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Belief revision generalized: a joint characterization of Bayes's and Jeffrey's rules

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Listed:
  • Dietrich, Franz
  • List, Christian
  • Bradley, Richard

Abstract

We present a general framework for representing belief-revision rules and use it to characterize Bayes's rule as a classical example and Jeffrey's rule as a non-classical one. In Jeffrey's rule, the input to a belief revision is not simply the information that some event has occurred, as in Bayes's rule, but a new assignment of probabilities to some events. Despite their differences, Bayes's and Jeffrey'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

  • Dietrich, Franz & List, Christian & Bradley, Richard, 2015. "Belief revision generalized: a joint characterization of Bayes's and Jeffrey's rules," LSE Research Online Documents on Economics 64836, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:64836
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    File URL: https://researchonline.lse.ac.uk/id/eprint/64836/
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    Cited by:

    1. is not listed on IDEAS
    2. Hill, Brian, 2022. "Updating confidence in beliefs," Journal of Economic Theory, Elsevier, vol. 199(C).
    3. 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.
    4. 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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    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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