Weighted averaging, Jeffrey conditioning and invariance

Theory and Decision 85 (1):21-39 (2018)
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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 and Jeffrey conditioning 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.



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Author Profiles

Denis Bonnay
Université Paris Nanterre
Mikael Cozic
Jean Moulin Lyon 3 University

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Support for Geometric Pooling.Jean Baccelli & Rush T. Stewart - 2023 - Review of Symbolic Logic 16 (1):298-337.

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References found in this work

Laws and symmetry.Bas C. Van Fraassen - 1989 - New York: Oxford University Press.
The Logic of Decision.Richard C. Jeffrey - 1965 - New York, NY, USA: University of Chicago Press.
Laws and Symmetry.Bas C. Van Fraassen - 1989 - Revue Philosophique de la France Et de l'Etranger 182 (3):327-329.
Probabilistic Opinion Pooling.Franz Dietrich & Christian List - 2016 - In Alan Hájek & Christopher Hitchcock (eds.), The Oxford Handbook of Probability and Philosophy. Oxford: Oxford University Press.
Conditionalization and observation.Paul Teller - 1973 - Synthese 26 (2):218-258.

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