Probabilistic Opinion Pooling with Imprecise Probabilities

Journal of Philosophical Logic 47 (1):17-45 (2018)

Rush T. Stewart
Ludwig Maximilians Universität, München
Ignacio Ojea Quintana
Australian National University
The question of how the probabilistic opinions of different individuals should be aggregated to form a group opinion is controversial. But one assumption seems to be pretty much common ground: for a group of Bayesians, the representation of group opinion should itself be a unique probability distribution, 410–414, [45]; Bordley Management Science, 28, 1137–1148, [5]; Genest et al. The Annals of Statistics, 487–501, [21]; Genest and Zidek Statistical Science, 114–135, [23]; Mongin Journal of Economic Theory, 66, 313–351, [46]; Clemen and Winkler Risk Analysis, 19, 187–203, [7]; Dietrich and List [14]; Herzberg Theory and Decision, 1–19, [28]). We argue that this assumption is not always in order. We show how to extend the canonical mathematical framework for pooling to cover pooling with imprecise probabilities by employing set-valued pooling functions and generalizing common pooling axioms accordingly. As a proof of concept, we then show that one IP construction satisfies a number of central pooling axioms that are not jointly satisfied by any of the standard pooling recipes on pain of triviality. Following Levi, 3–11, [39]), we also argue that IP models admit of a much better philosophical motivation as a model of rational consensus.
Keywords Aggregation Social epistemology  Consensus  Imprecise probabilities  Pooling  Social epistemology
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DOI 10.1007/s10992-016-9415-9
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References found in this work BETA

Imprecise Probabilities.Seamus Bradley - 2019 - Stanford Encyclopedia of Philosophy.
Probabilistic Opinion Pooling.Franz Dietrich & Christian List - 2016 - In A. Hajek & C. Hitchcock (eds.), Oxford Handbook of Philosophy and Probability. Oxford: Oxford University Press.
Decision Theory as Philosophy.Mark Kaplan - 1983 - Philosophy of Science 50 (4):549-577.

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Citations of this work BETA

Persistent Disagreement and Polarization in a Bayesian Setting.Michael Nielsen & Rush T. Stewart - forthcoming - British Journal for the Philosophy of Science:axy056.

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