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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. repec:bla:econom:v:65:y:1998:i:260:p:581-98 is not listed on IDEAS
    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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    6. Chew, Soo Hong, 1983. "A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox," Econometrica, Econometric Society, vol. 51(4), pages 1065-1092, July.
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    8. Blavatskyy, Pavlo R., 2008. "Stochastic utility theorem," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1049-1056, December.
    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.
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    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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