Preference, Belief, and Similarity Selected Writings Amos Tversky edited by Eldar Shafir Preference, Belief, and Similarity Preference, Belief, and Similarity Selected Writings Amos Tversky edited by Eldar Shafir Amos Tversky (1937–1996), a towering figure in cognitive and mathematical psychology, devoted his profes- 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- ically violated by the vagaries and consequences of human information processing. He created new areas of study and helped transform disciplines as varied as economics, law, medicine, political science, philosophy, and statistics. This book collects forty of Tversky’s articles, selected by him in collaboration with the editor during the last months of Tversky’s life. Included are several articles written with his frequent collaborator, Nobel Prize–winning economist Daniel Kahneman. Eldar Shafir is Professor of Psychology and Public Affairs at Princeton University. “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 intuitions go wrong. Is there a ‘hot hand’ in basketball? Is arthritis pain related to the weather? Why do we exaggerate certain risks? Why are some conflicts so hard to resolve? Tversky’s answers will surprise you. Indispensable reading, and full of implications, for everyone interested in social science.” —Cass R. Sunstein, Law School and Department of Political Science, University of Chicago “Amos Tversky’s research on preferences and beliefs has had a shattering and yet highly constructive influ- ence on the development of economics. The vague complaints of psychologists and dissident economists about the excessive rationality assumptions of standard economics, going back over a century, had little impact. It required the careful accumulation of evidence, the clear sense that Tversky did not misunder- stand what economists were assuming, and above all his formulation of useful alternative hypotheses to change dissatisfaction into a revolutionary change in perspective.” —Kenneth J. Arrow, Professor of Economics Emeritus, Stanford University “Amos Tversky’s work has produced an ongoing revolution in our understanding of judgment and choice. The articles in this book show why. They also show how: the articles are written with grace, wit, and a bril- liance that frequently verges on the pyrotechnic.” —Richard E. Nisbett, author of The Geography of Thought: How Asians and Westerners Think Differently . . . 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.” —George Akerlof, Koshland Professor of Economics, University of California, Berkeley, 2001 Nobel Laureate in Economic Sciences “It is deeply ironic that ‘similarity’ and ‘bounded rationality’ were two of the many topics that Amos Tversky studied—ironic because he seemed to be unboundedly rational and similar to no one. No one shared his combination of brilliance, precision, intuition, breadth, and enormous good humor. Few scholars change their own disciplines before they reach 40, as Tversky did, and even fewer then transform other disciplines, as he and Daniel Kahneman did for economics. Their influence on economics, recognized by the 2002 Nobel Prize, is still growing, and the discipline will never be the same. Nor will anyone who reads these papers: it 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 A Bradford Book The MIT Press Massachusetts Institute of Technology Cambridge, Massachusetts 02142 http://mitpress.mit.edu ,!7IA2G2-haajdb!:t;K;k;K;k 0-262-70093-X Tversky Shafir, editor tversky 12/16/03 12:58 PM Page 1 Preference, Belief, and Similarity Preference, Belief, and Similarity Selected Writings by Amos Tversky edited by Eldar Shafir A Bradfor d Book The MIT Press Cambridge, Massachusetts London, England 6 2004 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. This book was set in Times New Roman on 3B2 by Asco Typesetters, Hong Kong and was printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Tversky, Amos. Preference, belief, and similarity : selected writings / by Amos Tversky ; edited by Eldar Shafir. p. cm. ‘‘A Bradford book.’’ Includes bibliographical references and index. ISBN 0-262-20144-5 (alk. paper) — ISBN 0-262-70093-X (pbk. : alk. paper) 1. Cognitive psychology. 2. Decision making. 3. Judgment. 4. Tversky, Amos. I. Shafir, Eldar. II. Title. BF201 .T78 2003 153—dc21 2002032164 10987654321 Contents Introduction and Biography ix Sources xv SIMILARITY 1 Editor’s Introductory Remarks 3 1 Features of Similarity 7 Amos Tversky 2 Additive Similarity Trees 47 Shmuel Sattath and Amos Tversky 3 Studies of Similarity 75 Amos Tversky and Itamar Gati 4 Weighting Common and Distinctive Features in Perceptual and Conceptual Judgments 97 Itamar Gati and Amos Tversky 5 Nearest Neighbor Analysis of Psychological Spaces 129 Amos Tversky and J. Wesley Hutchinson 6 On the Relation between Common and Distinctive Feature Models 171 Shmuel Sattath and Amos Tversky JUDGMENT 187 Editor’s Introductory Remarks 189 7 Belief in the Law of Small Numbers 193 Amos Tversky and Daniel Kahneman 8 Judgment under Uncertainty: Heuristics and Biases 203 Amos Tversky and Daniel Kahneman 9 Extensional vs. Intuitive Reasoning: The Conjunction Fallacy in Probability Judgment 221 Amos Tversky and Daniel Kahneman 10 The Cold Facts about the ‘‘Hot Hand’’ in Bas ketball 257 Amos Tversky and Thomas Gilovich Editor’s Introductory Remarks to Chapter 11 267 11 The ‘‘Hot Hand’’: Statistical Reality or Cognitive Illusion? 269 Amos Tversky and Thomas Gilovich 12 The Weighing of Evidence and the Determinants of Confidence 275 Dale Gri‰n and Amos Tversky 13 On the Evaluation of Probability Judgments: Calibration, Resolution, and Monotonicity 301 Varda Liberman and Amos Tversky 14 Support The ory: A Nonextensional Representation of Subjective Probability 329 Amos Tversky and Derek J. Koehler 15 On the Belief That Arthritis Pain Is Related to the Weather 377 Donald A. Redelmeier and Amos Tversky 16 Unpacking, Repacking, and Anchoring: Advances in Support Theory 383 Yuval Rottenstreich and Amos Tversky PREFERENCE 403 Editor’s Introductory Remarks 405 Probabilistic Models of Choice 411 17 On the Optimal Number of Alternatives at a Choice Point 413 Amos Tversky 18 Substitutability and Similarity in Binary Choices 419 Amos Tversky and J. Edward Russo 19 The Intransitivity of Preferences 433 Amos Tversky 20 Elimination by Aspects: A Theory of Choice 463 Amos Tversky 21 Preference Trees 493 Amos Tversky and Shmuel Sattath Choice under Risk and Uncertainty 547 22 Prospect Theory: An Analysis of Decision under Risk 549 Daniel Kahneman and Amos Tversky vi Contents 23 On the Elicitation of Preferences for Alternative Therapies 583 Barbara J. McNeil, Stephen G. Pauker, Harold C. Sox, Jr., and Amos Tversky 24 Rational Choice and the Framing of Decisions 593 Amos Tversky and Daniel Kahneman 25 Contrasting Rational and Psychological Analyses of Political Choice 621 George A. Quattrone and Amos Tversky 26 Preference and Belief: Ambiguity and Competence in Choice under Uncertainty 645 Chip Heath and Amos Tversky 27 Advances in Prospect Theory: Cumulative Representation of Uncertainty 673 Amos Tversky and Daniel Kahneman 28 Thinking through Uncertainty: Nonconsequential Reasoning and Choice 703 Eldar Shafir and Amos Tversky 29 Conflict Resolution: A Cognitive Perspective 729 Daniel Kahneman and Amos Tversky 30 Weighing Risk and Uncertainty 747 Amos Tversky and Craig R. Fox 31 Ambiguity Aversion and Comparative Ignorance 777 Craig R. Fox and Amos Tversky 32 A Belief-Based Account of 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 Weighting in Judgment and Choice 845 Amos Tversky, Shmuel Sattath, and Paul Slovic 35 Anomalies: Preference Reversals 875 Amos Tversky and Richard H. Thaler Contents vii 36 Discrepancy between Medical Decisions for Individual Patients and for Groups 887 Donald A. Redelmeier and Amos Tversky 37 Loss Aversion in Riskless Choice: A Reference-Dependent Model 895 Amos Tversky and Daniel Kahneman 38 Endowment and Contrast in Judgments of Well-Being 917 Amos Tversky and Dale Gri‰ n 39 Reason-Based Choice 937 Eldar Shafir, Itamar Simonson, and Amos Tversky 40 Context-Dependence in Legal Decision Making 963 Mark Kelman, Yuval Rottenstreich, and Amos Tversky Amos Tversky’s Complete Bibliography 995 Index 1001 viii Contents Introduction and Biography Amos Tversky was a towering figure in the field of cognitive psychology and in the decision sciences. His research had enormous influence; he created new areas of study 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 who did not have the fortune to know him, and will provide a cherished memento to 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, but proved to be consequential once it accumulated across a number of such comparisons, yielding a reversal of preference between the first and the last. This was 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 processes involved in choices of that kind. In his now-famous model of similarity (chapter 1), Tversky made a number of simple psychol ogical assumptions: items are mentally represented as collect ions of features, with the similarity between them an increasing function of the features th at [...]... The contrast model expresses similarity between objects as a weighted Features of Similarity 15 di¤erence of the measures of their common and distinctive features, thereby allowing for a variety of similarity relations over the same domain The major constructs of the present theory are the contrast rule for the assessment of similarity, and the scale f, which reflects the salience or prominence of the. .. that the contrast model does not define a single similarity scale, but rather a family of scales characterized by di¤erent values of the parameters y, a, and b For example, if y ¼ 1 and a and b vanish, then Sða; bÞ ¼ fðA V BÞ; that is, the similarity between objects is the measure of their common features If, on the other hand, a ¼ b ¼ 1 and y vanishes then ÀSða; bÞ ¼ fðA À BÞ þ fðB À AÞ; that is, the. .. (from the second set) that di¤ers in complexity to use: ‘ The left figure is similar to the right figure,’’ or ‘ The right figure is similar to the left figure.’’ The positions of the stimuli were randomized so that p and q appeared an equal number of times on the left and on the right The results showed that in each one of the pairs, most of the subjects selected the form ‘‘q is similar to p.’’ Thus, the. .. formulated, therefore, in terms of the set-theoretical notion of a matching function rather than in terms of the geometric concept of distance In order to determine the functional form of the matching function, additional assumptions about the similarity ordering are introduced The major assumption of the theory (independence) is presented next; the remaining assumptions and the proof of the representation theorem... smaller than the sum of two others, and hence it cannot be readily refuted with ordinal or even interval data However, the triangle inequality implies that if a is quite similar to b, and b is quite similar to c, then a and c cannot be very dissimilar from each other Thus, it sets a lower limit to the similarity between a and c in terms of the similarities between a and b and between b and c The following... directional, and hence a and b may di¤er and symmetry need not hold If sða; bÞ is interpreted as the degree to which a is similar to b, then a is the subject of the comparison and b is the referent In such a task, one naturally focuses on the subject of the comparison Hence, the features of the subject are weighted more heavily than the features of the referent (i.e., a > bÞ Consequently, similarity. .. feature space and prove that the similarity ordering of object pairs coincides with the ordering of their contrasts, defined as linear combinations of the respective common and distinctive features Thus, the measure f and the contrast model are derived from qualitative axioms regarding the similarity of objects The nature of this result may be illuminated by an analogy to the classical theory of decision... chosen as the referent rather than the subject of similarity statements To test for asymmetry in judgments of similarity, we presented two groups of 67 subjects each with the same 16 pairs of figures and asked the subjects to rate (on a 20-point scale) the degree to which the figure on the left was similar to the figure on the right The two groups received identical booklets, except that the left and right... that theory, one starts with a set of prospects, characterized as probability distributions over some consequence space, and a preference order that is assumed to satisfy the axioms of the theory From these assumptions one derives a utility scale on the consequence space and proves that the preference order between prospects coincides with the order of their expected utilities Thus, the utility scale and. .. variety of similarity models that di¤er in the form of the matching function F and in the weights assigned to its arguments In order to apply and test the present theory in any particular domain, some assumptions about the respective feature structure must be made If the features associated with each object are explicitly specified, we can test the axioms of the theory directly and scale the features . Preference, Belief, and Similarity Selected Writings Amos Tversky edited by Eldar Shafir Preference, Belief, and Similarity Preference, Belief, and Similarity Selected Writings Amos. 12/16/03 12:58 PM Page 1 Preference, Belief, and Similarity Preference, Belief, and Similarity Selected Writings by Amos Tversky edited by Eldar Shafir A Bradfor d Book The MIT Press Cambridge, Massachusetts London,. reversal of preference between the first and the last. This was of theoretical significance since the transitivity of preferences is one of the funda- mental axioms of utility theory. At the same