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ECONOMETRICA

PROSPECT THEORY: AN ANALYSIS O F 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.

1. INTRODUCTION EXPECTED UTILITY 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 + p z + . . . +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...

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