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Belief revision generalized: A joint characterization of Bayes' and Je¤rey's rules

Author

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  • Franz Dietrich

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Christian List

    (LSE - London School of Economics and Political Science)

  • Richard Bradley

    (LSE - London School of Economics and Political Science)

Abstract

We present a general framework for representing belief-revision rules and use it to characterize Bayes' rule as a classical example and Jeffrey's rule as a non-classical one. In Je¤rey's rule, the input to a belief revision is not simply the information that some event has occurred, as in Bayes' rule, but a new assignment of probabilities to some events. Despite their differences, Bayes' and Je¤rey's rules can be characterized in terms of the same axioms: responsiveness, which requires that revised beliefs incorporate what has been learnt, and conservativeness, which requires that beliefs on which the learnt input is 'silent' do not change. To illustrate the use of non-Bayesian belief revision in economic theory, we sketch a simple decision-theoretic application.

Suggested Citation

  • Franz Dietrich & Christian List & Richard Bradley, 2016. "Belief revision generalized: A joint characterization of Bayes' and Je¤rey's rules," PSE-Ecole d'économie de Paris (Postprint) halshs-01249635, HAL.
    • Handle: RePEc:hal:pseptp:halshs-01249635
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01249635
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    References listed on IDEAS

    as
    1. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2006. "Interactive unawareness," Journal of Economic Theory, Elsevier, vol. 130(1), pages 78-94, September.
    2. Modica, Salvatore & Rustichini, Aldo, 1999. "Unawareness and Partitional Information Structures," Games and Economic Behavior, Elsevier, vol. 27(2), pages 265-298, May.
    3. Dietrich, Franz, 2012. "Modelling change in individual characteristics: An axiomatic framework," Games and Economic Behavior, Elsevier, vol. 76(2), pages 471-494.
    4. Eddie Dekel & Barton L. Lipman & Aldo Rustichini, 1998. "Standard State-Space Models Preclude Unawareness," Econometrica, Econometric Society, vol. 66(1), pages 159-174, January.
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    Cited by:

    1. Franz Dietrich & Wlodek Rabinowicz, 2018. "Introduction to the special issue “Beliefs in Groups” of Theory and Decision," Theory and Decision, Springer, vol. 85(1), pages 1-4, July.
    2. Hill, Brian, 2022. "Updating confidence in beliefs," Journal of Economic Theory, Elsevier, vol. 199(C).
    3. Denis Bonnay & Mikaël Cozic, 2018. "Weighted averaging, Jeffrey conditioning and invariance," Theory and Decision, Springer, vol. 85(1), pages 21-39, July.

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    More about this item

    Keywords

    fine-grained versus coarse-grained beliefs; axio-matic foundations; Belief revision; subjective probability; Bayes's rule; Je¤rey's rule; unawareness;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • 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
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

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