Support for Geometric Pooling

Review of Symbolic Logic:1-40 (forthcoming)
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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 non-trivially Bayes-compatible. We show by contrast that geometric pooling can be non-trivially 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.

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Author Profiles

Rush T. Stewart
King's College London
Jean Baccelli
Oxford University

Citations of this work

Social Choice Theory.Christian List - 2013 - Stanford Encyclopedia of Philosophy.
Peirce, Pedigree, Probability.Rush T. Stewart & Tom F. Sterkenburg - 2022 - Transactions of the Charles S. Peirce Society 58 (2):138-166.

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Experts: Which Ones Should You Trust?Alvin I. Goldman - 2001 - Philosophy and Phenomenological Research 63 (1):85-110.
Belief and the Will.Bas C. van Fraassen - 2010 - In Antony Eagle (ed.), Philosophy of Probability: Contemporary Readings. Routledge. pp. 235-256.

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