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On the Determination of Subjective Probability by Choices

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  • 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.

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File URL: http://dx.doi.org/10.1287/mnsc.46.2.233.11929
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Bibliographic Info

Article provided by INFORMS in its journal Management Science.

Volume (Year): 46 (2000)
Issue (Month): 2 (February)
Pages: 233-248

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Handle: RePEc:inm:ormnsc:v:46:y:2000:i:2:p:233-248

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Related research

Keywords: subjective probability; subjective expected utility; state-dependent utility;

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Cited by:
  1. Robert Nau, 2001. "De Finetti was Right: Probability Does Not Exist," Theory and Decision, Springer, vol. 51(2), pages 89-124, December.
  2. Brian Hill, 2009. "Living without state-independence of utilities," Theory and Decision, Springer, vol. 67(4), pages 405-432, October.
  3. Grant, S. & Karni, E., 2002. "Why Does it Matter that Beliefs and Valuations be Correctly Represented?," Discussion Paper 2002-12, Tilburg University, Center for Economic Research.
  4. Hill, Brian, 2010. "An additively separable representation in the Savage framework," Journal of Economic Theory, Elsevier, vol. 145(5), pages 2044-2054, September.
  5. Grant, Simon & Karni, Edi, 2004. "A theory of quantifiable beliefs," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 515-546, August.
  6. Sadowski, Philipp, 2008. "Conditional Preference for Flexibility: Eliciting Beliefs from Behavior," MPRA Paper 8614, University Library of Munich, Germany.
  7. Edi Karni, 2005. "Foundations of Bayesian Theory," Economics Working Paper Archive 524, The Johns Hopkins University,Department of Economics.
  8. DREZE , Jacques H. & RUSTICHINI, Aldo, 2000. "State-dependent utility and decision theory," CORE Discussion Papers 2000007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Peter J. Hammond, 2013. "Extending the Original Position: Revisiting the Pattanaik Critique of Vickrey/Harsanyi Utilitarianism," Global COE Hi-Stat Discussion Paper Series gd12-298, Institute of Economic Research, Hitotsubashi University.
  10. Brian, HILL, 2007. "When is there state independence?," Les Cahiers de Recherche 883, HEC Paris.
  11. Hill, Brian, 2007. "Three analyses of sour grapes," Les Cahiers de Recherche 873, HEC Paris.
  12. Giocoli, Nicola, 2011. "From Wald to Savage: homo economicus becomes a Bayesian statistician," MPRA Paper 34117, University Library of Munich, Germany.
  13. Mongin, Philippe, 2013. "La théorie de la décision et la psychologie du sens commun," Les Cahiers de Recherche 943, HEC Paris.

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