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Symmetry arguments against regular probability: a reply to recent objections. (English) Zbl 1428.60004

Summary: A probability distribution is regular if it does not assign probability zero to any possible event. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. C. Howson [ibid. 7, No. 1, 97–102 (2017; Zbl 1384.60011)] and V. Benci et al. [Br. J. Philos. Sci. 69, No. 2, 509–552 (2018; Zbl 1400.03006)] have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that T. Williamson’s “isomorphic” events [Analysis, Oxf. 67, No. 3, 173–180 (2007; Zbl 1158.60304)] are not in fact isomorphic, but Howson is speaking of set-theoretic representations of events in a probability model. While those sets are not isomorphic, Williamson’s physical events are, in the relevant sense. Benci et al. claim that all three arguments rest on a conflation of different models, but they do not. They are founded on the premise that similar events should have the same probability in the same model, or in one case, on the assumption that a single rotation-invariant distribution is possible. Having failed to refute the symmetry arguments on such technical grounds, one could deny their implicit premises, which is a heavy cost, or adopt varying degrees of instrumentalism or pluralism about regularity, but that would not serve the project of accurately modelling chances.

MSC:

60A05 Axioms; other general questions in probability
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