Random Binary Choices that Satisfy Stochastic Betweenness

Matthew Ryan ()
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Matthew Ryan: School of Economics, Faculty of Business and Law, Auckland University of Technology

No 2017-01, Working Papers from Auckland University of Technology, Department of Economics

Abstract: Experimental evidence suggests that the process of choosing between lotteries (risky prospects) is stochastic and is better described through choice probabilities than preference relations. Binary choice probabilities admit a Fechner representation if there exists a utility function u such that the probability of choosing a over b is a non-decreasing function of the utility di¤erence u (a) - u (b). The representation is strict if u (a) u (b) precisely when the decision-maker is at least as likely to choose a from fa; bg as to choose b. Blavatskyy (2008) obtained necessary and su¢ cient conditions for a strict Fechner representation in which u has the expected utility form. One of these is the common consequence independence (CCI) axiom (ibid.,Axiom 4), which is a stochastic analogue of the mixture independence condition on preferences. Blavatskyy also conjectured that by weakening CCI to a condition he called stochastic betweenness (SB) stochastic analogue of the betweenness condition on preferen-ces (Chew (1983)) - one obtains necessary and suffcient conditions for a strict Fechner representation in which u has the implicit expected utility form (Dekel (1986)). We show that Blavatskyys conjecture is false, and provide a valid set of necessary and su¢ cient conditions for the desired representation.

Pages: 22 pages
Date: 2017-01
New Economics Papers: this item is included in nep-upt
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