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Robust Maximum Likelihood Updating

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  • Elchin Suleymanov

Abstract

There is a large body of evidence that decision makers frequently depart from Bayesian updating. This paper introduces a model, robust maximum likelihood (RML) updating, where deviations from Bayesian updating are due to multiple priors/ambiguity. Using the decision maker's preferences over acts before and after the arrival of new information as the primitive of the analysis, I axiomatically characterize a representation where the decision maker's probability assessment can be described by a benchmark prior, which is reflected in her ex ante ranking of acts, and a set of plausible priors, which is revealed from her updated preferences. When new information is received, the decision maker revises her benchmark prior within the set of plausible priors via the maximum likelihood principle in a way that ensures maximally dynamically consistent behavior, and updates the new prior using Bayes' rule. RML updating accommodates most commonly observed biases in probabilistic reasoning.

Suggested Citation

  • Elchin Suleymanov, 2025. "Robust Maximum Likelihood Updating," Papers 2504.17151, arXiv.org.
  • Handle: RePEc:arx:papers:2504.17151
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    References listed on IDEAS

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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. Brian Hill, 2022. "Updating confidence in beliefs," Post-Print hal-03503986, HAL.
    3. Gary Charness & Edi Karni & Dan Levin, 2013. "Ambiguity attitudes and social interactions: An experimental investigation," Journal of Risk and Uncertainty, Springer, vol. 46(1), pages 1-25, February.
    4. Dominiak, Adam & Duersch, Peter & Lefort, Jean-Philippe, 2012. "A dynamic Ellsberg urn experiment," Games and Economic Behavior, Elsevier, vol. 75(2), pages 625-638.
    5. repec:dau:papers:123456789/7333 is not listed on IDEAS
    6. , G. & , & ,, 2008. "Non-Bayesian updating: A theoretical framework," Theoretical Economics, Econometric Society, vol. 3(2), June.
    7. Matthew Kovach, 2024. "Ambiguity and partial Bayesian updating," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(1), pages 155-180, August.
    8. 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.
    9. Terrance Odean., 1996. "Volume, Volatility, Price and Profit When All Trader Are Above Average," Research Program in Finance Working Papers RPF-266, University of California at Berkeley.
    10. Cheng, Xiaoyu, 2022. "Relative Maximum Likelihood updating of ambiguous beliefs," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    11. Barberis, Nicholas & Shleifer, Andrei & Vishny, Robert, 1998. "A model of investor sentiment," Journal of Financial Economics, Elsevier, vol. 49(3), pages 307-343, September.
    12. De Filippis, Roberta & Guarino, Antonio & Jehiel, Philippe & Kitagawa, Toru, 2022. "Non-Bayesian updating in a social learning experiment," Journal of Economic Theory, Elsevier, vol. 199(C).
    13. , & ,, 2007. "Updating preferences with multiple priors," Theoretical Economics, Econometric Society, vol. 2(3), September.
    14. Bleichrodt, Han & Eichberger, Jürgen & Grant, Simon & Kelsey, David & Li, Chen, 2021. "Testing dynamic consistency and consequentialism under ambiguity," European Economic Review, Elsevier, vol. 134(C).
    15. Dale O. Stah, 2014. "Heterogeneity of Ambiguity Preferences," The Review of Economics and Statistics, MIT Press, vol. 96(4), pages 609-617, October.
    16. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    17. 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.
    18. Ken Binmore & Lisa Stewart & Alex Voorhoeve, 2012. "How much ambiguity aversion?," Journal of Risk and Uncertainty, Springer, vol. 45(3), pages 215-238, December.
    19. Andrea Wilson, 2014. "Bounded Memory and Biases in Information Processing," Econometrica, Econometric Society, vol. 82, pages 2257-2294, November.
    20. ,, 2011. "Dynamic choice under ambiguity," Theoretical Economics, Econometric Society, vol. 6(3), September.
    21. 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.
    22. Larry G Epstein & Yoram Halevy, 2024. "Hard-to-Interpret Signals," Journal of the European Economic Association, European Economic Association, vol. 22(1), pages 393-427.
    23. Roland G FryerJr & Philipp Harms & Matthew O Jackson, 2019. "Updating Beliefs when Evidence is Open to Interpretation: Implications for Bias and Polarization," Journal of the European Economic Association, European Economic Association, vol. 17(5), pages 1470-1501.
    24. Sandeep Baliga & Eran Hanany & Peter Klibanoff, 2013. "Polarization and Ambiguity," American Economic Review, American Economic Association, vol. 103(7), pages 3071-3083, December.
    25. Ke, Shaowei & Wu, Brian & Zhao, Chen, 2024. "Learning from a black box," Journal of Economic Theory, Elsevier, vol. 221(C).
    26. 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.
    27. Hill, Brian, 2022. "Updating confidence in beliefs," Journal of Economic Theory, Elsevier, vol. 199(C).
    28. Epstein Larry G & Noor Jawwad & Sandroni Alvaro, 2010. "Non-Bayesian Learning," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-20, January.
    29. Cesaltina Pacheco Pires, 2002. "A Rule For Updating Ambiguous Beliefs," Theory and Decision, Springer, vol. 53(2), pages 137-152, September.
    30. repec:bla:jfinan:v:53:y:1998:i:6:p:1887-1934 is not listed on IDEAS
    31. Zhao, Chen, 2022. "Pseudo-Bayesian updating," Theoretical Economics, Econometric Society, vol. 17(1), January.
    32. Matthew Rabin, 1998. "Psychology and Economics," Journal of Economic Literature, American Economic Association, vol. 36(1), pages 11-46, March.
    33. Gul, Faruk & Pesendorfer, Wolfgang, 2021. "Evaluating ambiguous random variables from Choquet to maxmin expected utility," Journal of Economic Theory, Elsevier, vol. 192(C).
    34. repec:dau:papers:123456789/7357 is not listed on IDEAS
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