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Foundations of Bayesian Theory

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  • Edi Karni

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.

Suggested Citation

  • Edi Karni, 2005. "Foundations of Bayesian Theory," Economics Working Paper Archive 524, The Johns Hopkins University,Department of Economics.
    • Handle: RePEc:jhu:papers:524
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    File URL: http://www.econ2.jhu.edu/REPEC/papers/wp524karni.pdf
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    References listed on IDEAS

    as
    1. Skiadas, Costis, 1997. "Subjective Probability under Additive Aggregation of Conditional Preferences," Journal of Economic Theory, Elsevier, vol. 76(2), pages 242-271, October.
    2. Karni, Edi, 2003. "On the Representation of Beliefs by Probabilities," Journal of Risk and Uncertainty, Springer, vol. 26(1), pages 17-38, January.
    3. Costis Skiadas, 1997. "Conditioning and Aggregation of Preferences," Econometrica, Econometric Society, vol. 65(2), pages 347-368, March.
    4. Karni, Edi, 1996. "Probabilities and Beliefs," Journal of Risk and Uncertainty, Springer, vol. 13(3), pages 249-262, November.
    5. Edi Karni & Philippe Mongin, 2000. "On the Determination of Subjective Probability by Choices," Management Science, INFORMS, vol. 46(2), pages 233-248, February.
    6. 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.
    7. Fishburn, Peter C, 1973. "A Mixture-Set Axiomatization of Conditional Subjective Expected Utility," Econometrica, Econometric Society, vol. 41(1), pages 1-25, January.
    8. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 83-92.
    9. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
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    11. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63(4), pages 309-309.
    12. 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.
    13. Mongin Philippe, 1995. "Consistent Bayesian Aggregation," Journal of Economic Theory, Elsevier, vol. 66(2), pages 313-351, August.
    14. Grant, Simon & Karni, Edi, 2004. "A theory of quantifiable beliefs," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 515-546, August.
    15. Luce, R Duncan & Krantz, David H, 1971. "Conditional Expected Utility," Econometrica, Econometric Society, vol. 39(2), pages 253-271, March.
    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 1321-1336, November.
    17. Wakker, Peter, 1987. "Subjective probabilities for state dependent continuous utility," Mathematical Social Sciences, Elsevier, vol. 14(3), pages 289-298, December.
    18. Karni Edi, 1993. "Subjective Expected Utility Theory with State-Dependent Preferences," Journal of Economic Theory, Elsevier, vol. 60(2), pages 428-438, August.
    19. Karni, Edi & Schmeidler, David & Vind, Karl, 1983. "On State Dependent Preferences and Subjective Probabilities," Econometrica, Econometric Society, vol. 51(4), pages 1021-1031, July.
    20. 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. Thibault Gajdos & Feriel Kandil, 2008. "The ignorant observer," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(2), pages 193-232, August.
    2. Brian Hill, 2009. "Living without state-independence of utilities," Theory and Decision, Springer, vol. 67(4), pages 405-432, October.
    3. Luo, Xiao & Yang, Chih-Chun, 2009. "Bayesian coalitional rationalizability," Journal of Economic Theory, Elsevier, vol. 144(1), pages 248-263, January.
    4. Daniele Pennesi, 2017. "Uncertain discount and hyperbolic preferences," Theory and Decision, Springer, vol. 83(3), pages 315-336, October.
    5. Hamed Hamze Bajgiran & Houman Owhadi, 2021. "Aggregation of Models, Choices, Beliefs, and Preferences," Papers 2111.11630, arXiv.org.
    6. Ralph Keeney & Robert Nau, 2011. "A theorem for Bayesian group decisions," Journal of Risk and Uncertainty, Springer, vol. 43(1), pages 1-17, August.
    7. Karni, Edi, 2006. "Subjective expected utility theory without states of the world," Journal of Mathematical Economics, Elsevier, vol. 42(3), pages 325-342, June.
    8. 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.
    9. Eddie Dekel & Barton L. Lipman, 2010. "How (Not) to Do Decision Theory," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 257-282, September.
    10. Alexander M. Jakobsen, 2021. "An Axiomatic Model of Persuasion," Econometrica, Econometric Society, vol. 89(5), pages 2081-2116, September.

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