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Binary Choice Probabilities on Mixture Sets

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  • Matthew Ryan

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

Abstract

Experimental evidence suggests that choice behaviour has a stochastic element. Much of this evidence is based on studying choices between lotteries ñchoice under risk. Binary choice probabilities admit a strong utility representation (SUR) if there is a utility function such that the probability of choosing option A over option B is a strictly increasing function of the utility di§erence between A and B. Debreu (1958) obtained a simple set of su¢ cient conditions on binary choice probabilities for the existence of a SUR. More recently, Dagsvik (2008) considered binary choices between lotteries and provided axiomatic foundations for a SUR in which the underlying utility function is linear (i.e., conforms to expected utility). Our paper strengthens and generalises Dagsvikís result. We show that one of Dagsvikís axioms can be weakened, and we extend his analysis to encompass choices between uncertain prospects, as well as various non-linear speciÖcations of utility.

Suggested Citation

  • Matthew Ryan, 2015. "Binary Choice Probabilities on Mixture Sets," Working Papers 2015-01, Auckland University of Technology, Department of Economics.
    • Handle: RePEc:aut:wpaper:201501
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    References listed on IDEAS

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    1. Dagsvik, John K., 2008. "Axiomatization of stochastic models for choice under uncertainty," Mathematical Social Sciences, Elsevier, vol. 55(3), pages 341-370, May.
    2. Matthew J. Ryan, 2009. "Generalizations of SEU: a geometric tour of some non-standard models," Oxford Economic Papers, Oxford University Press, vol. 61(2), pages 327-354, April.
    3. Graham Loomes & Ganna Pogrebna, 2014. "Testing for independence while allowing for probabilistic choice," Journal of Risk and Uncertainty, Springer, vol. 49(3), pages 189-211, December.
    4. Ulrich Schmidt & Tibor Neugebauer, 2007. "Testing expected utility in the presence of errors," Economic Journal, Royal Economic Society, vol. 117(518), pages 470-485, March.
    5. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    6. John D. Hey, 2018. "Experimental investigations of errors in decision making under risk," World Scientific Book Chapters, in: Experiments in Economics Decision Making and Markets, chapter 17, pages 381-388, World Scientific Publishing Co. Pte. Ltd..
    7. Blavatskyy, Pavlo R., 2012. "Probabilistic subjective expected utility," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 47-50.
    8. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
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