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Amos Tversky, a cognitive psychologist, is regarded as a giant in the study of human judgment and decision making, and one of the founders of behavioural economics. Born on 16 March 1937 in Haifa, Israel, his father was a veterinarian and his mother was a social worker and member of the first Israeli Parliament and those following, for some 15 years. Tversky received his BA from the Hebrew University in Jerusalem in 1961, majoring in philosophy and psychology, and a Ph.D. in psychology from the University of Michigan in 1965.

The Early Work

Tversky’s early work in mathematical psychology focused on the study of individual choice behaviour and the analysis of psychological measurement, exploring almost from the beginning the surprising implications of simple and intuitively compelling psychological assumptions. In one early work, Tversky (1969) 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 differences on an important dimension were negligible between adjacent alternatives, but proved to be consequential once compounded across a number of options, yielding a reversal of preference between the first and the last. This pattern not only contradicted a fundamental assumption of utility theory; it also provided a revealing glimpse into the psychological processes involved in decisions of this kind.

For another example, Tversky’s (1977) highly influential model of similarity made a number of simple psychological assumptions: items are mentally represented as collections of features, with the similarity between items an increasing function of the features that they have in common, and a decreasing function of their distinct features. Feature weights are task-dependent, such that, for example, the features of the subject of comparison loom larger than the referent’s, and common features matter more in judgments of similarity, whereas distinctive features receive greater attention in judgments of dissimilarity. This simple and elegant theory was able to explain observed asymmetries in similarity judgments (A is more similar to B than B is to A), and the fact that item A may be perceived as quite similar to item B and item B quite similar to item C, but items A and C may be perceived as highly dissimilar. Foreshadowing the immensely elegant work to come, these early papers were predicated on the technical mastery of relevant normative theories, and explored simple and compelling psychological principles until their unexpected, and often striking, theoretical implications became apparent.

Another impressive project concerned the mathematical and axiomatic foundations of measurement, in the physical sciences, but especially in the study of behaviour. Although fundamental to modern science, measurement was long considered unproblematic. In fact, it represents non-trivial issues concerning the assignment of numbers to objects in terms of their structural correspondence. Our measurement models, for example, are often are not determined by the data. Tversky’s involvement in this project would stretch over two decades and result in three massive volumes (co-authored with Krantz, Luce, and Suppes 1971, 1989, 1990).

The Collaboration with Daniel Kahneman

Tversky’s long and extraordinarily influential collaboration with Daniel Kahneman began in 1969 and spanned the fields of judgment and decision making. Having recognized that intuitive predictions and likelihood estimates tend not to follow the principles of statistics or the laws of probability, Tversky and Kahneman (1974) embarked on the study of biases as a method for investigating judgmental heuristics. The beauty of the work was most apparent in the interplay of psychological intuition with normative theory, accompanied by memorable demonstrations. The research showed that judgments often violate basic normative principles despite the fact that people are quite sensitive to these principles’ normative appeal. An important theme in this work is a rejection of the claim that people are not able to grasp the relevant normative considerations. Rather, recurrent and systematic errors are attributed to people’s reliance on intuitive judgment and heuristic processes in situations where the applicability of normative criteria is not immediately apparent. The experimental demonstrations are noteworthy not only because they violate normative theory, but also because they contradict people’s own assumptions about how they make decisions.

Two early examples of judgmental heuristics illustrate this tension:

  1. 1.

    When presented with a description of Linda, a young, single, outspoken and very bright woman, who majored in philosophy, had participated in anti-nuclear demonstrations, and is concerned with issues of discrimination and social justice, most people think Linda is more likely to be a feminist bank teller than a bank teller – even though, of course, the likelihood of the latter must be greater than the former (since all feminist bank tellers are bank tellers).

  2. 2.

    When asked to estimate the number of seven-letter words on a typical page of English text, people are inclined to guess that there are fewer words whose penultimate letter is N than end in ING – even though the latter are necessarily a subset of the former.

In both cases, a heuristic judgment leads to what is known as the conjunction fallacy. In the first, people rely on the fact that Linda is more similar to a feminist bank teller than to a prototypical bank teller; in the second, frequency is judged via the ease with which examples can be brought to mind. In both cases, the reliance on intuitive heuristics leads people to ignore simple normative constraints that, upon reflection, they readily endorse.

In 1979, Kahneman and Tversky published their seminal paper on prospect theory. Although the theory is formally confined to the analysis of individual choice between binary monetary gambles, it incorporates fundamental insights that have revolutionized current theorizing about decision making more generally. Contrary to the notion of utility maximization, which focuses on final assets, the psychological carriers of value in prospect theory are gains and losses relative to some reference point, which is often the status quo. Diminishing sensitivity to greater amounts leads prospect theory’s value function to be concave for gains and convex for losses (that is, above and below the reference point, respectively), yielding risk aversion for gains and risk seeking for losses (except for very low probabilities, where these trends can reverse). Because prospects can often be framed as gains or as losses relative to some reference point, this can generate ‘framing effects’, wherein alternative descriptions trigger opposing risk attitudes and elicit discrepant preferences regarding the same final outcomes. For example, imagine being $300 richer than you are and having a choice between $100 for sure and an equal chance at $200 or nothing. Alternatively, imagine being $500 richer and having to choose between a sure $100 loss and an equal chance to lose $200 or nothing. Although the two scenarios offer the same final outcomes ($400 versus an equal chance at $300 or $500), people tend to prefer the certain $100 gain in the first and the chance of a greater loss or nothing in the second, thus expressing opposing preferences.

According to prospect theory, people are loss averse: the loss associated with giving up a good is greater than the pleasure associated with obtaining it. Loss aversion yields ‘endowment effects’ wherein the mere possession of a good can lead to higher valuation of it than if it were not in one’s possession (Kahneman et al. 1990), and it can create a general reluctance to negotiate or trade because the disadvantages of departing from the status quo loom larger than the advantages presented by possible alternatives (Samuelson and Zeckhauser 1988). Furthermore, the impact of probabilities in prospect theory is not linear; rather, it consists of a transformation of the relevant probabilities into ‘decision weights’ which capture the impact on decision makers, exhibited most clearly at the extremes of certainty and impossibility. For example, a reduction in the likelihood of a threatening outcome from.02 to 0 has a much greater impact on people (as exhibited, say, in their willingness to pay) than a comparable change in likelihoods from.67 to 65.

Later Work

Tversky returned to the study of judgment and in his work on support theory (Tversky and Koehler 1994), a theory of probabilistic judgment that formally distinguishes between events in the world and the manner in which they are mentally represented. Probabilities in support theory are attached not to events, as in standard models, but rather to descriptions of events, called hypotheses. Probability judgments are based on the support (strength of evidence) of the focal hypothesis relative to that of alternative, or residual, hypotheses. The theory distinguishes between explicit disjunctions, which are hypotheses that list their individual components (for example, ‘a car crash due to oil spill, or due to driver fatigue, or due to break failure’), and implicit disjunctions that do not (‘a car crash’). According to the theory, unpacking the description of an event from an implicit to an explicit disjunction generally increases its support and, hence, the perceived likelihood. As a result, alternative descriptions of an event can give rise to substantially different judgments.

A fundamental assumption underlying normative theories is the extensionality principle: options that are extensionally equivalent are assigned the same value, and extensionally equivalent events are assigned the same probability. Normative theories are concerned with options and events in the world: different descriptions of the same states are similarly evaluated. According to Tversky’s analyses, on the other hand, judgments and decisions are constructed, not merely revealed, during their elicitation, and their construction depends on the framing of the problem, the method of elicitation, and the valuations and attitudes that these trigger. The extensionality principle is deemed descriptively invalid because alternative decision contexts and alternative descriptions of options or events often produce systematically different judgments and preferences.

Behaviour, Tversky’s research made clear, is the outcome of normative ideals that people endorse upon reflection, combined with psychological processes that intrude upon and shape behaviour independently of any deliberative intent. These insights led to dramatic and memorable studies concerning, among others, the hot hand in basketball (Tversky and Gilovich 1989), the perceived relationship between weather and rheumatism (Redelmeier and Tversky 1996), money illusion (Shafir et al. 1997), self-deception (Quattrone and Tversky 1984), overconfidence (Griffin and Tversky 1992), and a variety of other economic, medical and political decisions. Tversky was an intellectual giant whose work had an exceptionally broad appeal, to economists, philosophers, statisticians, physicians, political scientists, sociologists and legal theorists, among others.

Tversky taught at Hebrew University (1966–78) and at Stanford University (1978–96), where he was the inaugural Davis–Brack Professor of Behavioral Sciences and Principal Investigator at the Stanford Center on Conflict and Negotiation. He spent leave periods at Harvard University, the Center for Advanced Studies in the Behavioral Sciences, the Center for Advanced Study at Hebrew University, and the Oregon Research Institute. After 1992 he 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 won many awards for diverse accomplishments. As a young officer in 1956, he earned Israel’s highest honour for bravery for rescuing a soldier who had frozen in panic after lighting an explosive charge. His dissertation, under the supervision of Clyde Coombs, won the University of Michigan’s Marquis Award. He won the Distinguished Scientific Contribution Award of the American Psychological Association in 1982, a MacArthur Prize in 1984, and the Warren Medal from the Society of Experimental Psychologists in 1995. He was a foreign member of the National Academy of Sciences, and a member of the Econometric Society and the American Academy of Arts and Sciences. He was awarded honorary doctorates by the University of Göteborg, the State University of New York at Buffalo, the University of Chicago, and Yale University.

Tversky was in the midst of an enormously productive time when he died of metastatic melanoma on 2 June 1996, at his home in Stanford, California. For a selection of his writings, as well as a complete bibliography, see Shafir (2004); for excellent collections of papers influenced by Tversky’s work on judgment and choice, respectively, see Gilovich et al. (2001), and Kahneman and Tversky (2000).

When it awarded Daniel Kahneman the 2002 Nobel Memorial Prize in Economic Sciences ‘for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty’, the Royal Swedish Academy of Sciences, which does not award prizes posthumously, took the unusual step of acknowledging Tversky in its Nobel citation, explaining that his joint work with Kahneman formulated alternative theories that better account for observed behaviour. Two months later, Tversky also posthumously won with Kahneman the prestigious 2003 Grawemeyer Award, which recognizes powerful ideas in the arts and sciences. The citation noted that it was ‘difficult to identify a more influential idea than that of Kahneman and Tversky in the human sciences’.

See Also

Selected Works

  • 1969. The intransitivity of preferences. Psychological Review 76: 31–48.

  • 1977. Features of similarity. Psychological Review 84: 327–352.

  • 1971. (With D.H. Krantz, R.D. Luce and P. Suppes.) Foundations of measurement: Vol. 1. Additive and polynomial representations. San Diego: Academic Press.

  • 1974. (With D. Kahneman.) Judgment under uncertainty: Heuristics and biases. Science 185: 1124–1131.

  • 1979. (With D. Kahneman.) Prospect theory: An analysis of decision under risk. Econometrica 47: 263–291.

  • 1984. (With G.A. Quattrone.) Causal versus diagnostic contingencies: On self-deception and on the voter’s illusion. Journal of Personality and Social Psychology 46: 237–248.

  • 1989. (With T. Gilovich.) The cold facts about the ‘hot hand’ in basketball. Chance 2(1): 16–21.

  • 1989. (With D.H. Krantz, R.D. Luce and P. Suppes.) Foundations of measurement: Vol. 2. Geometrical, threshold, and probabilistic representations. San Diego: Academic Press.

  • 1990. (With D.H. Krantz, R.D. Luce and P. Suppes.) Foundations of measurement: Vol. 3. Representation, axiomatization, and invariance. San Diego: Academic Press.

  • 1992. (With D. Griffin.) The weighing of evidence and the determinants of confidence. Cognitive Psychology 24: 411–435.

  • 1994. (With D.J. Koehler.) Support theory: A nonextensional representation of subjective probability. Psychological Review 101: 547–567.

  • 1996. (With D.A. Redelmeier.) On the belief that arthritis pain is related to the weather. Proceedings of the National Academy of Sciences 93: 2895–2896.

  • 1997. (With E. Shafir and P. Diamond.) On money illusion. Quarterly Journal of Economics 112: 341–374.

  • 2000. (With D. Kahneman, eds.) Choices, values, and frames. New York: Cambridge University Press/Russell Sage Foundation.