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A Joint Characterization of Belief Revision Rules

Author

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

Abstract

This paper characterizes different belief revision rules in a unified framework: Bayesian revision upon learning some event, Jeffrey revision upon learning new probabilities of some events, Adams revision upon learning some new conditional probabilities, and `dual-Jeffrey' revision upon learning an entire new conditional probability function. Though seemingly different, these revision rules follow from the same two principles: responsiveness, which requires that revised beliefs be consistent with the learning experience, and conservativeness, which requires that those beliefs of the agent on which the learning experience is `silent' (in a technical sense) do not change. So, the four revision rules apply the same revision policy, yet to different kinds of learning experience.

Suggested Citation

  • Dietrich, Franz & List, Christian & Bradley, Richard, 2012. "A Joint Characterization of Belief Revision Rules," MPRA Paper 41240, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:41240
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    File URL: https://mpra.ub.uni-muenchen.de/71304/1/MPRA_paper_71304.pdf
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    References listed on IDEAS

    as
    1. Wakker, Peter P, 2001. "Testing and Characterizing Properties of Nonadditive Measures through Violations of the Sure-Thing Principle," Econometrica, Econometric Society, vol. 69(4), pages 1039-1059, July.
    2. Franz Dietrich, 2010. "Bayesian group belief," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(4), pages 595-626, October.
    3. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521802345.
    4. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2006. "Interactive unawareness," Journal of Economic Theory, Elsevier, vol. 130(1), pages 78-94, September.
    5. Modica, Salvatore & Rustichini, Aldo, 1999. "Unawareness and Partitional Information Structures," Games and Economic Behavior, Elsevier, vol. 27(2), pages 265-298, May.
    6. Wakker,Peter P., 2010. "Prospect Theory," Cambridge Books, Cambridge University Press, number 9780521765015.
    7. Sarin, Rakesh & Wakker, Peter, 1994. "A General Result for Quantifying Beliefs," Econometrica, Econometric Society, vol. 62(3), pages 683-685, May.
    8. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    9. Eddie Dekel & Barton L. Lipman & Aldo Rustichini, 1998. "Standard State-Space Models Preclude Unawareness," Econometrica, Econometric Society, vol. 66(1), pages 159-174, January.
    10. Hylland, Aanund & Zeckhauser, Richard J, 1979. "The Impossibility of Bayesian Group Decision Making with Separate Aggregation of Beliefs and Values," Econometrica, Econometric Society, vol. 47(6), pages 1321-1336, November.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Subjective probability; Bayes's rule; Jeffrey's rule; axiomatic foundations; unawareness;

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D00 - Microeconomics - - General - - - General

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