Certainty effect

Abstract: Analysis of decision making under risk has been dominated by expected utility theory, which generally accounts for people's actions. Presents a critique of expected utility theory as a descriptive model of decision making under risk, and argues that common forms of utility theory are not adequate, and proposes an alternative theory of choice under risk called prospect theory. In expected utility theory, utilities of outcomes are weighted by their probabilities. Considers results of responses to various hypothetical decision situations under risk and shows results that violate the tenets of expected utility theory. People overweight outcomes considered certain, relative to outcomes that are merely probable, a situation called the "certainty effect." This effect contributes to risk aversion in choices involving sure gains, and to risk seeking in choices involving sure losses. In choices where gains are replaced by losses, the pattern is called the "reflection effect." People discard components shared by all prospects under consideration, a tendency called the "isolation effect." Also shows that in choice situations, preferences may be altered by different representations of probabilities. Develops an alternative theory of individual decision making under risk, called prospect theory, developed for simple prospects with monetary outcomes and stated probabilities, in which value is given to gains and losses (i.e., changes in wealth or welfare) rather than to final assets, and probabilities are replaced by decision weights. The theory has two phases. The editing phase organizes and reformulates the options to simplify later evaluation and choice. The edited prospects are evaluated and the highest value prospect chosen. Discusses and models this theory, and offers directions for extending prospect theory are offered. (TNM)

Abstract: 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. Expected utility theory reigned for several decades as the dominant normative and descriptive model of decision making under uncertainty, but it has come under serious question in recent years. There is now general agreement that the theory does not provide an adequate description of individual choice: a substantial body of evidence shows that decision makers systematically violate its basic tenets. Many alternative models have been proposed in response to this empirical challenge (for reviews, see Camerer, 1989; Fishburn, 1988; Machina, 1987). Some time ago we presented a model of choice, called prospect theory, which explained the major violations of expected utility theory in choices between risky prospects with a small number of outcomes (Kahneman and Tversky, 1979; Tversky and Kahneman, 1986). The key elements of this theory are 1) a value function that is concave for gains, convex for losses, and steeper for losses than for gains,

Abstract: The main body of current economic analysis of choice under uncertainty is built upon a small number of basic axioms, formulated in slightly different ways by von Neumann and Morgenstern (I 947), Savage (1 954) and others. These axioms are widely believed to represent the essence of rational behaviour under uncertainty. However, it is well known that many people behave in ways that systematically violate these axioms.' We shall initially focus upon a paper by Kahneman and Tversky (I 979) which presents extensive evidence of such behaviour. Kahneman and Tversky offer a theory, which they call 'prospect theory ', to explain their observations. We shall offer an alternative theory which is much simpler than prospect theory and which, we believe, has greater appeal to intuition. The following notation will be used throughout. The ith prospect is written as Xi. If it offers increments or decrements of wealth xl, ..., x. with probabilities Pi, .Pn (where p, + ... +pn = I) it may be denoted as (xi,pi; .. .; XwPn). Null consequences are omitted so that the prospect (x,p; o, I -p) is written simply as (x,p). Complex prospects, i.e. those which offer other prospects as consequences, may be denoted as (Xi,pi; ...; Xn,pn). We shall use the conventional notation >, > and to represent the relations of strict preference, weak preference and indifference. We shall take it that for all prospects Xi and Xk, Xi > Xk or Xi is transitive.

Abstract: When individuals choose among risky alternatives, the psychological weight attached to an outcome may not correspond to the probability of that outcome. In rank-dependent utility theories, including prospect theory, the probability weighting function permits probabilities to be weighted nonlinearly. Previous empirical studies of the weighting function have suggested an inverse S-shaped function, first concave and then convex. However, these studies suffer from a methodological shortcoming: estimation procedures have required assumptions about the functional form of the value and/or weighting functions. We propose two preference conditions that are necessary and sufficient for concavity and convexity of the weighting function. Empirical tests of these conditions are independent of the form of the value function. We test these conditions using preference "ladders" a series of questions that differ only by a common consequence. The concavity-convexity ladders validate previous findings of an S-shaped weighting function, concave up to p < 0.40, and convex beyond that probability. The tests also show significant nonlinearity away from the boundaries, 0 and 1. Finally, we fit the ladder data with weighting functions proposed by Tversky and Kahneman Tversky, Amos, Daniel Kahneman. 1992. Advances in prospect theory: Cumulative representation of uncertainty. J. Risk and Uncertainty5 297-323. and Prelec Prelec, Dražen. 1995. The probability weighting function. Unpublished paper..