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Foundations of Bayesian Theory

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Edi Karni

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Abstract

This paper states necessary and sufficient conditions for the existence, uniqueness, and updating according to Bayes?rule, of subjective probabilities representing individuals?beliefs. The approach is preference based, and the result is an axiomatic subjective expected utility model of Bayesian decision making under uncertainty with statedependent preferences. The theory provides foundations for the existence of prior probabilities representing decision makers?beliefs about the likely realization of events and for the updating of these probabilities according to Bayes?rule.

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Paper provided by The Johns Hopkins University,Department of Economics in its series Economics Working Paper Archive with number 524.

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Date of creation: Aug 2005
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Handle: RePEc:jhu:papers:524

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Skiadas, Costis, 1997. "Subjective Probability under Additive Aggregation of Conditional Preferences," Journal of Economic Theory, Elsevier, vol. 76(2), pages 242-271, October. [Downloadable!] (restricted)
  2. Karni, Edi, 1996. "Probabilities and Beliefs," Journal of Risk and Uncertainty, Springer, vol. 13(3), pages 249-62, November.
  3. Karni, Edi & Schmeidler, David, 1993. "On the Uniqueness of Subjective Probabilities," Economic Theory, Springer, vol. 3(2), pages 267-77, April.
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  4. Karni, Edi & Schmeidler, David & Vind, Karl, 1983. "On State Dependent Preferences and Subjective Probabilities," Econometrica, Econometric Society, vol. 51(4), pages 1021-31, July. [Downloadable!] (restricted)
  5. Wakker, Peter, 1987. "Subjective probabilities for state dependent continuous utility," Mathematical Social Sciences, Elsevier, vol. 14(3), pages 289-298, December. [Downloadable!] (restricted)
  6. E. Karni & Ph. Mongin, 1997. "On the determination of subjective probability by choices," THEMA Working Papers 97-37, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
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  7. Karni, Edi, 2003. " On the Representation of Beliefs by Probabilities," Journal of Risk and Uncertainty, Springer, vol. 26(1), pages 17-38, January. [Downloadable!] (restricted)
  8. Dreze, Jacques H. & Rustichini, Aldo, 1999. "Moral hazard and conditional preferences," Journal of Mathematical Economics, Elsevier, vol. 31(2), pages 159-181, March. [Downloadable!] (restricted)
  9. Mongin Philippe, 1995. "Consistent Bayesian Aggregation," Journal of Economic Theory, Elsevier, vol. 66(2), pages 313-351, August. [Downloadable!] (restricted)
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  10. Itzhak Gilboa & Dov Samet & David Schmeidler, 2004. "Utilitarian Aggregation of Beliefs and Tastes," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 932-938, August.
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  11. Grant, Simon & Karni, Edi, 2004. "A theory of quantifiable beliefs," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 515-546, August. [Downloadable!] (restricted)
  12. Karni, Edi, 1993. "A Definition of Subjective Probabilities with State-Dependent Preferences," Econometrica, Econometric Society, vol. 61(1), pages 187-98, January. [Downloadable!] (restricted)
  13. Luce, R Duncan & Krantz, David H, 1971. "Conditional Expected Utility," Econometrica, Econometric Society, vol. 39(2), pages 253-71, March. [Downloadable!] (restricted)
  14. Costis Skiadas, 1997. "Conditioning and Aggregation of Preferences," Econometrica, Econometric Society, vol. 65(2), pages 347-368, March.
  15. Hylland, Aanund & Zeckhauser, Richard J, 1979. "The Impossibility of Bayesian Group Decision Making with Separate Aggregation of Beliefs and Values," Econometrica, Econometric Society, vol. 47(6), pages 1321-36, November. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Edi Karni, 2007. "Bayesian Decision Theory and the Representation of Beliefs," Levine's Bibliography 321307000000000776, UCLA Department of Economics. [Downloadable!]
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  2. Thibault Gajdos & Feriel Kandil, 2008. "The ignorant observer," Social Choice and Welfare, Springer, vol. 31(2), pages 193-232, August. [Downloadable!] (restricted)
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  3. Eddie Dekel & Barton L. Lipman, 2009. "How (Not) to Do Decision Theory," Levine's Working Paper Archive 814577000000000339, David K. Levine. [Downloadable!]
  4. Grant, S. & Karni, E., 2002. "Why does it matter that beliefs and valuations be correctly represented?," Discussion Paper 12, Tilburg University, Center for Economic Research. [Downloadable!]
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  5. Edi Karni, 2005. "Subjective Expected Utility Theory without States of the World," Economics Working Paper Archive 523, The Johns Hopkins University,Department of Economics. [Downloadable!]
    Other versions:
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