Amos Tversky

Amos Tversky was a rising star in decision research when Daniel Kahneman invited him to speak at a seminar at the Hebrew University of Jerusalem in 1969. Thirty-two years old at the time, Tversky was already regarded by many acquaintances as the most intelligent person they had ever met. He was brilliant, voluble, and charismatic, with a perfect memory for jokes and an exceptional talent for using humor to make an argument. The meeting became the decisive beginning of the research partnership that would reshape modern thinking about judgment, uncertainty, and choice.

Identity and Introduction

Tversky entered Kahneman’s seminar carrying a question from an ongoing program at the University of Michigan: whether people were good intuitive statisticians. The comparison was with intuitive grammar. A four-year-old can speak according to grammatical rules without knowing that those rules exist; the question was whether people possessed a similarly reliable, unselfconscious grasp of basic statistical principles. Tversky and the class initially considered a qualified yes, but their lively discussion led them toward a qualified no.

The issue quickly became personal. Although both researchers had taught and used statistics for years, they recognized that their own intuitions were poor guides to the reliability of results based on small samples. They were too ready to believe findings supported by inadequate evidence and too willing to collect too few observations in their own research. At Café Rimon in Jerusalem, Tversky and Kahneman planned a survey to discover whether other sophisticated researchers suffered from the same weakness.

Tversky gathered responses from experts attending a meeting of the Society of Mathematical Psychology, including the authors of two statistical textbooks. The results were disquieting: the experts, like Tversky and Kahneman themselves, greatly overstated the likelihood that a small-sample experiment would successfully replicate its original result and gave poor advice to a fictitious graduate student about the number of observations she should collect. Expertise did not produce an intuitive command of statistics. Even statisticians were not good intuitive statisticians.

The Collaboration with Daniel Kahneman

The study became more than an empirical project because Tversky and Kahneman discovered that they enjoyed working together. Tversky’s humor made their long hours of work continuously amusing, and their shared pleasure made them unusually patient. They could pursue an idea toward perfection without the boredom that often turns criticism into impatience. Their working relationship was not free of argument: both were critical, and Tversky was even more argumentative than Kahneman. Yet during the collaboration neither dismissed the other’s ideas out of hand.

Their strengths were sharply complementary. Tversky was the more logical thinker, oriented toward theory and possessed of an unfailing sense of direction. Kahneman was more intuitive and rooted in the psychology of perception, a field from which the pair borrowed many ideas. They were similar enough to understand one another easily and different enough to surprise one another. Tversky could often see the point of Kahneman’s vague ideas more clearly than Kahneman himself could.

For fourteen years, the collaboration became the focus of both men’s lives. They spent much of their working days together, often walking through Jerusalem, and treated research as an extended conversation. They invented questions, examined their immediate answers, and treated each question as a small experiment. Their aim was not initially to find the formally correct answer to a statistical problem, but to identify the intuitive answer—the first response that came to mind, even when they already knew it might be wrong.

This method depended on their shared intuitions. When Tversky and Kahneman independently arrived at the same response, they believed that many other people would probably share it as well, and they could then design experiments to demonstrate its effects. Their private errors became instruments of public inquiry. Even an amusing exercise in which they assigned future professions to toddlers—an argumentative three-year-old as a lawyer, a nerdy child as a professor, an empathetic and mildly intrusive child as a psychotherapist—helped them recognize that predictions were being governed by resemblance to cultural stereotypes.

Heuristics, Biases, and Statistical Reasoning

Tversky and Kahneman spent several years studying biases in intuitive thinking across tasks involving probability assignment, forecasting, hypothesis assessment, and frequency estimation. Their central achievement was to show that ordinary errors were not random lapses caused only by emotion. They arose from the design of the cognitive machinery itself and could therefore be studied as systematic, predictable phenomena.

Their article “Judgment Under Uncertainty: Heuristics and Biases,” published in Science during the fifth year of their collaboration, described simplifying shortcuts of intuitive thought and explained roughly twenty biases as expressions of those heuristics. The article challenged two assumptions broadly accepted among social scientists in the 1970s: that people were generally rational and that departures from rationality were mainly produced by emotions such as fear, affection, or hatred. Tversky and Kahneman instead documented systematic errors in the thinking of normal people.

The program identified three central heuristics. Representativeness was used when people judged whether an object or event belonged to a class or process. Availability was used when they estimated the frequency of a class or the plausibility of a development by asking, implicitly, how easily examples or scenarios came to mind. Adjustment from an anchor shaped numerical prediction when a relevant starting value was available. These shortcuts were economical and often effective, but they also produced recurring errors.

The same framework explained why an apparently difficult question could receive an immediate answer. When a satisfactory answer to a hard target question was not quickly available, System 1 substituted a related heuristic question that was easier to answer. The resulting opinion could feel direct and confident even though it addressed a different problem. This account gave judgment errors a precise vocabulary rather than treating them as vague irrationality.

Tversky’s work also helped illuminate the necessity of Bayesian discipline. Bayes’s rule requires prior beliefs, or base rates, to be combined with the diagnosticity of evidence. If 3 percent of graduate students are enrolled in computer science and a description is four times more likely for a computer-science student than for students in other fields, the resulting probability is 11 percent, not the much higher probability suggested by the vivid description alone. If the base rate is 80 percent, the same evidence raises the probability to 94.1 percent. The lesson is that evidence does not erase prior probability, and intuitive impressions of diagnosticity are often exaggerated.

Prospect Theory and Decision Research

After the initial work on judgment, Tversky and Kahneman turned to decisions under risk. They continued their routine of long conversations, restaurant discussions, and walks through Jerusalem while inventing simple choice problems and asking themselves which option felt immediately tempting. They were not trying to determine the most rational or advantageous choice. Instead, they used their own shared preferences as rapid hypotheses about the preferences of other people, intending to test those hunches experimentally later.

Their five-year study of gambles culminated in “Prospect Theory: An Analysis of Decision under Risk.” The theory was modeled on utility theory but departed from it fundamentally. It was purely descriptive: its purpose was to document and explain systematic violations of the axioms of rationality in choices between gambles. The choice to submit the paper to Econometrica proved consequential. Because the journal published important theoretical work in economics and decision theory, the article reached an audience that a psychological journal might not have provided.

Prospect theory became the most significant work Tversky and Kahneman ever produced and one of the most frequently cited articles in the social sciences. Two years later, they published an account of framing effects in Science, showing that inconsequential changes in the wording of a choice problem could produce large changes in preferences. Their theory emerged from a dozen established facts about choices between risky options, several of them in direct conflict with expected utility theory. Rather than beginning with an abstract model and forcing observations into it, they modified expected utility theory only enough to explain the collection of regularities they had found.

Prediction, Calibration, and Intellectual Legacy

The consequences of Tversky’s research extended to the evaluation of experts. Philip Tetlock’s twenty-year study of 284 people who earned their living commenting on political and economic trends gathered more than 80,000 predictions. The experts were asked to assign probabilities to alternatives such as continuation of the status quo, an increase, or a decrease. Their performance was worse than an equal-probability baseline, and even in regions they knew best they were not significantly better than nonspecialists. Greater knowledge produced only a slight improvement, while the most knowledgeable participants could become less reliable because knowledge strengthened the illusion of skill and encouraged overconfidence.

The problem was not limited to political forecasting. A Duke University survey collected 11,600 forecasts from chief financial officers of large corporations about the following year’s Standard & Poor’s index. The correlation between their estimates and the actual value was slightly less than zero; when they predicted a decline, an increase was slightly more likely. Yet the financial officers did not appear to recognize that their forecasts were worthless. Their 80 percent confidence intervals produced surprises in 67 percent of cases rather than the expected 20 percent, demonstrating gross overconfidence.

Proper calibration made the same point formally. A judge who gives an X90 estimate should find that the true value exceeds it in only 10 percent of cases, while values should fall between X01 and X99 in 98 percent of problems. In practice, actual values fell outside such extreme bounds in about 30 percent of cases. Naive and sophisticated judges alike supplied confidence intervals that were too narrow, and proper scoring rules did not eliminate the effect. Anchoring offered part of the explanation: people began with a best estimate and adjusted insufficiently upward or downward, leaving their probability distributions too tight.

Tversky’s lasting importance lies in the union of conceptual clarity and experimental discipline. He helped turn the first, often misleading answer that comes to mind into an object of scientific study. With Kahneman, he showed that resemblance, availability, substitution, base-rate neglect, anchoring, and confidence could be investigated as recurring properties of judgment rather than as isolated personal failings. The resulting language made it possible to recognize errors in medicine, law, intelligence analysis, philosophy, finance, statistics, and military strategy—and, at least in some cases, to design interventions that limit the damage those errors cause.