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Bayesian updating rules and AGM belief revision

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  • Basu, Pathikrit

Abstract

We interpret the problem of updating beliefs as a choice problem (selecting a posterior from a set of admissible posteriors) with a reference point (prior). We use AGM belief revision to define the support of admissible posteriors after arrival of information, which applies also to zero probability events. We study two classes of updating rules for probabilities: 1) “lexicographic” updating rules where posteriors are given by a lexicographic probability system 2) “minimum distance” updating rules which select the posterior closest to the prior by some metric. We show that an updating rule is lexicographic if and only if it is Bayesian, AGM-consistent and satisfies a weak form of path independence. While not all lexicographic updating rules have a minimum distance representation, we study a sub-class of lexicographic rules, which we call “support-dependent” rules, which admit a minimum distance representation. Finally, we apply our approach to the problem of updating preferences.

Suggested Citation

  • Basu, Pathikrit, 2019. "Bayesian updating rules and AGM belief revision," Journal of Economic Theory, Elsevier, vol. 179(C), pages 455-475.
    • Handle: RePEc:eee:jetheo:v:179:y:2019:i:c:p:455-475
    DOI: 10.1016/j.jet.2018.11.005
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    References listed on IDEAS

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    Cited by:

    1. Evan Sadler, 2021. "A Practical Guide to Updating Beliefs From Contradictory Evidence," Econometrica, Econometric Society, vol. 89(1), pages 415-436, January.
    2. Li, Jinfang, 2022. "The sentiment pricing dynamics with short-term and long-term learning," The North American Journal of Economics and Finance, Elsevier, vol. 63(C).
    3. Michele Crescenzi, 2023. "Group knowledge and individual introspection," Papers 2305.08729, arXiv.org, revised Sep 2023.

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    More about this item

    Keywords

    Bayesian updating; AGM belief revision; Information processing; Lexicographic updating;
    All these keywords.

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • 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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