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An Axiomatic Characterization of Bayesian Updating

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  • Alós-Ferrer, Carlos
  • Mihm, Maximilian

Abstract

We provide an axiomatic characterization of Bayesian updating, viewed as a mapping from prior beliefs and new information to posteriors, which is disentangled from any reference to preferences. Bayesian updating is characterized by Non-Innovativeness (events considered impossible in the prior remain impossible in the posterior), Dropping (events contradicted by new evidence are considered impossible in the posterior), and Proportionality (for other events, the posterior simply rescales the prior’s probabilities proportionally). The result clarifies the differences between the normative Bayesian benchmark, alternative models, and actual human behavior.

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  • Alós-Ferrer, Carlos & Mihm, Maximilian, 2023. "An Axiomatic Characterization of Bayesian Updating," Journal of Mathematical Economics, Elsevier, vol. 104(C).
    • Handle: RePEc:eee:mateco:v:104:y:2023:i:c:s0304406822001252
    DOI: 10.1016/j.jmateco.2022.102799
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    1. Luca Rigotti & Chris Shannon, 2005. "Uncertainty and Risk in Financial Markets," Econometrica, Econometric Society, vol. 73(1), pages 203-243, January.
    2. David M. Grether, 1980. "Bayes Rule as a Descriptive Model: The Representativeness Heuristic," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 95(3), pages 537-557.
    3. 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.
    4. Charles A. Holt & Susan K. Laury, 2002. "Risk Aversion and Incentive Effects," American Economic Review, American Economic Association, vol. 92(5), pages 1644-1655, December.
    5. Andrew Caplin & Daniel Martin, 2015. "A Testable Theory of Imperfect Perception," Economic Journal, Royal Economic Society, vol. 125(582), pages 184-202, February.
    6. Anja Achtziger & Carlos Alós-Ferrer, 2014. "Fast or Rational? A Response-Times Study of Bayesian Updating," Management Science, INFORMS, vol. 60(4), pages 923-938, April.
    7. Grether, David M., 1992. "Testing bayes rule and the representativeness heuristic: Some experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 17(1), pages 31-57, January.
    8. Shleifer, Andrei, 2000. "Inefficient Markets: An Introduction to Behavioral Finance," OUP Catalogue, Oxford University Press, number 9780198292272, Decembrie.
    9. Barberis, Nicholas & Shleifer, Andrei & Vishny, Robert, 1998. "A model of investor sentiment," Journal of Financial Economics, Elsevier, vol. 49(3), pages 307-343, September.
    10. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    11. Mihm, Maximilian, 2016. "Reference dependent ambiguity," Journal of Economic Theory, Elsevier, vol. 163(C), pages 495-524.
    12. Fama, Eugene F., 1998. "Market efficiency, long-term returns, and behavioral finance," Journal of Financial Economics, Elsevier, vol. 49(3), pages 283-306, September.
    13. Larry G. Epstein, 2006. "An Axiomatic Model of Non-Bayesian Updating," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(2), pages 413-436.
    14. David Easley & Maureen O'Hara, 2009. "Ambiguity and Nonparticipation: The Role of Regulation," Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1817-1843, May.
    15. Camerer, Colin F, 1987. "Do Biases in Probability Judgment Matter in Markets? Experimental Evidence," American Economic Review, American Economic Association, vol. 77(5), pages 981-997, December.
    16. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    17. Dow, James & Werlang, Sergio Ribeiro da Costa, 1992. "Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio," Econometrica, Econometric Society, vol. 60(1), pages 197-204, January.
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    2. Breitmoser, Yves & Valasek, Justin, 2023. "Why do committees work?," Discussion Paper Series in Economics 18/2023, Norwegian School of Economics, Department of Economics.

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    Keywords

    Belief updating; Bayesian learning;

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