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Bayesian Decision Theory and the Representation of Beliefs

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  • Edi Karni

Abstract

In this paper, I present a Bayesian decision theory and define choice-based subjective probabilities that faithfully represent Bayesian decision makers’ prior and posterior beliefs regarding the likelihood of the possible effects contingent on his actions. I argue that no equivalent results can be obtained in Savage’s (1954) subjective expected utility theory and give an example illustrating the potential harm caused by ascribing to a decision maker subjective probabilities that do not represent his beliefs.

Suggested Citation

  • Edi Karni, 2007. "Bayesian Decision Theory and the Representation of Beliefs," Discussion Paper Series dp444, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp444
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    References listed on IDEAS

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    1. Karni, Edi, 2003. "On the Representation of Beliefs by Probabilities," Journal of Risk and Uncertainty, Springer, vol. 26(1), pages 17-38, January.
    2. Costis Skiadas, 1997. "Conditioning and Aggregation of Preferences," Econometrica, Econometric Society, vol. 65(2), pages 347-368, March.
    3. Karni, Edi, 1996. "Probabilities and Beliefs," Journal of Risk and Uncertainty, Springer, vol. 13(3), pages 249-262, November.
    4. Karni, Edi, 2006. "Subjective expected utility theory without states of the world," Journal of Mathematical Economics, Elsevier, vol. 42(3), pages 325-342, June.
    5. 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.
    6. Karni, Edi, 2007. "Foundations of Bayesian theory," Journal of Economic Theory, Elsevier, vol. 132(1), pages 167-188, January.
    7. Grossman, Sanford J & Hart, Oliver D, 1983. "An Analysis of the Principal-Agent Problem," Econometrica, Econometric Society, vol. 51(1), pages 7-45, January.
    8. 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.
    9. Wakker, Peter, 1987. "Subjective probabilities for state dependent continuous utility," Mathematical Social Sciences, Elsevier, vol. 14(3), pages 289-298, December.
    10. Karni, Edi, 1993. "A Definition of Subjective Probabilities with State-Dependent Preferences," Econometrica, Econometric Society, vol. 61(1), pages 187-198, January.
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    Cited by:

    1. Edi Karni, 2008. "Agency theory: choice-based foundations of the parametrized distribution formulation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(3), pages 337-351, September.
    2. Aurélien Baillon, 2008. "Eliciting Subjective Probabilities Through Exchangeable Events: An Advantage and a Limitation," Decision Analysis, INFORMS, vol. 5(2), pages 76-87, June.
    3. Sadowski, Philipp, 2008. "Conditional Preference for Flexibility: Eliciting Beliefs from Behavior," MPRA Paper 8614, University Library of Munich, Germany.

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