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Updating confidence in beliefs

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  • Hill, Brian

Abstract

This paper develops a belief update rule under ambiguity, motivated by the maxim: in the face of new information, retain those conditional beliefs in which you are more confident, and relinquish only those in which you have less confidence. We provide a preference-based axiomatisation, drawing on the account of confidence in beliefs developed in Hill (2013). The proposed rule constitutes a general framework of which several existing rules for multiple priors (Full Bayesian, Maximum Likelihood) are special cases, but avoids the problems that these rules have with updating on complete ignorance. Moreover, it can handle surprising and null events, such as crises or reasoning in games, recovering traditional approaches, such as conditional probability systems, as special cases.

Suggested Citation

  • Hill, Brian, 2022. "Updating confidence in beliefs," Journal of Economic Theory, Elsevier, vol. 199(C).
    • Handle: RePEc:eee:jetheo:v:199:y:2022:i:c:s0022053121000260
    DOI: 10.1016/j.jet.2021.105209
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    1. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    2. Charles F. Manski, 2013. "Response to the Review of ‘Public Policy in an Uncertain World’," Economic Journal, Royal Economic Society, vol. 0, pages 412-415, August.
    3. Ricardo J. Caballero & Arvind Krishnamurthy, 2008. "Collective Risk Management in a Flight to Quality Episode," Journal of Finance, American Finance Association, vol. 63(5), pages 2195-2230, October.
    4. Cohen, M. & Gilboa, I. & Jaffray, J.Y. & Schmeidler, D., 2000. "An experimental study of updating ambiguous beliefs," Risk, Decision and Policy, Cambridge University Press, vol. 5(2), pages 123-133, June.
    5. Dietrich, Franz & List, Christian & Bradley, Richard, 2016. "Belief revision generalized: A joint characterization of Bayes' and Jeffrey's rules," Journal of Economic Theory, Elsevier, vol. 162(C), pages 352-371.
    6. 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.
    7. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    8. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    9. Stalnaker, Robert, 1998. "Belief revision in games: forward and backward induction1," Mathematical Social Sciences, Elsevier, vol. 36(1), pages 31-56, July.
    10. Louis Anthony (Tony) Cox, 2012. "Confronting Deep Uncertainties in Risk Analysis," Risk Analysis, John Wiley & Sons, vol. 32(10), pages 1607-1629, October.
    11. , & ,, 2007. "Updating preferences with multiple priors," Theoretical Economics, Econometric Society, vol. 2(3), September.
    12. Pietro Ortoleva, 2014. "Hypothesis Testing and Ambiguity Aversion," Rivista di Politica Economica, SIPI Spa, issue 3, pages 45-64, July-Sept.
    13. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    14. Cosmin L. Ilut & Martin Schneider, 2014. "Ambiguous Business Cycles," American Economic Review, American Economic Association, vol. 104(8), pages 2368-2399, August.
    15. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January.
    16. Justin Gallagher, 2014. "Learning about an Infrequent Event: Evidence from Flood Insurance Take-Up in the United States," American Economic Journal: Applied Economics, American Economic Association, vol. 6(3), pages 206-233, July.
    17. De Bondt, Werner F M & Thaler, Richard, 1985. "Does the Stock Market Overreact?," Journal of Finance, American Finance Association, vol. 40(3), pages 793-805, July.
    18. Manski, Charles F., 2013. "Public Policy in an Uncertain World: Analysis and Decisions," Economics Books, Harvard University Press, number 9780674066892, Spring.
    19. Larry G. Epstein & Martin Schneider, 2007. "Learning Under Ambiguity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(4), pages 1275-1303.
    20. Epstein Larry G. & Le Breton Michel, 1993. "Dynamically Consistent Beliefs Must Be Bayesian," Journal of Economic Theory, Elsevier, vol. 61(1), pages 1-22, October.
    21. Hill, Brian, 2019. "Confidence In Beliefs And Rational Decision Making," Economics and Philosophy, Cambridge University Press, vol. 35(2), pages 223-258, July.
    22. Gilboa, Itzhak & Minardi, Stefania & Samuelson, Larry, 2020. "Theories and cases in decisions under uncertainty," Games and Economic Behavior, Elsevier, vol. 123(C), pages 22-40.
    23. Pietro Ortoleva, 2012. "Modeling the Change of Paradigm: Non-Bayesian Reactions to Unexpected News," American Economic Review, American Economic Association, vol. 102(6), pages 2410-2436, October.
    24. Hill, Brian, 2016. "Incomplete preferences and confidence," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 83-103.
    25. Brian Hill, 2019. "Confidence In Beliefs And Rational Decision Making," Post-Print hal-01966705, HAL.
    26. Gajdos, T. & Hayashi, T. & Tallon, J.-M. & Vergnaud, J.-C., 2008. "Attitude toward imprecise information," Journal of Economic Theory, Elsevier, vol. 140(1), pages 27-65, May.
    27. Lawrence Blume & Adam Brandenburger & Eddie Dekel, 2014. "Lexicographic Probabilities and Choice Under Uncertainty," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 6, pages 137-160, World Scientific Publishing Co. Pte. Ltd..
    28. Aurélien Baillon & Han Bleichrodt & Umut Keskin & Olivier l’Haridon & Chen Li, 2018. "The Effect of Learning on Ambiguity Attitudes," Management Science, INFORMS, vol. 64(5), pages 2181-2198, May.
    29. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
    30. Gilboa, Itzhak & Postlewaite, Andrew & Schmeidler, David, 2009. "Is It Always Rational To Satisfy Savage'S Axioms?," Economics and Philosophy, Cambridge University Press, vol. 25(3), pages 285-296, November.
    31. repec:hal:pseose:halshs-01249635 is not listed on IDEAS
    32. Reny, Philip J, 1992. "Backward Induction, Normal Form Perfection and Explicable Equilibria," Econometrica, Econometric Society, vol. 60(3), pages 627-649, May.
    33. 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.
    34. 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.
    35. Cesaltina Pacheco Pires, 2002. "A Rule For Updating Ambiguous Beliefs," Theory and Decision, Springer, vol. 53(2), pages 137-152, September.
    36. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    37. Gul, Faruk & Pesendorfer, Wolfgang, 2021. "Evaluating ambiguous random variables from Choquet to maxmin expected utility," Journal of Economic Theory, Elsevier, vol. 192(C).
    38. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    39. Hill, Brian, 2013. "Confidence and decision," Games and Economic Behavior, Elsevier, vol. 82(C), pages 675-692.
    40. Dietrich, Franz & List, Christian & Bradley, Richard, 2016. "Belief revision generalized: A joint characterization of Bayes' and Jeffrey's rules," Journal of Economic Theory, Elsevier, vol. 162(C), pages 352-371.
    41. Myerson, Roger B, 1986. "Multistage Games with Communication," Econometrica, Econometric Society, vol. 54(2), pages 323-358, March.
    42. Brian Hill, 2020. "Dynamic consistency and ambiguity: A reappraisal," Post-Print hal-02457455, HAL.
    43. Hill, Brian, 2020. "Dynamic consistency and ambiguity: A reappraisal," Games and Economic Behavior, Elsevier, vol. 120(C), pages 289-310.
    44. De Bondt, Werner F M & Thaler, Richard H, 1987. "Further Evidence on Investor Overreaction and Stock Market Seasonalit y," Journal of Finance, American Finance Association, vol. 42(3), pages 557-581, July.
    45. Raffaella Giacomini & Vasiliki Skreta & Javier Turen, 2020. "Heterogeneity, Inattention, and Bayesian Updates," American Economic Journal: Macroeconomics, American Economic Association, vol. 12(1), pages 282-309, January.
    46. 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.
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    More about this item

    Keywords

    Belief update; Ambiguity; Multiple priors; Confidence; Complete ignorance; Update on surprising or null events;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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