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Random Binary Choices that Satisfy Stochastic Betweenness

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  • Matthew Ryan

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

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.

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  • Matthew Ryan, 2017. "Random Binary Choices that Satisfy Stochastic Betweenness," Working Papers 2017-01, Auckland University of Technology, Department of Economics.
    • Handle: RePEc:aut:wpaper:201701
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    References listed on IDEAS

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    1. Graham Loomes, 2005. "Modelling the Stochastic Component of Behaviour in Experiments: Some Issues for the Interpretation of Data," Experimental Economics, Springer;Economic Science Association, vol. 8(4), pages 301-323, December.
    2. Dagsvik, John K., 2008. "Axiomatization of stochastic models for choice under uncertainty," Mathematical Social Sciences, Elsevier, vol. 55(3), pages 341-370, May.
    3. 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.
    4. Frederick Mosteller & Philip Nogee, 1951. "An Experimental Measurement of Utility," Journal of Political Economy, University of Chicago Press, vol. 59(5), pages 371-371.
    5. 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. Matthew Ryan, 2020. "Reconciling dominance and stochastic transitivity in random binary choice," Working Papers 2020-05, Auckland University of Technology, Department of Economics.
    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. 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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