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Stochastic utility theorem

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  • Blavatskyy, Pavlo R.
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    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].

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Mathematical Economics.

    Volume (Year): 44 (2008)
    Issue (Month): 11 (December)
    Pages: 1049-1056

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    Handle: RePEc:eee:mateco:v:44:y:2008:i:11:p:1049-1056

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    Web page: http://www.elsevier.com/locate/jmateco

    Related research

    Keywords: Expected utility theory Stochastic utility Fechner model Luce choice model Tremble;

    References

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    1. Blavatskyy, Pavlo R., 2006. "Violations of betweenness or random errors?," Economics Letters, Elsevier, Elsevier, vol. 91(1), pages 34-38, April.
    2. George Wu & Richard Gonzalez, 1996. "Curvature of the Probability Weighting Function," Management Science, INFORMS, INFORMS, vol. 42(12), pages 1676-1690, December.
    3. Chew, S H & Epstein, Larry G & Segal, U, 1991. "Mixture Symmetry and Quadratic Utility," Econometrica, Econometric Society, Econometric Society, vol. 59(1), pages 139-63, January.
    4. Starmer, Chris & Sugden, Robert, 1989. " Probability and Juxtaposition Effects: An Experimental Investigation of the Common Ratio Effect," Journal of Risk and Uncertainty, Springer, Springer, vol. 2(2), pages 159-78, June.
    5. Wu, George, 1994. "An Empirical Test of Ordinal Independence," Journal of Risk and Uncertainty, Springer, Springer, vol. 9(1), pages 39-60, July.
    6. Hey, John D. & Carbone, Enrica, 1995. "Stochastic choice with deterministic preferences: An experimental investigation," Economics Letters, Elsevier, Elsevier, vol. 47(2), pages 161-167, February.
    7. Faruk Gul & Wolfgang Pesendorfer, 2006. "Random Expected Utility," Econometrica, Econometric Society, Econometric Society, vol. 74(1), pages 121-146, 01.
    8. Hey, John D., 1995. "Experimental investigations of errors in decision making under risk," European Economic Review, Elsevier, Elsevier, vol. 39(3-4), pages 633-640, April.
    9. Harless, David W & Camerer, Colin F, 1994. "The Predictive Utility of Generalized Expected Utility Theories," Econometrica, Econometric Society, Econometric Society, vol. 62(6), pages 1251-89, November.
    10. Loomes, Graham & Sugden, Robert, 1998. "Testing Different Stochastic Specifications of Risky Choice," Economica, London School of Economics and Political Science, London School of Economics and Political Science, vol. 65(260), pages 581-98, November.
    11. Ballinger, T Parker & Wilcox, Nathaniel T, 1997. "Decisions, Error and Heterogeneity," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 107(443), pages 1090-1105, July.
    12. Camerer, Colin F, 1989. " An Experimental Test of Several Generalized Utility Theories," Journal of Risk and Uncertainty, Springer, Springer, vol. 2(1), pages 61-104, April.
    13. 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, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 19(3), pages 633-46, October.
    14. Carbone, Enrica, 1997. "Investigation of stochastic preference theory using experimental data," Economics Letters, Elsevier, Elsevier, vol. 57(3), pages 305-311, December.
    15. Loomes, Graham & Sugden, Robert, 1995. "Incorporating a stochastic element into decision theories," European Economic Review, Elsevier, Elsevier, vol. 39(3-4), pages 641-648, April.
    16. David Buschena & David Zilberman, 2000. "Generalized Expected Utility, Heteroscedastic Error, and Path Dependence in Risky Choice," Journal of Risk and Uncertainty, Springer, Springer, vol. 20(1), pages 67-88, January.
    17. Camerer, Colin F & Ho, Teck-Hua, 1994. "Violations of the Betweenness Axiom and Nonlinearity in Probability," Journal of Risk and Uncertainty, Springer, Springer, vol. 8(2), pages 167-96, March.
    18. Pavlo Blavatskyy, 2007. "Stochastic expected utility theory," Journal of Risk and Uncertainty, Springer, Springer, vol. 34(3), pages 259-286, June.
    19. Graham Loomes, 2005. "Modelling the Stochastic Component of Behaviour in Experiments: Some Issues for the Interpretation of Data," Experimental Economics, Springer, Springer, vol. 8(4), pages 301-323, December.
    20. Machina, Mark J, 1985. "Stochastic Choice Functions Generated from Deterministic Preferences over Lotteries," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 95(379), pages 575-94, September.
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    Citations

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    Cited by:
    1. Pavlo Blavatskyy, 2011. "Loss aversion," Economic Theory, Springer, Springer, vol. 46(1), pages 127-148, January.
    2. John D. Hey & Andrea Morone & Ulrich Schmidt, 2007. "Noise and Bias in Eliciting Preferences," Kiel Working Papers, Kiel Institute for the World Economy 1386, Kiel Institute for the World Economy.
    3. Pavlo Blavatskyy, 2014. "Stronger utility," Theory and Decision, Springer, Springer, vol. 76(2), pages 265-286, February.
    4. Pavlo Blavatskyy, 2012. "Probabilistic choice and stochastic dominance," Economic Theory, Springer, Springer, vol. 50(1), pages 59-83, May.
    5. 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, Elsevier, vol. 105(3), pages 330-332, December.
    6. Pavlo Blavatskyy & Ganna Pogrebna, 2010. "Reevaluating evidence on myopic loss aversion: aggregate patterns versus individual choices," Theory and Decision, Springer, Springer, vol. 68(1), pages 159-171, February.
    7. Blavatskyy, Pavlo R., 2011. "Probabilistic risk aversion with an arbitrary outcome set," Economics Letters, Elsevier, Elsevier, vol. 112(1), pages 34-37, July.
    8. Blavatskyy, Pavlo R., 2012. "Utility of a quarter-million," Economics Letters, Elsevier, Elsevier, vol. 117(3), pages 650-653.
    9. Blavatskyy, Pavlo, 2013. "Which decision theory?," Economics Letters, Elsevier, Elsevier, vol. 120(1), pages 40-44.

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