Amos Tversky

Judgment under Uncertainty: Heuristics and Biases

This article described three heuristics that are employed in making judgements under uncertainty: (i) representativeness, which is usually employed when people are asked to judge the probability that an object or event A belongs to class or process B; (ii) availability of instances or scenarios, which is often employed when people are asked to assess the frequency of a class or the plausibility of a particular development; and (iii) adjustment from an anchor, which is usually employed in numerical prediction when a relevant value is available. These heuristics are highly economical and usually effective, but they lead to systematic and predictable errors. A better understanding of these heuristics and of the biases to which they lead could improve judgements and decisions in situations of uncertainty.

Advances in Prospect Theory: Cumulative Representation of Uncertainty

We develop a new version of prospect theory that employs cumulative rather than separable decision weights and extends the theory in several respects. This version, called cumulative prospect theory, applies to uncertain as well as to risky prospects with any number of outcomes, and it allows different weighting functions for gains and for losses. Two principles, diminishing sensitivity and loss aversion, are invoked to explain the characteristic curvature of the value function and the weighting functions. A review of the experimental evidence and the results of a new experiment confirm a distinctive fourfold pattern of risk attitudes: risk aversion for gains and risk seeking for losses of high probability; risk seeking for gains and risk aversion for losses of low probability.This article has benefited from discussions with Colin Camerer, Chew Soo-Hong, David Freedman, and David H. Krantz. We are especially grateful to Peter P. Wakker for his invaluable input and contribution to the axiomatic analysis. We are indebted to Richard Gonzalez and Amy Hayes for running the experiment and analyzing the data. This work was supported by Grants 89-0064 and 88-0206 from the Air Force Office of Scientific Research, by Grant SES-9109535 from the National Science Foundation, and by the Sloan Foundation.

Availability: A heuristic for judging frequency and probability☆☆☆

Abstract This paper explores a judgmental heuristic in which a person evaluates the frequency of classes or the probability of events by availability, i.e., by the ease with which relevant instances come to mind. In general, availability is correlated with ecological frequency, but it is also affected by other factors. Consequently, the reliance on the availability heuristic leads to systematic biases. Such biases are demonstrated in the judged frequency of classes of words, of combinatorial outcomes, and of repeated events. The phenomenon of illusory correlation is explained as an availability bias. The effects of the availability of incidents and scenarios on subjective probability are discussed.

Loss Aversion in Riskless Choice: A Reference-Dependent Model

Much experimental evidence indicates that choice depends on the status quo or reference level: changes of reference point often lead to reversals of preference. We present a reference-dependent theory of consumer choice, which explains such effects by a deformation of indifference curves about the reference point. The central assumption of the theory is that losses and disadvantages have greater impact on preferences than gains and advantages. Implications of loss aversion for economic behavior are considered.

Rational choice and the framing of decisions

Alternative descriptions of a decision problem often give rise to different preferences, contrary to the principle of invariance that underlines the rational theory of choice. Violations of this theory are traced to the rules that govern the framing of decision and to the psychological principles of evaluation embodied in prospect theory. Invariance and dominance are obeyed when their application is transparent and often violated in other situations. Because these rules are normatively essential but descriptively invalid, no theory of choice can be both normatively adequate and descriptively accurate.

Features of similarity.

The metric and dimensional assumptions that underlie the geometric representation of similarity are questioned on both theoretical and empirical grounds. A new set-theoretical approach to similarity is developed in which objects are represented as collections of features, and similarity is described as a feature-matching process. Specifically, a set of qualitative assumptions is shown to imply the contrast model, which expresses the similarity between objects as a linear combination of the measures of their common and distinctive features. Several predictions of the contrast model are tested in studies of similarity with both semantic and perceptual stimuli. The model is used to uncover, analyze, and explain a variety of empirical phenomena such as the role of common and distinctive features, the relations between judgments of similarity and difference, the presence of asymmetric similarities, and the effects of context on judgments of similarity. The contrast model generalizes standard representations of similarity data in terms of clusters and trees. It is also used to analyze the relations of prototypicality and family resemblance

Subjective probability: A judgment of representativeness

This paper explores a heuristic — representativeness — according to which the subjective probability of an event, or a sample, is determined by the degree to which it: (i) is similar in essential characteristics to its parent population; and (ii) reflects the salient features of the process by which it is generated. This heuristic is explicated in a series of empirical examples demonstrating predictable and systematic errors in the evaluation of uncertain events. In particular, since sample size does not represent any property of the population, it is expected to have little or no effect on judgment of likelihood. This prediction is confirmed in studies showing that subjective sampling distributions and posterior probability judgments are determined by the most salient characteristic of the sample (e.g., proportion, mean) without regard to the size of the sample. The present heuristic approach is contrasted with the normative (Bayesian) approach to the analysis of the judgment of uncertainty.

Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment

Perhaps the simplest and the most basic qualitative law of probability is the conjunction rule: The probability of a conjunction, P (A&B) cannot exceed the probabilities of its constituents, P (A) and P (B), because the extension (or the possibility set) of the conjunction is included in the extension of its constituents. Judgments under uncertainty, however, are often mediated by intuitive heuristics that are not bound by the conjunction rule. A conjunction can be more representative than one of its constituents, and instances of a specific category can be easier to imagine or to retrieve than instances of a more inclusive category. The representativeness and availability heuristics therefore can make a conjunction appear more probable than one of its constituents. This phenomenon is demonstrated in a variety of contexts including estimation of word frequency, personality judgment, medical prognosis, decision under risk, suspicion of criminal acts, and political forecasting. Systematic violations of the conjunction rule are observed in judgments of lay people and of experts in both between-subjects and within-subjects comparisons. Alternative interpretations of the conjunction fallacy are discussed and attempts to combat it are explored.

Subjective Probability : Judgement of Representativeness

This paper explores a heuristic — representativeness — according to which the subjective probability of an event, or a sample, is determined by the degree to which it: (i) is similar in essential characteristics to its parent population; and (ii) reflects the salient features of the process by which it is generated. This heuristic is explicated in a series of empirical examples demonstrating predictable and systematic errors in the evaluation of uncertain events. In particular, since sample size does not represent any property of the population, it is expected to have little or no effect on judgment of likelihood. This prediction is confirmed in studies showing that subjective sampling distributions and posterior probability judgments are determined by the most salient characteristic of the sample (e.g., proportion, mean) without regard to the size of the sample. The present heuristic approach is contrasted with the normative (Bayesian) approach to the analysis of the judgment of uncertainty.

On the Elicitation of Preferences for Alternative Therapies

We investigated how variations in the way information is presented to patients influence their choices between alternative therapies. Data were presented summarizing the results of surgery and radiation therapy for lung cancer to 238 ambulatory patients with different chronic medical conditions and to 491 graduate students and 424 physicians. We asked the subjects to imagine that they had lung cancer and to choose between the two therapies on the basis of both cumulative probabilities and life-expectancy data. Different groups of respondents received input data that differed only in whether or not the treatments were identified and whether the outcomes were framed in terms of the probability of living or the probability of dying. In all three populations, the attractiveness of surgery, relative to radiation therapy, was substantially greater when the treatments were identified rather than unidentified, when the information consisted of life expectancy rather than cumulative probability, and when the problem was framed in terms of the probability of living rather than in terms of the probability of dying. We suggest that an awareness of these effects among physicians and patients could help reduce bias and improve the quality of medical decision making.