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SUPPORT FOR GEOMETRIC POOLING

Part of: Mathematical economics Foundations of probability theory Foundational and philosophical topics

Published online by Cambridge University Press:  21 October 2020

JEAN BACCELLI  and
RUSH T. STEWART
JEAN BACCELLI
Affiliation:
MCMP, LMU MUNICH MÜNCHEN, GERMANY E-mail: jean.baccelli@gmail.com
RUSH T. STEWART*
Affiliation:
MCMP, LMU MUNICH MÜNCHEN, GERMANY E-mail: jean.baccelli@gmail.com
*
E-mail: rush.stewart@lrz.uni-muenchen.de
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Abstract

Supra-Bayesianism is the Bayesian response to learning the opinions of others. Probability pooling constitutes an alternative response. One natural question is whether there are cases where probability pooling gives the supra-Bayesian result. This has been called the problem of Bayes-compatibility for pooling functions. It is known that in a common prior setting, under standard assumptions, linear pooling cannot be nontrivially Bayes-compatible. We show by contrast that geometric pooling can be nontrivially Bayes-compatible. Indeed, we show that, under certain assumptions, geometric and Bayes-compatible pooling are equivalent. Granting supra-Bayesianism its usual normative status, one upshot of our study is thus that, in a certain class of epistemic contexts, geometric pooling enjoys a normative advantage over linear pooling as a social learning mechanism. We discuss the philosophical ramifications of this advantage, which we show to be robust to variations in our statement of the Bayes-compatibility problem.

Keywords

supra-Bayesianismlinear poolinggeometric poolingBayes-compatibilitycommon priortotal evidencedeferencesynergy

MSC classification

Primary: 60A99: None of the above, but in this section
Secondary: 62A01: Foundations and philosophical topics 91B99: None of the above, but in this section
Type
Research Article
Information
The Review of Symbolic Logic , Volume 16 , Issue 1 , March 2023 , pp. 298 - 337
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Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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