Prospect Theory: An Analysis of Decision under RiskDaniel Kahneman; Amos TverskyEconometrica, Vol. 47, No. 2. (Mar., 1979), pp. 263-292.Stable URL:http://links.jstor.org/sici?sici=0012-9682%28197903%2947%3A2%3C263%3APTAAOD%3E2.0.CO%3B2-3Econometrica is currently published by The Econometric Society.Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtainedprior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content inthe JSTOR archive only for your personal, non-commercial use.Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained athttp://www.jstor.org/journals/econosoc.html.Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.JSTOR is an independent not-for-profit organization dedicated to and preserving a digital archive of scholarly journals. Formore information regarding JSTOR, please contact [email protected]://www.jstor.orgThu Apr 5 17:18:55 2007ECONOMETRICA 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 prob- abilities. Overweighting of low probabilities may contribute to the attractiveness of both insurance and gambling. 1. INTRODUCTION EXPECTEDUTILITY THEORY has dominated the analysis of decision making under risk. It has been generally accepted as a normative model of rational choice [24], and widely applied as a descriptive model of economic behavior, e.g. [15,4]. Thus, it is assumed that all reasonable people would wish to obey the axioms of the theory [47,36], and that most people actually do, most of the time. The present paper describes several classes of choice problems in which preferences systematically violate the axioms of expected utility theory. In the light of these observations we argue that utility theory, as it is commonly interpreted and applied, is not an adequate descriptive model and we propose an alternative account of choice under risk. 2. CRITIQUE Decision making under risk can be viewed as a choice between prospects or gambles. A prospect (xl, pl; . .. ;x,,, p,) is a contract that yields outcome xi with probability pi, where pl +pz+ . . .+p, = 1. To simplify notation, we omit null outcomes and use (x, p) to denote the prospect (x, p; 0, 1-p) that yields x with probability p and 0 with probability 1-p. The (riskless) prospect that yields x with certainty is denoted by (x). The present discussion is restricted to prospects with so-called objective or standard probabilities. The application of expected utility theory to choices between prospects is based on the following three tenets. (i) Expectation: U(x1, p~; . . .;x,, p,) =plu(xl)+ . . . +p,u(x,). 'This work was supported in part by grants from the Harry F. Guggenheim Foundation and from the Advanced Research Projects Agency of the Department of Defense and was monitored by Office of Naval Research under Contract N00014-78-C-0100 (ARPA Order No. 3469) under Subcontract 78-072-0722 from Decisions and Designs, Inc. to Perceptronics, Inc. We also thank the Center for Advanced Study in the Behavioral Sciences at Stanford for its support. 263264 D. KAHNEMAN AND A. TVERSKY That is, the overall utility of a prospect, denoted by U, is the expected utility of its outcomes. (ii) Asset Integration: (xl, pl; . . . ;x,, p,) is acceptable at asset position w iff U(w +XI, p1;. . . ;w +x", p,)> 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 [41). 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°/o chance to win 1,000, B: 450 for sure. 50% chance to win nothing;