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Weighted averaging, Jeffrey conditioning and invariance

Author

Listed:
  • Denis Bonnay

    (Université Paris-Ouest Nanterre and IHPST)

  • Mikaël Cozic

    (Université Paris-Est Créteil (EA LIS), IUF and IHPST)

Abstract

Jeffrey conditioning tells an agent how to update her priors so as to grant a given probability to a particular event. Weighted averaging tells an agent how to update her priors on the basis of testimonial evidence, by changing to a weighted arithmetic mean of her priors and another agent’s priors. We show that, in their respective settings, these two seemingly so different updating rules are axiomatized by essentially the same invariance condition. As a by-product, this sheds new light on the question how weighted averaging should be extended to deal with cases when the other agent reveals only parts of her probability distribution. The combination of weighted averaging (for the events whose probability the other agent reveals) and Jeffrey conditioning (for the events whose probability the other agent does not reveal) is a comprehensive updating rule to deal with such cases, which is again axiomatized by invariance under embedding. We conclude that, even though one may dislike Jeffrey conditioning or weighted averaging, the two make a natural pair when a policy for partial testimonial evidence is needed.

Suggested Citation

  • Denis Bonnay & Mikaël Cozic, 2018. "Weighted averaging, Jeffrey conditioning and invariance," Theory and Decision, Springer, vol. 85(1), pages 21-39, July.
    • Handle: RePEc:kap:theord:v:85:y:2018:i:1:d:10.1007_s11238-017-9639-3
    DOI: 10.1007/s11238-017-9639-3
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    References listed on IDEAS

    as
    1. Dietrich, Franz & List, Christian & Bradley, Richard, 2016. "Belief revision generalized: A joint characterization of Bayes' and Jeffrey's rules," Journal of Economic Theory, Elsevier, vol. 162(C), pages 352-371.
    2. Dietrich, Franz & List, Christian & Bradley, Richard, 2016. "Belief revision generalized: A joint characterization of Bayes' and Jeffrey's rules," Journal of Economic Theory, Elsevier, vol. 162(C), pages 352-371.
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