Your fifty years of work had a massive impact on different disciplines ranging from social sciences to psychology, from philosophy to economics. The Prize motivation states that you won the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2002 ‘for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty’.

My life changed when I invited my brilliant colleague Amos Tversky to give a guest lecture. Amos told my graduate seminar at the Hebrew University of Jerusalem about recent research at the University of Michigan, which had concluded that people are good intuitive statisticians. I thought that claim was completely wrong (Israelis tend not to mince words), and we had an intense and enjoyable conversation. Over the next few days we sketched an idea – perhaps the most productive either of us ever had – and decided to collaborate in the study of intuitive statistical thinking.

Our goal was to understand how people answer questions such as “what GPA will this student achieve?” or “what proportion of professors at our university have been divorced at least once?” We knew that people come up quickly with intuitive answers to such questions, without consulting statistical principles. How do they do it, and why are these intuitions so often wrong? In 1969 these were new questions. We reported our main conclusions five years later: “people rely on a limited number of heuristic principles which reduce the complex tasks of assessing probabilities and predicting values to simpler judgmental operations. In general, these heuristics are quite useful, but sometimes they lead to severe and systematic errors” (Tversky and Kahneman, 1974). We borrowed the term “heuristic” from the literature on problem solving, where it refers to computational short-cuts that are quick and efficient, but not guaranteed to produce the correct answer.

For an example of how intuitive statistical thinking can be analyzed, consider this question:

I expect that a number quickly came to your mind, probably not very far from 3.7. You were probably not aware of how the number came up, but there it was. The research program that Amos and I started has established that you – your mind, your memory – carried out several operations to produce your intuitive estimate.

1. (1) The evidence “read fluently at age 4” was assessed for precocity, yielding something like a percentile. This percentile was high – say, 95.

2. (2) The GPA that corresponds to the 95th percentile was identified.

The question of how people think of things that could have happened but did not has attracted increasing interest among psychologists in recent years (J. T. Johnson, 1986; Kahneman & Miller, 1986; Kahneman & Tversky, 1982a; Landman, 1987; D. T. Miller, Turnbull, & MacFarland, 1990; Wells & Gavanski, 1989; Wells, Taylor, & Turtle, 1987). As philosophers have long known, the study of counterfactuals cannot be separated from a conception of causality, and an understanding of causality requires a conception of possibility and conditional probability. Counterfactual assertions rest on causal beliefs, and causal attributions invoke counterfactual beliefs, for example, about what would have happened in the absence of a putative cause. Some counterfactual assertions assign degrees of probability or plausibility to unrealized outcomes, many causal beliefs are probabilistic, and judgments of probability often draw on impressions of causal tendencies or propensities. The present article is concerned with a psychological analysis of this nexus of issues.

Our study began with an attempt to understand the psychology of assertions of the form “X almost happened,” which we call close counterfactuals. An important characteristic of such assertions is that they are not expressed as a conditional with a specified antecedent, as counterfactual conditionals are. The close counterfactual does not invoke an alternative possible world, but states a fact about the history of this world – namely, that things were close to turning out differently than they did.

Uncertainty is an unavoidable aspect of the human condition. Many significant choices must be based on beliefs about the likelihood of such uncertain events as the guilt of a defendant, the result of an election, the future value of the dollar, the outcome of a medical operation, or the response of a friend. Because we normally do not have adequate formal models for computing the probabilities of such events, intuitive judgment is often the only practical method for assessing uncertainty.

The question of how lay people and experts evaluate the probabilities of uncertain events has attracted considerable research interest in the last decade (see, e.g., Einhorn & Hogarth, 1981; Kahneman, Slovic, & Tversky, 1982; Nisbett & Ross, 1980). Much of this research has compared intuitive inferences and probability judgments to the rules of statistics and the laws of probability. The student of judgment uses the probability calculus as a standard of comparison much as a student of perception might compare the perceived sizes of objects to their physical sizes. Unlike the correct size of objects, however, the “correct” probability of events is not easily defined. Because individuals who have different knowledge or who hold different beliefs must be allowed to assign different probabilities to the same event, no single value can be correct for all people. Furthermore, a correct probability cannot always be determined even for a single person.

INTRODUCTION

Economics and psychology offer contrasting perspectives on the question of how people value things. The economic model of choice is concerned with a rational agent whose preferences obey a tight web of logical rules, formalized in consumer theory and in models of decision making under risk. The tradition of psychology, in contrast, is not congenial to the idea that a logic of rational choice can serve double duty as a model of actual decision behavior. Much behavioral research has been devoted to illustrations of choices that violate the logic of the economic model. The implied claim is that people do not have preferences, in the sense in which that term is used in economic theory (Fischhoff, 1991; Payne, Bettman, & Johnson, 1992; Slovic, 1995). It is therefore fair to ask: If people do not have economic preferences, what do they have instead? Does psychology provide theoretical notions that can, at least in some contexts, account for both apparent violations of the rational model of preference and the regularities of observed choices? Behavioral research has documented several psychological processes that provide partial answers to this question, including concepts such as mental accounting, loss aversion, and hyperbolic discounting. To this set of conceptual tools the present treatment adds the concept of attitude, which we borrow from social psychology, and the core process – we label it affective valuation – which determines the sign and the intensity of the emotional response to objects.

Axiomatic theories of choice introduce preference as a primitive relation, which is interpreted through specific empirical procedures such as choice or pricing. Models of rational choice assume a principle of procedure invariance, which requires strategically equivalent methods of elicitation to yield the same preference order. Thus, if the decision maker prefers A to B, then the cash equivalent, or minimum selling price, of A should exceed that of B. However, there is a substantial body of evidence showing that the price ordering of risky prospects is systematically different from the choice ordering, contrary to standard theories of choice.

The effect of elicitation method on preference between gambles was first observed by Slovic and Lichtenstein (1968) who found that both buying and selling prices of gambles were primarily determined by the payoffs, whereas choices between gambles (and ratings of their attractiveness) were primarily influenced by the probabilities of winning and losing. Slovic and Lichtenstein reasoned that, if the method used to elicit preferences affected the weighting of the gambles' components, it should be possible to construct pairs of gambles such that the same individual would choose one member of the pair but set a higher price for the other. Lichtenstein and Slovic (1971, 1973) demonstrated such reversals in a series of studies, one of which was conducted on the floor of the Four Queens Casino in Las Vegas with experienced gamblers playing for real money.

The preference-reversal phenomenon involves a pair of gambles of comparable expected value.

INTRODUCTION

The assumption that agents are rational is central to much theory in the social sciences. Its role is particularly obvious in economic analysis, where it supports the useful corollary that no significant opportunity will remain unexploited. In the domain of social policy, the rationality assumption supports the position that it is unnecessary to protect people against the consequences of their choices. The status of this assumption is therefore a matter of considerable interest. This chapter argues for an enriched definition of rationality that considers the actual outcomes of decisions and presents evidence that challenges the rationality assumption in new ways.

The criteria for using the terms “rational” or “irrational” in nontechnical discourse are substantive: One asks whether beliefs are grossly out of kilter with available evidence and whether decisions serve or damage the agent's interests. In sharp contrast, technical discussions of rationality generally adopt a logical conception, in which an individual's beliefs and preferences are said to be rational if they obey a set of formal rules such as complementarity of probabilities, the sure thing principle, or independence of irrelevant alternatives. In the laissez-faire spirit of modern economics and decision theory, the content of beliefs and of preferences is not a criterion of rationality – only internal coherence matters (Sen, 1993). The methodology of the debate reflects this concern for consistency: In the classic paradoxes of Allais (1953) and Ellsberg (1961), for example, two intuitively compelling preferences are shown to be jointly incompatible with the axioms of expected utility theory, though each preference is unobjectionable on its own.

Uncertainty is an unavoidable aspect of the human condition. Many significant choices must be based on beliefs about the likelihood of such uncertain events as the guilt of a defendant, the result of an election, the future value of the dollar, the outcome of a medical operation, or the response of a friend. Because we normally do not have adequate formal models for computing the probabilities of such events, intuitive judgment is often the only practical method for assessing uncertainty.

The question of how lay people and experts evaluate the probabilities of uncertain events has attracted considerable research interest. (See, e.g., Einhorn & Hogarth, 1981; Kahneman, Slovic, & Tversky, 1982; Nisbett & Ross, 1980.) Much of this research has compared intuitive inferences and probability judgments to the rules of statistics and the laws of probability. The student of judgment uses the probability calculus as a standard of comparison much as a student of perception might compare the perceived size of objects to their physical sizes. Unlike the correct size of objects, however, the “correct” probability of events is not easily defined. Because individuals who have different knowledge or hold different beliefs must be allowed to assign different probabilities to the same event, no single value can be correct for all people. Furthermore, a correct probability cannot always be determined, even for a single person. Outside the domain of random sampling, probability theory does not determine the probabilities of uncertain events – it merely imposes constraints on the relations among them.

The program of research now known as the heuristics and biases approach began with a survey of 84 participants at the 1969 meetings of the Mathematical Psychology Society and the American Psychological Association (Tversky & Kahneman, 1971). The respondents, including several authors of statistics texts, were asked realistic questions about the robustness of statistical estimates and the replicability of research results. The article commented tongue-in-heek on the prevalence of a belief that the law of large numbers applies to small numbers as well: Respondents placed too much confidence in the results of small samples, and their statistical judgments showed little sensitivity to sample size.

The mathematical psychologists who participated in the survey not only should have known better – they did know better. Although their intuitive guesses were off the mark, most of them could have computed the correct answers on the back of an envelope. These sophisticated individuals apparently had access to two distinct approaches for answering statistical questions: one that is spontaneous, intuitive, effortless, and fast; and another that is deliberate, rule-governed, effortful, and slow. The persistence of large biases in the guesses of experts raised doubts about the educability of statistical intuitions. Moreover, it was known that the same biases affect choices in the real world, where researchers commonly select sample sizes that are too small to provide a fair test of their hypotheses (Cohen, 1969, 1992).