Generalized Probabilism: Dutch Books and Accuracy Domination [Book Review]

Journal of Philosophical Logic 41 (5):811-840 (2012)
Abstract
Jeff Paris (2001) proves a generalized Dutch Book theorem. If a belief state is not a generalized probability (a kind of probability appropriate for generalized distributions of truth-values) then one faces ‘sure loss’ books of bets. In <span class='Hi'>Williams</span> (manuscript) I showed that Joyce’s (1998) accuracy-domination theorem applies to the same set of generalized probabilities. What is the relationship between these two results? This note shows that (when ‘accuracy’ is treated via the Brier Score) both results are easy corollaries of the core result that Paris appeals to in proving his dutch book theorem (Minkowski’s separating hyperplane theorem). We see that every point of accuracy-domination defines a dutch book, but we only have a partial converse.
Keywords Dutch book  Probability  Accuracy  conditionalization
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References found in this work BETA
A. Hajek (2008). Arguments for-or Against-Probabilism? British Journal for the Philosophy of Science 59 (4):793-819.

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