Random binary choices that satisfy stochastic betweenness

Matthew Ryan

Journal of Mathematical Economics, 2017, vol. 70, issue C, 176-184

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 difference 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 {a,b} as to choose b. Blavatskyy (2008) obtained necessary and sufficient 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 we call Stochastic Betweenness–a stochastic analogue of the betweenness condition on preferences (Chew, 1983)–one obtains necessary and sufficient conditions for a strict Fechner representation in which u has the implicit expected utility form (Dekel, 1986). We show that Blavatskyy’s conjecture is false, and provide a valid set of necessary and sufficient conditions for the desired representation.

Keywords: Fechner model; Betweenness (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:70:y:2017:i:c:p:176-184

DOI: 10.1016/j.jmateco.2017.02.012

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