Distention for Sets of Probabilities

Philosophy of Science (forthcoming)
Download Edit this record How to cite View on PhilPapers
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.
PhilPapers/Archive ID
Upload history
First archival date: 2020-08-23
Latest version: 3 (2021-06-20)
View other versions
Added to PP index

Total views
94 ( #45,422 of 2,448,611 )

Recent downloads (6 months)
27 ( #24,358 of 2,448,611 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.