Prospect Theory: An Analysis of Decision under Risk

This paper presents a critique of expected utility theory as a descriptive model of decision making under risk, and develops an alternative model, called prospect theory.Choices among risky prospects exhibit several pervasive effects that are inconsistent with the basic tenets of utility theory.In particular, people underweight outcomes that are merely probable in comparison with outcomes that are obtained with certainty.This tendency, called the certainty effect, contributes to risk aversion in choices involving sure gains and to risk seeking in choices involving sure losses.In addition, people generally discard components that are shared by all prospects under consideration.This tendency, called the isolation effect, leads to inconsistent preferences when the same choice is presented in different forms.An alternative theory of choice is developed, in which value is assigned to gains and losses rather than to final assets and in which probabilities are replaced by decision weights.The value function is normally concave for gains, commonly convex for losses, and is generally steeper for losses than for gains.Decision weights are generally lower than the corresponding probabilities, except in the range of low probabilities.Overweighting of low probabilities may contribute to the attractiveness of both insurance and gambling. D. KAHNEMAN AND A. TVERSKYThat is, the overall utility of a prospect, denoted by U, is the expected utility of its outcomes.(ii) Asset Integration: (xi, Pi; ... ; Xn, P) is acceptable at asset position w iff U(w +x1, pl; ... ; w +Xn, Pn) > u(w).That is, a prospect is acceptable if the utility resulting from integrating the prospect with one's assets exceeds the utility of those assets alone.Thus, the domain of the utility function is final states (which include one's asset position) rather than gains or losses.Although the domain of the utility function is not limited to any particular class of consequences, most applications of the theory have been concerned with monetary outcomes.Furthermore, most economic applications introduce the following additional assumption.(iii) Risk Aversion: u is concave (u" < 0). A person is risk averse if he prefers the certain prospect (x) to any risky prospect with expected value x. In expected utility theory, risk aversion is equivalent to the concavity of the utility function. The prevalence of risk aversion is perhaps the best known generalization regarding risky choices. It led the early decision theorists of the eighteenth century to propose that utility is a concave function of money, and this idea has been retained in modern treatments (Pratt [33], Arrow [4]).In the following sections we demonstrate several phenomena which violate these tenets of expected utility theory.The demonstrations are based on the responses of students and university faculty to hypothetical choice problems.The respondents were presented with problems of the type illustrated below. Which of the following would you prefer?A: 50% chance to win 1,000, B: 450 for sure. 50% chance to win nothing;The outcomes refer to Israeli currency.To appreciate the significance of the amounts involved, note that the median net monthly income for a family is about 3,000 Israeli pounds.The respondents were asked to imagine that they were actually faced with the choice described in the problem, and to indicate the decision they would have made in such a case.The responses were anonymous, and the instructions specified that there was no 'correct' answer to such problems, and that the aim of the study was to find out how people choose among risky prospects.The problems were presented in questionnaire form, with at most a dozen problems per booklet.Several forms of each questionnaire were constructed so that subjects were exposed to the problems in different orders.In addition, two versions of each problem were used in which the left-right position of the prospects was reversed.The problems described in this paper are selected illustrations of a series of effects.Every effect has been observed in several problems with different outcomes and probabilities.Some of the problems have also been presented to groups of students and faculty at the University of Stockholm and at the