Dutch Book Arguments and Consistency

Abstract

I consider Dutch Book arguments for three principles of classical Bayesianism: (i) agents' belief-probabilities are consistent only if they obey the probability axioms. (ii) beliefs are updated by Bayesian conditionalisation. (iii) that the so-called Principal Principle connects statistical and belief probabilities. I argue that while there is a sound Dutch Book argument for (i), the standard ones for (ii) based on the Lewis-Teller strategy are unsound, for reasons pointed out by Christensen. I consider a type of Dutch Book argument for (iii), where the statistical probability is a von Mises one.