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Reconciling dominance and stochastic transitivity in random binary choice

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  • Matthew Ryan

    (School of Economics, Auckland University of Technology)

Abstract

Ryan (2017) introduces a condition on binary stochastic choice between lotteries which we call Weak Transparent Domniance (WTP). Consider a binary choice set containing two different mixtures over a "best" and "worst" possible prize, so that one option transparently dominates the other. The WTD axiom says that the probability of choosing the dominant alternative depends only on the difference in chance of winning the "best" prizea across the two lotteries. A person whose choices always respect first-order stochastic dominance (FOSD) will satisfy this condition, but WTD is a weaker requirement. We show that WTD and strong stochastic transitivity (SST), together with a mild technical condition, ensure the existence of a Fechner model for choice probabilities. this implies, in particular, that for choice probabilities satisfying WTD and our technical condition, there is no observable difference between scalability (Kants, 1964; Tversky and Russo, 1969) and compatability with a Fechner model.

Suggested Citation

  • Matthew Ryan, 2020. "Reconciling dominance and stochastic transitivity in random binary choice," Working Papers 2020-05, Auckland University of Technology, Department of Economics.
    • Handle: RePEc:aut:wpaper:202005
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    References listed on IDEAS

    as
    1. Matthew Ryan, 2017. "Random Binary Choices that Satisfy Stochastic Betweenness," Working Papers 2017-01, Auckland University of Technology, Department of Economics.
    2. Birnbaum, Michael H & Navarrete, Juan B, 1998. "Testing Descriptive Utility Theories: Violations of Stochastic Dominance and Cumulative Independence," Journal of Risk and Uncertainty, Springer, vol. 17(1), pages 49-78, October.
    3. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    4. Ryan, Matthew, 2017. "Random binary choices that satisfy stochastic betweenness," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 176-184.
    5. Pavlo R. Blavatskyy, 2011. "A Model of Probabilistic Choice Satisfying First-Order Stochastic Dominance," Management Science, INFORMS, vol. 57(3), pages 542-548, March.
    6. Blavatskyy, Pavlo R., 2008. "Stochastic utility theorem," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1049-1056, December.
    7. 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.
    8. Wilcox, Nathaniel T., 2011. "'Stochastically more risk averse:' A contextual theory of stochastic discrete choice under risk," Journal of Econometrics, Elsevier, vol. 162(1), pages 89-104, May.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    stochatic choice; risk; stochatic dominance; scalability; Fechner;
    All these keywords.

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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