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Conditional non-expected utility preferences induced by mixture of lotteries: a note on the normative invalidity of expected utility theory

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  • Gebhard Geiger

    (Technical University of Munich)

Abstract

This research note is concerned with static choices between alternative mixtures of lotteries with one common mixture component and identical mixture weights. It is shown that the common component induces a conditional preference relation on the underlying lottery space with given (unconditional) preference structure. Induced preferences of this type arise in the comparisons with which the independence axiom of expected utility theory is specifically concerned. Given a few obvious properties of the induced preferences, two basic results are obtained: first, the conditionalisation operation is an order-preserving isomorphism, and, secondly, if the conditional preferences satisfy stochastic dominance preference, they necessarily violate the independence axiom. Together, the two results preclude any possibility of postulating independence consistently for static decision making under risk. The independence axiom is thus generally invalid as a normative principle of rational risky choice.

Suggested Citation

  • Gebhard Geiger, 2020. "Conditional non-expected utility preferences induced by mixture of lotteries: a note on the normative invalidity of expected utility theory," Annals of Operations Research, Springer, vol. 289(2), pages 431-448, June.
    • Handle: RePEc:spr:annopr:v:289:y:2020:i:2:d:10.1007_s10479-020-03528-5
    DOI: 10.1007/s10479-020-03528-5
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    1. John Weymark, 2005. "Measurement theory and the foundations of utilitarianism," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(2), pages 527-555, December.
    2. Segal, Uzi, 1990. "Two-Stage Lotteries without the Reduction Axiom," Econometrica, Econometric Society, vol. 58(2), pages 349-377, March.
    3. Gebhard Geiger, 2012. "Multi-attribute non-expected utility," Annals of Operations Research, Springer, vol. 196(1), pages 263-292, July.
    4. Blanchet-Scalliet, Christophette & El Karoui, Nicole & Jeanblanc, Monique & Martellini, Lionel, 2008. "Optimal investment decisions when time-horizon is uncertain," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1100-1113, December.
    5. Mohammed Abdellaoui & Han Bleichrodt & Olivier L’Haridon, 2008. "A tractable method to measure utility and loss aversion under prospect theory," Journal of Risk and Uncertainty, Springer, vol. 36(3), pages 245-266, June.
    6. Machina, Mark J., 1984. "Temporal risk and the nature of induced preferences," Journal of Economic Theory, Elsevier, vol. 33(2), pages 199-231, August.
    7. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-1668, December.
    8. Günter Franke & Harris Schlesinger & Richard C. Stapleton, 2006. "Multiplicative Background Risk," Management Science, INFORMS, vol. 52(1), pages 146-153, January.
    9. Joao L. Becker & Rakesh K. Sarin, 1987. "Lottery Dependent Utility," Management Science, INFORMS, vol. 33(11), pages 1367-1382, November.
    10. Y Malevergne & B Rey, 2010. "Preserving preference rankings under non-financial background risk," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(8), pages 1302-1308, August.
    11. A. Nebout, 2014. "Sequential decision making without independence: a new conceptual approach," Theory and Decision, Springer, vol. 77(1), pages 85-110, June.
    12. ,, 2011. "Dynamic choice under ambiguity," Theoretical Economics, Econometric Society, vol. 6(3), September.
    13. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    14. Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
    15. Pratt, John W, 1988. "Aversion to One Risk in the Presence of Others," Journal of Risk and Uncertainty, Springer, vol. 1(4), pages 395-413, December.
    16. Sarin, Rakesh & Wakker, Peter P, 1998. "Dynamic Choice and NonExpected Utility," Journal of Risk and Uncertainty, Springer, vol. 17(2), pages 87-119, November.
    17. Ilia Tsetlin & Robert L. Winkler, 2005. "Risky Choices and Correlated Background Risk," Management Science, INFORMS, vol. 51(9), pages 1336-1345, September.
    18. David M. Kreps & Evan L. Porteus, 2013. "Temporal von Neumann—Morgenstern and Induced Preferences," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 11, pages 181-206, World Scientific Publishing Co. Pte. Ltd..
    19. Enrico Diecidue & Jeroen van de Ven, 2008. "Aspiration Level, Probability Of Success And Failure, And Expected Utility," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 49(2), pages 683-700, May.
    20. Karni, Edi & Schmeidler, David, 1991. "Atemporal dynamic consistency and expected utility theory," Journal of Economic Theory, Elsevier, vol. 54(2), pages 401-408, August.
    21. Geiger, Gebhard, 2008. "An axiomatic account of status quo-dependent non-expected utility: Pragmatic constraints on rational choice under risk," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 116-142, March.
    22. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    23. John Quiggin, 2003. "Background risk in generalized expected utility theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(3), pages 607-611, October.
    24. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, September.
    25. Lionel Martellini & Branko Uroševi'{c}, 2006. "Static Mean-Variance Analysis with Uncertain Time Horizon," Management Science, INFORMS, vol. 52(6), pages 955-964, June.
    26. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
    27. Tversky, Amos & Kahneman, Daniel, 1986. "Rational Choice and the Framing of Decisions," The Journal of Business, University of Chicago Press, vol. 59(4), pages 251-278, October.
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    More about this item

    Keywords

    Rational choice; Risky choice; Normative theory; Expected utility; Independence axiom;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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