Amos Tversky

Amos Tversky
Born	March 16 1937(1937-03-16)
Died	June 2 1996 (aged 59)
Education	University of Michigan
Occupation	Economist, Behavioral Economics, Psychologist
Known for	Prospect theory

Amos Nathan Tversky, (Hebrew: עמוס טברסקי;) (1937, 1996 ) was a cognitive and mathematical psychologist, and a pioneer of cognitive science, a longtime collaborator of Daniel Kahneman, and a key figure in the discovery of systematic human cognitive bias and handling of risk.

Life

Amos Tversky was born in Haifa, Israel, on March 16, 1937, to parents who had emigrated from Poland and Russia. His father, Yosef Tversky, was a veterinarian and his mother, Genia, was a member of the Knesset from its establishment in 1948 until her death in 1964. Tversky was an officer in the paratroopers, an elite unit, eventually rising to captain and serving in three wars. He became a "legend" within his unit, after he was awarded Israel's highest honor for personal bravery during a 1956 border skirmish.

Tversky earned a bachelor's degree from Hebrew University in 1961 and his doctorate in 1965 from the University of Michigan, where he met and married his wife, Barbara, a fellow student in cognitive psychology. Barbara Tversky became a professor of cognitive psychology at Stanford.

After holding several teaching positions at Michigan, Harvard, and Hebrew University, Amos Tversky went to Stanford in 1970 as a fellow at the Center for Advanced Study in the Behavioral Sciences. He joined the Stanford psychology faculty in 1978. At the time of his death in 1996, he was the Davis Brack Professor of Behavioral Sciences in the Department of Psychology.

When he won a five-year MacArthur Foundation fellowship in 1984, Tversky said with typical modesty that much of what he had studied was already known to "advertisers and used car salesmen." His theoretical modeling, however, elucidated the basis for such phenomena as consumers becoming upset if a store charged a "surcharge" for using a credit card but being pleased if a store offered a "discount" for paying with cash.

Tversky was elected to the American Academy of Arts and Sciences in 1980 and as a foreign associate of the National Academy of Sciences in 1985. He won the American Psychological Association's award for distinguished scientific contribution in 1982. He also was awarded honorary doctorates by the University of Chicago, Yale University, the University of Goteborg (Sweden) and the State University of New York at Buffalo. He served on Stanford's Faculty Senate from 1990 until his death and was a member of the Academic Council's advisory board to the president and provost.

Amos Tversky died in 1996 from metastatic melanoma.

Work

Tversky's professional ideas and contributions revolutionized not only his own field of cognitive psychology (Tversky 1970), but that of economics as well. Much of his early work concerned the foundations of measurement. He was co-author of a three-volume treatise, Foundations of Measurement (Tversky et al 1971, 1989, 1990). His early work with Daniel Kahneman focused on the psychology of prediction and probability judgment. Later, he and Kahneman originated prospect theory to explain irrational human economic choices. Tversky also collaborated with Thomas Gilovich, Paul Slovic, and Richard Thaler on several key papers.

Tversky's way of thinking established, signifies, and outlined the new meaning he brought into the study of political science. There are three specified foci:

• judgment under uncertainty (Tversky and Kahneman 1972)
• decision-making under risk (Tversky and Kahneman 1979), and
• reason-based choice (Tversky and Kahneman 1981).

Two noteworthy points emerge from review and analysis of his work:

First, Tversky's work stresses the importance of reason-based choice, whereby individuals actively seek to generate, understand, and justify their decisions.

Second, Tversky's work suggests that people do not act even as if' they were the value-maximizers they are purported to be by more rationally based theories, such as expected utility. Rather, individuals function as problem-solvers who creatively construct their choices and resolve complex problems which require trade-offs between values and goals. In this way, preferences are created, rather than elicited, within the process and context of choice itself (McDermott 2001).

Approach to cognitive science

Tversky's early work on judgment began in Israel with another Israeli-born psychologist, Daniel Kahneman. They detailed 11 "cognitive illusions," or biasing characteristics of human judgment, and proposed systematic explanations for them (Tversky and Kahneman 1974). This publication triggered a "cascade of related research," as Science News wrote in a 1994 article that was tracing the history of research on reasoning. Decision theorists in economics, business, philosophy, and medicine as well as psychologists cited their work.

Tversky's later work on decision making, some of it with Kahneman, showed how people make choices under conditions of uncertainty. His experiments and theories were so precise and broadly applicable that teachers can make up their own experiments, try them in any class and be reasonably certain the students will demonstrate the judgment pattern that Tversky has specified.

In psychology, heuristics are simple, efficient rules of thumb that people use to make decisions, typically when facing complex problems or incomplete information (Tversky 1972). These rules work well under most circumstances, but in certain cases lead to systematic cognitive biases. For instance, people may tend to perceive more expensive beers as tasting better than inexpensive ones. This finding holds even when prices and brands are switched; putting the high price on the normally relatively inexpensive brand is enough to lead experimental subjects to perceive that beer as tasting better than the beer that is normally relatively expensive. This is known as the "price infers quality" bias.

Tversky was the more mathematically minded of the two, colleagues say, but he also was an astute observer of how people made decisions and was good at explaining his ideas to others.

"One of his most beautiful pieces in recent years started out from observations he made at a Stanford faculty meeting," said his friend and collaborator Kahneman. Tversky observed that the faculty wanted to make appointment offers to two people for two vacancies but had decided to hold up the offer to one until after they had made the offer to the first, whom they wanted more. When Tversky pointed out that there was no reason to hold off on the offer to the second (since two positions were available), the committee made both offers. Tversky went on to demonstrate similar behavior in a number of laboratory experiments.

Two examples of his approach to “perceived” probability follows:

EXAMPLE A: In a 1972 paper ( Tversky 1972 ), Tversky conducted an experiment using the following story: Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in antinuclear demonstrations.

Participants were then asked to rank sentences by their probability. Among the sentences were the following:

• (1) Linda is a bank teller.

• (2) Linda is a bank teller and is active in the feminist movement.

As anyone familiar with probability can tell you, sentence (1) is more probable than sentence two, because the second involves a conjunction of (1) and another statement. However, participants almost always (86%) ranked (2) over (1), indicating that they thought it was more probable. This is the so-called "conjunction fallacy," and the standard explanation is that given her description, Linda is more representative of feminist banktellers than banktellers in general. When people refer to the conjunction fallacy, or the Kahneman and Tversky experiment, they often call the results the Linda the Feminist Bankteller problem/experiment.

EXAMPLE B: In an eye-opening 1985 journal article ( Tversky, Gillovich, Vallone 1985 ), Tversky and two other authors set out to correct the perception, common among basketball fans and players alike, that players tend to get hot - i.e., they sometimes hit a string of shots that is markedly longer than what you would have expected on the basis of their overall shooting percentage. Interviews with the Philadelphia 76ers revealed that the players put a good deal of faith in the hot hand concept, regularly passing the ball to a teammate who had made a series of consecutive shots so that he could shoot again. The 76ers' own shooting guard, Andrew Toney, was widely cited by fans as a classic streak shooter. But Tversky would have none of it. Analyzing the field-goal records for home games of individual members of the 1980-1981 76ers (including the famously streaky Toney), Tversky and his coauthors failed to find statistical evidence of the hot hand phenomenon. The paper also examined the data for all pairs of free throws by the Boston Celtics during the 1980-1981 and 1981-1982 seasons. None of the players - not Larry Bird, not Robert Parrish, not Kevin McHale - demonstrated a statistical tendency to have the success of their first shot affect the success of their second shot ( McDermott 2001 ).

The spectacle that basketball fans profess to see, Tversky argued, is nothing more than the standard laws of chance, observed through the imperfect lens of human cognition. Specifically, he noted, people have a tendency to expect the overall odds of a chance process (say, the 50 percent distribution of heads on a flipped coin, or the 46 percent accuracy of Toney's field-goal shooting ) to apply to each and every segment of the process. For instance, when flipping a coin 20 times, it's not uncommon to see a string of four heads in a row. Yet when people are paying attention to a shorter sequence of the 20 coin flips, they are inclined to regard a string of four heads as nonrandom - as a hot streak - even though a strict back-and-forth of heads and tails throughout the 20 flips would be far less likely ( McDermott 2001.)

Prospect Theory

Amos Tversky called the studies of how people manage risk and uncertainty Prospect Theory for no other reason than that it is a catchy, attention-getting name. This is much like Richard Bellman calling his algorithm of multistage decision-making Dynamic Programming because programming was a hot topic at the time he was choosing a label. Kahneman and Tversky's theory, developed over a thirty year period, is however highly important in economics and especially in financial economics ( Tversky and Kahneman 1979. )

Tversky started their research investigating apparent anomalies and contradictions in human behavior. Subjects when offered a choice formulated in one way might display risk-aversion but when offerred essentially the same choice formulated in a different way might display risk-seeking behavior. For example, people may drive across town to save $5 on a $15 calculator but not drive across town to save $5 on a $125 coat ( Bernstein 1996 )

One very important result of Tversky ( and Kahneman ) work is demonstrating that people's attitudes toward risks concerning gains may be quite different from their attitudes toward risks concerning losses. For example, when given a choice between getting $1000 with certainty or having a 50% chance of getting $2500 they may well choose the certain $1000 in preference to the uncertain chance of getting $2500 even though the mathematical expectation of the uncertain option is $1250. This is a perfectly reasonable attitude that is described as risk-aversion. But Kahneman and Tversky found that the same people when confronted with a certain loss of $1000 versus a 50% chance of no loss or a $2500 loss do often choose the risky alternative. This is called risk-seeking behavior. This is not necessarily irrational but it is important for analysts to recognize the asymmetry of human choices ( Bernstein 1996)

Peter Bernstein ( Bernstein 1996 ) reports some interesting results from a Tversky study of people's, in this case 120 Stanford graduates, estimates of the probability of dying from various causes.

Estimates of Probabilities of Death From Various Causes
Cause	Subject Estimates	Statistical Estimates
Heart Disease	0.22	0.34
Cancer	0.18	0.23
Other Natural Causes	0.33	0.35
All Natural Causes	0.73	0.92
Accident	0.32	0.05
Homicide	0.10	0.01
Other Unnatural Causes	0.11	0.02
All Unnatural Causes	0.53	0.08

The above table represent the probability estimate of one group in the study. Another group was not asked to estimate the probabilities for separate causes but only the probability of death by natural versus unnatural causes. The probability estimate of a natural death by this second group was 0.58, significantly lower than when the subjects considered each cause separately. The second group's estimate of an unnatural death was 0.32, again significantly lower than for the first group. The most notable aspect of the estimates is that the subjects significantly underestimated the probabilities for natural causes and vastly overestimated the probabilities for unnatural causes. This indicates that probably people give more attention to worrying about the unnatural dangers and not enough to the natural dangers ( Bernstein 1996 ).

Economics and law

The core of the economic analysis of law is a microeconomic approach defined by the Coase Theorem. The model of the individual is homo economicus. In Gary Becker's words:

"….All human behavior can be viewed as involving participants who…….maximize their utility from a stable set of preferences and accumulate an optimal amount of information and other inputs in a variety of markets…." (Becker, 1998: 3-4).

The Coase Theorem, which predicts how economically rational individuals will behave in free markets, is particularly important to legal rules and procedures. It asserts that, in the absence of transaction costs, no matter on whom the costs or liabilities of engaging in an activity are imposed, the parties will bargain to achieve the socially optimal level of that activity ( Brest 2006.)

This is pretty well what ruled the so called “law in economics” even though some of its proponents—Herbert Simon for one ( Simon 1955:99-118)—acknowledged that individuals do not always make rational choices but choices “boundedly rational.” But if humans were only "boundedly rational," the bounds were not very constraining and, more important, they did not bias decisions in any systematically predictable manner.

And then came Amos Tversky and Daniel Kahneman. While the, so-called, "behavioral law and economics" has not replaced the neoclassical tradition - and indeed has been strongly resisted by the neoclassicists - it has nevertheless been applied to virtually every area of the law, both to explain behavior and prescribe normative substantive and procedural rules ( Brest 2006.)

In recent years, a purely cognitive explanation of the phenomenon has been supplemented by one that focuses on affect. Cass Sunstein, a professor of law at Chicago, has coined the term probability neglect to describe how, when emotions run high - for example, when contemplating dreadful risks - people tend to greatly overweight probabilities or to ignore them altogether and focus only on the horrific, worst-case outcome. Indeed, affect is playing an increasingly important role in behavioral economics more broadly - for example, in understanding dynamically inconsistent preferences or hyperbolic discounting. Although this was not the major focus of Amos Tversky's work, the lines of thought certainly trace back to him, for example through the pioneering work of his collaborator Paul Slovic ( ibid. ).

EXAMPLE: Imagine you are a member of a jury judging a hit-and-run driving case. A taxi hit a pedestrian one night and fled the scene. The entire case against the taxi company rests on the evidence of one witness, an elderly man who saw the accident from his window some distance away. He says that he saw the pedestrian struck by a blue taxi. In trying to establish her case, the lawyer for the injured pedestrian establishes the following facts:

• 1. There are only two taxi companies in town, 'Blue Cabs' and 'Black Cabs'. On the night in question, 85% of all taxis on the road were black and 15% were blue.

• 2. The witness has undergone an extensive vision test under conditions similar to those on the night in question, and has demonstrated that he can successfully distinguish a blue taxi from a black taxi 80% of the time.

If you were on the jury, how would you decide?

If you are at all typical, faced with eye-witness evidence from a witness who has demonstrated that he is right 4 times out of 5, you might be inclined to declare that the pedestrian was indeed hit by a blue taxi, and assign damages against the Blue Taxi Company. Indeed, if challenged, you might say that the odds in favor of the Blue Company being at fault were exactly 4 out of 5, those being the odds in favor of the witness being correct on any one occasion.

The facts are quite different. Based on the data supplied, the mathematical probability that the pedestrian was hit by a blue taxi is only 0.41, or 41%. Less than half. In other words, the pedestrian was more likely to have been hit by a black taxi than a blue one. The error in basing your decision on the accuracy figures for the witness is that this ignores the overwhelming probability, based on the figures, that any taxi in the town is likely to be black. If the witness had been unable to identify the color of the taxi, but had only been able to state—with 100% accuracy, let us suppose—that the accident was caused by a taxi, then the probability that it had been a black taxi would have been 85%, the proportion of taxis in the town that are black. So before the witness testifies to the color, the chances are low—namely 15%—that the taxi in question was blue. This figure is generally referred to as the prior probability, the probability based purely on the way things are, not the particular evidence pertaining to the case in question. When the witness then testifies as to the color, that evidence increases the odds from the 15% prior probability figure, but not all the way to the 80% figure of the witness's tested accuracy. Rather the reliability figure for the witness's evidence must be combined with the prior probability to give the real probability. The exact mathematical manner in which this combination is done is known as 'Bayes' law', which gives the answer to be 41% ( Devlin 1997.)

Comparative Ignorance

Tversky and Fox ( Tversky 1995) addressed ambiguity aversion, the idea that people do not like ambiguous gambles or choices with ambiguity, with the comparative ignorance framework. Their idea was that people are only ambiguity averse when their attention is specifically brought to the ambiguity by comparing an ambiguous option to an unambiguous option. For instance, people are willing to bet more on choosing a correct colored ball from an urn containing equal proportions of black and red balls than an urn with unknown proportions of balls when evaluating both of these urns at the same time. However, when evaluating them separately, people are willing to bet approximately the same amount on either urn. Thus, when it is possible to compare the ambiguous gamble to an unambiguous gamble people are averse, but not when one is ignorant of this comparison.

One of the other common blunders of reasoning that Tversky discovered is the tendency to assess the frequency of a given event by how easy it is to think of examples of that event. Most people will estimate that there are more English words that begin with the letter k than those whose third letter is k - even though the opposite is true - simply because it's easier to think of examples of the former ( Brest 2006.)

Legacy

There is a famous Tversky quote:

“….It's what I do for a living: debugging human intuition. If you look at people as intuitive scientists, you find that we are very good at pattern generation, we are very good at generating hypotheses. It's just that we are not very good at all at testing hypotheses….” (Amos Tversky <http: //www.geom. umn.edu/locate/chance> )

With this in mind there is no wonder that most of the time Tversky's role in reshaping the cognitive sciences was in convincing economists to pay attention to what people actually do instead of what they would do if they behaved rationally. When he won a five-year MacArthur Foundation fellowship in 1984, Tversky said with typical modesty that much of what he had studied was already known to "advertisers and used car salesmen but not to economists."

Here is an example of what he was talking about. If there is a 10% chance that you will buy the blue Chevy when the salesman shows only that one car, then you will have a greater than 10% chance of buying it when the salesman shows you both the blue Chevy and a green Ford at same price but less desirable to you then the Chevy. A good car salesman would never show you just one car ( Lowenstein 1966, June 6.)

His theoretical modeling and carefully designed experiments, however, elucidated the basis for such phenomena as consumers getting upset if a store charged a "surcharge" for using a credit card but being pleased if a store offered a "discount" for paying with cash.

Another point came up in discussing the effect of Tversky's work in terms of behavioral economics applied to financial markets. This includes challenges to the efficient market hypothesis. The work of economists Robert Schelling and Richard Thaler is highlighted. Thaler observes that in 1926, when a ticket to the movies cost 25 cents, the average share on the Big Board was $35. It was still ( in 1996 ) , roughly, $35. Investors apparently like it that way. But there is no logic to it ( Lowenstein 1966, June 13.)

"…He certainly changed my life, applying just the concept that people's reasoning is imperfect, susceptible to error and amenable to corrective procedures….," said Donald Redelmeier, a physician at the University of Toronto who did research with Tversky. Tversky's and Kahneman's work on "framing" the idea that small differences in how data are presented to people have a substantial effect on their decisions has influenced the way doctors view informed consent from patients for medical procedures, according to Redelmeier and Barbara McNeil, the Ridley Watts Professor of Health Care Policy at Harvard. McNeil worked with Tversky on what she refers to as the 1 percent99 percent problem. One and 99 add up to 100, so that if someone is told he or she has a 1 percent chance of dying during a given medical procedure, that person also has a 99 percent chance of living. Their studies showed that people will be more optimistic or pessimistic about the procedure, depending upon which way the information was stated to them. "At a time when medical technology has advanced and patients are being asked to make more decisions about medical options, this is even more important than it was in 1980" when the research was done, McNeil said ( <960605tversky.sit>.)

Daniel Kahneman received the Nobel Prize 2002 for the work he did in collaboration with Amos Tversky, who would have no doubt shared in the prize had he been alive. Kahneman actually devoted substantial part of his acceptance speech to Tversky expressing regret that his longtime collaborator Amos Tversky wasn't able to share the distinction with him. A parallel would be just as Beatles fans couldn't fully appreciate the 1997 knighting of Sir Paul McCartney in the absence of the late John Lennon, so the announcement of 2002 Nobel Memorial Prize in Economic Science felt incomplete.

To summarize, Amos Tversky, a cognitive psychologist, was a dominant figure in decision research and a leading psychological theorist who seriously challenged economic theory by showing that people frequently do not behave rationally to maximize their welfare. His work on the limits of human rationality also had a major impact on philosophy, statistics, political science, law and medicine.

His work had a great impact on economics, said Kenneth Arrow, professor emeritus of economics, because he tested hypotheses of rationality that are central to predicting how economies behave. "...The hypothesis of rational behavior has been central to economics, though always held with some discomfort....," Arrow said from All Souls College, where he is on sabbatical. "...Previous criticism of economic postulates by psychologists had always been brushed off by economists, who argued, with some justice, that the psychologists did not understand the hypotheses they criticized. No such defense was possible against Amos' work....," he said. ( Arrow, www.stanfordu.edu/ dept/news/ pr/96/ 960605tversky.html )

Major publications

• Tversky, Amos, Coombs, C. H., and Robyn Dawes,, Mathematical psychology: An elementary introduction, Englewood Cliffs, N.J: Prentice-Hall, 1970
• Tversky, A., D. Kahneman, "Judgment under Uncertainty: Heuristics and Biases,"

Science, New Series, Vol. 185, No. 4157, 1974, pp. 1124-1131

• Tversky, A. and D.Kahneman, "Prospect theory: An analysis of decision making under risk," Econometrica, Vol. 47, No. 2., 1979, pp. 263-292 ( NOTE: The most cited article in the history of this premier economic journal and one of the most cited articles anywhere ever )
• Tversky, A., Kahneman, D. and P. Slovic, Judgement under uncertainty - Heuristics and biases, Cambridge University Press, Cambridge, 1981
• Tversky, A. and D. Kahneman "The Framing of Decisions and the Psychology of Choice," Science, 211, 1981:453-58
• Tversky, A., Gilovich, T., and R. Vallone, "The hot hand in basketball: On the misperception of random sequences," Cognitive Psychology 17, 295-314, 1985
• Tversky, Amos, Bell, D. E. and H. Raiffa, Decision making: Descriptive, normative, and prescriptive interactions, Cambridge and New York: Cambridge University Press, 1988

References

ISBN links support NWE through referral fees

• Becker, G. S., The Economic Approach to Human Behavior (5 ed.). Chicago: University of Chicago Press, 1998
• Bernstein, Peter, Against the Gods: The Remarkable Story of Risk, John Wiley & Sons, New York, 1996
• Brest, Paul,“Amos Tversky's contributions to legal scholarship,” Judgment and Decision Making, vol. 1, no. 2, November 2006, pp. 174-178.
• Devlin, Keith, Goodbye Descartes: The End of Logic and the Search for a New Cosmology of Mind, John Wiley and Sons, 1997
• Lowenstein, Roger “Outsider who challenged dismal science,” Wall Street Journal, 6 June 1996, C1
• Lowenstein, Roger “Sure, markets are rational, just like life,” Wall Street Journal, 13 June 1996, C1
• McDermott, Rose, "The Psychological Ideas of Amos Tversky and Their Relevance for Political Science," Journal of Theoretical Politics, Vol. 13, No. 1, 5-33, 2001
• Simon, H. A., Behavioral Model of Rational Choice, The Quarterly Journal of Economics, Vol. 69, No. 1.,1955, pp. 99-118.
• Tversky, A., D.H. Krantz, R.D. Luce, and P. Suppes, Foundations of measurement, volume 1: Additive and polynomial representations, Academic Press, New York, 1971
• Tversky, A., D.H. Krantz, R.D. Luce, and P. Suppes, Foundations of measurement, volume 2:

Geometrical, threshold and probabilistic representations, Academic Press, New York, 1989

• Tversky, A., D.H. Krantz, R.D. Luce, and P. Suppes, Foundations of measurement, volume 3:

Representation, axiomatisation and invariance, Academic Press, New York, 1990

• Tversky, A. and D.Kahneman, "Subjective probability: A judgment of representativeness," Cognitive Psychology, 3:430–454, 1972; see also Tversky, A. and Kahneman, D., "Extension versus intuititve reasoning: The conjunction fallacy in probability judgment," Psychological Review, 90, 293-315, 1983
• Tversky, A., and R.H. Thaler,"Preference Reversals" in R. H. Thaler, The Winner's Curse: Paradoxes and Anomalies of Economic Life, Princeton U. Press, pp. 79-91, 1992
• Tversky, A. < http://www.geom.umn.edu/locate/chance>
• Tversky, A., Craig R. Fox, "Ambiguity Aversion and Comparative Ignorance," Quarterly Economic Jopurnal, vol. 110, No. pp.585-603, 1995
• Tversky, A. and Daniel Kahneman, (editors), Choices, Values, and Frames, Cambridge University Press, 2000

External links

• Stanford Faculty Senate Memorial Resolution (PDF)
• The man who wasn't there Boston Globe.
• Daniel Kahneman – Autobiography
• Amos Tversky, leading decision researcher, dies at 59 Stanford University News Service.

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