Philosophy of Science:1-16 (forthcoming)

Rush T. Stewart
King's College London
Michael Nielsen
University of Sydney
A prominent pillar of Bayesian philosophy is that, relative to just a few constraints, priors “wash out” in the limit. Bayesians often appeal to such asymptotic results as a defense against charges of excessive subjectivity. But, as Seidenfeld and coauthors observe, what happens in the short run is often of greater interest than what happens in the limit. They use this point as one motivation for investigating the counterintuitive short run phenomenon of dilation since, it is alleged, “dilation contrasts with the asymptotic merging of posterior probabilities reported by Savage (1954) and by Blackwell and Dubins (1962)” (Herron et al., 1994). A partition dilates an event if, relative to every cell of the partition, uncertainty concerning that event increases. The measure of uncertainty relevant for dilation, however, is not the same measure that is relevant in the context of results concerning whether priors wash out or “opinions merge.” Here, we explicitly investigate the short run behavior of the metric relevant to merging of opinions. As with dilation, it is possible for uncertainty (as gauged by this metric) to increase relative to every cell of a partition. We call this phenomenon distention. It turns out that dilation and distention are orthogonal phenomena.
Keywords Consensus  dilation  distention  imprecise probabilities  merging of opinions  total variation distance  uncertainty  polarization
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DOI 10.1017/psa.2021.44
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Decision Theory as Philosophy.Mark Kaplan - 1983 - Philosophy of Science 50 (4):549-577.
Decision Theory as Philosophy.Mark Kaplan - 1996 - Cambridge University Press.

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