The paper’s target is the historically influential betting interpretation of subjective probabilities due to Ramsey and de Finetti. While there are several classical and well-known objections to this interpretation, the paper focuses on just one fundamental problem: There is a sense in which degrees of belief cannot be interpreted as betting rates. The reasons differ in different cases, but there’s one crucial feature that all these cases have in common: The agent’s degree of belief in a proposition A does not (...) coincide with her degree of belief in a conditional that A would be the case if she were to bet on A, where the belief in this conditional itself is conditioned on the supposition that the agent will have an opportunity to make such a bet. Even though the two degrees of belief sometimes can coincide (they will coincide in those cases when the bet has no expected causal bearings on the proposition A and the opportunity to bet have no evidential bearings on that proposition), it is the latter belief rather than the former that guides the agent’s rational betting behaviour. The reason is that this latter belief takes into consideration potential interferences that bet opportunities and betting itself might create with regard to the proposition to be betted on. It is because of this interference problem that the agent’s degree of belief in A cannot be interpreted as her betting rate for A. (shrink)

The Puzzle of the Hats is a puzzle in social epistemology. It describes a situation in which a group of rational agents with common priors and common goals seems vulnerable to a Dutch book if they are exposed to different information and make decisions independently. Situations in which this happens involve violations of what might be called the Group-Reflection Principle. As it turns out, the Dutch book is flawed. It is based on the betting interpretation of the subjective probabilities, but (...) ignores the fact that this interpretation disregards strategic considerations that might influence betting behavior. A lesson to be learned concerns the interpretation of probabilities in terms of fair bets and, more generally, the role of strategic considerations in epistemic contexts. Another lesson concerns Group-Reflection, which in its unrestricted form is highly counter-intuitive. We consider how this principle of social epistemology should be re-formulated so as to make it tenable. (shrink)