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Random binary choices that satisfy stochastic betweenness

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  • Ryan, Matthew

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.

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  • Ryan, Matthew, 2017. "Random binary choices that satisfy stochastic betweenness," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 176-184.
    • Handle: RePEc:eee:mateco:v:70:y:2017:i:c:p:176-184
    DOI: 10.1016/j.jmateco.2017.02.012
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    1. Loomes, Graham & Sugden, Robert, 1998. "Testing Different Stochastic Specifications of Risky Choice," Economica, London School of Economics and Political Science, vol. 65(260), pages 581-598, November.
    2. Blavatskyy, Pavlo R., 2006. "Violations of betweenness or random errors?," Economics Letters, Elsevier, vol. 91(1), pages 34-38, April.
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    7. Frederick Mosteller & Philip Nogee, 1951. "An Experimental Measurement of Utility," Journal of Political Economy, University of Chicago Press, vol. 59, pages 371-371.
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    9. Matthew Ryan, 2015. "A Strict Stochastic Utility Theorem," Economics Bulletin, AccessEcon, vol. 35(4), pages 2664-2672.
    10. Dekel, Eddie, 1986. "An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom," Journal of Economic Theory, Elsevier, vol. 40(2), pages 304-318, December.
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    Cited by:

    1. Addison Pan, 2022. "Empirical tests of stochastic binary choice models," Theory and Decision, Springer, vol. 93(2), pages 259-280, September.
    2. Matthew Ryan, 2021. "Stochastic expected utility for binary choice: a ‘modular’ axiomatic foundation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(2), pages 641-669, September.
    3. Matthew Ryan, 2020. "Reconciling dominance and stochastic transitivity in random binary choice," Working Papers 2020-05, Auckland University of Technology, Department of Economics.

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    Keywords

    Fechner model; Betweenness;

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