Reopening the Dutch Book

Probabilism is the thesis that the degrees of belief of rational agents behave like Kolmogorovian probabilities. There are quite different lines of argument for probabilism in the literature, including Dutch book arguments, arguments based on representation theorems, and epistemic utility arguments. This paper focusses on the Dutch book line of argument, the core idea of which is that nonprobabilistic degrees of belief generate irrational betting behavior. Different versions of the argument have been presented, often in response to objections to earlier versions. The aim of this paper is to develop a new, stronger version that avoids the problems of previous iterations—indeed to formulate the best possible argument based on the core idea.