Stochastic Utility Theorem

This paper analyzes individual decision making. It is assumed that an individual does not have a preference relation on the set of lotteries. Instead, the primitive of choice is a choice probability that captures the likelihood of one lottery being chosen over the other. Choice probabilities have a stochastic utility representation if they can be written as a nondecreasing function of the difference in expected utilities of the lotteries. Choice probabilities admit a stochastic utility representation if and only if they are complete, strongly transitive, continuous, independent of common consequences and interchangeable. Axioms of stochastic utility are consistent with systematic violations of betweenness and a common ratio effect but not with a common consequence effect. Special cases of stochastic utility include the Fechner model of random errors, Luce choice model and a tremble model of Harless and Camerer (1994). Stochastic Utility Theorem Pavlo R. Blavatskyy Institute for Empirical Research in Economics University of Zurich Winterthurerstrasse 30 CH-8006 Zurich, Switzerland Phone: +41(1)6343586 Fax: +41(1)6344978 e-mail: [email protected] October 2007 Abstract This paper analyzes individual decision making. It is assumed that an individual does not have a preference relation on the set of lotteries. Instead, the primitive of choice is a choice probability that captures the likelihood of one lottery being chosen over the other. Choice probabilities have a stochastic utility representation if they can be written as a nondecreasing function of the difference in expected utilities of the lotteries. Choice probabilities admit a stochastic utility representation if and only if they are complete, strongly transitive, continuous, independent of common consequences and interchangeable. Axioms of stochastic utility are consistent with systematic violations of betweenness and a common ratio effect but not with a common consequence effect. Special cases of stochastic utility include the Fechner model of random errors, Luce choice model and a tremble model of Harless and Camerer (1994).