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Weighted averaging, Jeffrey conditioning and invariance

Denis Bonnay () and Mikaël Cozic ()
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Denis Bonnay: Université Paris-Ouest Nanterre and IHPST
Mikaël Cozic: Université Paris-Est Créteil (EA LIS), IUF and IHPST

Theory and Decision, 2018, vol. 85, issue 1, 21-39

Abstract: 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.

Keywords: Jeffrey conditioning; Aggregations of opinion; Linear pooling; Weighted averaging; Geometric averaging; Testimony (search for similar items in EconPapers)
Date: 2018
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Handle: RePEc:kap:theord:v:85:y:2018:i:1:d:10.1007_s11238-017-9639-3