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Foundations of Bayesian theory

  • Karni, Edi

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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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 132 (2007)
Issue (Month): 1 (January)
Pages: 167-188

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Handle: RePEc:eee:jetheo:v:132:y:2007:i:1:p:167-188
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  1. Gilboa, I. & Samet, D. & Schmeidler, D., 2001. "Utilitarian Aggregation of Beliefs and Tastes," Papers 2001-17, Tel Aviv.
  2. Karni, E. & Mongin, P., 1997. "On the Determination of Subjective Probability by Choices," Papers 9737, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
  3. Karni, Edi & Schmeidler, David & Vind, Karl, 1983. "On State Dependent Preferences and Subjective Probabilities," Econometrica, Econometric Society, vol. 51(4), pages 1021-31, July.
  4. MONGIN, Philippe, 1993. "Consistent Bayesian Aggregation," CORE Discussion Papers 1993019, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Fishburn, Peter C, 1973. "A Mixture-Set Axiomatization of Conditional Subjective Expected Utility," Econometrica, Econometric Society, vol. 41(1), pages 1-25, January.
  6. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
  7. Karni, Edi & Schmeidler, David, 1993. "On the Uniqueness of Subjective Probabilities," Economic Theory, Springer, vol. 3(2), pages 267-77, April.
  8. Karni Edi, 1993. "Subjective Expected Utility Theory with State-Dependent Preferences," Journal of Economic Theory, Elsevier, vol. 60(2), pages 428-438, August.
  9. Dreze, Jacques H. & Rustichini, Aldo, 1999. "Moral hazard and conditional preferences," Journal of Mathematical Economics, Elsevier, vol. 31(2), pages 159-181, March.
  10. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63, pages 309.
  11. Wakker, Peter, 1987. "Subjective probabilities for state dependent continuous utility," Mathematical Social Sciences, Elsevier, vol. 14(3), pages 289-298, December.
  12. Karni, Edi, 1993. "A Definition of Subjective Probabilities with State-Dependent Preferences," Econometrica, Econometric Society, vol. 61(1), pages 187-98, January.
  13. Karni, Edi, 2003. " On the Representation of Beliefs by Probabilities," Journal of Risk and Uncertainty, Springer, vol. 26(1), pages 17-38, January.
  14. Grant, Simon & Karni, Edi, 2004. "A theory of quantifiable beliefs," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 515-546, August.
  15. Skiadas, Costis, 1997. "Subjective Probability under Additive Aggregation of Conditional Preferences," Journal of Economic Theory, Elsevier, vol. 76(2), pages 242-271, October.
  16. 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.
  17. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer, vol. 20(1), pages 83-92.
  18. Karni, Edi, 1996. "Probabilities and Beliefs," Journal of Risk and Uncertainty, Springer, vol. 13(3), pages 249-62, November.
  19. Luce, R Duncan & Krantz, David H, 1971. "Conditional Expected Utility," Econometrica, Econometric Society, vol. 39(2), pages 253-71, March.
  20. Costis Skiadas, 1997. "Conditioning and Aggregation of Preferences," Econometrica, Econometric Society, vol. 65(2), pages 347-368, March.
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