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On the Determination of Subjective Probability by Choices

Author

Listed:
  • Edi Karni

    (Department of Economics, Johns Hopkins University, Baltimore, Maryland 21218)

  • Philippe Mongin

    (THEMA, Centre National de la Recherche Scientifique and Université de Cergy-Pontoise, 33, Boulevard du Port, 95011 Cergy-Pontoise Cedex, France)

Abstract

The paper explores the uniqueness properties of the subjective probabilities in two axiomatizations of state-dependent preferences. Karni, Schmeidler, and Vind's (KSV 1983) system depends on selecting an arbitrary auxiliary probability, and as such, does not guarantee the uniqueness of the derived subjective probability. However, an axiom system initially designed by Karni and Schmeidler (KS 1981) and further elaborated upon here does guarantee the desired uniqueness as well as a useful property of "stability" of the derived solution. When the preference relation displays state-independence, even the KS probabilities may not agree with those derived from the classic Anscombe-Aumann (AA 1963) theorem. However, we claim that, in this case, the KS rather than the AA probabilities are the appropriate representation of the agent's beliefs.

Suggested Citation

  • Edi Karni & Philippe Mongin, 2000. "On the Determination of Subjective Probability by Choices," Management Science, INFORMS, vol. 46(2), pages 233-248, February.
    • Handle: RePEc:inm:ormnsc:v:46:y:2000:i:2:p:233-248
    DOI: 10.1287/mnsc.46.2.233.11929
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    References listed on IDEAS

    as
    1. Karni, Edi & Schmeidler, David, 1993. "On the Uniqueness of Subjective Probabilities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 267-277, April.
    2. Nau, Robert F, 1995. "Coherent Decision Analysis with Inseparable Probabilities and Utilities," Journal of Risk and Uncertainty, Springer, vol. 10(1), pages 71-91, January.
    3. Mark J. Schervish & Teddy Seidenfeld & Joseph B. Kadane, 1991. "Shared Preferences and State-Dependent Utilities," Management Science, INFORMS, vol. 37(12), pages 1575-1589, December.
    4. Karni, Edi & Schmeidler, David & Vind, Karl, 1983. "On State Dependent Preferences and Subjective Probabilities," Econometrica, Econometric Society, vol. 51(4), pages 1021-1031, July.
    5. Karni, Edi, 1996. "Probabilities and Beliefs," Journal of Risk and Uncertainty, Springer, vol. 13(3), pages 249-262, November.
    6. Karni, Edi, 1992. "Subjective Probabilities and Utility with Even-Dependent Preferences," Journal of Risk and Uncertainty, Springer, vol. 5(2), pages 107-125, May.
    7. Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, vol. 56(4), pages 279-279.
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    Citations

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    Cited by:

    1. Simon Grant & Edi Karni, 2005. "Why Does It Matter That Beliefs And Valuations Be Correctly Represented?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(3), pages 917-934, August.
    2. Brian Hill, 2009. "Living without state-independence of utilities," Theory and Decision, Springer, vol. 67(4), pages 405-432, October.
    3. Hammond, Peter J, 2013. "Extending the Original Position : Revisiting the Pattanaik Critique of Vickrey/Harsanyi Utilitarianism," The Warwick Economics Research Paper Series (TWERPS) 1008, University of Warwick, Department of Economics.
    4. Philippe Mongin, 2011. "La théorie de la décision et la psychologie du sens commun," Working Papers hal-00625445, HAL.
    5. Hill, Brian, 2010. "An additively separable representation in the Savage framework," Journal of Economic Theory, Elsevier, vol. 145(5), pages 2044-2054, September.
    6. Brian Hill, 2007. "Three Analyses of Sour Grapes," Working Papers hal-00582663, HAL.
    7. Blume, Lawrence E. & Cogley, Timothy & Easley, David A. & Sargent, Thomas J. & Tsyrennikov, Viktor, 2018. "A case for incomplete markets," Journal of Economic Theory, Elsevier, vol. 178(C), pages 191-221.
    8. DREZE , Jacques H. & RUSTICHINI, Aldo, 2000. "State-dependent utility and decision theory," LIDAM Discussion Papers CORE 2000007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Robert Nau, 2001. "De Finetti was Right: Probability Does Not Exist," Theory and Decision, Springer, vol. 51(2), pages 89-124, December.
    10. Giocoli, Nicola, 2011. "From Wald to Savage: homo economicus becomes a Bayesian statistician," MPRA Paper 34117, University Library of Munich, Germany.
    11. Karni, Edi, 2007. "Foundations of Bayesian theory," Journal of Economic Theory, Elsevier, vol. 132(1), pages 167-188, January.
    12. Jean Baccelli & Marcus Pivato, 2021. "Philippe Mongin (1950–2020)," Theory and Decision, Springer, vol. 90(1), pages 1-9, February.
    13. Stéphane Luchini, 2002. "De la singularité de la méthode d'évaluation contingente," Économie et Statistique, Programme National Persée, vol. 357(1), pages 141-152.
    14. Robert F. Nau, 2003. "A Generalization of Pratt-Arrow Measure to Nonexpected-Utility Preferences and Inseparable Probability and Utility," Management Science, INFORMS, vol. 49(8), pages 1089-1104, August.
    15. Hill, Brian, 2009. "When is there state independence?," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1119-1134, May.
    16. Helena Gaspars-Wieloch, 2018. "The Impact of the Structure of the Payoff Matrix on the Final Decision made Under Uncertainty," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(01), pages 1-27, February.
    17. Edi Karni & David Schmeidler, 2016. "An expected utility theory for state-dependent preferences," Theory and Decision, Springer, vol. 81(4), pages 467-478, November.
    18. Robert F. Nau, 2006. "Uncertainty Aversion with Second-Order Utilities and Probabilities," Management Science, INFORMS, vol. 52(1), pages 136-145, January.
    19. Sadowski, Philipp, 2008. "Conditional Preference for Flexibility: Eliciting Beliefs from Behavior," MPRA Paper 8614, University Library of Munich, Germany.
    20. Peter P. Wakker & Sylvia J. T. Jansen & Anne M. Stiggelbout, 2004. "Anchor Levels as a New Tool for the Theory and Measurement of Multiattribute Utility," Decision Analysis, INFORMS, vol. 1(4), pages 217-234, December.
    21. Grant, Simon & Karni, Edi, 2004. "A theory of quantifiable beliefs," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 515-546, August.

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    More about this item

    Keywords

    subjective probability; subjective expected utility; state-dependent utility;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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