tversky 12/16/03 12:58 PM Page 1 Preference, Belief, and Similarity T Selected Writings v e Amos Tversky r edited by Eldar Shafir s k Amos Tversky (1937–1996), a towering figure in cognitive and mathematical psychology, devoted his profes- y sional life to the study of similarity, judgment, and decision making. He had a unique ability to master the technicalities of normative ideals and then to intuit and demonstrate experimentally how they are systemat- P ically violated by the vagaries and consequences of human information processing. He created new areas of r study and helped transform disciplines as varied as economics, law, medicine, political science, philosophy, e and statistics. f This book collects forty of Tversky’s articles, selected by him in collaboration with the editor during the e r last months of Tversky’s life. Included are several articles written with his frequent collaborator, Nobel e Prize–winning economist Daniel Kahneman. n Preference, Belief, and Similarity Eldar Shafir is Professor of Psychology and Public Affairs at Princeton University. c e “Amos Tversky was one of the most important social scientists of the last century. This extraordinary collec- , tion demonstrates his range and brilliance, and in particular his genius for showing how and why human B intuitions go wrong. Is there a ‘hot hand’ in basketball? Is arthritis pain related to the weather? Why do we e exaggerate certain risks? Why are some conflicts so hard to resolve? Tversky’s answers will surprise you. l Indispensable reading, and full of implications, for everyone interested in social science.” i e —Cass R. Sunstein, Law School and Department of Political Science, University of Chicago f , “Amos Tversky’s research on preferences and beliefs has had a shattering and yet highly constructive influ- a Selected Writings ence on the development of economics. The vague complaints of psychologists and dissident economists n about the excessive rationality assumptions of standard economics, going back over a century, had little d impact. It required the careful accumulation of evidence, the clear sense that Tversky did not misunder- S stand what economists were assuming, and above all his formulation of useful alternative hypotheses to Amos Tversky i change dissatisfaction into a revolutionary change in perspective.” m —Kenneth J. Arrow, Professor of Economics Emeritus, Stanford University i l “Amos Tversky’s work has produced an ongoing revolution in our understanding of judgment and choice. a The articles in this book show why. They also show how: the articles are written with grace, wit, and a bril- r liance that frequently verges on the pyrotechnic.” it —Richard E. Nisbett, author of The Geography of Thought: How Asians and Westerners Think Differently . . . y and Why “Amos Tversky may have shown that basketball players do not have ‘hot hands,’ but he proved the opposite for psychologists. Tversky always made his basket, and in the process changed psychology, and also eco- nomics, forever.” S —George Akerlof, Koshland Professor of Economics, University of California, Berkeley, 2001 Nobel Laureate h in Economic Sciences a f i “It is deeply ironic that ‘similarity’ and ‘bounded rationality’ were two of the many topics that Amos Tversky r studied—ironic because he seemed to be unboundedly rational and similar to no one. No one shared his , e combination of brilliance, precision, intuition, breadth, and enormous good humor. Few scholars change d their own disciplines before they reach 40, as Tversky did, and even fewer then transform other disciplines, i t as he and Daniel Kahneman did for economics. Their influence on economics, recognized by the 2002 Nobel o Prize, is still growing, and the discipline will never be the same. Nor will anyone who reads these papers: it r is impossible to read Tversky without changing the way you think.” —Richard H. Thaler, Robert P. Gwinn Professor of Economics and Behavioral Science, University of Chicago “This collection offers the best of Tversky, the best of the best. It is amazing how many of these articles are already classics, not only in the fields of choice and decision making, but in psychology in general.” —Edward E. Smith, Arthur W. Melton Professor of Psychology, University of Michigan edited by Eldar Shafir A Bradford Book 0-262-70093-X The MIT Press ,!7IA2G2-haajdb!:t;K;k;K;k Massachusetts Institute of Technology Cambridge, Massachusetts 02142 http://mitpress.mit.edu Preference, Belief, and Similarity Preference, Belief, and Similarity Selected Writings by Amos Tversky edited by Eldar Shafir A BradfordBook The MIT Press Cambridge, Massachusetts London, England 62004MassachusettsInstituteofTechnology Allrightsreserved.Nopartofthisbookmaybereproducedinanyformbyanyelectronicormechanical means(includingphotocopying,recording,orinformationstorageandretrieval)withoutpermissionin writingfromthepublisher. ThisbookwassetinTimesNewRomanon3B2byAscoTypesetters,HongKongandwasprintedand boundintheUnitedStatesofAmerica. LibraryofCongressCataloging-in-PublicationData Tversky,Amos. Preference,belief,andsimilarity:selectedwritings/byAmosTversky;editedbyEldarShafir. p. cm. ‘‘ABradfordbook.’’ Includesbibliographicalreferencesandindex. ISBN0-262-20144-5(alk.paper)—ISBN0-262-70093-X(pbk.:alk.paper) 1.Cognitivepsychology. 2.Decisionmaking. 3.Judgment. 4.Tversky,Amos. I.Shafir,Eldar. II.Title. BF201 .T78 2003 153—dc21 2002032164 10 9 8 7 6 5 4 3 2 1 Contents Introduction and Biography ix Sources xv SIMILARITY 1 Editor’sIntroductory Remarks 3 1 Featuresof Similarity 7 Amos Tversky 2 Additive SimilarityTrees 47 ShmuelSattath and Amos Tversky 3 Studies of Similarity 75 Amos Tverskyand ItamarGati 4 WeightingCommonand DistinctiveFeatures inPerceptual and 97 Conceptual Judgments Itamar Gati and Amos Tversky 5 NearestNeighbor Analysis ofPsychological Spaces 129 Amos Tverskyand J.Wesley Hutchinson 6 On theRelation between Common and DistinctiveFeatureModels 171 ShmuelSattath and Amos Tversky JUDGMENT 187 Editor’sIntroductory Remarks 189 7 Belief in theLaw of Small Numbers 193 Amos Tverskyand Daniel Kahneman 8 Judgment under Uncertainty: Heuristics andBiases 203 Amos Tverskyand Daniel Kahneman 9 Extensional vs.Intuitive Reasoning: The Conjunction Fallacy in 221 Probability Judgment Amos Tverskyand Daniel Kahneman 10 The Cold Factsaboutthe ‘‘Hot Hand’’ inBasketball 257 Amos Tverskyand Thomas Gilovich Editor’sIntroductory Remarksto Chapter11 267 vi Contents 11 The ‘‘HotHand’’: Statistical Reality orCognitive Illusion? 269 Amos Tversky and Thomas Gilovich 12 The Weighing ofEvidenceandthe Determinants ofConfidence 275 Dale Gri‰n and Amos Tversky 13 On theEvaluation of Probability Judgments: Calibration, Resolution, 301 and Monotonicity Varda Liberman and Amos Tversky 14 SupportTheory:A NonextensionalRepresentationof Subjective 329 Probability Amos Tversky and Derek J. Koehler 15 On theBelief That ArthritisPain Is Related to theWeather 377 Donald A. Redelmeier and Amos Tversky 16 Unpacking, Repacking, and Anchoring: Advances inSupport Theory 383 Yuval Rottenstreich and Amos Tversky PREFERENCE 403 Editor’s Introductory Remarks 405 Probabilistic Models of Choice 411 17 On theOptimal Numberof Alternatives ata Choice Point 413 Amos Tversky 18 Substitutability and Similarityin Binary Choices 419 Amos Tversky and J.Edward Russo 19 The Intransitivity of Preferences 433 Amos Tversky 20 Elimination by Aspects: ATheory of Choice 463 Amos Tversky 21 Preference Trees 493 Amos Tversky and ShmuelSattath Choiceunder Risk and Uncertainty 547 22 Prospect Theory:An Analysisof Decision under Risk 549 Daniel Kahneman and Amos Tversky Contents vii 23 On theElicitation of Preferences forAlternative Therapies 583 Barbara J.McNeil, Stephen G. Pauker,HaroldC. Sox, Jr., and Amos Tversky 24 Rational Choice and theFraming of Decisions 593 Amos Tverskyand Daniel Kahneman 25 Contrasting Rational andPsychological Analyses of Political Choice 621 George A. Quattrone and Amos Tversky 26 Preference and Belief:Ambiguity and Competence in Choice under 645 Uncertainty Chip Heath and Amos Tversky 27 Advancesin Prospect Theory:Cumulative Representationof 673 Uncertainty Amos Tverskyand Daniel Kahneman 28 Thinkingthrough Uncertainty: Nonconsequential Reasoning and 703 Choice Eldar Shafir and Amos Tversky 29 ConflictResolution: ACognitive Perspective 729 Daniel Kahneman and Amos Tversky 30 WeighingRisk and Uncertainty 747 Amos Tverskyand Craig R. Fox 31 Ambiguity AversionandComparative Ignorance 777 Craig R. Fox and Amos Tversky 32 ABelief-Based Accountof Decision under Uncertainty 795 Craig R. Fox and Amos Tversky Contingent Preferences 823 33 Self-Deception and the Voter’s Illusion 825 George A. Quattrone and Amos Tversky 34 Contingent Weightingin JudgmentandChoice 845 Amos Tversky,ShmuelSattath, and Paul Slovic 35 Anomalies: Preference Reversals 875 Amos Tverskyand Richard H. Thaler viii Contents 36 Discrepancy between MedicalDecisions for Individual Patientsand for 887 Groups Donald A. Redelmeier and Amos Tversky 37 LossAversion inRisklessChoice: AReference-DependentModel 895 Amos Tversky and Daniel Kahneman 38 Endowment andContrastin Judgments ofWell-Being 917 Amos Tversky and Dale Gri‰n 39 Reason-Based Choice 937 EldarShafir,Itamar Simonson,and Amos Tversky 40 Context-Dependence inLegal Decision Making 963 MarkKelman,Yuval Rottenstreich, and Amos Tversky Amos Tversky’sComplete Bibliography 995 Index 1001 Introduction and Biography Amos Tversky was a towering figure in the field of cognitive psychology and in the decisionsciences.Hisresearchhadenormousinfluence;hecreatednewareasofstudy and helped transform related disciplines. His work was innovative, exciting, aes- thetic, and ingenious. This book brings together forty of Tversky’s original articles, which he and the editor chose together during the last months of Tversky’s life. Because it includes only a fragment of Tversky’s published work, this book cannot provide a full sense of his remarkable achievements. Instead, this collection of favorites is intended to capture the essence of Tversky’s phenomenal mind for those whodidnothavethefortunetoknowhim,andwillprovideacherishedmementoto those whose lives he enriched. Tversky was born on March 16, 1937, in Haifa, Israel. His father was a veterinar- ian, and his mother was a social worker and later a member of the first Israeli Parliament. He received his Bachelor of Arts degree, majoring in philosophy and psychology, from Hebrew University in Jerusalem in 1961, and his Doctor of Phi- losophy degree in psychology from the University of Michigan in 1965. Tversky taught at Hebrew University (1966–1978) and at Stanford University (1978–1996), where he was the inaugural Davis-Brack Professor of Behavioral Sciences and Prin- cipal Investigator at the Stanford Center on Conflict and Negotiation. After 1992 he also held an appointment as Senior Visiting Professor of Economics and Psychology and Permanent Fellow of the Sackler Institute of Advanced Studies at Tel Aviv University. Tversky wrote his dissertation, which won the University of Michigan’s Marquis Award, under the supervision of Clyde Coombs. His early work in mathematical psychology focused on the study of individual choice behavior and the analysis of psychological measurement. Almost from the beginning, Tversky’s work explored the surprising implications of simple and intuitively compelling psychological assumptions for theories that, until then, seemed self-evident. In one oft-cited early work (chapter 19), Tversky showed how a series of pair-wise choices could yield intransitive patterns of preference. To do this, he created a set of options such that the di¤erence on an important dimension was negligible between adjacent alter- natives,butprovedtobeconsequentialonceitaccumulatedacrossanumberofsuch comparisons,yieldingareversalofpreferencebetweenthefirstandthelast.Thiswas of theoretical significance since the transitivity of preferences is one of the funda- mental axioms of utility theory. At the same time, it provided a revealing glimpse into the psychological processesinvolved inchoices of thatkind. In his now-famous model of similarity (chapter 1), Tversky made a number of simple psychological assumptions: items are mentally represented as collections of features, with the similarity between them an increasing function of the features that