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Stochastic utility theorem

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  • Blavatskyy, Pavlo R.

Abstract

This paper analyzes individual decision making. It is assumed that an individual does not have a preference relation on the set of lotteries. Instead, the primitive of choice is a choice probability that captures the likelihood of one lottery being chosen over the other. Choice probabilities have a stochastic utility representation if they can be written as a non-decreasing function of the difference in expected utilities of the lotteries. Choice probabilities admit a stochastic utility representation if and only if they are complete, strongly transitive, continuous, independent of common consequences and interchangeable. Axioms of stochastic utility are consistent with systematic violations of betweenness and a common ratio effect but not with a common consequence effect. Special cases of stochastic utility include the Fechner model of random errors, Luce choice model and a tremble model of [Harless, D., Camerer, C., 1994. The predictive utility of generalized expected utility theories. Econometrica 62, 1251-1289].

Suggested Citation

  • Blavatskyy, Pavlo R., 2008. "Stochastic utility theorem," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1049-1056, December.
  • Handle: RePEc:eee:mateco:v:44:y:2008:i:11:p:1049-1056
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    References listed on IDEAS

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    1. Fishburn, Peter C, 1978. "A Probabilistic Expected Utility Theory of Risky Binary Choices," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 19(3), pages 633-646, October.
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    9. 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.
    10. Starmer, Chris & Sugden, Robert, 1989. "Probability and Juxtaposition Effects: An Experimental Investigation of the Common Ratio Effect," Journal of Risk and Uncertainty, Springer, vol. 2(2), pages 159-178, June.
    11. Blavatskyy, Pavlo R., 2006. "Violations of betweenness or random errors?," Economics Letters, Elsevier, vol. 91(1), pages 34-38, April.
    12. Harless, David W & Camerer, Colin F, 1994. "The Predictive Utility of Generalized Expected Utility Theories," Econometrica, Econometric Society, vol. 62(6), pages 1251-1289, November.
    13. Machina, Mark J, 1985. "Stochastic Choice Functions Generated from Deterministic Preferences over Lotteries," Economic Journal, Royal Economic Society, vol. 95(379), pages 575-594, September.
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    16. Hey, John D., 1995. "Experimental investigations of errors in decision making under risk," European Economic Review, Elsevier, vol. 39(3-4), pages 633-640, April.
    17. Pavlo Blavatskyy, 2007. "Stochastic expected utility theory," Journal of Risk and Uncertainty, Springer, vol. 34(3), pages 259-286, June.
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    Citations

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    Cited by:

    1. John Hey & Andrea Morone & Ulrich Schmidt, 2009. "Noise and bias in eliciting preferences," Journal of Risk and Uncertainty, Springer, vol. 39(3), pages 213-235, December.
    2. Pavlo Blavatskyy, 2012. "Probabilistic choice and stochastic dominance," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(1), pages 59-83, May.
    3. Dagsvik, John K., 2015. "Stochastic models for risky choices: A comparison of different axiomatizations," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 81-88.
    4. Dino Borie, 2016. "Expected Multi-Utility Representations by "Simplex" with Applications," GREDEG Working Papers 2016-10, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), University of Nice Sophia Antipolis.
    5. Blavatskyy, Pavlo, 2013. "Which decision theory?," Economics Letters, Elsevier, vol. 120(1), pages 40-44.
    6. repec:kap:jrisku:v:54:y:2017:i:1:d:10.1007_s11166-017-9251-5 is not listed on IDEAS
    7. Matthew Ryan, 2015. "A Strict Stochastic Utility Theorem," Economics Bulletin, AccessEcon, vol. 35(4), pages 2664-2672.
    8. Michael H. Birnbaum & Ulrich Schmidt & Miriam D. Schneider, 2017. "Testing independence conditions in the presence of errors and splitting effects," Journal of Risk and Uncertainty, Springer, vol. 54(1), pages 61-85, February.
    9. Blavatskyy, Pavlo R., 2012. "Utility of a quarter-million," Economics Letters, Elsevier, vol. 117(3), pages 650-653.
    10. Blavatskyy, Pavlo, 2015. "Behavior in the centipede game: A decision-theoretical perspective," Economics Letters, Elsevier, vol. 133(C), pages 117-122.
    11. repec:eee:mateco:v:70:y:2017:i:c:p:176-184 is not listed on IDEAS
    12. Pavlo Blavatskyy, 2011. "Loss aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(1), pages 127-148, January.
    13. repec:eee:mateco:v:73:y:2017:i:c:p:142-148 is not listed on IDEAS
    14. Blavatskyy, Pavlo R., 2011. "Probabilistic risk aversion with an arbitrary outcome set," Economics Letters, Elsevier, vol. 112(1), pages 34-37, July.
    15. Pavlo Blavatskyy, 2014. "Stronger utility," Theory and Decision, Springer, vol. 76(2), pages 265-286, February.
    16. Dagsvik, John K, 2017. "Invariance Axioms and Functional Form Restrictions in Structural Models," Memorandum 08/2017, Oslo University, Department of Economics.
    17. Blavatskyy, Pavlo R., 2009. "How to extend a model of probabilistic choice from binary choices to choices among more than two alternatives," Economics Letters, Elsevier, vol. 105(3), pages 330-332, December.
    18. Blavatskyy, Pavlo, 2016. "Probability weighting and L-moments," European Journal of Operational Research, Elsevier, vol. 255(1), pages 103-109.
    19. Pavlo R. Blavatskyy, 2011. "A Model of Probabilistic Choice Satisfying First-Order Stochastic Dominance," Management Science, INFORMS, vol. 57(3), pages 542-548, March.
    20. repec:eee:matsoc:v:91:y:2018:i:c:p:85-95 is not listed on IDEAS
    21. Pavlo Blavatskyy & Ganna Pogrebna, 2010. "Reevaluating evidence on myopic loss aversion: aggregate patterns versus individual choices," Theory and Decision, Springer, vol. 68(1), pages 159-171, February.

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