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.

The relation of preference between acts or options is the key element of decision theory that provides the basis for the measurement of utility or value. In axiomatic treatments of decision theory, the concept of preference appears as an abstract relation that is given an empirical interpretation through specific methods of elicitation, such as choice and matching. In choice the decision maker selects an option from an offered set of two or more alternatives. In matching the decision maker is required to set the value of some variable to achieve an equivalence between options (e.g., what chance to win $750 is as attractive as 1 chance in 10 to win $2,500?).

The standard analysis of choice assumes procedure invariance: Normatively equivalent procedures for assessing preferences should give rise to the same preference order. Indeed, theories of measurement generally require the ordering of objects to be independent of the particular method of assessment. In classical physical measurement, it is commonly assumed that each object possesses a well-defined quantity of the attribute in question (e.g., length, mass) and that different measurement procedures elicit the same ordering of objects with respect to this attribute. Analogously, the classical theory of preference assumes that each individual has a well-defined preference order (or a utility function) and that different methods of elicitation produce the same ordering of options. To determine the heavier of two objects, for example, we can place them on the two sides of a pan balance and observe which side goes down.

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.

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 weighing of evidence and the formation of belief are basic elements of human thought. The question of how to evaluate evidence and assess confidence has been addressed from a normative perspective by philosophers and statisticians; it has also been investigated experimentally by psychologists and decision researchers. One of the major findings that has emerged from this research is that people are often more confident in their judgments than is warranted by the facts. Overconfidence is not limited to lay judgment or laboratory experiments. The well-publicized observation that more than two-thirds of small businesses fail within 4 years (Dun & Bradstreet, 1967) suggests that many entrepreneurs overestimate their probability of success (Cooper, Woo, & Dunkelberg, 1988). With some notable exceptions, such as weather forecasters (Murphy & Winkler, 1977), who receive immediate frequentistic feedback and produce realistic forecasts of precipitation, overconfidence has been observed in judgments of physicians (Lusted, 1977), clinical psychologists (Oskamp, 1965), lawyers (Wagenaar & Keren, 1986), negotiators (Neale & Bazerman, 1990), engineers (Kidd, 1970), and security analysts (Staël von Holstein, 1972). As one critic described expert prediction, “often wrong, but rarely in doubt.”

Overconfidence is common, but not universal. Studies of calibration have found that with very easy items, overconfidence is eliminated and underconfidence is often observed (Lichtenstein, Fischhoff, & Phillips, 1982). Furthermore, studies of sequential updating have shown that posterior probability estimates commonly exhibit conservatism or underconfidence (Edwards, 1968).

Both laypeople and experts are often called upon to evaluate the probability of uncertain events such as the outcome of a trial, the result of a medical operation, the success of a business venture, or the winner of a football game. Such assessments play an important role in deciding, respectively, whether to go to court, undergo surgery, invest in the venture, or bet on the home team. Uncertainty is usually expressed in verbal terms (e.g., unlikely or probable), but numeric estimates are also common. Weather forecasters, for example, often report the probability of rain (Murphy, 1985), and economists are sometimes required to estimate the chances of recession (Zarnowitz, 1985). The theoretical and practical significance of subjective probability has inspired psychologists, philosophers, and statisticians to investigate this notion from both descriptive and prescriptive standpoints.

Indeed, the question of whether degree of belief can, or should be, represented by the calculus of chance has been the focus of a long and lively debate. In contrast to the Bayesian school, which represents degree of belief by an additive probability measure, there are many skeptics who question the possibility and the wisdom of quantifying subjective uncertainty and are reluctant to apply the laws of chance to the analysis of belief. Besides the Bayesians and the skeptics, there is a growing literature on what might be called revisionist models of subjective probability.

In describing an outstanding performance by a basketball player, reporters and spectators commonly use expressions such as “Larry Bird has the hot hand” or “Andrew Toney is a streak shooter.” These phrases express a belief that the performance of a player during a particular period is significantly better than expected on the basis of the player's overall record. The belief in “the hot hand” and in “streak shooting” is shared by basketball players, coaches, and fans, and it appears to affect the selection of plays and the choice of players. In this chapter, we investigate the origin and the validity of these beliefs.

People's intuitive conceptions of randomness depart systematically from the laws of chance. It appears that people expect the essential characteristics of a chance process to be represented not only globally in the entire sequence, but also locally, in each of its parts. For instance, people expect even short sequences of heads and tails to reflect the fairness of a coin and contain roughly 50% heads and 50% tails. This conception of chance has been described as a “belief in the law of small numbers” according to which the law of large numbers applies to small samples as well (Tversky & Kahneman, 1971). A locally representative sequence, however, deviates systematically from chance expectation: It contains too many alternations and not enough long runs.

One of the main ideas that has emerged from behavioral decision research is a constructive conception of judgment and choice. According to this view, preferences and beliefs are actually constructed – not merely revealed – in the elicitation process. This conception is entailed by findings that normatively equivalent methods of elicitation often give rise to systematically different responses (e.g., Slovic, Fischhoff, & Lichtenstein, 1982; Tversky, Sattath, & Slovic, 1988). To account for these data within a constructive framework, we seek explanatory principles that relate the characteristics of the task to the attributes of the objects under study. One such notion is the compatibility hypothesis, which states that the weight of a stimulus attribute is enhanced by its compatibility with the response.

The rationale for this hypothesis is twofold. First, noncompatibility between the input and the output requires additional mental operations, which often increase effort and error and may reduce impact. Second, a response mode may prime or focus attention on the compatible features of the stimulus. Common features, for example, are weighted more heavily in judgments of similarity than in judgments of dissimilarity, whereas distinctive features are weighted more heavily in judgments of dissimilarity (Tversky, 1977). Consequently, entities with many common and many distinctive features (e.g., East and West Germany) are judged as both more similar to each other and as more different from each other than entities with relatively fewer common and fewer distinctive features (e.g., Sri Lanka and Nepal).

The theory of rational choice assumes that preference between options does not depend on the presence or absence of other options. This principle, called independence of irrelevant alternatives, is essentially equivalent to the assumption that the decision maker has a complete preference order of all options, and that -given an offered set - the decision maker always selects the option that is highest in that order. Despite its simplicity and intuitive appeal, experimental evidence indicates that this principle is often violated (see Huber et al. 1982, Simonson and Tversky 1992).