Weighted averaging, Jeffrey conditioning and invariance
Theory and Decision 85 (1):21-39 (2018)
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 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.Author Profiles
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Citations of this work
Support for Geometric Pooling.Jean Baccelli & Rush T. Stewart - forthcoming - Review of Symbolic Logic:1-40.
Learning from others: conditioning versus averaging.Richard Bradley - 2017 - Theory and Decision 85 (1):5-20.
An Interpretation of Weights in Linear Opinion Pooling.Jan-Willem Romeijn - forthcoming - Episteme:1-15.
References found in this work
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 Hajek & Christopher Hitchcock (eds.), Oxford Handbook of Philosophy and Probability. Oxford: Oxford University Press.