NEUROECONOMICS Decision Making and the Brain SECOND EDITION Edited by PAUL W. G LIMCHER New York University, New York, NY, USA ERNST FEHR University of Zurich, Switzerland AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEW YORK • OXFORD • PARIS • SAN DIEGO SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Academic Press is an imprint of Elsevier Academic Press is an imprint of Elsevier 32 Jamestown Road, London NW1 7BY, UK 225 Wyman Street, Waltham, MA 02451, USA 525 B Street, Suite 1800, San Diego, CA 92101-4495, USA Copyright r 2014, 2008 Elsevier Inc. 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 electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher. Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone (144) (0) 1865 843830; fax (1 44) (0) 1865 853333; email: permissions@elsevier. com. 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British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress ISBN : 978-0-12-416008-8 For information on all Academic Press publications visit our website at elsevierdirect.com Typeset by MPS Limited, Chennai, India www.adi-mps.com Printed and bound in United States of America 1415161710987654321 CHAPTER 3 Computational and Process Models of Decision Making in Psychology and Behavioral Economics Eric J. Johnson and Roger Ratcliff OUTLINE Introduction 35 Models of Choice Over Time 39 History 35 Computational Process Models 40 Models of Risky Choice 36 Diffusion Models of Rapid Decisions 41 Normative Origins 36 Boundaries, Speed-Accuracy, and Bias Effects 42 Descriptive Modifications 36 Model Constraints 42 Heuristic Models of Risky Choice 37 Competing Models 43 Models of Riskless Choice 38 Use in Neuroscience 44 Multi Attribute Utility Theory 38 Judgment 44 Cognitive Limitations and Context Effects 38 Conclusion 45 Heuristic Models of Riskless References 45 Choice 39 INTRODUCTION These days, that first glance would be very mis- leading. Neuroeconomics today makes great use of History both models that are meant to provide accounts of what should be chosen (normative models) and At first glance, historically, models in decision- models that describe what is actually chosen (descrip- making research seem to have very little in common tive models). This has been facilitated by two impor- with neuroscience. Most decision-making models have tant trends: the first is that there is increasing been concerned with predicting outcomes, or more pre- evidence of brain processes that correspond, in some cisely choices, from a set of inputs, the characteristics of areas, to the output generated by the mathematical the options, and have been mute about the underlying expressions employed by some of these historical cognitive and neuronal processes underlying choice. models. For example, for simple choices, the value of This interest in predicting outcomes has been associated an option described by some of these models seems with a reliance on algebraic models that specify a trans- to be encoded by the medial orbitofrontal cortex and formation of these properties of external options to a ventral striatum (see Chapters 8 and 20; Kable and rank ordering of the attractiveness of options, an idea Glimcher, 2007; Knutson et al., 2007; Plassmann et al., developed in some detail in Chapter 1. These models 2007; Rangel et al., 2008). The second is that said little about how the brain and cognition might trans- models of decision making are changing: faced with form these inputs into output. Neuroeconomics. DOI: http://dx.doi.org/10.1016/B978-0-12-416008-8.00003-6 35 © 2014 Elsevier Inc. All rights reserved. 36 3. COMPUTATIONAL AND PROCESS MODELS OF DECISION MAKING IN PSYCHOLOGY AND BEHAVIORAL ECONOMICS a plethora of possible accounts mapping inputs to in our coin flip example, .5 3 $0 1 .5 3 $20 5 $10. options, there is an emerging consensus that models However appealing the idea of weighting payoffs by that make predictions about additional data, data their probability might have been in this early expected emerging from an understanding of cognitive pro- value theory, this approach implied the uncomfortable cesses, would both winnow this plethora of possible fact that the value of each increasing dollar to every accounts and would help build more robust, useful chooser was the same: it required that the pleasure gen- and reliable models. erated by increasing one’s wealth, x, from $10 to $20 is, This chapter consists of two parts. The first part according to Expected Value, exactly the same as the describes the history of modeling in choice with an impact of an increase from $999,980 to $1,000,000. emphasis on the psychological, from normative to In response to this uncomfortable fact, Bernoulli descriptive and from algebraic to process models. (1738) proposed that the decision maker should instead This review of the major areas of the psychology pick the gamble with the highest expected utility where: of decision making focuses on three topics that are X central to the study of choices: (1) choice under EUðXÞ 5 pðxÞuðxÞð3:2Þ uncertainty (such as deciding whether or not to buy x a lottery ticket, a stock, or an insurance policy), where the outcomes are uncertain; (2) choice under The function that maps actual wealth, x, on the certainty where the outcomes are known (such as x-axis into utility for wealth, u(x), is in this formulation deciding which car to buy); and finally (3) choice no longer linear but usually “concave,” for example, 5 θ θ across time (such as deciding whether to study in a power function of the form, u(x) x , where is a θ hopes of doing better in a distant exam or to, number less than or equal to 1. The exponent is thus instead, party tonight). The second part of this chap- a parameter that describes the curvature of this func- ter illustrates the newer style of computational pro- tion and serves as an index of an individual’s degree θ , cess models which describe the psychological and of risk aversion. Put another way 1 corresponds to neural processes in addition to predicting choices, money having diminishing marginal returns, a point and illustrates this class of models in detail using developed in Chapter 1. This idea of expected utility one important subclass that has had a great impact has been the dominant normative theory in economics, in neuroscience: diffusion models. in part because von Neumann and Morgenstern (1953) provided an intuitively appealing axiomatic founda- tion for expected utility (EU) maximization, which made it a normatively attractive decision criterion not MODELS OF RISKY CHOICE only for repeated decisions in the long run, but when extended by Savage (1954) also for unique risky Normative Origins decisions even when the true probabilities are not known to the decision maker. Here we gloss over the Most theories of choice are either normative models very foundational conceptual differences between the that advise people about how they should make classical economic approach of Bernoulli and the neo- choices, or descriptive models, portraying how they classical approach of von Neumann and Morgenstern actually make choices. The origins of normative that are the subject of Chapter 1. models of how to make choice under risk occurred in the eighteenth century, in response to questions presented by gambling. Recall that most gambles Descriptive Modifications consist of a set of outcomes and their associated probabilities. Imagine simply flipping a coin to dou- Starting as early as the 1950s, empirical evidence, ble your money, say an initial stake of $10, or lose however, began to cast doubt on EU as a descriptive it all. The coin flip gives each outcome a probability choice model (Allais, 1953). While these data did not of .5, and the two outcomes are either $0 or $20. The catch the attention of many economists, by the early early normative advice about how to choose between 1970s there were a significant number of empirical two gambles was simply to choose the one with the observations that could not be accounted for by highest expected payoff: expected utility (Kahneman and Tversky, 1979; see Wu et al., 2004 for a historical overview). While there had X been piecemeal attempts to account for each of the fail- EVðXÞ 5 pðxÞUx ð3:1Þ x ures of expected utility, prospect theory (Kahneman and Tversky, 1984; Kahneman and Tversky, 1979) where x is the payoff for each outcome, 1...X,andp is presented three major changes to expected utility the probability associated with that outcome. Thus, intended to account for many of these known failures NEUROECONOMICS MODELS OF RISKY CHOICE 37 as well as several new problems identified by Kahneman these related models share important properties with and Tversky (see the Appendix for a detailed descrip- expected value and expected utility theories: they define tion of prospect theory). These changes were: (1) intro- a mapping between characteristics of the objects under ducing a transformation relating objective probabilities consideration and their value, but are mute to the cogni- to subjective probabilities; (2) defining outcomes tive computations that may construct this mapping (utilities) not on total wealth as in expected utility but (Brandsta¨tter et al., 2006; Johnson et al., 2008), as in fact rather on gains and losses relative to a dynamic reference do most of the alternatives to this class of theory.