption that implementing the measures will lead to a stable or increasing cougar population while not implementing the measures will lead to a cougar population that continues to decline. This would be, in effect, a problem of decisionmaking under certainty and can be tackled within the parameters of decision theory (provided that the scale on which costs and benefits are calculated satisfies the completeness and transitivity requirements). As has been much discussed by environmentalists, however, there are further factors that need to be taken into account. There is no single outcome of a stable or increasing cougar population. At the very least one needs to take into account the implications of a stable or increasing cougar population for the big horn sheep population. So the outcomes contingent on implementing the measures need at least to include Stable or Increasing Cougar Population + Declining Big Horn Sheep Population and Stable or Increasing Cougar Population + Stable or Increasing Big Horn Sheep Population. By symmetry the different possible consequences for the Big Horn Sheep Population need to be factored into the consequences of not implementing the measures. The problem has to be construed as a problem of decision-making under risk, if probabilities can meaningfully be assigned, or under uncertainty, otherwise. These are all cases where the agent underestimates the number of possible outcomes. There are breaches of rationality that take the opposite form, where agents identify distinct outcomes in situations where there is really only one outcome. One of the best-known studies in the extensive literature on framing effects is the Asian disease paradigm developed by Tversky and Kahneman (1981). Subjects are asked to make two choices with respect to a scenario in which the outbreak of a

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disease threatens the lives of 600 people. In the first choice subjects are asked which of the following two outcomes is least bad: A. 200 people are saved B. There is a 1/3 probability that 600 people will be saved and 2/3 probability that nobody will be saved. There is, of course, no correct answer to this question. If you are completely risk-neutral and think that each life is worth, say, one unit of utility then you will be neutral between A and B. But of course you may be risk-averse and/or think that the value of saving 200 lives is not equivalent to 1/3 of the value of saving 600 lives. Nonetheless, however you choose between A and B your choice seems to commit you to choosing a certain way between the following two options: C. 400 lives are lost D. There is a 1/3 probability that no lives are lost and 2/3 probability that 600 lives are lost. The only difference between the A/C and B/D outcome pairs is in how the outcomes are ‘‘framed’’. The first choice presents the outcomes in a positive light (in terms of people being saved), while the second presents the outcomes negatively (in terms of people being lost). It is striking that participants in the study had plainly inconsistent patterns of preference, with 72% preferring A over B and 78% preferring D over C. Framing effects extend to the preferences of extremely sophisticated reasoners working within areas in which they are expert. Tversky and Kahneman (1986) report an earlier study in the New England Journal of Medicine (McNeil et al. 1982) revealing that experienced physicians are subject to exactly the same framing effect as in the Asian disease study. Once again the issue is statistical information about the percentage of a given population that will live as opposed to the percentage that will die. Three groups of subjects (experienced physicians, business school students, and medical patients) were given the following description of two treatments of lung cancer and asked to state which they preferred: Surgery: Of 100 people having surgery 90 live through the postoperative period; 68 are alive at the end of the first year; and 34 are alive at the end of 5 years. Radiation: Of 100 people having radiation therapy all live through the treatment; 77 are alive at the end of the first year and 22 are alive at the end of 5 years.

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Here the statistics are framed in terms of survival rates. Similar groups of subjects were presented with the same statistical information, only this time formulated in terms of mortality rates. Surgery: Of 100 people having surgery 10 die during surgery; 32 die by the end of the first year; and 66 die by the end of 5 years. Radiation: Of 100 people having radiation therapy none die during treatment; 23 die by the end of the first year and 78 die by the end of 5 years. There were no statistically significant divergences between the three groups of subject, but there was a very significant framing effect. The percentage of respondents who preferred radiation over surgery was dramatically higher (44%) in the mortality frame than in the survival frame (18%). Unlike the Asian disease study, agents were not asked to make two choices and so none of them can be charged with straightforward inconsistency. However, the wide divergence between the two groups surely betokens a widespread tendency to value outcomes differently depending upon whether they are described positively (e.g. in terms of survival rates) or negatively (in terms of mortality rates). It seems safe to say that something is going badly wrong in these patterns of preferences. A requirement of rationality is being breached. Tversky and Kahneman identify it as the principle of invariance, which they characterize in the following terms: An essential condition for a theory of choice that claims normative status is the principle of invariance: different representations of the same choice problem should yield the same preference. That is, the preference between options should be independent of their description. Two characterizations that the decision-maker, on reflection, would view as alternative descriptions of the same problem should lead to the same choice—even without the benefit of such reflection. ( Tversky and Kahneman 1986, 253)

The precise formulation of an invariance principle depends on certain technicalities of the theory within which it is embedded. Theories differ in how they understand the outcomes that actions can yield and to which utilities and probabilities are assigned. A theorist might take outcomes to be states of affairs, for example. Or she might take outcomes to be propositions (as in Jeffrey 1983). In the first case a numerical utility and probability is assigned to the fact that a state of affairs holds, while in the second they are assigned to the circumstance of a proposition being true. In either case, however, the principle of invariance states in

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essence that equivalent outcomes must not be treated differently. The rub comes, of course, in spelling out what it is for outcomes to be equivalent. Suppose we work with specifications of outcomes as propositions. Theorists have typically taken propositions in either a thick or a thin sense (see e.g. Loux 2001, ch. 4). In the thick sense, propositions are abstract entities that stand in a many–one relation to facts.¹ We might take a proposition in the thick sense to be a way of thinking about a state of affairs (either possible or actual). Plainly, there are many different ways of thinking about a given state of affairs and correspondingly many thick propositions corresponding to that state of affairs. In the thin sense, propositions stand in a one–one relation to facts. If I assign utilities/probabilities to propositions in the thick sense then those assignments will have the property of intensionality. That is, it is perfectly possible for me to assign different utilities/probabilities to two or more of the thick propositions corresponding to a given fact. Trivially, this cannot occur when propositions are understood in the thin sense, since to each fact there corresponds only one proposition. It is far from clear that it even makes sense to think of probabilities and utilities being assigned to propositions in the thin sense. When we specify a decision problem we do so in words and we inevitably find ourselves thinking of outcomes in particular ways, which are often simply a function of the words chosen. This is what Tversky and Kahneman exploit in the two experiments described earlier. We think about an outcome differently when it is characterized in terms of a 10% mortality rate as opposed to a 90% survival rate. This is simply a fact about human psychology. From a normative point of view, however, the invariance principle bids us proceed as if we were individuating propositions in the thin sense. We cannot help thinking about outcomes under particular descriptions, but we should abstract away from those particular descriptions as much as possible. Of course, as Tversky and Kahneman recognize in their formulation of the invariance principle, we cannot be expected to proceed exactly as if propositions were individuated in the thin sense. It cannot be a requirement of rationality that we treat all descriptions of the same state of affairs as equivalent. It might not be reasonable, for example, ¹ I am assuming that facts, or states of affairs, are always to be understood in a thin sense.

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to expect us to know that two propositions correspond to the same state of affairs. However, the diverging descriptions in the two pairs of experimental vignettes are such that brief reflection ought to convince the decision-maker that they are descriptions of the same state of affairs. Plausibly, it is irrational to treat two propositions differently when it would be easy enough to establish that they correspond to the same state of affairs. What counts as ‘‘easy enough’’ will vary from context to context, but invariance theorists are unlikely to think that descriptions involving synonymous words such as ‘‘dying’’ and ‘‘failing to survive’’ will ever fail to fall within the scope of the invariance principle. Let us follow Frederic Schick (1991, 74–5) in defining the coreportiveness of propositions as follows. Two propositions are coreportive just if they are materially equivalent (i.e. they coincide in truth value) and their material equivalence is a function of independent physical self-identities. So, for example, the two propositions expressed by ‘‘Cicero was a famous Roman orator’’ and ‘‘Tully was a famous Roman orator’’ are co-reportive as a function of the fact that Cicero and Tully are the same person. The invariance principle, as formulated by Tversky and Kahneman, states that different utilities and probabilities should never be assigned to propositions that brief reflection can establish to be co-reportive. They are not alone in this. Many theorists are committed either to their version of the invariance principle or to the slightly weaker version spelled out (but not, as we shall see, accepted) by Schick, which is that it is a basic requirement of rationality that decisionmakers assign the same probabilities and utilities to propositions believed to be co-reportive.

P S YC H O LO G I C A L E X P L A N AT I O N A N D T H E I N D I V I D UAT I O N O F O U TC O M E S What matters for explanation and prediction is how decision-makers actually individuate outcomes, not how they ought to individuate them. If we are to succeed in making sense of other people’s actions we need to think about the decision problem that they take themselves to be confronting, not about the decision problem that they ought to take themselves to be confronting. Can we use decision theory to do this in a way that leaves open the possibility of stepping outside the agent’s perspective for the purposes of normative assessment? In brief, can

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decision theory be deployed from both an internal and an external perspective? There is a prima facie tension here. If, as the psychological literature on framing effects strongly suggests, the decision problems that people take themselves to be confronting frequently fail to satisfy certain basic requirements on how one should construe the available actions and outcomes, then one might think that this jeopardizes using decision theory as a predictive/explanatory theory at all. Perhaps we should follow the lead of Tversky and Kahneman and conclude that the normative core theory is of no use as an explanatory/predictive tool. On this view, decision theory is a theory of rationality that brings with it certain auxiliary requirements, such as the requirements of comprehensiveness and invariance, and if those requirements are not satisfied then decision theory cannot be brought to bear. Let us call this the incompatibilist approach (where what are being held to be incompatible are, of course, the normative and explanatory/predictive dimensions of rationality). On the other hand, however, it might be argued that there is no particular difficulty here. If we are trying to predict behavior then we do the best we can at spelling out how the agent views the available actions and outcomes, and then assigning probabilities and utilities in a way that reflects what we take to be the agent’s beliefs and desires. Once we have done that we work out what the agent is going to do by applying the decision rule for decision-making under risk. That is, we assume that the agent will perform the act that maximizes expected utility. And, one might think, we can do all this without endorsing the way the agent has configured the decision problem. After all, once the numbers are in, elementary arithmetic is enough to identify the uniquely admissible action (assuming that there is only one maximizing action). It does not matter how the agent has parsed the possible outcomes and determined the available actions. All that matters is the numbers that have been assigned relative to that parsing, whatever it is. Of course, this line of reasoning might continue, we are perfectly able to switch perspectives and critically evaluate the parameters of the decision problem. When we do this it might turn out that the decision problem, as the agent formulated it, does not bear scrutiny. Nonetheless, this has no bearing on how we might apply the expected utility maxim from the internal perspective. The expected utility maxim simply identifies a uniquely admissible action relative to an assignment of utilities and probabilities that satisfies the axioms of decision theory. Let us call this the compatibilist approach.

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The compatibilist approach holds that external normative requirements upon the framing of decision problems are extraneous to decision theory, so that the working of decision theory is independent of whether or not those requirements are satisfied. It rests upon the possibility of insulating the efficacy of the expected utility principle from the parsing of the decision problem and the assignment of utilities and probabilities. But this is hardly something that can be taken for granted. It could well be that the requirements of psychological explanation and prediction lead us to assignments of probabilities and utilities that are incompatible with applying the expected utility principle. It might be the case, for example, that suitably empathetic probability and utility assignments regularly breach the axiomatic basis of decision theory. In order to explore the dialectic between the compatibilist and incompatibilist approaches we can focus on the invariance requirement highlighted in the previous section. This has been the subject of considerable scrutiny from Frederic Schick. In a series of writings Schick (1991, 1997, 2003) has argued that decision theory should be reconfigured in a way that severely limits the scope of the invariance principle, which he terms the extensionality principle and formulates in terms of propositions known to be co-reportive (as defined in the previous section). Extensionality requires that different utilities not be assigned to two propositions known to be co-reportive (where two propositions are co-reportive just if they are materially equivalent as a function of certain physical self-identities). With a range of well-crafted examples that have far more psychological depth than the experimental scenarios constructed by Tversky and Kahneman, Schick argues both that, as a matter of empirical fact, there are widespread breaches of extensionality and that many such breaches are rationally defensible. One example that he discusses at length emerges from a passage from George Orwell’s essay ‘‘Looking back at the Spanish Civil War’’. Orwell is describing an episode in which, after a long wait for a soldier to come out of the Fascist trenches and within range, a soldier finally did come out: [The soldier] jumped out of the trench and ran along the parapet in full view. He was half-dressed and was holding up his trousers with both hands as he ran. I refrained from shooting at him . . . I did not shoot partly because of that detail about the trousers. I had come here to shoot at ‘‘Fascists’’; but a man holding up his trousers isn’t a ‘‘Fascist’’, he is visibly a fellow-creature, similar to yourself, and you don’t feel like shooting at him. (Orwell 1957, 199)

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As Schick puts it, the propositions I shoot that Fascist and I shoot that fellow-creature are plainly co-reportive. They coincide in truth value as a function of the fact that the Fascist in view just is the fellowcreature in view. Orwell, of course, knows that. Nonetheless, he assigns different utilities to the two propositions—a high utility to the first and a low utility to the second—and acts on the second assignment rather than the first. This is a flagrant breach of the invariance principle, but Schick does not think that it should automatically be described as irrational. Schick produces a number of further examples with very similar structures. Here is one. We are asked to imagine a doctor who learns that the patient whom he is struggling to keep alive is in fact guilty of a heinous murder (and we might, although Schick doesn’t, imagine that the doctor has good reason to think that the murderer will go unpunished if he lives). Here the two co-reportive propositions are The patient lives and The murderer lives. Such a doctor may well assign different utilities here. If the possible outcomes of continuing treatment are The murderer lives (high probability and low utility) and The murderer dies (low probability and high utility) then continuing treatment looks much less attractive than it would do if the possible outcomes are The patient lives (high probability and high utility) and The patient dies (low probability and low utility). But of course, from an extensional point of view, there is no difference between the two ways of thinking about the outcomes. The patient lives just if the murderer lives, and dies just if the murderer dies, because the patient is the murderer. And the doctor knows this. Again, the invariance principle is breached, but Schick wants to leave open the possibility of describing the doctor as rational. For Schick these and comparable examples point to the psychological significance of what he calls understandings (Schick 1991, ch. 3). Understandings are psychological states that, like propositions, can stand in a many–one relation to facts. I can understand the same fact in a number of different ways. An understanding, for Schick, is really the way that a particular individual sees a fact. There is no requirement that understandings be communicable or shareable. Nor need they be truth-evaluable, in the way that a proposition has to be. There is a basic difference between understanding a particular fact in a certain way, and believing certain things about that fact. We can have an understanding without a belief. The doctor, for example, might understand the (possible) fact of his saving the patient in a

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certain way (as saving the murderer, rather than as abiding by the Hippocratic oath) without believing that he will save the murderer. In fact, his understanding the fact in that way might be what leads him to decide not to save the patient, and hence makes it the case that he cannot believe that he will save the patient. Conversely, as the Orwell example shows, one can believe something about a (possible) fact without having the corresponding understanding. Orwell presumably believed the proposition If I shoot the man with his trousers down I will be shooting a Fascist, but his reason for not shooting is simply that he did not understand the fact in that way. In effect what Schick is proposing is adding a third factor into the standard belief-desire model of action/explanation. The standard model, as we find it for example in Davidson 1963, holds that actions are caused by belief-desire pairs (or, more realistically, by combinations of beliefs and what Davidson calls pro-attitudes) that stand in the appropriate rationalizing relation to the action they bring about/explain. As Schick (and many others) note, however, this cannot be the whole story about the genesis of behavior (Schick 1991, 55–60). For one thing, beliefs and desires are standing states. What explains why they should suddenly become effective at this particular moment? Explanations are contrastive. Citing a particular belief-desire pair might adequately explain why I did this rather than that (say, why I ϕ-ed rather than ψ-ed). But it does nothing to explain why I ϕ-ed at this time, rather than at that time. For another, agents frequently have belief-desire pairs that yield different prescriptions for action. Once again Orwell is a case in point. On the one hand he wanted to shoot Fascists and believed that the man on the parapet was a Fascist. On the other, he desired to live in harmony with his fellow creatures and believed that the man on the parapet was a fellow creature. Plainly, both belief-desire pairs cannot feed into action. So, what explains why one pair is effective, but not the other? Bringing understandings into the picture solves both these problems. According to Schick, beliefs and desires gain their causal force from their psychological context and, in particular, from how the agent understands the facts associated with the different possible actions. For Orwell, understanding the action as the shooting of a fellow human being was enough to rule it out. Something similar might hold for the doctor. In the case of standing beliefs and desires, one can imagine that the precipitating cause of an action might be coming to understand the facts associated with it in a new way that ‘‘activates’’ standing states that

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were previously inert. I do not need a new belief or a new desire to be moved to action. It can happen simply that understanding the facts in a new way leads me to see how the beliefs and desires I already have, and know that I have, apply to this particular situation. There is a further problem solved by the appeal to understandings. It emerges naturally from the discussion in the previous chapter. If we abandon the operational construal of utility and preference we commit ourselves to no longer taking the fact of choice as explanatorily basic in the way that it is in, for example, the theory of revealed preference. Whether we try to develop a more robust notion of preference, or whether we move away from the idea of preference to a more substantive way of understanding what I termed relation R, the fact that an agent chooses one option over another reflects (and indeed is caused by) some underlying motivational state. The fact that the agent is in this underlying motivational state is what explains the choice that she makes. But this raises an interesting psychological question. Sticking for simplicity with the language of preference and confining ourselves to decision-making under certainty (it is easy to see how the basic points carry across to other types of decision-making), we can ask what it is about an option that makes it motivating for the agent. The basic assumption of consequentialism in decision theory is that an option is chosen because of its consequences. But this simply pushes the question back one stage. What makes the consequences of an option motivating for the agent? In decision-making under certainty we understand the consequences of an option in terms of a particular state of affairs (what is sometimes called a prospect—e.g. in Pettit 1991). So we can ask why prospects are motivating—and what makes one prospect more motivating than another. A natural answer here is that prospects are motivating to the extent that they are valued, and that they are valued because of characteristics that they display. These characteristics may well be different for different people and for the same person in different contexts. In one context I might value the prospect in which I give $1000 to international disaster relief because it allows me to make a modest but positive contribution to global well-being. In another context I might value the same prospect because it allows me to flaunt my disposable income. Another person, a misanthrope (in the first case) or someone not wanting to be taken to be a ‘‘flaunter’’ of any type (in the second case), might disvalue the prospect for the very reason that I value it. But these reasons for valuing prospects are, quite plainly, functions of how the prospects are

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understood, in exactly the way that Schick understands understandings. My choices among prospects are determined by the characteristics I take them to have and the characteristics I take them to have are determined by how I understand them. So, allowing understandings into decision theory solves what we might think of as the problem of grounding choice behavior.² From the point of view of the psychology of reasoning and, more generally, of the theory of rationality as an explanatory/predictive tool, there are good reasons for trying to accommodate understandings within decision theory. As we shall see in the next section, this can be done, but the price to be paid is the invariance principle.

A B A N D O N I N G T H E I N VA R I A N C E P R I N C I P L E The invariance principle states that an agent must assign the same utility to two propositions known to be co-reportive, where co-reportiveness requires material equivalence (i.e. sameness of truth-value).³ Since this principle would rule out counting Orwell and the doctor as rational, Schick argues that we should replace it with a weaker principle that rules out simply assigning different utilities to propositions that are known to be (or that might easily be worked out to be) co-reportive where the coreportiveness is a function of their logical equivalence (i.e. the fact that, as a matter of necessity, they have the same truth value). This version of the invariance principle would still count as irrational the patterns of preference revealed in the Tversky and Kahneman experiments, since a 23% death rate is logically equivalent to a 77% survival rate. But it would have nothing to say about Orwell and the doctor, since it is ² For some similar ideas about the psychology of valuing prospects see Pettit 1991. Pettit suggests that what are fundamental for agents are what he calls their propertydesires (desires that particular properties be realized) rather than their prospect-desires. Agents desire prospects because of the properties that they realize. Pettit, however, takes it as given that decision theory cannot accommodate this desiderative structure and argues on that basis that decision theory is incomplete, non-autonomous, and non-practical. This seems to me to be rather too hasty. What this chapter is trying to show is, in effect, that desiderative structure can be accommodated within decision theory, but only at the cost of compromising its suitability as a theory of normative assessment. Pettit’s views will be discussed further in Chapter 5. ³ To my knowledge no one has ever proposed that it might be rational to assign different probabilities to propositions believed to be co-reportive. Henceforth only utilities are at stake.

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obviously contingent that the man holding his trousers is a Fascist, or that the patient is a murderer (even those who believe in the necessity of identity do not think that this extends to identity statements where one of the terms is a definite description). This creates problems, however, because (as Schick recognizes) the invariance principle is entailed by a principle governing conditional utilities that can itself be derived from the expected utility principle. Here is Schick’s reasoning. Suppose, for the sake of simplicity, that we are dealing with a situation where there are only two relevant states of the world, k and m. We are trying to work out the expected utility of an available action h. Decision theory tells us that this expected utility is given by summing the utilities of the outcomes in each state, where those utilities are weighted by the conditional probabilities of the relevant state occurring if one performs h. More succinctly, where u(oh,k ) is the utility of the outcome of performing h in state k and p(k/h) the probability of k conditional on h, (A) u(h) = p(k/h).u(oh,k ) + p(m/h).u(oh,m ) The basic principle of consequentialism states that actions are to be evaluated solely by their outcomes, so that the utility of an action in a given state (the utility of the action and the state holding together, which Schick symbolizes as h-θ-k) is identical to the utility of the outcome of h in state k, i.e. (B)

u(h-θ-k) = u(oh,k ).

Putting the consequentialist assumption back into (A) gives an alternative formulation of the expected utility principle (C)

u(h) = p(k/h).u(h-θ-k) + p(m/h).u(h-θ-m).

We are assuming that the agent knows h and n to be co-reportive. Let us write what the agent knows as h-iff-n. Suppose we substitute h-iff-n for k and ¬(h-iff-n) for m in (C). This gives (1) u(h) = p(h-iff-n/h).u(h-θ-h-iff-n) + p(¬(h-iff-n)/h).u(h-θ-¬(h-iff-n)) Since the agent knows h and n to be co-reportive, we have p(h-iff-n/h) = 1 and p(¬(h-iff-n)/h) = 0. This gives (2) u(h) = u(h-θ-h-iff-n) + 0

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and hence (3) u(h) = u(h-θ-n). Repeating exactly the same reasoning with n in place of h gives (4) u(n) = u(h-θ-n). Combining these yields (5) u(h) = u(n). This is exactly what the invariance principle requires. So, we can in effect derive the invariance principle from principle C, which is an alternative formulation of the expected utility principle derivable from the more familiar formulation in principle A via the unimpeachable consequentialist assumption given by principle B. So, rejecting the invariance principle means that we cannot accept the expected utility principle in anything like its standard formulation. Schick is prepared to bite the bullet. He argues that the expected utility principle should be revised in a way that reflects the agent’s understandings. He introduces some new terminology. A proposition is compelling just if it reports a fact in the way that the agent understands it. It might be the case, for example, that for the doctor the murderer is saved is compelling, whereas the patient is saved is not. Let us go back to principle A: (A) u(h) = p(k/h).u(oh,k ) + p(m/h).u(oh,m ) Principle A should only be taken to hold, Schick suggests, when the outcome-reporting propositions are compelling for the agent. The same holds for the consequentialist assumption built into principle B. In effect, what Schick is proposing is a trade-off between explanatory/predictive adequacy and normative force. He sees decision theory as primarily a formal theory of motivation—a theory that regiments both our intuitive notion of what it is to act for reasons and our commonsense explanatory and predictive practices.⁴ The rejection of the invariance principle is motivated primarily by its apparent incompatibility with ⁴ In the Introduction to Schick 1991, for example, he writes: ‘‘What follows is about the motivation of action, about the reasons that people have. The study of human motivation is known as the study of practical reason’’ (p. 8). He summarizes his position in Essay 4 of Schick 2003 as follows. ‘‘The common theory of motivation refers to what

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widespread patterns of practical reasoning, patterns exemplified in the examples of Orwell and the doctor. What Schick is aiming to provide is a formal model of human motivation. The obvious question to ask, therefore, is whether interpreting decision theory in this way, and making the modifications required, can be reconciled with the theory’s normative dimension.

I N T E N S I O N A L D E C I S I O N T H E O RY A N D T H E D I M E N S I O N O F N O R M AT I V E ASSESSMENT In one obvious sense Schick’s rejection of the invariance principle (or rather: restriction of the invariance principle to cases of logical equivalence) severely restricts the normative scope of decision theory by limiting our ability to take an external perspective on how an agent individuates outcomes. The concept of rationality can only get a grip within the framework set by the agent’s understandings (provided that the agent is not breaching the restricted version of the extensionality principle by assigning different utilities to logically equivalent propositions). We do not have a perspective from which we can normatively assess an agent’s understandings. Or rather, we do not have a perspective for normatively assessing the rationality of an agent’s understandings. Schick makes a number of suggestions about how we might normatively assess an agent’s understandings in moral terms. There are various motivations that an agent might have for particular combinations of understandings and some of those motivations are at best morally equivocal. He considers the example of a judge taking a bribe but who understands it as receiving some money in return for a service that he is duty bound to perform The judge who in fact sees the bribe as a payment wants to avoid having to censure himself. He wants to look good in his own eyes, whatever others may people want and believe. It speaks of motives as reasons, and it holds that people’s reasons are composed of desires and beliefs, that a person has a reason for choosing (and for doing) a where he wants to choose (or take) an action of a certain sort b and believes a is of sort b. I have argued that this is too thin, that we need to bring in also how he sees or understands a, that he has a reason for choosing (and for doing) a where he wants to choose (or take) an action of a certain sort b and believes a is of sort b—and sees a as being of that sort’’ (p. 60).

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think. Formally put, the situation is this. He expects to do x (to take some money). He believes that h and k are propositions co-reportive of x (h is I accept a bribe and k is I accept payment for services). He does not approve of actions reported as x is reported in h but approves of these same actions reported in terms of k. He wants to feel good about himself. He has therefore got to get himself to understand x in terms of k. (Schick 1991, 156)

Schick is surely correct that there is something very suspect about proceeding in this manner. Quite apart from the moral dubiousness of a judge taking bribes there is clearly something wrong with this type of self-serving, deliberate self-delusion. Schick himself describes it as inauthentic and dishonest. But taking the ‘‘moralistic turn’’ in the manner that Schick recommends does not really resolve the tension between the projects of explanation/prediction and normative. For one thing there will be many cases where the motivation is not ‘‘impure’’ in the way that it is in the judge case. Some faulty understandings, and the breaches of invariance that go with them, are misguided for reasons that have nothing to do with the moral sphere. Suppose, for example, that I have a mortgage of $100,000 with 25 years outstanding on which, taking tax relief into account, I am paying an interest rate of 5%. I inherit $100,000 and choose to invest the money in 25-year long-term bonds that are illiquid until maturity. Suppose that these bonds are paying a coupon of 4% and suppose that, in general, I prefer more money to less. This is a situation that I might rationalize to myself with different understandings of the possible outcomes of paying down the mortgage and investing in the bonds. I might think of the first as giving $100,000 to the bank and never seeing it again and the second as putting away $100,000 towards my retirement. Some would think that this is perfectly acceptable. I am not so sure, however, and I think that majority opinion would be on my side. In effect I would be paying to own the bonds, when the only point to owning the bonds is to gain a modest but steady and safe return. One would be hard-pressed to find a moral failing here, however. I am not doing anything self-serving. Quite the opposite, in fact. Nor am I engaged in some form of self-delusion. It just seems that I am in the grip of a straightforward failing of rationality, no more and no less. But this description of the situation is not available on Schick’s reconstruction of decision theory. If putting away $100,000 towards my retirement is compelling (in his technical sense), while gaining a lower return than otherwise possible is not compelling, then my behavior is perfectly acceptable.

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The problem runs deeper than this, however. Let us suppose that we are dealing with a situation that does, plausibly, have a moral dimension. This would be a situation where the agent is subject to moral censure for assigning different utilities to outcomes that he knows to be equivalent. What is the source of the moral censure? We can take the judge case. Here is what Schick has to say about why the judge should be described as dishonest and inauthentic (his terms): Take the judge who describes some money he was given as a payment for services. He is likely to see it as before, as an incentive to favor who gave it—that is, as a plain bribe. The point of the pretense is clear. The judge describes the affair as he does in order to get others to see it so, or at least to get them to think that he himself now sees it that way. He hopes in this manner to avoid their censure. No question about his purposes here. (Schick 1991, 156)

The question, of course, is what is wrong with his purpose. We can take as given that it is morally wrong to take a bribe. The question is: Why is it morally wrong to put a favorable ‘‘spin’’ on something that is morally wrong? Put another way: Why is it morally wrong to find one understanding of an outcome compelling and another not compelling? The moral wrongness cannot be derived solely from the moral wrongness of the outcome. If it were then there would be no significant difference between simply taking a bribe and the complicated contortions that Schick’s judge gets himself into. But where then does it come from? Schick’s judge is trying to avoid the censure of others by describing taking a bribe as receiving a payment for services rendered. But what is wrong with that? There is nothing wrong with trying to avoid the censure of others. The point, surely, is how the judge tries to do this—and, in particular, that in the circumstances there is no relevant difference between taking a bribe and receiving a payment for services rendered—and the judge knows this perfectly well. Or, to put it another way, what is wrong is that I am taking a bribe and I am receiving a payment for services rendered are co-reportive and the judge is well aware of this. Because the judge knows the two propositions to be co-reportive he is required to assign them equal utility. It is because his attempt to avoid the censure of others involves him doing this that it is subject to censure. And this censure is grounded in a requirement of rationality that can be traced ultimately to the principle of invariance. But this, according to Schick, is precisely what we are not allowed to say about the case. There is no rational requirement of invariance, since the two propositions are not logically equivalent.

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So, a theorist sympathetic to Schick’s reconstruction of decision theory is in an uncomfortable position. She has a basic decision to make. On the one hand she can adopt the extreme position of withholding normative censure from all breaches of invariance that do not involve assigning different utilities to logically equivalent outcomes. This will strike many as a desperate course of action. Certainly it is not one that can be accepted by anyone who thinks that there is something wrong with the type of reasoning engaged in by Schick’s judge. It seems unlikely that many will want to bite this bullet. Most theorists (including of course Schick himself) who are sympathetic to the idea that decision theory must in some sense accommodate understandings in addition to extensionally individuated outcomes will want to keep open the possibility of criticizing those understandings. But what is the perspective from which such criticism can be made? There is no possibility of criticizing from the perspective of rationality, since the principles that would make such criticism possible have been excised from decision theory in order to make room for different understandings in the first place. But can we be confident that there will always be a normative perspective other than the perspective of rationality from which breaches of invariance can be criticized? And, even in those situations in which there is such a perspective, can we be sure that what makes the criticism appropriate is not at bottom best characterized as a breach of rationality? The significance of the points just made is contingent, of course, upon the importance attached to the invariance principle and to the availability of a perspective from which breaches of invariance can be criticized. And it is open to a theorist to argue that breaches of invariance are sufficiently rare and/or insignificant for the gain in predictive/explanatory power achieved by accommodating understandings within decision theory to outweigh the correlative loss in the normative assessment dimension. On this view, what we have uncovered is not a tension between the predictive/explanatory and normative assessment dimensions, but simply a trade-off that may be well motivated on pragmatic grounds. We turn now to a more fundamental worry with Schick’s reconstruction of decision theory that cannot be finessed in this way. The normative force of decision theory is very closely connected to the possibility of giving it an axiomatic basis. The representation theorems of expected utility theory assure us that, given a complete and transitive preference ordering over simple lotteries satisfying the substitution and continuity axioms, we can define a utility function over

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outcomes in such a way that an agent prefers one lottery to another just if the expected utility of the first lottery exceeds the expected utility of the second lottery. This gives us a solid reason to follow the theory’s basic principle for decision-making under risk—if we fail to maximize expected utility in the way that decision theory prescribes then we must be breaching the minimal consistency requirements imposed by the axioms. The axioms on which the representation theorem is based are independently plausible, but that plausibility is reinforced by the fact that those axioms entail the expected utility principle. In short the axioms and the expected utility principle stand in complex relations of mutual support that are fundamental to the theory’s normative force. This creates a basic problem for any proposal to reconstruct decision theory along the lines that Schick proposes. As he recognizes, and as we saw above, the revision of the invariance principle that Schick proposes has as a straightforward consequence that we cannot continue to maintain the expected utility principle in anything like its standard form. The expected utility principle only applies for Schick to propositions that report outcomes in ways that reflect the agent’s understanding of those outcomes. Plainly, therefore, Schick cannot be committed to the axioms that jointly entail the expected utility principle. This in itself will strike many as troubling, and it is certainly the case that the principles enshrined in the axioms ought not to be abandoned lightly. Schick himself briefly addresses the question of axiomatizability (1991 n. 27 on p. 94). He considers the potential objection that his proposed reconstruction of choice theory eliminates principles that can be shown to follow from ‘‘basic theses about coherent preferences’’ (i.e. the axioms of decision theory). But the axioms that he considers are the Jeffrey-Bolker axioms and he responds by rejecting their axiom of impartiality, pointing out that Jeffrey and Bolker themselves think that it has no independent plausibility. For our purposes, however, it is more relevant to consider his attitude to the substitution axiom. Here too Schick is prepared to bite the bullet. He claims that the axiom becomes much less straightforward to apply when we broaden our perspective on actions to take into account how agents understand outcomes. We can appreciate Schick’s position through his analysis of the wellknown Allais ‘‘paradox’’ (Allais 1979). In essence Schick suggests that the apparent irrationality of the pattern of choices that Allais drew to our attention is dispelled when we factor in agents’ different understandings

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of the possible outcomes. The Allais phenomenon (robustly confirmed by experimental studies, including those reported in Kahneman and Tversky 1979) arises when subjects are asked how they would choose in a pair of situations, each of which involves a choice between two options. In the first situation subjects are asked to choose between (A) a certain return of $1,000,000 and (B) a lottery that pays $5,000,000 with probability 0.1, $1,000,000 with probability 0.89 and nothing with probability 0.01. In the second situation subjects are asked to choose between two lotteries. The first lottery, (C), pays $1,000,000 with probability 0.11 and $0 with probability 0.89, while the second, (D), pays $5,000,000 with probability 0.1 and $0 with probability 0.9.

A B C D

0.89

0.1

0.01

$1,000,000 $1,000,000 $0 $0

$1,000,000 $5,000,000 $1,000,000 $5,000,000

$1,000,000 $0 $1,000,000 $0

The Allais pattern of choices is A over B and D over C. It is easy to see that this pattern cannot be utility-maximizing, on the orthodox way of parsing the decision problem. Let u be the utility of receiving $1,000,000; v the utility of receiving $5,000,000; and w the utility of receiving $0. The choice of A over B implies that u > 0.89u + 0.1v + 0.01w and hence that 0.11u > 0.1v + 0.01w. On the other hand, the choice of D over C implies that 0.9w + 0.1v > 0.11u + 0.89w, and hence that 0.01w + 0.1v > 0.11u. Plainly, one of the axioms on consistent choice is being breached and from the table we see that it is the substitution axiom. This application of the substitution axiom requires that we view outcomes with the same monetary value as equivalent when they are embedded in different compound lotteries (as indeed does any application of the substitution axiom). But Schick thinks that this assumption is not warranted. Here is what he has to say: For a person who sees the outcomes in money terms only, Allais is right: choices of A and D can’t both be expectedness maximizing. But what if the chooser sees things differently? What if he sees the zero-money outcome of Allais’s option B as getting nothing when I was sure to get a million if I took option A or getting

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nothing and kicking myself for choosing as I did ? For a person who sees the outcomes in a way that takes in what might have been—what would have been, had he been prudent—the choice of both A and D may well be expectednessmaximizing. So also for someone who sees the outcomes in terms of the regret (or relief ) they would yield him. It could be argued that such a person should choose A and D on expectedness grounds, and nothing worrisome therefore follows from the fact that many people did. (Schick 1991, 125)

It is important to get clear on the dialectic of the argument. Schick is not, as far as I can see, arguing that the possibility of construing the Allais choices in the way that he suggests is a counterexample to the substitution axiom. The point, rather, is that it is possible to reconfigure the Allais choices in such a way that the substitution axiom cannot be brought to bear. If, as Schick proposes, the outcome that yields $0 with probability 0.01 in B is understood as getting nothing when I was sure to get a million if I took option A while the outcome that yields $0 with probability 0.01 in D is understood as, say, a slight increase in what is already a considerable increase in the probability of ending up with nothing, then options B and D cannot both be viewed as compound lotteries that each involve lottery Q. And this means that the substitution axiom cannot get a grip—which is just as it should be, according to Schick, since if the substitution axiom were applicable then the choices would come out as irrational, which he thinks they are not. Nonetheless, although Schick’s manoeuvre shows that one can allow the Allais choices to be rational without directly compromising the substitution axiom, that is not the end of the story. It is well documented that many Allais choosers stand by their choices even when the (putative) inconsistency is pointed out to them (see e.g. Slovic and Tversky 1974). Let α be the proposition getting nothing when I was sure to get a million if I took option A and β be the proposition getting nothing with a probability of 0.01. An Allais chooser who stands by her choices after the ‘‘debriefing’’ is aware that α and β are co-reportive, but she thinks of option B in terms of α while she thinks of option D in terms of β. What rationalizes her choices is that she assigns a lower utility to α than to β. But then such a chooser is clearly in breach of the invariance principle, which demands that a rational decision-maker not assign different utilities to outcomes believed to be co-reportive, and hence, by the reasoning outlined earlier, the unrestricted expected utility principle cannot apply, which means that the axioms cannot be being adhered to. This is the real nub of the problem. Schick’s own perspective on his modified version of expected utility theory is that it is primarily a theory

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of practical reason, which he thinks of in terms of human motivation, so that decision theory comes out as in essence a formal theory of human motivation. From that perspective the loss of an axiomatic basis may well seem a price worth paying for a gain of psychological realism and increased explanatory/predictive power. From the perspective of normative assessment, however, the cost seems too high, given how the axiomatic basis of expected utility theory serves as a foundation for the normative assessment dimension of decision theory. We are looking for a theory to serve the aims of both normative assessment and explanation/prediction. Eliminating the axiomatic basis of decision theory is not an option. The question arises, therefore, whether it is possible to do justice to the psychological subtleties drawn to our attention by Schick without compromising the axiomatic basis of decision theory. We have seen that allowing for understandings is not a viable way of doing this. Is there another possibility? We turn in the next section to a proposal for individuating outcomes that has been made by John Broome. Although not motivated by the sorts of concerns that we have been exploring, Broome’s proposal preserves extensionality while accommodating a more fine-grained approach to individuating outcomes than is standard among utility theorists. B RO O M E O N I N D I V I D UAT I N G O U TC O M E S It is clear what we need to avoid. The problems for the axiomatic basis of decision theory all stem from breaches of the invariance principle, which in turn come from allowing it to be legitimate to assign different utilities to propositions known to be co-reportive. Of course, we can only have two or more co-reportive propositions if we individuate outcomes less finely than we individuate propositions. So, our best hope is to find a way of individuating outcomes that is both principled and sufficiently fine-grained to obviate the need to allow for different understandings of individual outcomes. Broome’s account of outcome individuation is developed in the context of arguing that the transitivity of preferences and the substitution axiom are indeed requirements of rationality. We can consider his argument in the context of the Allais puzzle, about which he makes a telling observation (Broome 1991, ch. 5). The Allais choices are proposed as counter-examples to the substitution axiom, with the argument depending upon the twin claims, first, that the choices are rational and,

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second, that they present a counter-example to the substitution axiom. Broome argues that these claims cannot both be true. What would it be, Broome asks, for it to be rational to prefer A over B and D over C. Given that the two pairs of options have the same outcomes in two of the three states (i.e. those whose probability of occurring is 0.1 and 0.89) the only possible way of rationalizing the Allais choices is going to involve finding a difference between the outcome in the other state (the state with probability 0.01) in option B and in option D. There is a number of ways of doing this, one of which bears a certain similarity to Schick’s proposal. The difference might be that, if the outcome in the 0.01 state occurs and the agent has chosen option B, then she will receive $0 and will also suffer a certain amount of psychological distress as a consequence of failing to choose the option with the guaranteed outcome—whereas, if the same outcome occurs and the agent has chosen D then, although the monetary outcome is the same, she will not feel the same amount of distress.⁵ If the two outcomes do indeed differ in this respect then there is no counter-example to the substitution axiom, which of course applies only when we have the same outcome embedded in different compound lotteries. But Broome continues, if the outcomes are not distinguished in this or some other way then the Allais choices cannot be rational—we would have a distinction without a difference. The point Broome is making is simply one of consistency (as I understand it he is agnostic about the Allais choices), to the effect that the reasons one might have for viewing the Allais choices as rational militate against viewing them as a counter-example to the substitution axiom, and vice versa. Both Schick and Broome highlight the psychology of the Allais chooser, but they do so in different ways. Schick individuates the outcomes in monetary terms in the standard manner and then builds the psychological dimension of regret and self-recrimination into how those outcomes are understood. This is how he ends up with a breach of invariance, since we have a single outcome (receiving $0) that is assigned different utilities depending upon how it is understood. Broome’s account, on the other hand, makes it possible to individuate the outcomes more finely, so that the feeling of regret and the urge towards self-recrimination are actually built into the outcomes. Doing this preserves the invariance principle. ⁵ For a discussion of this general approach to the Allais paradox see Weber 1998.

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One might wonder whether Broome’s points do not beg the question against someone who believes that the Allais choices are both rational and breaches of the substitution axiom. After all, Broome’s argument depends upon the tacit assumption that any reason for choosing A over B and D over C must be a function of what happens in the 0.01 state. The justification for this is obvious and intuitive, namely, that each pair of options is identical with respect to the other two states (the 0.89 state and the 0.1 state). Where else could a reason be found? But this obvious and intuitive justification is simply the substitution axiom, which is precisely what is at issue. Those, such as Allais himself, who think that choosing A over B and D over C is both rational and contravenes the substitution axiom simply deny that we can think about outcomes in different states independently of each other. There are, so they think, ‘‘complementarities’’ between outcomes in different states that undercut the line of reasoning Broome canvasses. In any event, the validity of Broome’s argument is not our principal concern. What is interesting about his position is the proposal it contains about how to individuate outcomes. Broome offers the following principle: Principle of individuation by justifiers. Outcomes should be distinguished as different if and only if they differ in a way that can make it rational to have a preference between them. If outcomes are individuated by justifiers then there is no difficulty in seeing how the type of phenomena that Schick draws to our attention can be accommodated at the level of outcomes rather than the level of understandings. If it is indeed rational to assign different utilities to shooting the Fascist soldier and shooting the man holding up his trousers then Broome’s principle has it that these are different outcomes. This means that there would be no breach of the invariance principle, as characterized by Tversky and Kahneman, since we do not have different utilities being assigned to different descriptions of the same outcome. Things are slightly more complicated with the version of the invariance principle that Schick rejects. Recall that this version requires decision-makers to assign the same utilities to propositions believed (or easily worked out) to be co-reportive, where two propositions are co-reportive just if they are materially equivalent (they always have the same truth value) and their material equivalence is a function of independent physical self-identities. Even if we grant that the propositions I will shoot the Fascist soldier and I will shoot the man holding his trousers

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up describe different outcomes, according to Broome’s way of individuating outcomes, they may still come out as being co-reportive. It all depends upon whether we can make sense of their not being materially equivalent. It does not obviously follow from the fact that two propositions report different outcomes that they can differ in truth value. But it may well be the case that, whenever we have two propositions reporting outcomes between which it can be rational to have a preference, those two propositions fail to be materially equivalent.⁶ In any event, this proposal for individuating outcomes cannot solve the problem with which we began (although, in fairness to Broome, we should note that our problem is not his problem). We need a way of individuating outcomes that is independent of, and logically prior to, our theory of rational preferences. Recall that what gave rise to the discussion of outcomes was a perceived need, from the viewpoint of normative assessment, to be able to take an external perspective on how agents parse decision problems. It is, I have argued in several places, a basic requirement upon a theory of rationality that it yield a way of individuating outcomes that allows us to assess how individual decisionmakers individuate outcomes. Even though an agent’s decision-making may be impeccable relative to the parameters set by the decision problem that he took himself to be facing, there are always questions to be asked about how those parameters are set. We can ask, for example, how rationally the decision-maker assessed the available actions, or how rationally he construed the outcomes. The type of situation where these normative questions arise is typically one where it is far from clear how to individuate the outcomes. A course of action may come out as rational when the outcomes are individuated one way and as irrational when they are individuated another way. Plainly, we need a way of individuating outcomes that will determine in an absolute sense whether or not the action is rational and Broome’s proposal, which presupposes an independent triangulation on what qualifies as a rational preference, takes us outside the realm of decision theory. The principle of individuation by justifiers is itself a normative principle. It is a principle about how decision-makers should discriminate ⁶ Of course, Broome is not committed to there being two different outcomes in this case. But many of Schick’s examples are very plausible from a psychological point of view and any principle for individuating outcomes that is to do justice to the explanatory/predictive dimensions of the concept of rationality will have to accommodate some if not most of the cases that he discusses. It is unclear how important this is to Broome, since his emphasis is primarily on the normative dimension of rationality.

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between outcomes and what preference between outcomes they are permitted to have. We need to ask, therefore, about the source of this normativity. If we were interested in decision theory solely from the point of view of explanation/prediction we could resolve this question by looking at the discriminations that people standardly make and the preferences that they standardly have. We might conclude, for example, that anecdotal and experimental evidence suggest that it is indeed appropriate to distinguish in the Allais situation between the outcome in the state with probability 0.01 in option B and in option D. We might argue, for example, that outcomes should be distinguished as different just if they are so distinguished by sufficiently many people, which thereby makes it rational to have a preference between them. But this of course is exactly what we cannot do, if we want decision theory to be normatively valid, since normative validity requires us to reserve the right to accuse the majority of irrationality. So, we need an independent grounding for the normative force of the principle of individuation by justifiers. As the formulation of the principle makes clear, this independent grounding presupposes an account of what it is for a preference to be rational. But, since we cannot bring decision theory to bear without a principled way of individuating outcomes, it is clear that we need to go beyond decision theory if we are to have a full account of rationality. Broome is explicit about where the independent triangulation is supposed to come from, namely, what he calls external criteria of goodness. He writes, ‘‘it is rational to have a preference between two alternatives only if they differ in some good or bad respect’’ (1991, 106). The theory of rationality, therefore, has to be grounded, if not on a theory of the good, then at least on certain pretheoretical criteria for judging the goodness of acts. There are both similarities and differences with the position that Schick ends up in. For both Broome and Schick the theory of rationality is ultimately constrained by considerations of value. Schick thinks that there are limits on what can count as an acceptable understanding of a given state of affairs. These are moral limits. He gives examples of unacceptable understandings that betray character flaws and failings (inauthenticity, dishonesty, self-deception, and so on). To put it in terms of goodness, what is at stake is the goodness of the agent. So, both theorists at some level take rationality (or at least, the way in which a rational agent can parse a decision problem) to be constrained

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by considerations of goodness. But the details are very different in the two cases. For Broome, as we saw in the previous chapter, betterness is relation R. That is to say, outcomes and prospects are evaluated, compared, and ranked in terms of their relative degrees of goodness. It is hardly surprising, therefore, that Broome takes it to be axiomatic that a rational agent should be indifferent between alternatives that do not differ in some good or bad respect. In this sense, therefore, his principle for individuating outcomes is entirely continuous with the rest of his theory. For Schick, in contrast, the considerations that he thinks constrain acceptable understandings are extrinsic to his recasting of decision theory. The psychological theory of motivation that he develops is formulated entirely in terms of beliefs, desires, and understandings. Character traits such as sincerity and authenticity have no role to play. It is unsurprising, therefore, that there seem to be inadmissible understandings that fall outside the scope of Schick’s moral criteria—and also that Schick’s position seems to sidestep the apparent irrationality of (at least some) breaches of invariance. In these respects, at least, Broome’s position is more secure. But there are, however, serious difficulties with using Broome’s proposal to reconcile the tension between the explanatory/predictive and normative assessment dimensions of rationality (which, it should be repeated, is not the problem that Broome sets out to address—and so these difficulties are not proposed as difficulties for him). As we saw earlier, if we take relation R to be the betterness relation then we can understand betterness in either an internal or an external sense, depending on whether or not the fact that relation R holds between two outcomes or lotteries is cognitively accessible to the agent. To understand betterness in the internal sense is to understand it in terms of some psychological quantity, such as pleasure or, more plausibly, apparent good (what the agent perceives to be good for her). To understand betterness in the external sense is to understand it in terms of what is good for the person tout court. The problem with the internal reading is that it lacks the normative force to do the work required. The whole point of the discussion of individuation through justifiers is to find a vantage point from which it is possible normatively to assess how an agent has framed the relevant decision problem. We are looking for a perspective from which we might say, for example, that an agent is treating as distinct outcomes what is really a single outcome. But we have no such external vantage

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point if betterness is construed internally. Suppose, for example, that an agent judges one description of an outcome to be more pleasant than another description of what turns out to be the same outcome. On at least some such occasions we want to be able to say that the agent is acting irrationally. But Broome’s criterion will not allow us to do this, if betterness is construed internally in terms, say, of apparent good. The fact that the agent judges the first description to be better for her than the second shows (on the internal construal) that the outcomes as described differ in some good or bad respect. They differ in respect of apparent goodness, which is a justifier. And so it is rational for the agent to have a preference between them. The same will hold for any other candidate for the internal construal of betterness. On the internal construal of betterness, therefore, the principle of individuation by justifiers does not give the external vantage point we need. It cannot do justice to the requirements of normative assessment. This problem disappears if we construe betterness externally. The decision-maker does not have the last word on whether or not two outcomes differ with respect to goodness externally construed. But a different problem emerges. Broome is explicit that the principle of individuation by justifiers effectively abdicates responsibility for individuating outcomes to external criteria of goodness, recognizing in effect that a theory of rationality built around decision theory is not autonomous and self-contained. This already places limits on the scope of decision theory (limits that do not exist for interpretations of decision theory that individuate outcomes according to the extensionality principle, given the close connections explored above between the extensionality principle and the expected utility principle). Moreover, some theorists might be concerned about the existence of external criteria of goodness, or about how to appeal to them in normatively assessing how agents construe decision problems. But let us put all these worries aside. The real problem with using Broome’s principle with goodness construed externally is that the criteria of goodness to which it appeals are dependent upon the facts about rational preference that they are intended to explain. It is often not possible to agree on the facts about goodness unless one already agrees on the facts about rational preference. This emerges from an example that Broome himself discusses. Imagine a couple with a single child who are trying to decide whether to have another. In thinking about this they consider both the possibility of dividing their resources equally between the two children, and that

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of concentrating on the eldest. Suppose that the three alternatives look like this, with the units representing each child’s degree of well-being. Broome imagines the couple reasoning as follows. The status quo (alternative A) is better than alternative B, because A is better for the first child and there is no one in A for whom it is worse than alternative B. They might also think that B is better than C, because the overall quantity of well-being is greater and it is evenly distributed. Finally, they may well think C to be better than A, since in C the eldest child is better off and nobody is worse off. CHILDREN First 11 ALTERNATIVE A

CHILDREN First Second 7

7

ALTERNATIVE B

CHILDREN First Second 12

1

ALTERNATIVE C

If this line of reasoning is rational then it is rational to have cyclical preferences. But there are ways of individuating the relevant outcomes so that something like these preferences would be rational without compromising acyclicality. The couple might, for example, think of alternative B as really two different outcomes. They might think of B differently when it results from rejecting A from when it is the result of rejecting C. Would this be rational? Broome thinks that the principle of individuation by justifiers can be straightforwardly applied to show that it is not. If outcome B comes about, I cannot see that it makes any difference to its value whether it comes about as a result of rejecting A or not. What matters about B is that there are two children living two equally good lives. I cannot see that it matters what choices their parents are faced with in bringing about this result. Comparing B with different alternatives may bring to mind different considerations, but it does not alter B’s actual goodness. In this case, the difference in the rejected alternatives is not a justifier. (Broome 1991, 106)

We can certainly concede that the well-being of the two children remains constant however B is brought about (since any variation in the well-being will ipso facto count as a justifier). And we can also concede that (on Broome’s assumptions) if the actual goodness of B is not altered by how it comes about then there can only be one outcome. But the question is how we get from the first claim to the

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antecedent of the second. Broome needs it to be the case that the goodness of B is fixed by the well-being of the individual children. I have no views about whether or not this is the case. My point is simply that one cannot decide for or against this claim without deciding whether it is rational to have a preference between an outcome brought about one way and an outcome brought about another way. If it is rational to have a preference between them, then the goodness of B need not be fixed by the well-being of the individual children. If it is not rational, then the goodness of B must be fixed by the wellbeing of the individual children. So, how are we to decide whether or not it is rational to have a preference between the two ways in which outcome B might come about? It is plain that the principle of individuation by justifiers cannot be applied to tackle the question, since we cannot apply the principle without having answered the question. It follows that Broome’s external criteria fail to be sufficiently independent to anchor the principle of individuation by justifiers. As a consequence, the external construal of the betters relation also fails to give the required vantage point for normatively assessing how agents individuate actions. ASSESSING THE SECOND CHALLENGE We can summarize the dialectic as follows. If decision theory is to do justice to the normative assessment dimension of rationality, then it must offer a vantage point from which we can assess how agents parse decision problems. Some ways of parsing decision problems are acceptable and others unacceptable, and at least some of the unacceptable ways of parsing decision problems are unacceptable precisely because they are irrational. The most obvious area in which these issues arise is determining when to count outcomes as the same or different. One answer to the problem, implicit in standard presentations of decision theory (and indeed entailed by them), is to adopt some version of the invariance principle. We have discussed a formulation due to Schick, according to which it is irrational to assign different utilities to propositions that are known to be co-reportive in the material equivalence sense of co-reportiveness. This preserves the normative assessment dimension, but placing such a strong constraint upon how decision problems are parsed runs into conflict with the explanatory/predictive dimension of the concept of rationality. There are powerful reasons for

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thinking that an extensional decision theory cannot serve as a theory of motivation. It cannot do justice to why people make the choices that they make—and hence cannot serve as a way of understanding and predicting their behavior. Schick’s own answer to the problem is to replace the standard twocomponent theory of motivation (which we see reflected in orthodox decision theory, taking utilities to be formal analogs of the commonsense notion of desire and probability assignments to correspond to beliefs) with a three-component theory that allows for a single outcome to be understood in different ways. The immediate consequence is that the invariance principle no longer holds. With it goes the expected utility principle in its standard formulation. Schick’s proposed replacement is relativized to understandings. This manoeuvre allows decision theory to serve as a theory of motivation and hence as a tool for predicting and explaining behavior. But the price to be paid is that the theory is severely compromised on the normative assessment dimension. The failure of the expected utility principle prevents us from placing decision theory on a firm axiomatic basis, which strikes hard at the project of normative assessment, given the importance of axiomatizability for grounding the normative force of the theory. And second, on Schick’s construal decision theory cannot settle questions about the rationality of a decision-maker’s understandings, provided that those understandings meet the minimal extensionality requirement (i.e. that it is irrational to assign different utilities to two propositions known, or easily worked out to be, logically equivalent). He proposes to use what are in effect moral criteria of inauthenticity, dishonesty, and inattention to distinguish ‘‘right’’ understandings from ‘‘wrong’’ understandings. As we saw, this is at best only a partial solution. These moral criteria cannot get a grip on many, ordinary, apparently irrational understandings that are less dramatic than the corrupt judges and war criminals whom Schick considers. Even in the cases to which they do apply they leave unanswered the important question of what is wrong with the ‘‘wrong’’ understandings, over and above the wrongness of the action that is being characterized. And, of course, the appeal to morality is an admission that Schick’s version of decision theory cannot itself determine the rationality of how agents parse decision problems, so that the theory fails one of the crucial demands posed by the normative assessment dimensions of the theory of rationality. The principal problems here are not specific to Schick’s theory. The expected utility theorem will fail in any theory that breaches the

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requirement of invariance, and so no such theory will be axiomatizable. And any version of decision theory that allows breaches of invariance must distinguish those breaches that are normatively acceptable from those that are not. These criteria will have to come from outside decision theory. A third response to the problem is to individuate outcomes in a more fine-grained way. Whereas Schick allows for multiple ways of understanding a single outcome, we can individuate outcomes so that our way of individuating outcomes does the job that Schick brings in understandings to do. Any such way of individuating outcomes has to respect Broome’s principle of individuation by justifiers, which holds that two outcomes should be distinguished if and only if it is rational to have a preference between them. In principle this leaves it open for a rational agent to assign different utilities to two propositions known to be co-reportive (in the material equivalence sense of co-reportiveness). Broome’s development of his individuation principle hinges on the idea that it is rational to have a preference between two outcomes only if they differ in some good or bad respect. This raises once again the issue that we discussed at some length in the last chapter. Should goodness be understood internally or externally? On either interpretation we saw that there are problems for using the principle of individuation by justifiers. On the internal construal the principle fails to provide an external vantage point for overriding how an agent distinguishes outcomes. The agent comes out as the ultimate arbiter on whether or not outcomes differ in some good or bad respect, and hence on whether or not it can be rational to have a preference between them. Construing goodness externally gets round this problem, but raises new problems for the normative assessment dimension. We cannot decide whether or not two outcomes differ in some good or bad respect without deciding which respects can legitimately be taken into account in comparing the two outcomes. But this decision will often depend upon a prior decision about whether or not it is rational to have a preference between the two outcomes. Applying Broome’s principle requires there to be an independent tribunal of facts about goodness to appeal to in fixing whether or not there are rational requirements of indifference (i.e. whether a decision-maker is rationally mandated not to have a (strict) preference between two outcomes). But fixing the facts about goodness often requires prior fixing of the facts about rational preference.

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As we did in the previous chapter we can represent the dialectic in tabular form: STRATEGY Extensional approach (invariance principle) Intensional approach Individuation by justifiers

AG

NA

E/P

✓ ✓ ✓

✓ ✕ ✕

✕ ✓ ✓

As before we see that none of the three strategies considered can accommodate all three of the dimensions. The tensions explored in the chapter have all been between the explanatory/predictive and normative assessment dimensions. Developing decision theory in accordance with the first strategy fails to meet the requirements of explanation and prediction. Developing it in accordance with the second or third strategy falls foul of the requirements of normative assessment.

4 The Third Challenge: Rationality Over Time We can think about rationality from a synchronic or a diachronic perspective. Synchronic rationality is concerned with preferences, probability assignments, and choices at a time. Diachronic rationality is concerned with preferences, probability assignments, and choices over time. Up to now we have been discussing decision theory from a purely synchronic point of view. We have been thinking about how to resolve individual decision problems; about how one might normatively assess an individual’s solution to a particular decision problem; and about how one might either work forwards from preferences and probability assignments to predict choices or work backwards from choices to preferences and probability assignments. In many respects this restriction to individual decision problems is highly artificial. As agents we engage in sequences of choices that are not always reducible to a series of independent, individual choices. We make choices about how we will choose, and we make choices in the light of earlier commitments to choose in certain ways. We make plans for the future and we have a degree of concern for the plans that we have made in the past. The way in which we carry these plans through depends upon how things turn out. The third challenge for decision theory is accommodating the basic phenomenon of sequential choice.¹ ¹ What I am calling sequential choice others call dynamic choice. The terminology of dynamic choice (and dynamic (in-)consistency) is well established in the literature. However, as a referee pointed out, it is standard when discussing a situation that changes over time to distinguish what the changes are (the kinematics of the situation) from what causes those changes (the dynamics of the situation). Since I will sometimes be talking about dynamics and sometimes about kinematics I will use the neutral term ‘sequential’.

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T H E S U B S T I T U T I O N A X I O M A N D S E QU E N T I A L CHOICE Although decision theory does not explicitly have a diachronic dimension, it does have implications for sequential choice. The theory is a theory of consistency and there are complex relations between consistency at a time and consistency over time. We can see this by considering the implications for sequential choice of having preferences that are synchronically inconsistent in virtue of breaching the substitution axiom. There is a powerful argument that agents with preferences contravening the substitution axiom (and hence who cannot, by the representation theorems, be maximizers of expected utility) are committed to a form of sequential inconsistency if they have to make a suitably structured sequence of choices.² Their pattern of preferences commits them to deciding to choose in a particular way at a later time and then, when that time comes, to choosing differently. Recall that the substitution axiom requires that an agent prefer one lottery to another if and only if he prefers a complex lottery in which the first is embedded to an identical lottery in which the second is embedded. More precisely, for every lottery X, Y, Z (including of course degenerate lotteries with a certain outcome) and non-zero probability p we have X ≥ Y ⇔ {X, p; Z, 1 − p} ≥ {Y, p; Z, 1 − p} where {X, p; Z, 1 − p} is the compound lottery that gives X with probability p and Z otherwise. So, for example, if I prefer a helping of sorbet to a helping of mint chocolate chip then I should prefer a lottery that offers an 80% chance of a helping of sorbet and a 20% chance of a packet of popcorn to a lottery that offers an 80% chance of a helping of mint chocolate chip and a 20% chance of an equally sized packet of popcorn. Consider an agent with preferences breaching the substitution axiom. For some lotteries X, Y, Z and a non-zero probability p, this agent has the following preferences: ² See Raiffa 1968, 82 for an early formulation of the argument. For detailed discussion see, inter alia, McClennen 1983, Machina 1989, McClennen 1990, and Rabinowicz 1995.

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Decision Theory and Rationality X ≥ Y and {Y, p; Z, 1 − p} ≥ {X, p; Z, 1 − p}³

It might be the case that, although he prefers the helping of sorbet to the helping of mint chocolate chip, he prefers the 80:20 chance of mint chocolate chip rather than popcorn to the 80:20 chance of sorbet rather than popcorn. We can construct a sequential choice problem that exploits this pattern of preferences to generate a sequential inconsistency. Sequential inconsistency occurs when an agent makes a plan to choose in a particular way at a later time and then, when that time comes, chooses differently. If I make a plan to choose a helping of sorbet and then, when the times comes, I choose a helping of mint chocolate chip, then I am being sequentially inconsistent. Assume that E is an event that takes place with probability p—a lottery, for example, in which the agent’s chance of success is p. If E occurs (e.g. if the agent wins the lottery) then he wins the opportunity to choose between X and Y (e.g. between the helping of sorbet and the helping of mint chocolate chip). If he loses then he receives Z (e.g. the consolation prize of the packet of popcorn). Let t1 be the time at which E either occurs or fails to occur and t2 the later time at which the choice between X and Y is made. The situation is represented in Figure 4.1, where the box represents the choice node (where the agent has to make a choice) and the circle the chance node (where it is determined whether E occurs or not). The agent is asked at a time t0 before t1 (and hence before it is known whether E will occur) how he plans to choose between X and Y at the still later time t2 . Of course, there will only be such a choice if E occurs. So the agent is choosing between {X, if E occurs; Z, otherwise} and {Y, if E occurs; Z otherwise}. Since the probability of E is p the choice is effectively between {X, p; Z, 1 − p} and {Y, p; Z, 1 − p} and we know that the agent prefers the latter. So, at time t0 the agent chooses to go across rather than down at the choice node. In our example he chooses at t0 to choose mint chocolate chip at t2 . Suppose, then, that E occurs and that the agent arrives at the choice node. Faced with a choice between X and Y the agent consults his preferences and chooses X over Y. But then he ends up going down at t2 , contrary to the plan decided upon at t0 . This is a textbook case of sequential inconsistency. ³ {Y, p; Z, 1 − p} is the lottery that yields Y with probability p and Z otherwise.

Rationality Over Time t0

t1

115

t2 E

Y (mint chocolate chip)

¬E

Z (popcorn)

X (sorbet)

Figure 4.1 Illustration of how preferences breaching the substitution axiom lead to sequential inconsistency. The circle represents a chance node and the square a choice node. The solid line represents what the agent does at t2 , while the dotted line represents what, at t0 , he had planned to do.

For another example, imagine an agent with Allais-type preferences contravening the substitution axiom (as discussed in Chapter 3). Recall that this involves simultaneous preference for lottery A over lottery B and for lottery D over lottery C when the pay-offs are as presented in the table.

A B C D

0.89

0.1

0.01

$1,000,000 $1,000,000 $0 $0

$1,000,000 $5,000,000 $1,000,000 $5,000,000

$1,000,000 $0 $1,000,000 $0

It is easy to present the Allais scenario as a sequential choice problem. This is done in Figure 4.2, where E and F are ethically neutral events with the appropriate probabilities. The figure illustrates both problems, the only difference between them being what happens if E does not occur at the first chance node. In the first problem (between A and B in the table, with $1,000,000 pay-off at the first chance node) an agent with the Allais preferences opts to go down at the choice node at t2 . In the second problem (between C and D in the table, with $0 pay-off at the first chance node) the same agent opts for the gamble at t3 .

116 t0

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t2

t3

t4 $5M

F (10/11) E (0.11)

(Allais B/D)

¬ F (1/11) $0 ¬ E (0.89)

$1M or $0

$1M (Allais A/C)

Figure 4.2 Illustration of a sequential form of the pair of Allais problems. The two problems differ only in the pay-off at the first chance node ( t1 ).

It is evident that an agent with the Allais preferences will be sequentially inconsistent. Any such agent plans to go down at the choice node in the first problem and across in the second problem. Now, she either prefers a certain prospect of $1,000,000 to the gamble {$5,000,000, 10/11; $0, 1/11} or not. If she prefers the certain prospect then she will go down at the choice node in the second problem, despite having planned to continue across to the gamble. While if she prefers the gamble, then she will go across at the choice node in the first problem, despite having planned to go down and take the certain $1,000,000. The consequences for an agent who prefers the certain prospect are illustrated in Figure 4.3. There are some prominent dissenters from this line of argument. Machina and McClennen, for example, claim that agents can have preferences that fail to satisfy the substitution axiom without necessarily falling into sequential inconsistency (Machina 1989; McClennen 1990; 1998). We will be considering some of the issues they raise later in the chapter. At the very least, however, it must be conceded (and surely is conceded even by Machina and McClennen) that having preferences contravening the substitution axiom opens the door to a type of sequential inconsistency to which agents with consistent preferences are not exposed. And, by the same token, having (constant) preferences that conform to the substitution axiom guarantees that one will not be sequentially inconsistent. Conformity to the substitution axiom ensures

Rationality Over Time t0

t1

t2

t3

117 t4 $5M

F (10/11)

E (0.11)

(Allais D) ¬ F (1/11) $0

¬E (0.89)

$0

$1M (Allais C)

Figure 4.3 Illustration of sequential inconsistency in the second Allais problem, assuming that the agent prefers the certainty of $1,000,000 to the gamble at t2 . The solid line represents what the agent does at t2 , while the dotted line represents what, at t0 , he had planned to do.

that I will carry through plans upon which I embark—or at least that my preferences will not stand in the way of my carrying them through. We see, then, that decision theory does have implications for sequential choice in the (admittedly indirect) sense that agents who are not utility maximizers because their preferences breach the substitution axiom are susceptible to sequential inconsistency. We shall see later in the chapter that the phenomenon of sequential inconsistency crystallizes some important tensions between the three dimensions of rationality. Before going on to explore these we need to characterize sequential inconsistency more precisely.

T WO T Y PE S O F S E QU E N T I A L I N C O N S I S T E N C Y There are two types of sequential inconsistency. The distinction between them emerges when we ask the following question. Granted that breaching the substitution axiom can lead to sequential inconsistency, does the converse hold? Does sequential inconsistency inevitably involve a contravention of the substitution axiom? One might reason as follows. Instances of sequential inconsistency have the following general structure. An agent, at time t0 , makes a plan

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to choose in a certain way at a later time t2 , with it being contingent on some event E at an intervening time t1 whether or not he gets to choose at t2 . Were E not to occur then there would be some other outcome, say W. When E occurs and he makes his choice, however, he goes against his earlier plan. Suppose, for simplicity, that the choice at t2 is between two lotteries, L1 and L2 ; that he prefers L1 to L2 ; and that event E has probability p. Since the agent is sequentially inconsistent it must be the case that, at t0 , the agent preferred the compound lottery {L2 , p; W, 1 − p} to the compound lottery {L1 , p; W, 1 − p}. If we assume that the agent assigns a probability p to E, then we have a straightforward contravention of the substitution axiom, since the agent prefers L1 to L2 , but prefers the compound lottery {L2 , p; W, 1 − p} to {L1 , p; W, 1 − p}. However, the fact that the agent prefers {L2 , p; W, 1 − p} to the lottery {L1 , p; W, 1 − p} at t0 and L1 to L2 at t2 , is perfectly compatible with his having consistent preferences at both times. For all that has been said the agent might, at time t0 , have the consistent set of preferences {L2 , p; W, 1 − p} ≥ {L1 , p; W, 1 − p} and L2 ≥ L1 . In fact, the second preference might be the reason for the first. Nonetheless, something might happen between t0 and t2 that reverses both preferences, so that at t2 the agent has the equally consistent preferences {L1 , p; W, 1 − p} ≥ {L2 , p; W, 1 − p} and L1 ≥ L2 . There is no time at which such a sequentially inconsistent agent has inconsistent preferences. Plainly, we need to distinguish two types of sequential inconsistency. On the one hand there is sequential inconsistency that results from a constant set of inconsistent preferences. We can term this constant preference sequential inconsistency. The sequential choice problems that we have been considering can all be viewed in this light. And, given that most of the discussion in this area has focused on the pragmatic implications of preferences that contravene the substitution axiom, this is a natural way of looking at them. But it is not the only way. The extensive form diagrams that we have used to illustrate these sequential choice problems are silent about those preferences that are not directly manifested in choice at a particular time. It is perfectly possible that sequential inconsistency can result from preference change over time, rather than inconsistency at a time. We can call this preference reversal sequential inconsistency. This distinction gives us two ways of thinking about the relation between sequential inconsistency and the substitution axiom. On the

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one hand, we can take a narrow reading of the substitution axiom (holding that it applies only to simultaneously held preferences). This allows for cases of sequential inconsistency that do not breach the substitution axiom. Alternatively, we can read the substitution axiom broadly, as applying to preferences over time as well as at a time. This makes every case of sequential inconsistency into a contravention of the substitution axiom. One reason for adopting the narrower reading is that the principal cases where the two readings yield different verdicts already involve diachronic inconsistency of a more fundamental kind. The cases at issue are those where the agent has consistent and comprehensive preferences both at t0 and at t2 , but there is preference reversal between those times with regard to the choice to be made at t2 . If at t2 the agent chooses X over Y, then it must be the case that he preferred Y over X at t0 . But then there is no need to bring the substitution axiom into play to explain why his preferences are inconsistent when viewed diachronically. In any event, it makes most sense to distinguish explicitly between synchronic and diachronic applications of the substitution axiom, and it will turn out to be important for the following that we recognize the difference between sequential inconsistency that involves preference change and sequential inconsistency that does not. We have so far been considering only sequential inconsistency that occurs in the context of sequential choice, where sequential choice in turn involves the resolution of some uncertainty between the moment of choosing a plan and the moment of making the choice that the plan determines. This is unsurprising since we have been thinking about the relation between sequential inconsistency and breaches of the substitution axiom. The intervening uncertainty allows us to think of the plan as a compound lottery and the choice that the agent confronts after the resolution of the uncertainty as a simpler lottery embedded within that compound lottery. If we assume that preferences remain constant during the choice sequence then sequential inconsistency (as we have defined it) is the only form of sequential inconsistency that does not involve having contradictory preferences. But considering the possibility of preference reversal points to a much simpler kind of sequential inconsistency, occurring when preferences change between the moment of choosing a plan and the moment of executing it. This type of inconsistency need not have anything to do with the substitution axiom.

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S E QU E N T I A L I N C O N S I S T E N C Y A N D T H E AC T I O N - G U I D I N G D I M E N S I O N With a clearer understanding of sequential inconsistency in hand we can now pose the following questions. (i) Is preference reversal sequential inconsistency always irrational? (ii) Is constant preference sequential inconsistency always irrational? (iii) Is there a distinction between rational and irrational preference change? (iv) If there is such a distinction can it be reflected in decision theory? We shall see that these questions receive different answers depending on the uses to which decision theory is being put. In this section our concern is with questions (i) and (ii), relative to decision theory considered from the action-guiding perspective. We begin with the first question. Suppose that my preferences change between t0 and t2 . At t0 I prefer X over Y and {X, p; Z, 1 − p} over {Y, p; Z, 1 − p}, where p is the probability of some ethically neutral event E. So I plan to choose X over Y at t2 . By the time E occurs and I arrive at t2 , however, my preferences have changed and I now prefer Y to X and, since I am consistent, I also prefer {Y, p; Z, 1 − p} over {X, p; Z, 1 − p}. What does decision theory tell me to do? Most decision theorists think that decision theory tells me to maximize in the light of my preferences at t2 . If that requires me to discard the plan made at t0 , so be it. Everything depends upon how much value I attach at t2 to adhering to my earlier plan. If my preference for consistency outweighs the value I attach to Y then decision theory tells me to be consistent. If, on the other hand, the value I attach to Y is greater than the value I attach to sticking by my plan, then decision theory tells me to be sequentially inconsistent. This is so, one might argue, in virtue of a basic characteristic of decision theory considered as an action-guiding theory. The theory offers a way of solving individual decision problems, where the parameters of the decision problem are fixed by the agent’s preferences and probabilities at the moment of deliberation. As such, it is implicitly indexical. It tells the agent to maximize (expected) utility in the light of what she wants to achieve at that moment and the information she currently has available

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to her. In this respect decision theory is purely forward-looking. There is no scope for ‘‘looking backwards’’ at earlier decisions and plans unless it is part of what one currently wants to achieve that an earlier decision should be respected and an earlier plan implemented. It is easy to see why decision theory, considered from an actionguiding perspective, has this indexical property. It proposes the following method for solving a decision problem. Consider the possible consequences of the courses of action available to you. If each action has a certain outcome, consult your preferences to rank those outcomes. Then choose the most highly ranked outcome (or find a way of settling the tie, if there is more than one most highly ranked outcome). If each action has a number of possible outcomes, assign probabilities to them and consult your preferences to determine the expected utility of each action. Then choose the action with the highest expected utility. There is no room for anything to feature as a reason for action other than one’s current preferences and one’s beliefs about the likelihood of different outcomes. This seems compelling in the limited case of preference reversal sequential inconsistency. We are envisaging at t2 that the agent both prefers Y over X and prefers {Y, p; Z, 1 − p} to {X, p; Z, 1 − p}. So, it is not just that at t2 the agent prefers Y over X in the decision problem that confronts her at t2 . At t2 she also prefers the plan of choosing Y over X if E occurs to the plan of choosing X over Y if E occurs. It is true that at t0 she preferred X over Y and the plan of choosing X over Y if E occurs to the plan of choosing Y over X if E occurs. But, it is tempting to say, t0 was then and t2 is now. Unless the agent’s preferences at t2 somehow bring her preferences at t0 back into the frame, it is hard to see why those earlier preferences should be relevant to the process of decision-making, which is fixed by the preferences and probability assignments at t2 . Can this line of reasoning be extended to the case of constant preference sequential inconsistency? Is the agent with constant preferences breaching the substitution axiom doing what decision theory mandates when she acts in a sequentially inconsistent manner? In one sense, of course, she cannot be, since decision theory mandates maximizing expected utility, which is not an option for agents with preferences that fail to respect the substitution axiom. In another sense, however, it looks very much as if the indexical nature of decision theory will be decisive in mandating sequential inconsistency at t2 . The choice at t2 is simply a choice between X and Y and only the preference of Y over X is relevant,

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in the sense that this is the only preference that I need to consult. My earlier preference for X if E occurs and Z otherwise over Y if E occurs and Z otherwise is no longer relevant because I now know that E has happened and so there is no point in thinking about what might have happened had E not occurred. This property of decision theory is sometimes described by saying that the theory tacitly involves a separability principle (e.g. McClennen 1990). There is a number of ways of formulating the separability principle, but they all have in common the basic idea that the options available at a particular choice node determine the preferences that should be taken into account at that choice node. So, if we think of a sequential choice problem as a decision-tree (of exactly the type diagrammed in Figures 4.1–4.3), the separability principle states that at any given choice node n on that tree we should choose as if we were confronting a decision problem identical to the decision problem diagrammed in the sub-tree that begins at n. We need only consider the preferences that we have for those options that remain options in the sub-tree that begins at n. There is a strong case to be made that the separability principle is built into decision theory, construed as an action-guiding theory. The action-guiding problem, as we have been construing it, is the problem of how to choose in a decision problem, where a decision problem is fixed by the currently available courses of action and the preferences one has over the possible outcomes of those actions. The assumption of separability is built into the very characterization of a decision problem, given that changing the past is not an available option. But since separability mandates sequential inconsistency (in both the constant preference and preference reversal cases), we should conclude that decision theory mandates sequential inconsistency. If we remain within the confines imposed by the parameters of the decision problem, then decision theory requires us to have separable preferences.

S E QU E N T I A L I N C O N S I S T E N C Y A N D T H E N O R M AT I V E A S S E S S M E N T A N D P R E D I C T I V E / E X P L A N ATO RY D I M E N S I O N S Things look very different from the other two perspectives. As far as the normative assessment dimension is concerned, it is quite plain that

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we frequently want to condemn sequential inconsistency as irrational. That is why there is an extensive literature on the subject. The problem is that decision theory has implications from one perspective (the action-guiding perspective) that seem unacceptable from another perspective (the normative assessment perspective). What is rational from a perspective internal to the decision problem that the agent confronts is often not rational when viewed from a perspective external to the decision problem. Let us say that a choice is hypothetically rational if it is mandated by decision theory when the parameters are set according to the agent’s parsing of the decision problem, where this includes her preferences. It is plainly the case that some hypothetically rational choices fail to be all-things-considered rational (where an all-things-considered characterization of rationality extends to how the agent parses the decision problem). I suggested in the previous section that the assumption of separability can make sequentially inconsistent choice hypothetically rational. This is most obvious in the case of preference reversal, but it also extends (so I claim) to cases where agents have constant, but inconsistent, preferences. There are many such cases, however, that it would be truly desperate to count as all-things-considered rational. This applies most obviously to constant preference sequential inconsistency, but it also applies in the preference reversal case (which we saw to be the case where the separability principle is most compelling). Suppose, for example, that my preferences change between the time of formulating a plan and the moment at which I make my choice. At the time of choosing my preferences clearly mandate choosing what I earlier decided not to choose. I know that my preferences will revert back to what they were when I formulated the plan, but I do not give this any weight. My sequentially inconsistent choice is out of kilter not only with my plans and my past preferences, but also with my future preferences. Only the most die-hard defender of the separability principle is likely to think that the sequentially inconsistent choice is rational in the all-things-considered sense. Yet, choosing in a sequentially inconsistent way is hypothetically rational by the earlier argument. On the other hand, however, some instances of sequential inconsistency do seem to be rational in the all-things-considered sense. We can give a nice example by extending our notion of preference to include second-order preferences. Suppose (as in Chapter 2) that we allow preferences to stand in the preference relation to other preferences. If ‘‘X Pref Y’’ represents the agent’s preference for X over Y then

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we can write ‘‘(Y Pref X) Pref (X Pref Y)’’ to represent the agent’s preference for preferring Y over X over preferring X over Y. One way of giving content to the idea that it is simultaneously true for some agent both that X Pref Y and that (Y Pref X) Pref (X Pref Y) would be that in some sense preferring Y over X is not an option for the agent, for if it were an option it would be mysterious why the agent continues to prefer X over Y. We can represent this by writing ‘‘¬ O (Y Pref X)’’.⁴ Suppose, then, that we are dealing with a standard case of sequential choice (taking the general form illustrated in Figure 4.1). At t0 the agent has to make a choice between two compound lotteries: L1 = {X, p; Z, 1 − p} and L2 = {Y, p; Z, 1 − p}. We assume that his preferences at t0 are consistent with the substitution axiom so that there will be no sequential inconsistency if E occurs and he reaches the choice node at t2 . But we also assume that he has a second-order preference for not having the preference that he actually does have. The situation at t0 is as follows: X Pref Y L1 Pref L2 ¬O(Y Pref X)

(Y Pref X) Pref (X Pref Y)

Choosing L1 at t0 is perfectly consistent—particularly if, as we can stipulate to be the case, the agent does not anticipate (Y Pref X) becoming an option by t2 . Suppose now that all that changes between t0 and t2 is that (Y Pref X) does in fact (and contrary to the agent’s expectations) become an option for the agent. Since (Y Pref X) is now an option, the secondorder preference (Y Pref X) Pref (X Pref Y) trumps the first-order preference (X Pref Y). The ensuing preference shift generates a sequential inconsistency—if the agent acts on his new preferences then he will be sequentially inconsistent. But this sequential inconsistency arises because the agent’s first-order preferences have been brought into line with his second-order preferences. It is not hard to imagine scenarios on which this type of sequential inconsistency is normatively acceptable (and perhaps even normatively commendable). We might imagine, for example, that ¬O(Y Pref X) holds because the agent is weak-willed. To take the classic example, the addicted smoker prefers smoking (X) to not smoking (Y) but at the same ⁴ I borrow this notational device from Jeffrey 1974.

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time prefers a preference for not smoking (Y Pref X) over a preference for smoking (X Pref Y). At t0 the agent does not foresee that his preferences will be any different at t2 and so consistently chooses L1 over L2 . Nonetheless, as things turn out (and contrary to his expectations), by t2 the agent has become stronger-willed, which allows him to have the first-order preferences that he prefers to have. Acting on those preferences brings sequential inconsistency. Yet if we take it that, in at least some such cases, an agent’s second-order preferences reflect their ‘‘real’’ preferences more than their first-order preferences, then in those cases sequential inconsistency seems rational in the all-things-considered sense, as well as being hypothetically rational. From the perspective of normative assessment, therefore, sequential inconsistency poses in a particularly stark way the need to find a way of extending decision theory to mark the crucial distinction between hypothetical rationality and rationality in the all-things-considered sense. The way we have set up the problem makes clear how we need to proceed. Assessments of hypothetical rationality are reached by confining attention to the preferences and options that an agent has at the moment of decision and requiring that the agent maximize in the light of those preferences. The only hope of using decision theory to develop an account of all-things-considered rationality that can potentially trump considerations of hypothetical rationality is to lift the restriction to occurrent preferences and options. At a minimum this involves lifting the assumption of separability. But doing that only brings past preferences into play. It may well be that the door also needs to be opened to future preferences that are not reflected either in current preferences or in past preferences. A different set of pressures arises from the perspective of explanation and prediction. Our practices of explanation and prediction, and indeed the very possibility of social interaction in a more general sense, rest upon assumptions of stability and continuity that come into conflict with the principle of separability. As Bratman has put it, ‘‘Coordinated, organized activity requires that we be able reliably to predict what we will do; and we need to be able to predict this despite both the complexity of the mechanisms underlying our behavior and our cognitive limitations in understanding those mechanisms’’ (Bratman 1999, 59; for further discussion see his 1987). This is most obvious in the case of prediction. If you undertake in good faith (or what I plausibly consider to be good faith) to do something then I am typically justified in making plans that assume

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your going through with your commitment. Of course, my plans are contingent upon it remaining within your power to do that thing. If we plan to meet at a downtown restaurant for lunch next Thursday then when I make my own plans to get there on time I am tacitly assuming that none of an indefinite number of possible defeaters will hold (that you are not summoned away by a family illness, that you have adequate means of transportation, and so on). But these defeaters are all exogenous. I do not typically take into account endogenous defeaters. In particular, I do not typically take into account the possibility that you will be sequentially inconsistent. Even if I think that, when next Thursday comes and you have to decide whether to carry through with the plan, you will find the prospect of spending the day at the swimming pool more appealing than the prospect of joining me for lunch, I still expect you to come to lunch. It is hard to see how there could be any type of coordinated social life if every agreement, promise, or commitment, were assumed to be constantly up for reevaluation and open to being reneged upon in the light of how things seem to the agent at the time of reevaluation. The enterprise of explanation is no less dependent upon assumptions of stability and continuity. When I try to work out why you behaved in certain ways I assume that you do things for a reason; that what you do at one time is connected to what you do at another time; and that it is reasonable to take your stated plan, when you have one, to be a good explanation of why you did what you did, even if it were made long before the time of acting. None of this would make sense if we took decision-making to be governed by some version of the separability principle. The separability principle has the consequence that the only relevant deliberation is that immediately preceding the action. Let us call this the proximal deliberation. No earlier deliberation (say, the deliberation that results in formulating a plan to ϕ when the time comes) can be decisive. If the earlier deliberation is recapitulated in the proximal deliberation (if, that is, the proximal deliberation results in a decision to ϕ) then it is redundant, while if it conflicts with the proximal deliberation then it is irrelevant. The only exception will come when the proximal deliberation is informed by a concern for the earlier plan. But, as was just noted, social interaction depends upon our being able to rely upon plans that are, by their very nature, non-proximal. The general lesson is that our practices of explanation and prediction involve relying upon commitments and plans in a way that would not

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be justified if decision-making were governed by some version of the separability principle. The problem here is distinct from the normative concerns raised earlier. The point is that the separability principle does not seem descriptively adequate. Psychological explanation and prediction works on the assumption that people do what it is rational for them to do. But explanation and prediction would break down if we were to assume that people only do what it is hypothetically rational for them to do (in the sense discussed earlier). When we are dealing with diachronic choosers we do not view them as synchronic expected utility maximizers. This obvious psychological fact raises two important questions. First, what is the conception of rationality that governs how we view diachronic choosers? Second, can that conception of rationality be derived from decision theory? R E S O LV I N G T H E T E N S I O N S ? The structure of the debate here is interestingly analogous to a familiar discussion in consequentialist moral theory. Just as decision theory is governed by the overarching principle of maximizing utility, so too are consequentialist moral theories committed to maximizing a particular quantity, which might be happiness, or preference satisfaction, or items on a list of ‘‘approved goods’’. The consequentialist principle can be applied either to individual actions (act consequentialism) or to rules and practices (rule consequentialism). The dialectic between act consequentialism and rule consequentialism raises issues of sequential consistency. Suppose that I am participating in a consequentially justified practice (the practice, let us say, of paying for the services that I receive). When the time comes to make the payment, however, I calculate that the consequences of not paying are preferable to the consequences of paying. The act-consequentialist maxim mandates non-payment, contravening my earlier commitment to paying and hence making me sequentially inconsistent. The problem is that if we consider individual actions in isolation, abstracting from the trajectory that has taken us there, then the act-consequentialist maxim trumps other considerations. On the other hand, however, there are often good normative grounds for not following the act-consequentialist maxim in a sequentially inconsistent manner. And, from a descriptive point of view, it is hard to see how social coordination could work if rules and commitments were always open to being trumped by act-consequentialist considerations.

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As John Rawls famously put it, social rules are more than mere maxims (Rawls 1955). On the other hand, to make the parallel even closer, only the most die-hard rule-consequentialist would hold that the actconsequentialist principle can never trump rules (think of the innocent person who must be sacrificed to save the entire human race from certain destruction). Unfortunately, although the literature on consequentialist ethical theory is a good place to look for structurally analogous tensions, it is not a good place to look for resolutions of those tensions. We need to return to sequential choice and decision theory to find a way or ways of using decision theory to impose a balance between hypothetical rationality and all-things-considered rationality. In its standard, synchronic formulation, decision theory is governed by the separability principle and does not permit any distinction between hypothetical and all-things-considered rationality. This introduces a serious tension between the action-guiding dimension of rationality on the one hand, and the normative assessment and explanatory/predictive dimensions on the other. The remainder of this chapter considers three strategies for resolving this tension, which is so sharply crystallized in the phenomenon of sequential inconsistency. As we have characterized sequential inconsistency there are three focal points to which such a strategy might be directed. It might be directed, first, at the process of deciding upon a plan; second, at possible changes of preference between deciding on a plan and implementing it; and third, at what happens when the time comes to implement the plan. The following three strategies tackle these focal points in order. The sophisticated choice strategy. Any instance of sequential inconsistency involves two components—a plan to choose in a certain way at a certain time and a subsequent departure from that plan. This strategy focuses on the initial plan, rather than the subsequent departure. It argues that sophisticated choosers (Strotz 1956) will foresee their own inability to carry through their own plans and hence realize that plans that will generate sequential inconsistency are not feasible for them. So they will never get started on the course that leads to sequential inconsistency and the conflict between hypothetical and all-things-considered rationality will not appear. The rational preference change strategy is directed at preference reversal sequential inconsistency. It proposes to distinguish rational changes

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of preference from irrational changes of preference, thereby providing the tools for arguing that preference reversal sequential inconsistency can be rational in the all-things-considered sense when it is consequent upon a rational change of preference. This provides a principled way of distinguishing between different forms of sequential inconsistency. The resolute choice strategy. McClennen and Machina both reject the separability principle and propose models of rational choice that mandate taking previously formulated plans into account (Machina 1989; McClennen 1990; 1998). A resolute chooser takes herself to be constrained by the plans that she has made, so that her decision at a given choice node may differ from what it would be had she not made an earlier decision to choose in a certain way. Sequential inconsistency drops out of the picture, and with it goes the tension between hypothetical and all-things-considered rationality. Both the sophisticated choice and resolute choice strategies are essentially action-guiding. They offer ways of parsing the decision problem that will block the tension between the action-guiding and normative assessment dimensions. The rational preference change strategy works in the opposite direction, aiming for a principled way of distinguishing normatively acceptable from normatively unacceptable changes of preference. T H E S O PH I S T I C AT E D C H O I C E S T R AT E G Y The sophisticated choice strategy can best be appreciated in the context of a well-known pragmatic argument that preferences breaching the substitution axiom are fundamentally irrational, according to criteria of rationality ultimately derivable from decision theory. What makes the preferences irrational is that they can expose an agent to a set of choices that is to his guaranteed disadvantage.⁵ This type of pragmatic defense of the substitution axiom is a close relative of the money-pump and so-called Dutch Book arguments that have been used to argue for the irrationality of having intransitive preferences and degrees of belief that fail to satisfy the probability axioms respectively.⁶ ⁵ For an early version of the argument see Raiffa 1968. For critical discussion see Machina 1989; McClennen 1990; and Rabinowicz 1995. ⁶ The basic idea can be found in Ramsey 1931. For a more formal version see e.g. Kemeny 1955 and for philosophical discussion see the first two chapters of Kaplan 1996.

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We can illustrate the pragmatic argument through the earlier discussion of a sequential version of the Allais problems. In Figure 4.3 we saw how an agent who has the Allais preferences and who prefers the certainty of $1,000,000 to the gamble {$5,000,000, 10/11; $0, 1/11} ends up being sequentially inconsistent. In order to see how this pattern of preferences can be turned to his guaranteed disadvantage, we extend the scenario in Figure 4.3 by adding an additional option at t0 . In effect, adding this extra option turns the two-way choice of the sequential choice version of the second Allais decision problem (as presented in Figure 4.3) into a three-way choice. The additional option is a lottery very similar to the C option in Allais’s second problem, but with a slightly more attractive pay-off. Consider Figure 4.4. At the first choice node the agent has to decide between three options. She can either decide to go up and then, if she arrives at t2 , to go down in order to receive a guaranteed $1,000,000. This is Allais’s C lottery. Alternatively, she can decide to go up and then, if she arrives at t2 , to continue across to Allais’s D lottery. Third, she can choose to go down and accept a third lottery. As in the other two options, the pay-off in

t0

t1

t2

t3 F (10/11)

$5M

E (0.11)

(Allais D) F (1/11) $0

¬E (0.89)

$0

E (0.11)

$1M (Allais C) $1M + ε Lottery C+

¬ E (0.89)

$0 + ε

Figure 4.4 A sequential choice problem illustrating the pragmatic argument for the substitution axiom. See text for explanation.

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this third lottery depends upon whether or not event E occurs (recall that event E is an ethically neutral event with probability 0.11). If E occurs then the pay-off is $1, 000, 000 + ε, while if E does not occur then the pay-off is simply ε, where ε is an additional reward that may be monetary (but need not be). The crucial factor here is the value of ε. Basically, we assume that ε is large enough for the agent to prefer the gamble {$1, 000, 000 + ε, 0.11; $0 + ε, 0.89} to Allais’s gamble C, which is the gamble {$1,000,000, 0.11; $0, 0.89}. However, ε is small enough that the agent still prefers Allais’s gamble D to going down at the first choice node.⁷ We can term this third lottery C+. It follows from all our assumptions that at t0 the agent will plan to go up and then to go across at the second choice node. In effect, he will decide to implement the plan associated with Allais’s gamble D. This is the right thing to do given his preferences because going up requires making a choice between Allais’s gambles C and D; he knows that his preference is for D; and ex hypothesi he prefers D to C+, the lottery yielded by going down. So, he goes up. If E does not occur then he receives nothing, while if E does occur then he arrives at the second choice node. This is where the contravention of the substitution axiom kicks in. Recall that we are assuming that the agent prefers the certainty of $1,000,000 to the gamble {$5,000,000, 10/11; $0, 1/11}.⁸ Hence he will be sequentially inconsistent and go down at the second choice node, rather than implementing his plan by going across. So, he will receive $1,000,000. But consider how this compares to what would have happened had the agent chosen C+ at the first choice node. Had he chosen C+ and gone down the pay-off would have been determined by whether or not E occurred. Had E occurred then the pay-off would have been $1, 000, 000 + ε. Had E not occurred then the pay-off would have been ⁷ It is a consequence of the continuity axiom (see Chapter 1) that there will always be such a value of ε. ⁸ We can make this assumption without loss of generality, since a very similar argument can be run if the agent prefers the gamble to the certain pay-off. We change the decision problem so that the third option involves a gamble that yields $0 + ε if E does not occur and a gamble if E does occur. The gamble if E does occur pays $5, 000, 000 + ε with probability 10/11 and $0 + ε with probability 1/11. We assume that the agent prefers Allais’s option C to the third option, which he prefers to Allais’s option D. His preferences lead him at t0 to choose option C, but then at time t2 he goes across rather than down. He is guaranteed to be worse off than he would have been had he chosen to go down at t0 .

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$0 + ε. Either way the agent would have received ε more than he in fact received. In this case, then, the agent with preferences contravening the substitution axiom is guaranteed to do less well than he might have done. In fact, he is guaranteed to take a dominated option, where an option is dominated just if there is another option that is better however events turn out. So, the argument goes, there is a high price to pay for contravening the substitution axiom—the price of conspicuously failing to maximize—and no agent who conspicuously fails to maximize in this way can be counted as rational. Proponents of the sophisticated choice strategy (Schick 1986; Strotz 1956) deny that events will unfold in the way the argument assumes. Imagine that you are a reasonably self-aware and reflective agent with the described preferences at t0 . You consider your options, in the light of what you know of your preferences. It is true that your preferred strategy is D (going up and then across to the lottery). However, you know that your preferences will prevent you from carrying through your plan to continue across at the second choice node. You know this because you are able to put yourself now in the shoes of your future self at t2 . Your future self at t2 will be confronting a choice between $1,000,000 and the lottery {$5,000,000, 10/11; $0, 1/11} and you know that, given such a choice, your preference is for $1,000,000. This may be the preference that you have at t0 . Or it might be a preference that you do not have at t0 , but can be reasonably confident you will have by t2 . In the first case you would be anticipating constant preference sequential inconsistency, and in the second preference reversal sequential inconsistency. In either case, however, you determine that D is not feasible for you. It is a strategy that you could embark upon but not carry through. So you realize that the real choice you face at t0 is between C and C+ and, in accordance with your preferences, you choose C+. You are maximizing in the light of the options that are feasible for you—and that, surely, is all that decision theory can reasonably demand. The sophisticated chooser acknowledges the power of the separability principle and avoids getting into a position where separability will force them to thwart their own plans. It is easy to see that a sophisticated chooser will not be sequentially inconsistent in any case in which they can foresee the prospect of sequential inconsistency, either because they know that they have inconsistent preferences or because they have good grounds for thinking that their preferences will change. Whenever sophisticated choosers anticipate that they will behave irrationally in the future they take measures to thwart that irrationality.

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Let me distinguish two ways in which an agent might take steps to thwart anticipated irrationality. One way would be to adopt some form of precommitment strategy that effectively blocks them from making any choice at all at the point when they anticipate making a sequentially inconsistent choice. So, for example, an agent might engage a third party to tie them to the mast—either literally (as in the much discussed case of Ulysses and the sirens⁹), or metaphorically (by removing some item of temptation from their reach). A second way would be to employ a form of backwards induction argument to identify the courses of action that are genuinely feasible. This is the strategy that we see in the situation envisaged by the pragmatic argument for the substitution axiom. The terminology of ‘‘sophisticated choice’’ is often used to cover both strategies. There are, however, potentially important differences between them. In some cases, for example, adopting a precommitment strategy effectively changes the sequential decision problem. The sequential decision problems in which we are interested are those where an agent has the option of making a plan at some time t0 . This plan commits the agent to choosing in a certain way at some later time t1 . The agent does not need to adopt the plan. That is, she does not need to move towards the choice node at t1 . But if she does move towards it, she is still moving towards a choice node. Conversely, if there isn’t really a choice to be made (because the agent has adopted a precommitment strategy) then the agent has made it the case that he is moving to a node where there is a single outcome. This node is not the original choice node. And, if it was not explicitly represented in the original decision problem, then adopting a precommitment strategy has effectively placed the agent in a new decision problem. In contrast, an agent who adopts a backward induction argument to identify the plans that are really feasible (given his anticipated future preferences) is reasoning within the parameters set by the decision problem as originally set up. It is true that his reasoning leads him to conclude that not every option within the decision problem is a genuine option for him. But this does not change the decision problem—any more than an agent who uses a backwards induction argument to defect on the first play of a finitely iterated prisoner’s dilemma is changing the decision problem. For this reason, therefore, I propose only to count precommitment strategies as instances of sophisticated choice ⁹ See Elster 1979; 2000, for example.

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where the precommitment strategy is explicitly included in the decision problem. In this respect I follow authors such as Hammond (1976), but diverge from many others. The terminological issue is not particularly important. What is important is that sophisticated choice, as I am understanding it, should be a strategy that can be applied to a given sequential choice problem without transforming it into another. It is sometimes suggested that sophisticated choice involves a very basic type of inconsistency, contravening what Sen has called the αproperty (Sen 1969). An agent’s choices respect the α-property just if, whenever that agent chooses an option, say c, from a menu of options, he chooses c from a subset of the menu that contains c. Equivalently, if an agent rejects c from a menu, then he will continue to reject c however that menu is expanded. Hammond proposes a classic example of sophisticated choice—an agent who is wondering whether or not to start taking a drug that they know to be addictive (Hammond 1976).¹⁰ The three options are: a = Take the drug until it is about to impair health and then stop b = Become an addict c = Refuse the drug altogether As a sophisticated chooser, the agent realizes that starting to take the drug will inevitably lead to addiction so that, when the drug begins to impair his health and he has to decide whether to continue taking it (at t1 , let us say) his preferences will stand in the way of his stopping taking the drug. At t1 he will have a choice between a and b and he foresees that he will choose b. So, as a sophisticated chooser, he decides that a is not a feasible option and chooses c from the menu {a, b, c}. If we suppose that the agent prefers a to c, then (Hammond argues) he is breaching the α property, since he chooses a from the menu {a, c} but c from the expanded menu {a, b, c}. Hammond is mischaracterizing the situation, however. The αproperty (or any other constraint upon coherent choice) is only defined relative to menus of feasible options and the whole point of the sophisticated choice strategy is that some options that appear to be feasible are really not feasible—and some apparent menus of options are not really menus at all. The agent does not choose from the menu {a, b, c}, since he realizes that a is not a feasible option. The apparent menu {a, b, c} ¹⁰ Hammond distinguishes sophisticated choice from precommitment strategies. As noted above, the literature has not generally followed him in this.

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contracts into the genuine menu {b, c} and the choice of c from {b, c} cannot possibly contravene the α-property since {b, c} is not a proper subset of any menu of feasible options that the agent confronts. Nonetheless, the sophisticated choice strategy needs careful scrutiny. We should distinguish two questions. First, does sophisticated choice block pragmatic arguments of the type sketched above? Second, does sophisticated choice solve the tensions created by sequential choice? The first question need not detain us long. We should concede that sophisticated choice does block the pragmatic argument, in the sense that it provides a perfectly cogent reason for thinking that a rational agent might not be compelled to take a dominated option in the sequential choice problem. Whether it is the best way of blocking the pragmatic argument is a different matter, and defenders of the resolute choice strategy such as McClennen have proposed pragmatic arguments to the effect that sophisticated choosers always do less well than they could do if they were resolute (i.e. if they stuck by their original plans and were not swayed by their preferences at the moment of implementation). In any event what really matters for our purposes is whether the sophisticated choice strategy resolves the tensions between the three different dimensions of rationality. There is a class of cases for which sophisticated choice seems highly appropriate. If I foresee the inevitability of my better judgment being overpowered by the irresistible song of the sirens, for example, then it is surely right that hearing the song of the sirens and remaining unrestrained on the deck of my ship is not a feasible option. So I should ensure that I am not on the deck (recalling that I am not taking the precommitment strategy of tying myself to the mast to be a version of sophisticated choice). Somewhat less dramatically, I might know myself well enough to know that the temptations of a well-stocked bar will be overpowering and so that the option of going to the bar and having a single drink is not feasible, so that my real choice is between avoiding the bar and feeling the worse for wear the next morning. In both cases I anticipate a preference reversal that will prevent me from carrying through one of the plans that appears to be open to me. And in both cases the preference reversal would lead to an outcome that would plainly not be desired. But the problem is that these are not the only cases of sequential inconsistency—and nor, correspondingly, do they exhaust the scope for sophisticated choice. As we saw earlier, it can be rational to be sequentially inconsistent—not just from an internal perspective but

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also from an external perspective. In these cases it would be irrational to be a sophisticated chooser. The fundamental question that the proponent of sophisticated choice has to answer is how an agent is to decide when to choose in a sophisticated way and when not to. Consider the following example. Suppose that although I would rather have a preference for non-smoking over smoking than a preference for smoking over non-smoking, I still prefer smoking (X) to not smoking (Y). I also prefer smoking to having a preference for non-smoking over smoking. My preferences at t0 can be represented as follows (recalling that ¬O (Y Pref X) is to be read as Y Pref X is not an option for me): X Pref Y

(Y Pref X) Pref (X Pref Y) ¬O(Y Pref X)

X Pref (Y Pref X)

However, it is hard work for me to retain these preferences. It requires constantly avoiding having to consider medical evidence about the harmful effects of smoking and when I cannot avoid the evidence I have to go to all sorts of contortions to explain it away so that it will not strengthen my will and make it an option for me to prefer not smoking to smoking. As a self-aware agent I realize that I am not going to be able to do this for much longer and I foresee a time (say, t1 ) in the not too distant future when it will no longer not be an option for me to prefer not smoking over smoking—that is, when it will become an option for me to prefer not smoking over smoking. And I can clearly see that, once it is an option for me to prefer not smoking to smoking, I will no longer prefer smoking to preferring not smoking over smoking (i.e. O(Y Pref X) → ¬(X Pref (Y Pref X))). Since I do now prefer smoking over not smoking this is a source of concern. The way things are shaping up I anticipate a preference reversal that will lead me to prefer not smoking to smoking. Suppose that I have open to me (as part of the decision problem at t1 ) some way of safe-guarding my current first-order preference for smoking over non-smoking—such as hypnosis that will eliminate my second-order preference for (Y Pref X) over (X Pref Y). Should I adopt it? As far as the sophisticated choice strategy is concerned, this would be a perfectly rational thing to do. I foresee that my future preferences will thwart my current preferences and I take appropriate action to safeguard my current preferences. Yet there is something self-defeating about this—self-defeating from the perspective of my preferences at t1 . The point is that at t1 I prefer having a preference for not smoking over

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smoking to having a preference for smoking over not smoking. It is not news that my strategy of sophisticated choice is counter-preferential from the perspective of my preferences at the later time, since the whole point of sophisticated choice is that it tries to work around the efficacy of future preferences. But in this case my sophisticated choice is counter-preferential even at the moment at which it is engaged in. What I am doing is ensuring that I continue to prefer smoking to not smoking, in the face of my second-order preference for preferring not smoking to smoking. From this point of view, sophisticated choice does not make good sense. It is certainly not obvious in this case what I should do. There are reasons to choose in a sophisticated manner and reasons not to. Both sets of reasons are available to me at t1 . There seems to be no perspective available to the agent from which to choose whether or not to be a sophisticated chooser. The two sets of reasons are close to symmetrical. What would motivate sophisticated choice is an anticipated preference reversal. That preference reversal, if left unchecked, would actually bring my first-order preferences at t2 , the later time, into line with my t1 second-order preference (Y Pref X) Pref (X Pref Y)—and t1 is the time at which I have to make the decision. If I choose in a sophisticated manner, on the other hand, I will be bringing my secondorder preferences at t2 into line with my first-order preferences at t1 as well as with my second-order preference X Pref (Y Pref X). Either way, my first- and second-order preferences will become aligned with each other at t2 . The question is the form that that alignment will take. In particular, will they become aligned with my first-order preferences at t1 together with my second-order t1 preference X Pref (Y Pref X), or will they become aligned with my second-order t1 preference (Y Pref X) Pref (X Pref Y)? I simply don’t have any preferences between first-order and second-order preferences. And even if I did it would be easy enough to run a similar argument at the next level up. One might wonder whether, at least in this particular case, the t1 preferences could settle the matter. After all, the anticipated preference change is actually desired at t1 . Perhaps this is enough to decide the issue against sophisticated choice? Certainly, it is true that the anticipated preference change is desired at t1 in the sense that at t1 I prefer having the preference I will have at t2 to the preferences that I have at t1 . But, on the other hand, at t1 I still prefer smoking to having the preferences that I will have at t2 —and I can see that changing my preferences will result in my not smoking. So, the anticipated preference change is both

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desired and not desired. It is hard to see how appealing to t1 preferences is going to settle the issue. And in any case it cannot be a general principle of rationality that a rational agent should respect foreseen preference changes that are preferred at the time of considering them. We can see this by supposing that the sequence of choices we have been considering is embedded within a longer sequence. Suppose that my second-order preference (Y Pref X) Pref (X Pref Y) is the result of brainwashing by the anti-smoking lobby, against my will and better judgment. Before that happened, at t0 , I had the consistent preferences X Pref Y and (X Pref Y) Pref (Y Pref X). Relative to my preferences at t0 , therefore, the anticipated t2 preference reversal is straightforwardly counter-preferential. So, which preferences should we look to in evaluating the t2 preference reversal? It seems implausible that the mere fact that t1 is the time at which I am considering the matter should mean that they fix the rationality of the t2 preference reversal. But nor, on the other hand, do we have a clear reason for thinking that the t0 preferences should decide the matter. In sum, since sequential inconsistency is not necessarily irrational, sophisticated choice cannot be universally adopted. So we need principled reasons for deciding whether or not it is rational to choose in a sophisticated manner. And we need to do this from the perspective both of normative assessment and of explanation/prediction. We want some way of working out whether an agent is to be censured or praised for avoiding sequential inconsistency by sophisticated choice, and whether a rational agent who confronts the prospect of sequential inconsistency will fall into it, or take a sophisticated avoidance strategy. The problem is that there are many cases where this is simply not possible. The rationality of sophisticated choice rests upon determining where the agent’s real preferences lie. It is plain enough that Ulysses does not really prefer hurling himself into the sea with the sounds of the sirens’ song in his ears to living to sail another day, even though that is what he would prefer when listening to the sirens’ song. But this is the exception rather than the rule in cases of potential sequential inconsistency. Perhaps, though, if we could make a principled distinction between rational and irrational preference change then we would be in a better position to identify real preferences. (This would certainly help in the last case discussed, given how the preference change between t0 and t1 is supposed to have come about.) This brings us to the rational preference change strategy.

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R AT I O N A L P R E F E R E N C E C H A N G E ? How do preferences change? Sometimes they change because tastes change. There is more to preference than taste, but preferences certainly reflect tastes. Preferences also reflect beliefs and preferences can change on the receipt of new information. In both cases what changes is the agent’s (subjective) utility function. In the second case but not the first this change is a function of changes in the agent’s probability function. Since the general topic of rational changes in probability assignments has been well studied, this second type of preference change seems a good place to look for a distinction between rational and irrational changes in preference. One way of thinking about this is in terms of how utilities or desirabilities can change as a function of changes in belief. The classic approach to updating probabilities is Bayesian conditioning, according to which my new degree of belief in some proposition q on learning some evidence A is given by my prior degree of belief conditional upon A.¹¹ Can something similar be applied to changes in desirability or utility? Can we apply some form of Bayesian updating to the utility function? The idea of conditional desirability has a certain intuitive appeal. It seems perfectly possible that, although I am now indifferent between fillet steak and pizza margarita and completely ignorant of how much money I have to spend, I would no longer be indifferent if I had more information about my disposable income. It might be the case, for example, that if I were to find out that I have more than $200 in my bank account, then I would find fillet steak more desirable than pizza margarita, while if I were to find out that I have less than $200 in my bank account then I will find pizza margarita more desirable than fillet steak. When I check my bank balance I discover than it is $151. As a consequence my utility function changes and pizza margarita comes out above fillet steak. So far this is simply the acquisition of a new utility function conditional upon coming to learn that some condition is satisfied. ¹¹ Standard Bayesian conditionalization rests upon two assumptions: Certainty (that my degree of belief in A is 1) and Rigidity (that learning that A holds does not change my degree of belief in q conditional upon A). The first assumption in particular seems too restrictive and models of conditionalization have been developed without it—most famously the probability kinematics developed by Richard Jeffrey ( Jeffrey 1983; 1992).

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The new utility function is a causal consequence of the receipt of the new information. If we think about conditional desirabilities in this way, as dispositions to acquire preferences upon the receipt of certain types of information, then there is no space for considerations of rationality to gain purchase (other than indirectly, in terms of the rationality of the new information). But we can think about conditional desirabilities in a richer way. We can think of them as attitudes that one currently takes to some possible state of affairs on the assumption that some condition holds. Richard Bradley has persuasively argued both that we should think about conditional desirabilities in this way and that we can do so within an extension of Jeffrey-Bolker decision theory (Bradley 1999). He argues, surely correctly, that an agent’s conditional desirabilities can diverge from their dispositions to change their utility function upon receipt of new information, because the new information might have non-rational effects. As a generally reptile-friendly person, for example, it is certainly true of me that I desire that, if I run into a non-threatening snake, I will retreat rather than attack. However, it might also be true that the shock of seeing a snake, however non-threatening, creates in me an urge to kill the snake, which flies in the face of what we are assuming to be my conditional desire. Bradley’s suggestion (simplifying slightly) is that we think of the desirability of X given Y as the difference between the desirability of X and Y and the desirability of Y. So, for example, the conditional desirability of going to the museum given that it is raining is the desirability of going to the museum and it raining, minus the desirability of rain. He motivates this with a form of Dutch book argument. Let the desirability of X and Y be given by the sum of money one would pay for a ticket that guarantees that XY holds (say, $n) and let the desirability of Y be given the same way (in this case, $m). Let p = n − m, so that by Bradley’s measure the desirability of X given Y is p. Suppose that you are prepared to pay $p + ε for a ticket that guarantees that X holds if Y does. A canny entrepreneur will buy the XY ticket from you for $n and then sell you both the Y ticket and the X if Y ticket securing a guaranteed return of $ε. If you are prepared to pay $p − ε then the entrepreneur will buy from you the Y ticket and the X if Y ticket, once again guaranteeing herself a painless gain of $ε. For present purposes the details of Bradley’s account are less important than the general lesson we learn from the possibility of defining conditional desirabilities. This is that it allows us to make sense of the idea of conditionalizing on conditional desirabilities. If I come

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to learn with probability 1 that Y holds, then (provided the Rigidity assumption holds), the new desirability of X should be given by Bayesian conditioning upon the conditional desirability of X given Y. Where my degree of belief is less than 1 we can use a different type of conditioning, perhaps some version of Jeffrey conditioning (Bradley 2005). This seems to give one way of identifying rational change of preference. We might say that an agent’s preferences change rationally if her new preferences result from conditionalizing on her former conditional desirabilities. Changes in probability assignments can also result in rational changes of preference. Suppose for example that I have a strong preference for backpacking without encountering a grizzly bear to running into a grizzly bear while in the wilderness. The desirability for me of backpacking is plainly going to be a function of the probability I assign to encountering a grizzly bear. If I learn that the grizzlies are roaming further north this year, so that there is less chance of my running into one, then the desirability of backpacking will increase. The generalization is obvious. If the desirability of some prospect depends upon the likelihood of some condition holding, then a change in the likelihood of the condition should bring about a change in the desirability of the prospect. A second class of cases arises because the desirability of prospects can be a function of their perceived instrumental value, which itself depends upon assessments of conditional probability. Suppose that I have weight management as a goal and I come to learn that I am more likely to lose weight in a controlled and sustained manner if I go for a long jog than if I run harder for a shorter period of time. This new information will increase the desirability of jogging. Can these three different ways of thinking about preference change help make sense of the rationality of sequential choice? In particular, can they help make sense of what an agent’s real preferences might be? Recall one type of situation that proved problematic for the sophisticated choice strategy. It is not always the case that I should prioritize my current preferences over my future preferences (although if I do prioritize my current preferences then I can follow the sophisticated choice strategy to make sure that those preferences are not thwarted). It all depends upon which ones count as my ‘‘real’’ preferences. So, one suggestion might be that my future preferences will count as my real preferences if and only if they are rationally derived from my current preferences in one of the ways just outlined. The claim is one of both necessity and sufficiency.

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We begin with the sufficiency claim. Making an account of rational preference change dependent upon ways of rationally updating one’s current preferences still places all the weight on one’s current preferences. Rationally updating current preferences that are problematic to begin with need not eliminate whatever problems there were. It is easy to see how Allais-type sequential inconsistency might be generated through problematic conditional desirabilities. Suppose that I am confronting an extended Allais-type sequential choice as depicted in Figure 4.2 (with $0 the pay-off if E does not occur). At t0 my preference is for Allais’s D strategy (going across at t2 and taking the lottery at t3 ) over the C strategy (going down at t2 and taking the $1,000,000 guaranteed pay-off ). At the same time, however, the conditional desirability of preferring the guaranteed pay-off over the lottery, given E, outweighs the conditional desirability of the lottery relative to the guaranteed pay-off, given E. If E occurs then I conditionalize on my conditional desirabilities and as a result end up taking the guaranteed pay-off. In this case no one who thinks that the Allais sequential choice is inconsistent could possibly think that rational preference updating is sufficient to determine one’s real preferences—that is, those preferences on which it is rational to act. Of course, there is a sense in which in this situation I start out from a position of inconsistency. Suppose we define a notion of conditional preference. Let ‘‘ϕ ≤A ψ’’ stand for ϕ being weakly preferred to ψ, on the assumption that A is true. It seems plausible that ϕ ≤A ψ is true of an agent iff that agent unconditionally weakly prefers A and ϕ holding simultaneously to A and ψ holding simultaneously.¹² Hence ϕ ≤A ψ iff (ϕ & A) ≤ (ψ & A). It is plausible to demand that conditional desirabilities are related to conditional preferences in the following way (where ‘‘DesA ϕ’’ stands for the conditional desirability of ϕ given A): DesA ϕ ≤ DesA ψiff ϕ ≤A ψ.¹³ It follows that in the case envisaged I have inconsistent preferences. Take ϕ to be the guaranteed pay-off and ψ to be the lottery. The two ¹² This is Bradley’s axiom of conditional preference (Bradley 1999). ¹³ Bradley (1999) shows that this holds by showing that, given the axiom of conditional preference, the ≤A relation satisfies the Bolker-Jeffrey axioms for consistent preference. In effect this gives a representation theorem for consistent preference.

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principles jointly yield ϕ ≤ ψ, once E has occurred, which essentially gives me the (unconditional) Allais preferences. Perhaps then we should restrict the rational updating requirement so that it holds only for consistent preferences? This would preserve the sufficiency claim, but the price is too high. The rational preference change strategy now fails to get to grips with, let alone solve, one of the basic problems that we are trying to solve. Our account of rational preference change now has nothing to say to agents with inconsistent preferences. But we need an account that will tell such an agent how to restore consistency. This is one of the lessons of the earlier discussion of sophisticated choice. As a self-aware agent I realize that, if E occurs, I will update my desirabilities by conditionalizing on these conditional desirabilities, with the result that at t2 my preference will be for the certain pay-off over the lottery. What should I do? If E occurs then my current preferences will be thwarted by my future preferences. The strategy of sophisticated choice instructs me to adopt any measures to prevent this happening that are open to me in the decision problem. I could, for example, pay someone else to make my choice for me at t2 , instructing them to opt for the lottery, whatever I might say at t2 (in effect, I would be tying myself to the mast). On the other hand, however, those future preferences will be arrived at by updating my conditional desirabilities with the information that E has occurred, in full conformity with the procedure sketched out above. So we are left with the problem with which we ended up at the end of the last section. How are we to determine when to apply the strategy of sophisticated choice? So rational updating of preferences of the type just described does not guarantee immunity from sequential inconsistency. The sufficiency claim fails (or becomes unhelpfully narrow). And so does the necessity claim. Rational updating of preferences is not necessarily involved in everything that one might wish to describe as rational change in preference. Suppose, to go back to a case that we considered earlier, that my first-order and second-order preferences are out of kilter, but that it is not an option for me to acquire the first-order preferences that I would rather have. Let L1 be the compound lottery {X, if E; Z, otherwise} and L2 the compound lottery {Y, if E; Z, otherwise}. At t0 the situation is as follows L1 Pref L2 X Pref Y ¬O(Y Pref X)

(Y Pref X) Pref (X Pref Y)

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At t0 I choose L1 over L2 , thereby committing myself to choosing X over Y at t2 , should E occur at t1 . This is consistent with my firstorder preference for X over Y, but not with my second-order preference for preferring Y over X to preferring X over Y. Between t0 and t2 two things happen. The first is that E occurs, opening up the possibility of a choice between X and Y at t2 . The second is that it becomes an option for me to prefer Y over X. As a consequence I choose Y over X at t2 . I suggested earlier that this kind of sequential inconsistency could sometimes be rational (in the case, for example, where Y is not smoking and X is smoking and what happens between t0 and t2 is that I become stronger willed). As such it would presumably involve a rational preference change (rather than simply a change in taste). But this rational preference change would not result from any of the types of updating that we have been considering. T H E R E S O LU T E C H O I C E S T R AT E G Y The sophisticated choice strategy aims to resolve the problems posed by sequential choice by constraining the decision-making processes that might lead to sequential inconsistency. In effect, the strategy blocks potential clashes between the action-guiding and normative assessment dimensions by proposing a way of parsing decision-problems that rules out as unfeasible precisely those options that might lead to such clashes. The basic problem with it is that some cases of sequential inconsistency can be perfectly rational but the would-be sophisticated chooser may well not have the resources to distinguish those cases where it would be rational to be a sophisticated chooser from those where it would be irrational to be a sophisticated chooser. There is little prospect of using the distinction between rational and irrational preference change to salvage the situation. We turn then to the final strategy. The resolute choice strategy is focused not on the original moment of choosing a plan (what we have been calling t0 ) nor on how preferences might change between t0 and the moment of making a decision (t2 ), but rather on the weight one should give to one’s prior commitments at t2 , the moment of implementing one’s earlier plan. A sophisticated chooser’s choice of plan is constrained by what she thinks her future preferences will be. In particular, she does not adopt any plan that she thinks she will be unable to carry through, either because she currently has inconsistent preferences that breach the substitution

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axiom or because she anticipates a preference reversal between the moment of making the plan and the moment of carrying it through. As McClennen puts it (1990, 156–7), the sophisticated chooser’s ex ante choice of plan is tailored to her projected ex post preferences. In contrast, the resolute chooser’s ex post choice is constrained by her ex ante choice of plan. Here is how McClennen characterizes a resolute agent: The agent can be interpreted as resolving to act in accordance with a particular plan and then subsequently intentionally choosing to act on that resolve, that is, subsequently choosing with a view to implementing the plan originally adopted. In each such case, the plan that is judged most attractive from an ex ante perspective calls for an ex post choice that the agent would otherwise not be disposed to make, but the agent consciously makes that choice nonetheless. In doing this, the agent can be said to act on his previous decision—and in so doing to act resolutely. (McClennen 1990, 157–8)

The resolute agent abides by her commitments, even when this means choosing in a way that fails to maximize in the sub-tree that she confronts at that moment. That is, in the type of situation we have been considering, a resolute agent will choose in accordance with their plan at t2 even though, when the decision problem at t2 is considered independently of how the agent arrived at it, the agent would act differently. In this respect, then, the resolute agent breaches the principle of separability. The advantages of the resolute choice strategy for the problems we have been considering are clear. A resolute chooser will not be sequentially inconsistent. If she has preferences that breach the substitution axiom, those preferences will not be efficacious. They will be overridden by the agent’s resolute commitment. Likewise for the preferences that might result from preference reversal. Those new preferences are trumped by the resolute agent’s ex ante decision. What is not so clear, however, is how exactly resolute choice is supposed to work in practice. It cannot simply be that the resolute chooser attaches high utility to maintaining their commitments. This would make resolute choice into a straightforward maximizing choice at t2 , whereas the whole point of resolute choice is supposed to be that the resolute chooser abides by her commitments even when doing so fails to maximize at the moment of decision. Bearing this in mind there are two ways of interpreting the kinematics of resolute choice. The first way is not dissimilar to sophisticated choice. We might see resolute choosers as taking their earlier commitment to narrow down what is really feasible

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for them at the moment of decision to a single option, namely, the option that implements their earlier plan. On this view the resolute chooser’s changed or inconsistent preferences cannot get a grip at t2 , simply because implementing them is not a feasible option—although if implementing them were an option, that is the option that they would prefer. On the second interpretation, resolute choosers effectively confront reconfigured decision problems. Their ex ante commitments change the ex post decision problem. On this way of thinking about resolute choice, developed in most detail by Mark Machina, the route by which the agent has arrived at the decision problem is built into the characterization of the options available to him (Machina 1989). The first interpretation is explicitly rejected by McClennen (see McClennen 1990, 160) and it is certainly not very explanatory. We are told that the resolute chooser only has one feasible option at t2 , but no explanation is given of why this should be the case. Surely it cannot be that simply committing oneself at t0 to choose in a certain way at t2 forecloses on any possibility of choosing otherwise. If this were the case then sequential inconsistency would be impossible, and there would be no content to the notion of resolute choice. So there must be something specific to resolute choosers that closes off all other feasible options, but it is hard to see what this might be. In any case, the suggestion is not very plausible. In what sense is sequential inconsistency not a feasible option for the resolute chooser? Imagine that all that it takes for the resolute chooser to fail to be resolute at t2 is that they refrain from doing anything. We might imagine, in our familiar example of the sequential Allais problem, that doing nothing at t2 automatically results in receiving the $1,000,000 pay-off (which would involve sequential inconsistency), while opting for the lottery (which would be the resolute choice) requires some form of action (perhaps posting a letter rejecting the certain pay-off and applying to enter the lottery). It is hard to think of any non-question-begging sense in which doing nothing is not a feasible option. This brings us to the second interpretation of resolute choice. Machina proposes an account of nonseparable preferences, which allows what he thinks of as past consumption to be built into current preferences (in a way that plainly breaches the separability principle). Machina is not suggesting that all preferences are nonseparable (in the sense to be described), but simply that it can be rational for an agent to have nonseparable preferences. He motivates the suggestion with the following example. Imagine an individual with the following preference ranking:

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(pizza, pizza, salad, salad) > (pizza, pizza, pizza, pizza) > (pizza, pizza) > (salad, salad) where (pizza, pizza, salad, salad) is the option of eating two small pizzas in succession followed by two small salads at t3 and t4 . The individual arrives at a pizza and salad bar, consults his preferences, and starts out on the pizza. At t2 he reaches the end of his second pizza and wonders what to do, since he is now confronting a choice between two more pizzas and two salads and, given that choice, his preferences mandate eating two more pizzas, even though he prefers a pair of pizzas and a pair of salads to four pizzas. Machina suggests that the preference for (pizza, pizza) over (salad, salad) should be read as a preference for two pizzas over two salads, conditional on not having already eaten anything. As such it is not relevant at t2 , when the agent has already consumed two pizzas. We need to find some way of taking into account at t2 what the agent has already consumed. Machina’s proposal is that we can simply use the original preference function using some way of tracking what has been consumed. The choice confronting the agent at t2 is between (pizza, pizza, salad, salad) and (pizza, pizza, pizza, pizza), where the underlining and italics indicated items that have already been consumed, rather than between (salad, salad) and (pizza, pizza). In making this choice the agent can simply consult his original preference function, with (pizza, pizza, salad, salad) > (pizza, pizza, pizza, pizza) ⇔ (pizza, pizza, salad, salad) > (pizza, pizza, pizza, pizza) The threat of sequential inconsistency is kept at bay, since the potentially problematic preference of (pizza, pizza) over (salad, salad) does not come into the calculation at t2 . Unlike the first interpretation, however, there is no suggestion that it is not feasible for the agent to opt for two further pizzas over the two salads. It is a feasible option, but the agent prefers not to take it. As with the sophisticated choice strategy, we need to distinguish two questions. We can ask, first, whether this way of thinking about resolute choice shows how an agent with appropriately inconsistent (i.e. nonseparable) preferences can avoid the type of problems raised by

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pragmatic arguments in support of the substitution axiom. The answer to this question is straightforward. Machina’s model of resolute choice blocks pragmatic arguments such as that represented in Figure 4.4. The pragmatic argument assumes that at t2 the agent confronts a choice between a certainty of $1,000,000 and the gamble {$5,000,000, 10/11; $0, 1/11}. This is what generates sequential inconsistency, since we are assuming that the agent prefers the certain return to the gamble. However, if we represent the situation as Machina suggests, then the agent is really facing an updated version of the decision problem at t0 , which he can solve in a way entirely consistent with his earlier choice. So, as far as responding to the pragmatic argument is concerned, the resolute choice strategy is just as successful as the sophisticated choice strategy. But the interesting question is whether resolute choice solves the more general tensions raised by sequential inconsistency. Here things are less straightforward. As in the case of sophisticated choice, the principal source of difficulty is that sequential inconsistency is not always irrational. Plainly, it cannot be rational to be resolute in situations where sequential inconsistency is rationally preferable to sequential consistency. Can the resolute choice strategy offer a way of identifying when it is rational to be resolute and when not? The most obvious approach for the resolute choice theorist (and almost certainly the only approach that remains within the domain of decision theory) is to offer a pragmatic answer—to say that resolute choice is rational just when the agent fares better according to some maximizing criterion by choosing resolutely than by failing to choose resolutely. One well-known application of a general pragmatic strategy in the interpersonal case is Gauthier’s theory of constrained maximization in repeated interactions (Gauthier 1986, ch. 6). A constrained maximizer decides whether or not to adopt a cooperative joint strategy (in, for example, a prisoner’s dilemma) by considering (i) whether the outcome, were everyone to adopt that strategy, approaches ideals of fairness and optimality and (ii) whether the outcome she reasonably expects would afford her greater utility than universal non-cooperation. Gauthier argues that it is rational to be a constrained maximizer in situations where constrained maximizers do better than straightforward maximizers and he gives a fairly precise characterization of what has to hold in such situations, in terms of the prevalence of other constrained maximizers in the general population and the agent’s ability to detect those constrained maximizers. In essence, Gauthier tries to identify those situations in

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which the constrained maximizer beats the straightforward maximizer at his own game. The resolute theorist needs to do something comparable—that is, to argue that there are situations where the resolute chooser’s apparently counter-preferential (and hence non-maximizing) choice makes possible a more overarching maximization than is available to the sophisticated or sequentially inconsistent chooser.¹⁴ McClennen explores some possible pragmatic arguments against sophisticated and sequentially inconsistent choice (which he, following standard terminology, calls myopic choice) in ch. 11 of his 1990 book. There is no need to go into the details of these arguments. We can illustrate the general difficulty with pragmatic arguments of this type through some comments he makes in a later article about the much simpler sequential decision problem given in Figure 4.5. This is a standard problem of preference reversal sequential inconsistency. At t1 the agent’s preferences lead him to choose to go across to the second choice node with the intention of choosing a3 at t2 . But his preferences at t2 lead him to abandon that plan. McClennen’s pragmatic argument is directed primarily at the precommitment strategy, which he identifies with a2 (in essence, this is the t1

t2 a1

a2

O2

a3

O3

a4

O4

Figure 4.5 Illustration of McClennen’s pragmatic argument for resolute choice. Each ai is a strategy and each Oi an outcome. We assume that the agent’s preferences at t1 are O3 > O2 > O4 , and at t2 O4 > O3 > O2 . ¹⁴ In fact, if she can do this then the resolute chooser will have provided important support for Gauthier’s constrained maximization strategy, since a constrained maximizer is of necessity resolute. The relations between interpersonal and intrapersonal resoluteness are explored by McClennen in his 1998. Gauthier has explored versions of resolute choice in his 1994, 1996, and 1998.

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strategy of paying an agent to ensure that a3 rather than a4 is chosen at the second choice node). He writes: [The precommitment strategy] is the best option consistent with the separability principle. But if you are resolute you can realize the very same outcome, without having to pay an agent. On the assumption that each of your time-defined selves prefers more to less money, to reason in a separable manner is to create a real intrapersonal dilemma for yourself, in which ‘‘rational’’ interaction with your own future selves leads to an outcome that is intrapersonally suboptimal or ‘‘second-best’’. That is, each time-defined self does less well than it would have done, if the selves had simply coordinated with each other. Other values must be sacrificed as well. Precommitment devices limit your freedom, since they involve placing you in situations in which you do not choose, but have choices made for you. Moreover, they expose you to the risks associated with any procedure that is inflexible. In contrast the resolute approach is not subject to any of these difficulties. Scarce resources do not have to be expended on precommitment devices or to pay agents; you are the one doing the choosing, and you retain the option of reconsideration insofar as events turn out to be different from what you had anticipated. (McClennen 1998, 24)

As I suggested earlier in this chapter, however, there may be problems with taking precommitment to be an instance of sophisticated choice properly speaking. These problems do not arise in this case (since the possibility of precommitment is built into the decision problem as the a2 strategy and a2 is precisely the strategy that the sophisticated chooser in the backwards induction sense would choose). But it will make the argument much clearer (without weakening it) if we reformulate it in the following way. Consider the following table, which indicates how each time-defined self ranks the outcome it would receive under each of the three strategies. I am assuming that the myopic chooser goes across at the first node (because that will open up the possibility of choosing O3 , which is preferred to O2 ) and then down at the second node (because at t2 he prefers O4 to O3 ). The sophisticated chooser at t1 forsees his t2 preferences and, observing that his t1 most preferred outcome of O3 is not really feasible, opts to go down at the first node because he prefers O2 to O4 . The resolute chooser, on the other hand, manages to hold out for O3 . If we compare the outcomes of resolute and sophisticated choice as presented here we see that the resolute-self-at-t1 fares better than the sophisticated-self-at-t1 and the resolute-self-at-t2 fares better than the sophisticated-self-at-t2 . It is in this sense that the sophisticated choice

Rationality Over Time

Myopic (O4 ) Sophisticated (O2 ) Resolute (O3 )

151

t1 –self

t2 –self

3rd 2nd 1st

1st 3rd 2nd

strategy is claimed to be suboptimal. It is strictly dominated by resolute choice both at t1 and at t2 . So, when we factor in the extra costs of precommitment, it looks very much as if resolute choice is to be preferred on pragmatic grounds. This particular pragmatic argument is at best inconclusive, however. Even if it is granted that resolute choice dominates sophisticated choice, it certainly does not even weakly dominate myopic choice, since the myopic-self-at-t2 ends up with his most preferred outcome (and does not incur any costs) while the resolute-self-at-t2 only obtains his second most preferred outcome. And the proponent of sophisticated choice might reasonably object that at least one important question has been begged against her. The whole point of sophisticated choice is that not every apparently feasible option is genuinely feasible. The sophisticated chooser at t1 works through the decision problem in the light of what she knows her future preferences will be. In particular, realizing that she will not be able to carry through the plan that involves choosing a3 at t2 she no longer considers O3 to be an attainable outcome. If we consider preferences over outcomes that the agent takes to be attainable then things look very different for the sophisticated chooser. The sophisticated-self-at-t1 ends up with her most preferred (attainable) outcome, while the sophisticated-self-at-t2 ends up with her second most preferred attainable outcome. Looked at in this way the sophisticated choice strategy is not weakly dominated by the resolute choice strategy either. The real issue for resolute choice, however, is not the details of the pragmatic argument, but rather the presuppositions of there being a pragmatic argument at all. The problem is that pragmatic arguments are constructed in a way that prevents them from performing the twin functions of action-guidance and normative assessment. Pragmatic arguments of the type given by McClennen depend upon being able to weigh up and compare, for each strategy, the extent to which each time-defined self satisfies their goals. Viewed sub specie aeternitatis we can determine that in a particular decision problem each time-defined

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self will do better if resolute choice is adopted than if sophisticated choice is adopted. From the same Olympian perspective we might decide that, by standard maximizing criteria, this makes the strategy of resolute choice more rational in that decision problem. This plainly fits the requirements of normative assessment. But the very feature that makes such pragmatic arguments suitable for normative assessment stands in the way of their being effective for action-guidance. Pragmatic arguments work by aggregating the fortunes of all the different time-defined selves, giving each equal weight. This can only be done from a perspective that is not the perspective of any single time-defined self. We can see this by asking why any time-defined self should find a pragmatic argument of the type that McClennen raises convincing. Suppose we encounter someone about to act irresolutely in a situation of the type that McClennen considers. We might point out to him that he would do better overall by acting resolutely, even if his current preference is to be irresolute, running through a line of reasoning very much like that canvassed a few paragraphs ago. The problem is that the pragmatic argument in support of resoluteness depends upon the individual identifying with his past and future selves in such a way that it makes sense for him to be concerned with the extent to which the preferences of each are satisfied. We only have such identification when an individual is capable of abstracting away from his current situation and taking a detached perspective on his personal history. An individual who can be persuaded by the pragmatic argument is an individual who is prepared to align his current preferences with the preferences of his past and future selves. But such an individual is not going to be susceptible to sequential inconsistency in the first place! The whole problem of sequential inconsistency only arises when an individual’s current preferences do not take account of his past and future preferences, and for such an individual pragmatic arguments of the type that McClennen and others have proposed will have no force. The claim here is not that pragmatic arguments in support of resoluteness are not effective.¹⁵ It is that they can only be effective in a ¹⁵ Such claims have been made. Michael Bratman, for example, argues that resolute choice is flawed in the emphasis it places on ‘‘courses of action that typically include elements no longer in the agent’s causal control. This seems to me not to do justice to the significance of temporal and causal location to our agency . . . A reply will be that in giving such priority to intentional structure a resolute agent employs a deliberative procedure that is, in the words of Gauthier, ‘maximally conducive to one’s life going as well as possible’. . . But it is difficult to see that this shows that at the time of action one

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restricted way. They can serve the purposes of third-person normative assessment. Someone else can use pragmatic considerations to determine whether or not I am acting irrationally in failing to be resolute. They can do this because they have no reason to privilege the time-defined self who is acting irresolutely—or any other time-defined self. They are able to put the interests of all the relevant time-defined selves into the balance equally; determine my interests as a person as the sum of the interests of the time-defined selves; and then work out whether I am better off overall by acting resolutely or irresolutely. But this is not something that I can do myself. Or rather, if I can do it then the question of resoluteness does not arise. Suppose that at t2 it is pointed out to me that acting counter-preferentially will yield a greater return than following my preferences, where the greater return is calculated by comparing the returns to my t1 and t2 time-defined selves. So (putting aside the earlier reservations with the interpretation proposed on McClennen’s behalf ) my t1 -self will receive his most preferred option if my t2 -self acts resolutely, while my t2 -self will receive his second most preferred option. At t2 sophisticated choice is no longer an option, so the comparison has to be with myopic choice, which we have agreed to be not even weakly dominated by resolute choice. If I choose myopically at t2 then my t2 -self receives his most preferred option, while my t1 -self receives his least preferred option. In this case being resolute requires my t2 -self to value the interests of my t1 -self over the interests of my t2 -self. To find the pragmatic argument compelling my t2 -self has to identify with the interests of my t1 -self. But how could my t2 -self identify with the interests of my t1 -self in a way that would lead it to act counter-preferentially unless my t1 -preferences were incorporated into my t2 -preferences? But if the t1 -preferences are incorporated into the t2 preferences then my t2 -self is not really choosing counter-preferentially at all—which means that the notion of resolute choice fails to get a grip. The argument here does not depend upon any particular metaphysics of the self, or upon any particular view about how the good for a person is distributed over time. John Broome has argued (drawing upon the work of Derek Parfit) in support of the claims, first, that everything will not reasonably consult one’s ranking of options that are at that time in one’s control’’ (Bratman 1999, 73. The reference to Gauthier is to Gauthier 1994, 701). It seems to me that Bratman’s point is more circumscribed than he takes it to be. Temporal and causal location is certainly relevant from the action-guiding perspective, but to assume that it is decisive from the normative assessment perspective is essentially to beg the normative question in favor of the separability principle.

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that is good for a person is good for that person at some time (and so is good for at least one person-stage, or temporally-indexed self ) and, second, that a person’s intertemporal betterness relation is given by the sum of her temporally-indexed betterness relations (Broome 1991, ch. 11; 2004, ch. 15; and Parfit 1984). His argument rests upon what he calls a ‘‘disuniting metaphysics of personhood’’, to the effect that a person is nothing over and above a succession of person-stages. If Broome’s argument is sound, then it certainly gives us a very clear way of aggregating the good for a person over time (we simply sum the good of the individual person-stages). This yields a determinate way of applying the type of pragmatic arguments that we have been considering. We can compare with respect to goodness the individual histories that result from being resolute and irresolute respectively (calculating the goodness of each history by summing the goodness of its stages). And of course, on Broome’s disuniting metaphysics, it is very clear that this type of intertemporal aggregation is not something that can be done from the perspective of an individual temporal stage. On Broome’s view, the relations between successive person-stages are akin to the relations between different persons, and just as I am under no particular rational requirement to take into account the interests of other people, so too is no person-stage rationally obligated to take into account the interests of another person-stage in the same history. Of course, I may do so without being obligated to do so. I may be what might be termed intertemporally coherent. But if I am intertemporally coherent then, almost as a matter of definition, I am not going to have the disconnect between different stages in my person history that will generate potential irresoluteness. Rejecting Broome’s disuniting metaphysics does not eliminate the problem that I have raised. It certainly makes it more difficult from the perspective of normative assessment to run pragmatic arguments in support of resoluteness, because it make it more difficult to see how we can aggregate good over time. The pragmatic arguments assume that it makes sense to attribute preferences and hence individual good to individual person-stages. But this assumption surely does not stand or fall with the disuniting metaphysics. It is hard to see how there could be any metaphysical perspective on the self on which it does not make sense to aggregate good over time. And the fact remains that, however closely one thinks individual person-stages are connected (and should take each other into account), the decision-maker who feels the pull of irresoluteness is not one for whom individual person-stages are connected in a way that would give the pragmatic argument purchase.

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Whatever the fact of the matter is concerning the identity of selves over time, if I am sufficiently detached from the preferences of my earlier self to be considering breaching them by acting irresolutely, then I am not going to be moved by arguments that rest upon my now valuing the future satisfaction of my earlier self ’s desires and preferences. For these reasons, then, the pragmatic argument cannot work at the action-guiding level, although it can be effective as a device of normative assessment. It will not persuade a decision-maker on the cusp of irresoluteness into choosing resolutely, but it does provide a benchmark and set of criteria by which we might, from a third-person perspective, determine whether an irresolute decision-maker is irrational. Pragmatic arguments of this type give us a way of assessing whether a particular choice is rational, even though a decision-maker not already disposed to choose in accordance with them will not find them persuasive. This is a fairly common phenomenon in philosophy. Consider, for example, the exercise of justifying a deductive rule, such as the rule of modus ponens. It is plain that any such justification will end up employing the very rule that it is trying to justify. And so no such justification is likely to convince someone skeptical about modus ponens (assuming that there could be such a person)—just as a McClennen-style pragmatic argument could not persuade an agent to be resolute who was not already disposed to be resolute. This does not prevent such a justification from explaining why it is rational to reason according to modus ponens.¹⁶ Nor, by analogy, does the pragmatic argument’s lack of suasive force stand in the way of its explaining why it is rational to be resolute (or why, on some occasions, it fails to be rational). But nonetheless, a pragmatic argument can be effective only from the external perspective of normative assessment. It cannot get a grip on internal problems of action guidance. OV E RV I EW: T H E T H I R D C H A L L E N G E The third challenge is the challenge of developing decision theory to do justice to the sequential and diachronic nature of decision-making. ¹⁶ Michael Dummett terms this type of circularity pragmatic circularity and suggests that it is relatively harmless, as opposed to the circularity involved in taking a conclusion as a premise, which is to be censured precisely because it guarantees success (Dummett 1978). For further discussion of the epistemic peculiarities of the project of justifying deduction see Boghossian 2002 and Wright 2002.

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Can this be done in a way that accommodates all three dimensions of rationality? Once again we run into tensions between the different dimensions. These tensions are precipitated by a distinctive feature of decision theory considered as a synchronic theory of decision-making at a time, namely, the fact that it is governed by the principle of separability. If we think of a sequential choice problem as a decisiontree, the separability principle states that at any given choice node n on that tree we should choose as if we were confronting a decision problem identical to the decision problem diagrammed in the sub-tree that begins at n. The separability principle opens up the possibility of sequential inconsistency, which occurs when a decision-maker plans to choose in a particular way but then, when the time for choice arrives, fails to carry through his plan. Sequential inconsistency can come about through simple preference reversal, or through having preferences that fail to satisfy the substitution axiom. The phenomenon of sequential inconsistency raises a very basic tension between the action-guiding dimension of decision theory and the normative assessment and explanatory/predictive dimensions. Since the justification for separability comes from the limited range of factors that are relevant to decision-making—viz. the decision-maker’s probability and utility functions at the moment of decision-making—we can see the separability principle as linked to the action-guiding dimension of rationality. The agent deciding how to act in a given situation does indeed have only the resources that the separability principle says he has. From the perspective of normative assessment and explanation/prediction, however, the separability principle has much less appeal. It is easy to think of examples where sequential inconsistency is plainly to be censured from a normative point of view, and our practices of explanation and prediction rest upon stable expectations that could not hold if every plan were open to revision in the light of the agent’s preferences at the time of choice. The problem, then, is the problem of dealing with sequential inconsistency. There are three relevant aspects to sequential inconsistency. The first is fixing an initial plan. The second is the possible change of preferences that might take place in the interval between fixing on a plan and acting on it. The third is the decision-making that leads up to the sequentially inconsistent choice. There is a strategy for dealing with sequentially inconsistent choice corresponding to each aspect. The first strategy is known as the strategy of sophisticated choice. The focus here is the initial plan. The sophisticated chooser identifies

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plans that he cannot carry through (plans that he knows will lead to sequential inconsistency) and realizes that they are not feasible. Since they cannot be carried through, they cannot be chosen. So the sophisticated chooser confines himself to the remaining feasible options. Plainly this eliminates the possibility of sequential inconsistency—at least, of anticipated sequential inconsistency. The separability principle is not permitted to get a grip. However, the sophisticated choice strategy fails to strike the required balance between decision-making/action-guidance and normative assessment. Sophisticated choice certainly resolves the decision-making problem. It tells the agent what to do to avoid sequential inconsistency. But there are still issues that can be raised from the perspective of normative assessment. Sequential inconsistency is not always irrational and the strategy of sophisticated choice has no guidance to offer as to when it is rational to be sequentially inconsistent (and hence when it is rational to abstain from sophisticated choice) and when not. By the same token, therefore, it gives us little predictive leverage on what a rational agent will do in a given situation. An agent who adopts sophisticated choice knows what to do. But the assumption that the agent is rational does not tell us whether or not she will be a sophisticated chooser. One way of dealing with this problem, at least in the case of sequential inconsistency due to preference reversal, is to distinguish rational from irrational changes in preference through an account of rational updating of preferences comparable to a broadly Bayesian account of rational updating of probabilities. This would underwrite a distinction between rational and irrational sequential inconsistency, with sequential inconsistency counting as rational if and only if it is consequent upon an appropriately rational updating of preferences. Yet rational updating of preferences (at least in the most obvious ways of thinking about it) neither guarantees immunity from sequential inconsistency, nor is involved in everything that one might think of as rational change of preference. This has obvious implications for the project of normative assessment and for the project of explanation/prediction. The rational preference strategy does not fix the domain of rational preference change. Nor does it allow us to predict how rational agents will change their preferences. It does, however, serve a limited action-guiding role, since it gives decision-makers tools for restoring consistency both within their utility functions and between their utility and probability functions. A third strategy for dealing with the problems crystallized in the phenomenon of sequential inconsistency is to eliminate the force of the

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separability principle at the moment of choice. This is the strategy of resolute choice, which proposes that decision-makers be bound by their earlier plans. The justification for resolute choice is pragmatic. Resolute choosers can do better, in the standard maximizing sense of decision theory, than sophisticated choosers or myopic choosers (the name given to agents who always make separable choices). Of course, they do not always do better. But this is an advantage, not a disadvantage. It gives the resolute choice theorist a way of solving the problem that arises for the sophisticated chooser, namely, the problem of determining when it is rational to be sequentially inconsistent and when not. We can use pragmatic considerations to determine when it is rational to be irresolute (and hence sequentially inconsistent). The problem here is that this pragmatic justification for resolute choice cannot be deployed from the first-person, action-guiding perspective. No decision-maker susceptible to irresoluteness will be concerned with the interests of her different time-defined selves in the manner required for the pragmatic argument to have leverage. The pragmatic justification can be deployed from the third-person perspective of normative assessment. So the basic tension reappears. As before we can represent the tensions between the different dimensions in a tabular form. Once again we see that each of the strategies considered fails to satisfy the requirements of at least one of the three dimensions. STRATEGY Sophisticated choice Rational preferences Resolute choice

AG ✓ ✓ ✕

NA ✕ ✕ ✓

E/P ✕ ✕ ✓

5 Rationality: Crossing the Fault Lines? Decision theory is a theory of great elegance and power. It goes right to the heart of some aspects of how we think about rationality. But just how comprehensive is it? Can it do justice to the multiplicity of tasks that the concept of rationality has been called upon to play in different academic disciplines and different explanatory projects? In particular, can it do justice simultaneously to the three basic dimensions of the concept of rationality—to its action-guiding dimension; to its normative assessment dimension; and to its explanatory/predictive dimension? It is tempting to think that decision theory can serve such a foundational role. This would certainly provide a unifying thread across the social and human sciences. We have been exploring three challenges for the view that decision theory is the core of our theory of rationality. The first of these challenges has to do with how we interpret decision theory—in particular, how we understand the key notions of preference and utility at the heart of the mathematical theory. We cannot take these notions as theoretical primitives. They must be interpreted and brought into line with some of the pretheoretical concepts that they might plausibly be taken to clarify or regiment. If decision theory is to be a theory of rationality then its basic notions must be continuous with the basic notions in the domains in which the theory of rationality applies. If, as many have thought, the theory of rationality applies in the domain of psychological explanation and prediction, where the key notions are commonsense psychological notions of belief and desire, then there must be meaningful connections between how we think about utility and preference, on the one hand, and how we think about desire, on the other. The second challenge emerges when we think about the domain and scope of decision theory. The canonical application of decision theory is to decision problems understood in a very particular way.

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An agent confronts a decision problem when she has a number of courses of action available to her, each of which she thinks leads to one or more possible outcomes, to each of which she attaches a certain value (utility). But what are those outcomes? And what constraints (if any) are there on how the decision-maker identifies and distinguishes different outcomes? It is natural to think that a theory of rationality must itself be capable of answering this question. Some ways of individuating outcomes seem irrational, while others are perfectly acceptable. But can decision theory provide a principled way of distinguishing these? The third challenge emerges when we ask how decision theory can be extended and developed to accommodate rationality over time. Decision theory is a synchronic theory, in the sense that every decision problem is considered ab initio, to be solved as a function solely of the agent’s probability and utility assignments at the time of deliberation and decision. But rationality is a diachronic notion. We enter into commitments that make it rational (or at least: that we think make it rational) to act in certain ways, irrespective of how our utility and probability assignments might change in the interval between making a commitment and acting upon it. Can decision theory accommodate this diachronic aspect of rationality? Exploring these three challenges has exposed some serious problems for the thesis that decision theory can serve as a universal theory of practical rationality. The difficulty is not that any of the three challenges is intractable. Quite the opposite. The challenges have been extensively discussed and, as the discussion has shown, each challenge can be met in a number of different ways. The problem is that each way of meeting the challenges fails to do justice to at least one of the three dimensions of rationality. There is no way of meeting any of the challenges that can simultaneously do justice to the action-guiding, normative assessment, and explanatory/predictive dimensions of the concept of rationality. These three challenges expose in a particularly acute way that there are fault lines between the three different dimensions of rationality. Each dimension places constraints upon the theory of rationality that decision theory can satisfy only at the cost of failing to satisfy the constraints imposed by one or both of the other two dimensions. The dialectic is summarized in the following table, which simply combines the tables that we have seen at the end of each chapter.

Crossing the Fault Lines?

Challenge 1: (a) Challenge 1: (b) Challenge 1: (c) Challenge 2: (a) Challenge 2: (b) Challenge 2: (c) Challenge 3: (a) Challenge 3: (b) Challenge 3: (c)

161

STRATEGY

AG

NA

E/P

Formal understanding of utility and preference Relation R as considered preference Moving away from preference Extensional approach (invariance principle) Intensional approach Individuation by justifiers Sophisticated choice Rational preferences Resolute choice

✓

✕

✕

✕

✕

✓

✕

✓

✕

✓

✓

✕

✓ ✓

✕ ✕

✓ ✓

✓ ✓ ✕

✕ ✕ ✓

✕ ✕ ✓

I will not repeat the reasoning summed up in the table. Summaries will be found at the end of the relevant chapters. The dialectical situation can be read off the table. There is no way to negotiate any of the three challenges that accommodates all three dimensions of rationality. (Every row has at least one cross in it.) The three dimensions of rationality pose inconsistent demands. In fact, the situation is even worse than this. The dimensions of rationality are pairwise inconsistent. Removing one of the dimensions will not restore consistency. (There is no column such that its removal would leave a row with no crosses in it for each challenge.) If we drop the requirement that decision theory serve as an explanatory/predictive theory, for example, this would certainly give us a way of resolving the second challenge. Decision theory could do justice both to the action-guiding and normative assessment dimensions of rationality if it were interpreted (as it is standard to do) in a purely extensional manner. But the first and third challenges would still retain all their force. Dropping the action-guiding dimension opens up the possibility of a resolution to the third challenge (via resolute choice), but leaves the first and second challenges untouched. Putting the normative assessment dimension to one side would allow us to resolve the second and third challenges (by means of an intensional

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approach that adopted sophisticated choice), but would still leave us with the first. It remains true, however, that no one of the dimensions of rationality is eliminated by the challenges we have been considering. (No column has a cross in it for each approach to a given challenge.) The implication is clear. Decision theory cannot yield a theory of rationality that accommodates all three dimensions. In fact, it cannot yield a theory of rationality that accommodates any two of them. But, one might think, this is not too fatal. If we confine ourselves to just one dimension of rationality, then there is no reason to think that decision theory cannot meet all three challenges. Surely we can take decision theory to be a theory of rationality, provided that we are clear that it is being proposed only as a theory of deliberation, or only as a theory of normative assessment, or only as an explanatory/predictive theory of human behavior. But which one? Decision theory is standardly taken to apply paradigmatically to the action-guiding dimension of rationality. As its name suggests, decision theory tells us how to choose. One response to the arguments of this book would be to say that what has been shown is that it is quite simply a mistake to think of decision theory as anything other than a theory of rational deliberation. We should look elsewhere for a psychological theory of reasoning that can be used for explaining and predicting behavior, and in a third place for a normative theory that can be used for what we have termed the external assessment of an agent’s probability and utility assignments and how they are put to work to solve decision problems. It is certainly hard to imagine the form that such a normative theory might take. Part of the appeal of decision theory, particularly for social scientists, is that it has struck many as the only way of bringing the normative concept of rationality in from the realm of hand-waving and appeals to intuition. But we are in a much better position when it comes to the psychology of reasoning. Here there is a number of well worked out alternatives to decision theory—worked out both from theoretical and experimental perspectives. Prospect theory, as originally proposed by Daniel Kahneman and Amos Tversky, is a good example (Kahneman and Tversky 1979). Prospect theory was developed in direct response to experimental evidence seeming to show that reasoners regularly contravene the basic principles of decision theory. We have reviewed some of this evidence above when discussing the invariance principle, and indirectly touched upon it in the context of the Allais

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paradox. Prospect theory responds to the apparent divergence between the normative and the descriptive by proposing a descriptive model of decision-making. It sets out to capture the psychology of individual decision-making in a way that explains the experimentally observed departures from decision theory. So, for example, whereas decision theory takes outcomes and probabilities as given, prospect theory proposes two stages in the choice process, each of which diverges substantially from the prescriptions of decision theory. The first is an editing stage that involves interpreting the presented prospects—coding them in terms of gains and losses relative to a neutral starting-point, for example; discarding extremely unlikely outcomes; and canceling out components that are shared by different outcomes. The second is the process of choosing the prospect with the highest value, where value is derived from, but in no sense determined by, the probabilities and utilities of its possible outcomes. Even when objective probabilities are known for particular outcomes, these are weighted by a decision function π that reflects the impact of that probability on the overall value of the prospect. There is no requirement that π(p) and π(1 − p) sum to 1. And the value function measures the magnitude of the deviation from the neutral starting-point identified in the editing phase. As one might expect, given that prospect theory is a theory designed to explain experimentally identified anomalies in reasoning, prospect theory serves much better as a tool of explanation and prediction than decision theory, at least in most types of situations that have been experimentally studied.¹ In effect, Kahneman and Tversky propose a division of labor. For deliberation we should use decision theory. For explaining and predicting behavior we should use prospect theory. But, as even the briefest sketch of prospect theory illustrates, it differs in very fundamental ways from decision theory. This raises an obvious question. Is it possible to separate completely the action-guiding dimension of rationality from the explanatory/predictive dimension in the way that such a division of labor would require? It is far from obvious that they can be. There are good reasons for thinking that, if decision theory is to serve as a theory of deliberation then it must be explanatory/predictive. ¹ See the papers in Kahneman and Tversky 2000 for detailed discussion of the current state of prospect theory.

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We can approach the issues here by asking why we should accept decision theory as a theory of deliberation. As we have seen on a number of occasions, the standard answer appeals to the representation theorems. The representation theorems show that the cost of failing to maximize (expected) utility is inconsistent choice. But this does not really get to the heart of the issue. Why should we care about the consistency of our choices? What is so terrible about choosing inconsistently? The most plausible answer, I think, is that our choices are a function of our beliefs and desires. They reflect what we want to achieve and the information that we possess about the world. If our choices are consistent in the ways delineated by the representation theorems then they represent our best attempt to achieve what we want to achieve in the light of the information we possess. This is really why we care about consistency. If we choose consistently (if, that is, our choices respect the relevant axioms) then we can be sure that we are being true to our beliefs and desires. And, by extension, what decision theory tells us is how to ensure that we are being true to our beliefs and desires in those situations where we know what our beliefs and desires are (where we have sufficiently determinate probability and utility assignments). But being true to our desires and beliefs in this way is, plausibly, what we are trying to do all the time, since beliefs aim at truth and desires aim at satisfaction. The appeal of decision theory as a theory of deliberation, then, is that it tells us how to achieve what we are already trying to achieve. If this is right then it follows that we should view the probability and utility functions at the heart of decision theory as regimentations, or calibrations, of our beliefs and desires. It is highly implausible that decision-makers have beliefs and desires as fine-grained and/or as articulated as the probability and utility functions that can be attributed to them (or that they can work out for themselves by applying the techniques sketched out by Ramsey). But it is even more implausible that an agent’s probability and utility functions should be systematically in tension with her beliefs and desires. When a decision-maker thinks through the implications of the choices that she has actually made and thinks about the choices that she would make in given counterfactual situations in a way that might allow her (or a conveniently located choice theorist) to delineate her probability and utility functions, what she is doing is uncovering a structure that is implicit in the beliefs and desires that she would acknowledge before setting out on the process. The structure is implicit because there is scope for tension between

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the agent’s utility function and what she takes to be her desires, and between her probability functions and what she takes to be her beliefs. Desire is comparative and the agent can always ask, for any outcome that her utility function has her preferring to another, whether she desires the former more than the latter. If utilities and desires come into conflict then something has gone wrong. The agent is either mistaken about what her desires or utilities really are, or she has uncovered an internal inconsistency. In either case the agent is committed to restoring consistency. The same holds for beliefs. If the agent’s probability function has her holding e1 to be more probable than e2 , the agent can always ask herself whether she believes e1 to be more probable than e2 . As in the case of desires and utilities, the derivation of a probability function might reveal commitment to assigning probabilities to outcomes about whose probability she is not aware of having any beliefs. But conflict is not acceptable here either. Suppose, then, that taking decision theory as a theory of deliberation presupposes taking the probability and utility functions as regimentations of our commonsense notions of belief and desire. Our argument for this rested in part upon the thesis that people generally act in ways that seem to them best to satisfy their desires in the light of their beliefs. Many philosophers call this the ‘‘belief-desire law’’ and take it to be a very basic platitude of ‘‘folk psychology’’—of the implicit theory of human motivation and behavior that is widely held to govern our social interactions and how we make sense of ourselves and other people. The thrust of the early argument was, in essence, that decision theory’s suitability as a theory of deliberation is underwritten by the belief-desire law. The principle of maximizing expected utility is, on this view, the belief-desire law writ large—a codification and regimentation of a basic principle of human psychology. We can leave aside the question of whether or not this way of thinking about social interaction and social understanding is correct.² What is important is that something like it seems to be built into the idea that decision theory can serve as a theory of practical deliberation. This has an important consequence. If the belief-desire law is, broadly speaking, true (if, that is, it is sufficiently true for decision theory to be a useful ² See Bermúdez 2005 for further discussion of different ways of thinking about folk psychology. It is no easy matter to give a precise formulation of the ‘‘belief-desire’’ law. This is brought out in Gauker 2005, which also is very skeptical about the idea that decision theory can serve as a regimentation of commonsense belief-desire psychology.

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guide to deliberation) and if the expected utility principle is really a regimentation of the belief-desire law, then it follows that agents must, broadly speaking, be maximizers of expected utility. But this, of course, entails that decision theory must be explanatory and predictive—that it should serve not just as a tool for deliberation, but also as a tool for explaining why people choose the way they do and predicting how they will choose. This is a conditional claim. The point is that our reasons for thinking that decision theory can serve as a useful theory of deliberation are equally reasons for thinking that it should serve as an explanatory/predictive tool. To the extent, then, that we have good reasons for thinking that decision theory is a tool for deliberation we have good reasons for thinking that decision theory serves as a psychological theory that can be explanatory and predictive. This makes the kind of strategy adopted by Kahneman and Tversky very problematic. The functions that play the role in prospect theory that probability and utility functions play in decision theory are fundamentally different from those probability and utility functions. So we can ask: Which pair of functions best corresponds to our pretheoretical notions of belief and desire? There is a dilemma here for the two-pronged strategy of using separate theories for deliberation, on the one hand, and explanation/prediction on the other. Suppose we look to probability functions standardly construed for regimentations of our pretheoretical notions of belief and desire. The previous argument entails that decision theory has to be an explanatory/predictive theory. This is because reformulating the belief-desire law with beliefs viewed in terms of probabilities and desires in terms of utilities simply gives us the descriptive claim that people are maximizers of expected utility. But if people are maximizers of expected utility then there is no need for prospect theory to explain and predict behavior. So the two-pronged strategy fails. Suppose, on the other hand, that we take something like prospect theory’s π function and value function as formal analogs of belief and desire. This undercuts the argument for taking decision theory to be a theory of deliberation. If we are supposed to understand the beliefdesire law in terms of the theoretical posits of prospect theory, then why should we take decision theory as a theory of deliberation? In what sense does it help us better to satisfy our desires in the light of our beliefs (the information that we possess about the environment and the possible outcomes of our actions), now that we have decided that the theoretical posits of prospect theory give a more accurate picture of

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the structure of our beliefs and desires than the probability and utility functions of decision theory? What is the point of making decisions according to the principle of maximizing expected utility when what we are really trying to do (according to our explanatory/predictive theory of motivation) is to maximize the quantity discussed in prospect theory? The problem is not peculiar to prospect theory. It is quite general. Any proposal that has different theories playing the deliberation role and the explanatory/predictive role will confront an analogous dilemma, since we will have to map one (but not both) of the theories onto our pretheoretical notions of belief and desire. So there are grave problems for thinking that decision theory can serve solely as a theory of deliberation, with some other theory of decision-making and practical reasoning serving as a theory of explanation and prediction. But does the converse hold? Could decision theory serve as an explanatory/predictive theory without being a theory of deliberation? The discussion in earlier chapters has shown that this would require, at a minimum, reconstruing decision theory to allow for a more fine-grained individuation of outcomes and to accommodate the welldocumented patterns of preferences that gave rise to prospect theory. But even if we assume that this can be done without prospect theory’s radical departure from standard construals of decision theory, the proposal runs into difficulties. The difficulties come when we think about the relation between a theory of behavior and a theory of motivation. There are descriptive theories of behavior that are not in any sense theories of motivation. Optimal foraging theory is a case in point. It is possible to model certain aspects of animal behavior by making the heuristic assumption that animals are performing complex cost-benefit calculations. The guiding assumption of optimal foraging theory is that animals optimize the net amount of energy obtained in a given period of time. Foraging behavior is described using a cost-benefit analysis on which acquired energy is the benefit. For a foraging bird, for example, faced with the ‘‘decision’’ of whether to keep on foraging in the location it is in or to move to another location, the costs are the depletions of energy incurred through flight from one location to another and during foraging activity in a particular location. The cost-benefit analysis can be carried out once certain basic variables are known, such as the rate of gaining energy in one location, the energy cost of flying from one location to another and the expected energy gain in the new location. It turns out that optimality modeling makes robust

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predictions of foraging behavior in many different species of animal. Of course, as optimal foraging theorists themselves are often the first to point out, there is no suggestion that the great tits or starlings really are carrying out complex calculations about how net energy gain can be maximized within a particular set of parameters and background constraints. The animal optimizes by following a set of relatively simple rules of thumb or heuristics, which are most likely to be innate rather than learned. Evolution has worked in such a way (at least according to the proponents of optimal foraging theory) that foraging species have evolved sets of heuristic strategies that result in optimal adaptation to their ecological niches. This optimal adaptation can be mathematically modeled, but the behaviors in which it manifests itself do not result from the application of such a theory. Theories such as optimal foraging theory are purely instrumental. They have nothing to say about the mechanisms that explain the behaviors that they model and predict. This is certainly not how Schick, for example, views his revisionary construal of decision theory, which he explicitly presents as a theory of motivation. Schick is proposing a psychological theory of the springs of action. Plainly we can take decision theory as an explanatory/predictive theory in one or other of these two ways—as an instrumental theory or as a theory of motivation. But there are problems on each construal. Suppose we take it to be a theory of motivation. Since we are assuming that the theory does indeed work well we need to explain why that is so. The most natural explanation is that the theory works as well as it does because it exploits the very same processes by which people solve decision problems. Or, more accurately, the theory exploits the processes by which people could solve decision problems. Even if the way that people actually solve those problems in practice often involves heuristic shortcuts (of the sort discussed in other writings by Kahneman and Tversky and by Gigerenzer and his collaborators), these heuristic shortcuts must take them to the very place to which decision theory would have taken them.³ If they did not, then decision theory would not be a very useful tool for explanation and prediction. But if they do, then it is hard to see why decision theory should not also serve as a theory of deliberation. If we take decision theory to be a theory of motivation then it is hard to avoid the conclusion that the processes of explanation and prediction ³ See the essays in Gigerenzer et al. 1999 and 2001, as well as the discussion of the representativeness and availability heuristics in Kahneman and Tversky 1982.

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are the reciprocal of the process of deliberation. A theory can only serve the one role to the extent that it serves the other. Suppose, then, that we take decision theory in a purely instrumental sense. We will still need a supplementary theory of motivation. Descriptive adequacy is not a brute fact. A descriptively adequate instrumental theory needs to be grounded in an account of how and why the successfully described behaviors occur. We would need something that stands to decision theory in the same relation that an account of evolved heuristics might stand to optimal foraging theory. Certainly we have at present no idea what such a theory might look like. There is an extensive literature on heuristics and biases that proposes to understand decision-making in terms of simple psychological rules, such as the rule of   . This requires a decision-maker faced with a choice between several alternatives to apply a series of cues in order of cue validity and to choose the first alternative that is selected by one of the cues—for examples of the explanatory power of    see Gigerenzer et al. 1999, 2001. But this line of research is generally proposed as an alternative to taking decision theory as a predictive/explanatory theory. The central claim of Gigerenzer and his school is that the simple heuristics that they discuss are what they term ecologically rational, even though they fail to be rational according to standard criteria of rationality (such as those associated with decision theory). The precise definition of ecological rationality is not easy to pin down, but the important point is that ecological rationality is an alternative to optimizing rationality, not a way of understanding how decision-makers end up maximizing expected utility without explicitly reasoning according to the expected utility principle, or adhering to the axioms. The same holds for the heuristics discussed by Kahneman, Tversky, and their collaborators (such as the representativeness heuristic and the availability heuristic). These are proposed to explain why people regularly make decisions in ways that directly contravene decision theory. These are all models of what is often termed bounded rationality (Simon 1957), proposed as a corrective to taking decision theory as an explanatory/predictive theory, not as a theory of motivation to supplement it. The prospects for taking decision theory to be a purely instrumental explanatory/predictive theory seem very dim indeed. If decision theory is to be an explanatory/predictive theory at all then it will have to serve as a theory of motivation. But then, for the reasons sketched earlier, we have a theory that could equally serve as a theory of deliberation. What this means is that the action-guiding and explanatory/predictive

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dimensions of rationality cannot be separated. We cannot take decision theory to be a theory of deliberation without also taking it to be an explanatory/predictive theory. And vice versa. But, if the arguments of the earlier chapters are sound, it follows that no version of decision theory can be both a theory of deliberation and an explanatory/predictive theory. This emerged most clearly in the discussion of the first challenge. By default, then, decision theory has to be viewed through the lens of the normative assessment dimension of the concept of rationality. This would chime with how decision theory is often described. It is often said, for example, that decision theory is a normative rather than a descriptive theory. A particularly trenchant illustration comes from the writings of Isaac Levi, who has argued in several places that decision theory has little or no use as a tool of explanation and prediction, and instead should properly be viewed as yielding ‘‘norms for self-criticism’’ (Levi 1989, 19). Levi holds that decision theory gives ‘‘weak principles of rationality . . . that could be deployed by deliberating agents to evaluate their options, full beliefs, probability judgments and value judgments to ascertain whether they satisfy the requirements of a weak account of coherence and consistency’’ (Levi 1989, 25). For Levi, then, decision theory is a theory of normative assessment without being an explanatory/predictive theory. In the light of the argument just canvassed for the interdependence of the action-guiding and explanatory/predictive dimensions, Levi’s position is stable only if decision theory can be a theory of normative assessment without being a theory of deliberation.⁴ Prima facie this seems implausible. Levi’s ‘‘norms for self-criticism’’ seem to straddle the boundary between the action-guiding and the normative assessment conceptions of the concept of rationality. Why should we want to ascertain whether our probability and value judgments satisfy the requirements of coherence and consistency (as laid down in decision theory)? Surely only because our probability and value judgments are the basis for our deliberations. The norms of self-criticism obtained from decision theory are norms that we ought to take seriously because they are norms that tell us how we ought to deliberate. But it is hard to see how decision theory can ⁴ I should stress that Levi does not see matters this way. As I read him he does not see a distinction between the action-guiding and normative assessment dimensions of rationality. The reason for this, I conjecture, is that he would not see what I am calling external questions of rationality as falling within the province of decision theory (or perhaps even the theory of rationality at all).

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do this without itself actually being a theory of deliberation. How can a theory that tells us how we ought to solve a particular type of decision problem be anything but a theory of deliberation for decision problems of that type? Philip Pettit has proposed answers to these questions. He has explicitly argued that decision theory provides what he calls a ‘‘canon of rationality’’, but not a ‘‘calculus of deliberation’’—or, in my terms, that decision theory offers a theory of normative assessment, but not an action-guiding theory. Here is a representative passage. Decision theory is non-practical: It offers no guide to how an agent ought to deliberate about what to do . . . It tells us that whenever someone makes a rational decision certain constraints will be fulfilled—thus it provides a canon or test of rationality—but it does not offer any information on how deliberation proceeds, or any advice, therefore, on how it ought to proceed: It may give us a canon of rationality but it does not describe a calculus such that by following it an agent may hope to be rational. (Pettit 1991; 2002, 166)

Pettit’s reasons for thinking this are subtle, and rest upon a distinctive account of practical reasoning. He sees practical deliberation as starting from probability and value judgments. These value judgments share their objects with the value judgments of decision theory. That is to say, they are defined over prospects, which Pettit understands in a fairly standard way. But he thinks that value judgments about prospects are neither psychologically nor normatively basic. Agents value prospects because of the properties that they display (or promise to display). These properties are the real motors of decision-making, although they manifest themselves in value judgments about prospects. We choose between prospects in virtue of the desires that we have for the properties that we see in the prospects. Since decision theory does not, at least in its classical forms, accommodate this distinction between properties and prospects, Pettit claims that it is an incomplete account of the factors relevant to decision-making. And so he concludes that it cannot serve as a theory of deliberation—although it can still serve as a theory of normative assessment, as what he terms a canon of rationality. I find Pettit’s position inherently unstable, however. In its actionguiding guise, decision theory does not claim to be a complete account of the factors relevant to decision-making. It claims only to be an account of rational decision-making. So, for the distinction between prospects and the properties that they display to show that decision theory is not a theory of deliberation it must be the case that thinking about

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prospects in terms of properties raises rationality-relevant considerations that do not emerge when decision theorists think about prospects in what one might term an extensional sense. To put it another way, it must be the case that the consistency and coherence relations between prospects differ depending on whether one is viewing those prospects extensionally or intensionally. In the absence of such divergence there seems to be no reason to think that decision theory fails as a theory of deliberation. The idea that there might be such a divergence will be familiar from our earlier discussions of intensional decision theory. In essence, as I noted in Chapter 3 (see n. 2), Pettit’s thesis of desiderative structure should be read as a version of the call for an intensional decision theory. Pettit’s properties are, to a first approximation, very similar to Schick’s ‘‘understandings’’. That is to say, the way in which we understand a prospect is a function of the properties that we see in it. And, as we saw at some length, Schick is quite explicit that the relations of consistency and coherence between prospects look very different depending on whether or not one takes into account how those prospects are understood. On his version of intensional decision theory, for example, it can be perfectly rational for an agent to assign different values to a single outcome understood in two different ways (even when the agent is aware that there is only one outcome), whereas this is plainly not something that would be condoned by classical (extensional) decision theory. It seems to me that Pettit’s argument requires there to be a comparable divergence between what happens when one thinks about prospects tout court in the manner of orthodox decision theory and when one thinks about them in terms of the properties that they display (or promise to display). So, suppose that there is a divergence between what decision theory identifies as the rational relations within a certain set of prospects and what those rational relations turn out to be when one takes into account the properties for which those prospects are valued. If this divergence is significant enough to disqualify orthodox decision theory as a calculus of deliberation then it is surely significant enough to disqualify it as a canon of rationality. Schick and other proponents of intensional decision theory are prepared to bite the bullet. They reject the normative pretensions of orthodox decision theory. Consistency requires Pettit to do the same. And so his position faces a fatal dilemma. If there is no significant divergence with respect to rationality between decision-theoretic prospects and prospects viewed intensionally, then

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there is no reason to think that decision theory cannot be a theory of deliberation. But, on the other hand, if there is significant divergence then this undermines the plausibility of taking decision theory to be a normatively compelling canon of rationality. There is a more general point to be extracted here. At the most basic level using decision theory as a canon of rationality is a matter of examining probability and value judgments in the light of the fundamental requirements of consistency and coherence that decision theory lays down. But why should we do this? Why should we care whether probability and value judgments satisfy these consistency and coherence requirements? Surely only because our probability and value judgments are the basis for our deliberations. If the starting-points of deliberation are something other than our probability and value judgments, then why should we care whether those probability and value judgments are coherent and consistent. More to the point, why should we be rationally obliged to care? The normative force of decision theory comes from the fact that having appropriately consistent probability and value judgments generates choices that maximize expected utility. Why should we want to be coherent and consistent in this way? Plainly because maximizing expected utility is the rational thing to do in decision problems of the relevant type. But to say that maximizing expected utility is the rational thing to do in decision problems of the relevant type just is to say that decision theory is a theory of deliberation. It tells us what to do when we confront decision problems that have the appropriate form. There is no prospect here of separating normative assessment from deliberation. It is true that decision theory can prescribe not using decision theory as a theory of deliberation. An expected utility calculation across different decision-making procedures might well come up with the conclusion that utility would be maximized by not setting out to maximize expected utility. This would be perfectly rational if the expected benefits of being a utility maximizer outweigh the expected costs.⁵ But this sort of reasoning would itself be an application of decision theory as a theory of deliberation. A decision-maker who decides that it does not maximize expected utility to set out to maximize expected utility is ⁵ Although there is room for doubt about the practical possibility of making this sort of expected utility calculation over different decision-making procedures. See Selten 2001.

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simply deliberating at a higher level, where the options are different strategies for decision-making and the outcomes are the anticipated results of putting those strategies into practice. This would not be an example of how decision theory can serve as a theory of normative assessment without being a theory of deliberation. Exactly the same point made earlier holds here. If decision theory prescribes not pursuing a strategy of maximizing expected utility in a particular (temporally extended) situation, then a decision-maker in that situation both can and should deliberate in a way that applies decision theory to rule out the strategy of maximizing expected utility. Putting this discussion of normative assessment together with our earlier discussion of the interrelations between the action-guiding and explanatory/predictive dimensions of rationality gives us reasons for thinking that the three dimensions of rationality are highly interdependent. We saw that our best reasons for taking decision theory seriously as a theory of deliberation are themselves reasons for taking decision theory to be an explanatory/predictive theory. Conversely, we saw that, if it turned out that we had good reasons for thinking that decision theory can be a tool for explanation and prediction, we would by the same token have good reasons for thinking that decision theory was a theory of deliberation. So, the action-guiding and explanatory/predictive dimensions go hand in hand. But, as has just emerged, we cannot take decision theory to be purely a theory of normative assessment, since decision theory can only yield ‘‘norms for self-criticism’’ if what are being criticized are processes of deliberation that set out to conform to decision theory. The problem that this leaves us with is stark. On the one hand, the discussion in the main part of the book appears to show that decision theory cannot serve as a universal theory of rationality. Decision theory cannot be simultaneously a theory of deliberation; a theory for normatively assessing actions and choices; and a theory for explaining and predicting behavior. In fact, it can perform at most one of these explanatory tasks. On the other hand, decision theory cannot be a theory of any one of these types without being a theory of all of them. The three dimensions of rationality cannot be separated out. This leaves us with only a limited number of theoretical possibilities. It may be that decision theory can shed no light on the concept of rationality. Or perhaps there is a way of developing, expanding, and elucidating decision theory that meets all three of the challenges identified while still accommodating the different dimensions of rationality.

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Alternatively, one or more of the challenges may turn out to be spurious. Finally, it might be that, contrary to initial appearances, it is indeed possible to separate out the three dimensions of rationality in a way that allows decision theory to be a theory of one without being a theory of the other two. To end this book on a personal note, I would like the first possibility not to hold. But on the other hand the case against the last three seems strong.

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Index α-property 134, see also inconsistency; sophisticated choice action-guiding dimension 5, 12–14, 20–27, 48–51, 71–73, 120–122 canon of rationality vs. calculus of deliberation 171–173 deliberation 5, 13, 48, 164–165, 173 hypothetical rationality 6 instrumental rationality 20 substantive vs. operational conceptions of utility 48–51 vs. explanatory/predictive dimension 122–127, 156, 163–170 vs. normative assessment dimension 122–127, 151–152, 155–156, 162–163, 170–174 see also dimensions of rationality; decision-making; decision problem; principle of expected utility all-things-considered rational 6, 123, 125, see also inconsistency; normative assessment dimension Allais, M. 7 Allais paradox 78, 97–100, see also sequential choice Allen, R. 45 Anand, P. 30n14, 33n17 Arrhenius, G. 33n17 Arrow, K. 54n5 Arrow’s axiom 30n13 Asian disease paradigm 80–81 axiomatic method 28–35, see also normative assessment dimension; principle of expected utility; representation theorems; weak axiom of revealed preference axioms of consistency 32, 51–52, see also axiomatic method; continuity axiom; rationality axiom; reduction of compound lotteries; substitution axiom

Bayesianism 1, 5, 22, 26–27 conditionalization 139 insufficient reason, see principle of insufficient reason belief-desire law 53, 165, see also commonsense psychology Bentham, J. 43, 44 Berm´udez, J. 165n2 Blackburn, S. 15n2 Boghossian, P. 155n16 Bolker, E. 31n15, 49n3, 140 bounded rationality 169 Bradley, R. 140–142 Bratman, M. 125, 152n15 Broome, J. 14, 43, 44, 46, 65, 67n10, 68–74, 78, 100–108, 110, 153–154 calculus of deliberation 171–173, see also action-guiding dimension Cannan, E. 45 canon of rationality 171–173, see also normative assessment dimension cardinal utilities, see utility challenges to decision theory 8–9, 159–162 diachronic rationality 9, 112, 155–158, 160, see also sequential choice interpreting preferences and utility 8, 43, 74–76, 159, see also preferences; utility individuating outcomes 8–9, 77–78, 108–111, 159–160, see also outcomes tables summarizing challenges for different dimensions 76, 111, 158, 161 see also dimensions of rationality Chang, R. 33n17 change (in preferences), see preference; rational preference change Chater, N. 19 Chernoff, H. 29n12

184 choice 28–30 all-things-considered vs. hypothethically rational 6, 123 choice behavior and preferences 46–47, 57 choice function 28–29 feasible sets 28 motivation 89–90 myopic choice, see sophisticated choice sequential choice, see sequential choice see also representation theorems; weak axiom of revealed preference. Christensen, D. 15n1, 32n16 co-reportiveness, see propositions common prior assumption 40 commonsense psychology 7, 37–38, 52–53, 88–90, 164–166 belief-desire law 53, 165–166 decision problems 37–38 desires as dispositional states 37–38 information about available options 38 limits of belief-desire explanations 88 motivation, see motivation rationality assumption 7, 17–19, 37 regimented by decision theory 7, 52–53, 164–165 social interactions 125–127 understandings, see understandings vs. Ramsey’s method 38–40 compatibilism 85–86 conditionalization 139, see also Bayesianism consequentialism 89, 91, 127–128 considered preferences 57–65, 75, see also preferences ideal conditions theory 57–58 regress problem 61–64 revealed vs. expressed preferences 59–60 weakness of will 58–59 constrained maximization 148–149 continuity axiom 32 Cooter, R. 43, 44, 45 Davidson, D. 15n1, 16, 37, 88 decision-making 20–26 proximal deliberation 126 risk vs. uncertainty 35–36

Index under certainty 20–21, 80 under risk 23–24 under uncertainty 24–27 see also action-guiding dimension; decision problem decision problem 12–14, 20–26, see also action-guiding dimension; decision-making available options 12, 14, 28 in the explanation of action 37–38 outcomes 12, see also outcomes principle of separability 122, see also principle of separability sequential form 155, see also sequential choice solving a problem vs. having a reason 13–14 solving vs. resolving a problem 12 states of the world 12, 22–23 weakness of the will as a decision problem 61–62 deliberation 5, 13, 48, see also action-guiding dimension; decision-making desiderative structure 90n2 diachronic rationality 112, see also sequential choice dimensions of rationality 5–8, 19–20, 42, 74–76, 85–86, 108–111, 155–158, 159–175, see also action-guiding dimension; normative assessment dimension; explanatory/predictive dimension tables summarizing challenges for different dimensions 76, 111, 158, 161 disunity metaphysics 153–154, see also resolute choice Dummett, M. 155n16 Dutch book (for conditional desirability) 140, see also rational preference change Dynamic choice 112, see also sequential choice Edgeworth, F. 44 Ellsberg, D. 7, 43, 46, 47 Elster, J. 45, 133n9 expected utility 23–24, see utility expected utility theorem 32, 38, see also principle of expected utility; representation theorems

Index explanatory/predictive dimension 7, 16–19, 35–41, 52–56, 71–73, 85–90 idealization 35 identification of a decision problem 37 incompatibilism vs. compatibilism 85–86 instrumental approach vs. theory of motivation approach 167–169 intensional decision theory 92–100 operational vs. substantive conceptions of utility 52–54, see also Utility psychological explanation, see commonsense psychology psychological realism of decision theory 7, 8–9 Ramsey’s method 38–40 social interactions 125–126 vs. action-guiding dimension 35, 122–127, 156, 163–170 vs. normative assessment dimension 85–86, 92–93, 96–100, 108–111, 162–163, 170–171 extensional decision-theory, see outcomes; principle of invariance Fishburn, F. 31n15 framing effects 15, 80–82, 85, see also outcomes Friedman, M. 7 G¨ardenfors, P 26 Gauker, C. 53, 165n2 Gauthier, D. 14, 58–65, 148, 149n14, 152n15 Gigerenzer, G. 168–169 goodness 67–74, 104–108, see also R-relation; moral reasons; utility actual-preference-satisfaction theory 72–73 constraining rationality 105–108 expectational 68–71 external criteria 104–106 non-expectational 68 outcomes vs. lotteries 70–72 problems for action-guidance dimension 72–74 Gordon, R. 18

185 Hammond, P. 134 Hampton, J. 33n17 Hansson, B. 54 Harsanyi, J 40, 48, 54 Harsanyi doctrine 40 Heal, J. 18 heuristics 168–169 Hicks, J. 45 Hollis, M. 3 homo economicus vs. homo sociologus 3 Hume, D. 15, 43 Hurwitz α-criterion 25 hypothethically rational 6, 123, 125, see also inconsistency; normative assessment dimension ideal conditions theory 57–58, see also choice and preferences inconsistency α-property 134 Allais choices 78, 97–100, 115–116, 130–132, 142 failures to maximize expected utility 28–33 normative vs. explanatory/predictive dimension 125–126, see also explanatory/predictive dimension; normative dimension pragmatic argument 129–132 principle of separability 122, see also principle of separability problem with choice inconsistencies 164 rational inconsistencies 120–122, 123–124, 148–150 substitution axiom and inconsistency 113–117, 119 two types of sequential inconsistency 113, 119–120 under different conceptions of utility 49–57 see also axioms of consistency; sequential choice; representation theorems; substitution axiom individuation by justifiers, see outcomes; principle of individuation by justifiers; principle of invariance insufficient reason, see principle of insufficient reason

186 intensional decision-theory 8, 77, 82–84, 93–100 as a theory of motivation 92–93, 100, 167–169 decisions based on desires 172 explanatory/predictive vs. normative dimension 92–100 intensionality of utility assignments 83 see also principle of invariance; outcomes; understandings introspective measurement of utility 47, see also utility invariance principle, see principle of invariance Jeffrey, R. 5, 20n4, 31n15, 38n19, 48, 49n3, 82, 124n4, 139n11, 140 Jevons, W. 44, 47 Kahneman, D. 7, 8, 19, 80–84, 90, 98, 162–163, 166, 168–169 Kaplan, M. 15n1, 32n16, 129n6 Kemeny, J. 129n6 Kolodny, N. 14 Korsgaard, C. 2 Kyburg, H. 26 Kyburg’s principle III, 26 Lepore, E. 37n18 Levi, I. 26, 170 Lewis, D. 7, 53 Loomes, G. 33n17 Loux, M. 83 Luce, R. 20n3, 25, 46, 49 Ludwig, K. 37n18 McClennen, E 113n2, 116, 122, 129, 135, 145, 146, 149–153 Machina, M. 113n2, 116, 129, 146 McKinsey, J. 15n1 McNeil, B. 81 Mandler, M. 33n17 Marshall, A. 45 Maximin 25 Minimax regret criterion 25 modus ponens (justification of) 155 money pump arguments 15n1, 28, 129 moral reasons 14, 93–95 constraints on rationality 105–108

Index morally wrong understandings 95 normative vs. moral assessment 93–94 principle of individuation by justifiers 104 see also goodness; reasons for action Morgestern, O. 31, 46 motivation 89–90, 92–93, 100, 167–169 Myerson, R. 40 normative assessment dimension 6, 14–17, 27–34, 51–52, 68–70, 78–84 all-things-considered vs. hypothetically rational 6, 123, 125 answerability to reasons 2–3 axiomatic method 30–34, 97–100, see also axioms of consistency; representation theorems evaluative facts 66n9 instrumental reasons 2, 13 internal vs. external perspective 78–79 incompatibilism vs. compatibilism 85–86 intensional decision-theory 94–100 individuation of outcomes 77–78, 103–104, 108–111, see also outcomes vs. explanatory/predictive dimension 85–86, 92–93, 96–100, 108–111, 170–171 vs. action-guiding dimension 17, 122–127, 151–152, 156, 170–174 vs. moral assessment 93–94 prospect theory 162–163 canon of rationality vs. calculus of deliberation 171–173 norms for self-criticism 170–171 norms of consistency 2, see also axioms of consistency Oaksford, M. 19 optimal foraging theory 167–168 ordinal utilities, see utility Orwell, G. 86 Outcomes 77–111 extensional vs. intensional interpretations 8, 77, 83–84

Index failures of outcome identification 77–80. framing effects 80–82 individuation by justifiers 102–104 normative assessment dimension 78–84 outcomes as propositions 82–84 outcomes vs. lotteries 48–49, 70–71 simple vs. compound lotteries 31 states of affairs vs. propositions 82–83 vs. understandings 89–90, 101, see also understandings see also intensional decision theory; preferences; principle of invariance; understandings; utility Pareto, V. 45 Parfit, D. 153–154 Pettit, P., 90n3, 171–172 Pigou, A. 45 precommitment 133–134, 149–150, see also sophisticated choice preferences 57–65, 74–76 considered preferences, see considered preferences higher(second)-order preferences 62–63, 123–125 ideal conditions theory 57–58 inconsistent preferences 50, 113–119, see also inconsistency; sequential choice intransitive preferences 28–30 new preferences 49–50 nonseparable preferences 146–147 operational conception 46, see also utility-operational conception preference relation 21–22, see also R-relation principle of individuation by justifiers 103, 106–108 revealed preferences 46–47, 56, 57–58, see also utilityoperational conception strict vs. weak preference 21, see also R-relation see also axioms of consistency; representation theorems; utility; weak axiom of revealed preference

187 principle of expected utility 2, 5, 27–34, 109 belief-desire law 164–165 breaching the principle 27–29 principle of invariance 91–92, see also principle of invariance see also axiomatic method; expected utility theorem; representation theorems; weak axiom of revealed preference. principle of individuation by justifiers 102–108 as a normative principle 104 goodness 104–106 rational preferences 103, 106–108 see also outcomes principle of insufficient reason 26, 36 principle of invariance 82–84, 90–100, 108–109 breaching the principle 86–87 defined over co-reportive propositions 84 derivation from the principle of expected utility 91–92 understandings 90, 93–95 see also intensional decision-theory; outcomes; understandings principle of separability 122, 123, 125–126, 132, 156 nonseparable preferences 146–147 propositions 82–84 coreportiveness 84, 90, see also principle of invariance ethically neutral 38–39 thick vs. thin 83 vs. states of affairs 82 prospect theory 19, 162–163, 166 psychological explanation 16–18, 37–38, 41, 88, see also commonsense psychology; explanatory/predictive dimension R-relation 21–22, 65–67 completeness 21 transitivity 21 considered preference 58–65 internal relation 65–66 external relation 66–67 comparative goodness 67–74, 105–108

188 R-relation (cont.) numerical representation 22, see also utility see also preference Rabinowicz, W. 33n17, 113n2, 129n5 Raiffa, H. 20n3, 25, 46, 49, 113n2, 129n5 Ramsey, F., 31n15, 38–39, 129n6 Rappoport , P. 43, 45 rational analysis of cognition 19 rational preference change 128–129, 139–144, 157 conditional desirability 139–140 different kinds of changes 141 shortcomings of strategy 142–144 see also sequential choice rationality axiom 32 Rawls, J. 128 Raz, J. 66n9 reasons for action individual vs. collective reasons 3 vs. norms of consistency 2 vs. solutions of a decision problem 13–14 see also action-guiding dimension; goodness; moral reasons reduction of compound lotteries 32, see also axioms of consistency reflective endorsement 61, see also considered preferences regret, see minimax regret criterion representation theorems 30–33, 51–52, 65 expected utility theorem 31–33, 38 normative assessment 34, see also normative assessment dimension see also axiomatic method; axioms of consistency; principle of expected utility Resnik, M. 20n3, 31n15, 32 resolute choice 129, 144–155, 157–158 argument against inconsistency 148 argument against precommitment 149–151 nonseparable preferences 146–147 prior commitments 144–145 problem of time-defined selves 152–155 shortcomings of the strategy 148–150

Index two interpretations of the strategy 145–146 see also sequential choice revealed preferences, see preferences; representation theorems; weak axiom of revealed preference Rey, G. 1997 risk aversion 54–55, 69–70 Roemer, E. 45 Rosenberg. A. 53 Sahlin, N. 26 Savage, L. 31n15 Schick, F, 15n1, 78, 84, 86–100, 101, 102, 104–105, 108, 109, 132, 168, 172 Selten, R. 173n5 Sen, A. 29n12, 134 separability principle, see principle of separability sequential choice 9, 112–158 Allais choices 115–116, 130–132, 142 constant preference sequential inconsistency 118, 120–121 dynamic choice 112n1 inconsistency and the pragmatic argument 129–132 preference reversal sequential inconsistency 118, 121–122 principle of separability, see principle of separability rational preference change strategy 128–129, see also rational preference change resolute choice strategy 129, see also resolute choice sequential inconsistency 9, 113–117, 123–125, 135–136 sophisticated choice strategy 128, see also sophisticated choice substitution axiom 113–119 Sidgwick, H. 71 Simon, H. 169 Skyrms, B. 38n19 Slovic, P. 99 Smith, M. 15n2 sophisticated choice 128, 129–138, 156–157 argument against inconsistency 129–132, 135

Index argument against precommitment 149–150 precommitment vs. backward induction 133–134 separability 132, see also principle of separability shortcomings of the strategy 135–138 see also sequential choice Starmer, C. 20n4, 33n17 states of affairs, see outcomes; propositions Strotz, R. 128, 132 substitution axiom 32, 97–100, 113–119 breaching the axiom leads to inconsistency 113–117 pragmatic argument for 129–130 sequential inconsistency 118, 120–122, see also inconsistency synchronic vs. diachronic applications 119 without principle of invariance 97–99 see also axioms of consistency; preferences; sequential choice synchronic vs. diachronic rationality 42, see also substitution axiom and sequential choice Sudgen, R. 20n4, 30n14, 33n17 Suppes, P. 15n1 Suzumura, K. 30n13 Temkin, L. 33n17 theory of deliberation 13, see also deliberation theory of mind 18, see also commonsense psychology Tversky, A. 7, 8, 19, 80–84, 90, 98, 99, 162–163, 166, 168–169 understandings 87–90, 93–95, 101 commonsense psychology 87–88 moral reasons 94–95 motivation 89–90 principle of invariance 93–95 see also intensional decision theory; principle of invariance; outcomes

189 utilitarianism 44 utility 8, 22–24, 43–57, 65–76 action guiding dimension 48–51, 71–73 cardinal vs. ordinal 22–24, 35–36, 44–45 categorical vs. dispositional 44 comparative goodness 67–74 desirability vs. usefulness 46–47 different conceptions 43–47 expected utility 23–24 explanatory and predictive dimension 52–56, 71–73 in the von Neumann-Morgenstern theorem 46 introspective measurements 47 linear transformations 22, 24 normative assessment dimension 51–52, 68–70 operational conception 46–47, 56, 74, see also preference-revealed preferences operational vs. substantive conceptions 48–57 representation of preference 46 stereotypical utility functions 41, 56n1 substantive conception 47, 56, 75, see also goodness see also preferences von Neumann 31, 46 von Neumann-Morgenstern representation theorem 31, 38, 71n11 Wald maximin, 26 weak axiom of revealed preference 29–30, see also representation theorems weakness of the will 58–59, 61, 124–125, see also considered preferences Weber, Max 3n1 Weber, M. 101n5 Weirich, P 19n3 Williams, B. 15n2 Wright, C. 155n16