Coin flips, credences and the Reflection Principle

Abstract

One recent topic of debate in Bayesian epistemology has been the question of whether imprecise credences can be rational. I argue that one account of imprecise credences, the orthodox treatment as defended by James M. Joyce, is untenable. Despite Joyce's claims to the contrary, a puzzle introduced by Roger White shows that the orthodox account, when paired when Bas C. van Fraassen's Reflection Principle, can lead to inconsistent beliefs. Proponents of imprecise credences, then, must either provide a compelling reason to reject Reflection or admit that the rational credences in White's case are precise.

Global Constraints on Imprecise Credences: Solving Reflection Violations, Belief Inertia, and Other Puzzles

“…22 For similar remarks, see Schoenfield ( 2012 ) and Topey ( 2012 ). 23 For an early discussion of the rational permissibility of dilation, see Seidenfeld and Wasserman ( 1993 ).…”

“…The idea of tempering Value Reflection in response to dilation examples is discussed briefly by Schoenfield ( 2012 ) and Topey ( 2012 ). Both authors consider something like the following substitute for Value Reflection :…”

“…So, if Reflection is to be at all useful as a principle, some psychological differences must be irrelevant to its applicability. (Topey 2012, 485)…”

Distention for Sets of Probabilities

“…Some see in dilation grounds for rejecting the notion that imprecise probabilities provide a normatively permissible generalization of standard Bayesian probability theory (e.g., White, 2010;Topey, 2012). It is not just that it seems intuitively wrong that learning should increase uncertainty.…”