In Alan Hajek & Christopher Hitchcock (eds.), Oxford Handbook of Philosophy and Probability. Oxford: Oxford University Press (2016)

Franz Dietrich
Centre National de la Recherche Scientifique
Christian List
Ludwig Maximilians Universität, München
Suppose several individuals (e.g., experts on a panel) each assign probabilities to some events. How can these individual probability assignments be aggregated into a single collective probability assignment? This article reviews several proposed solutions to this problem. We focus on three salient proposals: linear pooling (the weighted or unweighted linear averaging of probabilities), geometric pooling (the weighted or unweighted geometric averaging of probabilities), and multiplicative pooling (where probabilities are multiplied rather than averaged). We present axiomatic characterisations of each class of pooling functions (most of them classic, but one new) and argue that linear pooling can be justified procedurally, but not epistemically, while the other two pooling methods can be justified epistemically. The choice between them, in turn, depends on whether the individuals' probability assignments are based on shared information or on private information. We conclude by mentioning a number of other pooling methods.
Keywords Probabilistic opinion pooling  Judgment aggregation  Peer disagreement  Linear, geometric, and multiplicative pooling  Eventwise independence  Unanimity preservation  External Bayesianity  Credence aggregation
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Social Choice and Individual Values.Irving M. Copi - 1952 - Science and Society 16 (2):181-181.
Logical Constraints on Judgement Aggregation.Marc Pauly & Martin van Hees - 2006 - Journal of Philosophical Logic 35 (6):569 - 585.

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On the Accuracy of Group Credences.Richard Pettigrew - 2019 - Oxford Studies in Epistemology 6.
On the Accuracy of Group Credences.Richard Pettigrew - 2019 - Oxford Studies in Epistemology 6.

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