http://repub.eur.nl/res/aut/28291/ List of Publications en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/23032/ 2000-09-01T00:00:00Z Machina and Schmeidler [Econometrica, 60 (1992) 745–780] gave preference conditions for probabilistic sophistication, i.e. decision making where uncertainty can be expressed in terms of (subjective) probabilities without commitment to expected utility maximization. This note shows that simpler and more general results can be obtained by combining results from qualitative probability theory with a ‘cumulative dominance’ axiom. http://repub.eur.nl/res/pub/23086/ 1998-11-01T00:00:00Z This paper explores how some widely studied classes of nonexpected utility models could be used in dynamic choice situations. A new "sequential consistency" condition is introduced for single-stage and multi-stage decision problems. Sequential consistency requires that if a decision maker has committed to a family of models (e.g., the multiple priors family, the rank-dependent family, or the betweenness family) then he use the same family throughout. Conditions are presented under which dynamic consistency, consequentialism, and sequential consistency can be simultaneously preserved for a nonexpected utility maximizer. An important class of applications concerns cases where the exact sequence of decisions and events, and thus the dynamic structure of the decision problem, is relevant to the decision maker. It is shown that for the multiple priors model, dynamic consistency, consequentialism, and sequential consistency can all be preserved. The result removes the argument that nonexpected utility models cannot be consistently used in dynamic choice situations. Rank-dependent and betweenness models can only be used in a restrictive manner, where deviation from expected utility is allowed in at most one stage. http://repub.eur.nl/res/pub/23085/ 1998-05-01T00:00:00Z Nonadditive expected utility models were developed for explaining preferences in settings where probabilities cannot be assigned to events. In the absence of probabilities, difficulties arise in the interpretation of likelihoods of events. In this paper we introduce a notion of revealed likelihood that is defined entirely in terms of preferences and that does not require the existence of (subjective) probabilities. Our proposal is that decision weights rather than capacities are more suitable measures of revealed likelihood in rank-dependent expected utility models and prospect theory. Applications of our proposal to the updating of beliefs and to the description of attitudes towards ambiguity are presented. http://repub.eur.nl/res/pub/23088/ 1997-07-01T00:00:00Z Anscombe and Aumann showed that if one accepts the existence of a physical randomizing device such as a roulette wheel then Savage's derivation of subjective expected utility can be considerably simplified. They, however, invoked compound gambles to define their axioms. We demonstrate that the subjective expected utility derivation can be further simplified and need not invoke compound gambles. Our simplification is obtained by closely following the steps by which probabilities and utilities are elicited. http://repub.eur.nl/res/pub/23011/ 1997-01-01T00:00:00Z Two core meanings of “utility” are distinguished. “Decision utility” is the weight of an outcome in a decision. “Experienced utility” is hedonic quality, as in Bentham’s usage. Experienced utility can be reported in real time (instant utility), or in retrospective evaluations of past episodes (remembered utility). Psychological research has documented systematic errors in retrospective evaluations, which can induce a preference for dominated options. We propose a formal normative theory of the total experienced utility of temporally extended outcomes. Measuring the experienced utility of outcomes permits tests of utility maximization and opens other lines of empirical research. http://repub.eur.nl/res/pub/23123/ 1994-05-01T00:00:00Z This note demonstrates that two minimal requirements of decision tree analysis, the folding back procedure and the interchangeability of consecutive event nodes, imply independence http://repub.eur.nl/res/pub/23125/ 1994-05-01T00:00:00Z http://repub.eur.nl/res/pub/23188/ 1994-01-01T00:00:00Z This paper provides a simple approach for deriving cumulative prospect theory. The key axiom is a cumulative dominance axiom which requires that a prospect be judged more attractive if in it greater gains are more likely and greater losses are less likely. In the presence of this cumulative dominance, once a model is satisfied on a "sufficiently rich" domain, then it holds everywhere. This leads to highly transparent results. http://repub.eur.nl/res/pub/23210/ 1992-11-01T00:00:00Z This paper provides an extension of Savage's subjective expected utility theory for decisions under uncertainty. It includes in the set of events both unambiguous events for which probabilities are additive and ambiguous events for which probabilities are permitted to be nonadditive. The main axiom is cumulative dominance, which adapts stochastic dominance to decision making under uncertainty. We derive a Choquet expected utility representation and show that a modification of cumulative dominance leads to the classical expected utility representation. The relationship of our approach with that of Schmeidler, who uses a two-stage formulation to derive Choquet expected utility, is also explored. Our work may be viewed as a unification of Schmeidler (1989) and Gilboa (1987).