Betting Interpretation and the Problem of Interference

We consider a fundamental problem for the betting interpretation of degrees of belief: There is a sense in which degrees of belief cannot be interpreted as betting rates. The bets we are disposed to accept do not reflect our current unconditional degrees of belief in various propositions. Whether a bet on A would be accepted or not does not depend on the agent’s degree of belief in A but rather on the degree of belief she would have if she were confronted with this bet proposal, or – more generally – the degree of belief she would have if she were in a position to bet on A. Assuming the conditionalization model for belief change, this means that whether the agent would be willing to bet depends on her current conditional beliefs concerning A on the supposition that she has an opportunity to make this bet. Furthermore, her disposition to bet also depends on the expected effects the act of betting would have on the truth of the proposition to be betted on. Both these phenomena imply that finding oneself in a betting situation might alter one’s expectations in important ways. Consequently, the identification of (unconditional) degrees of belief with betting rates is a mistake. The reason is, to put it shortly, that we need to take 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. This suggestion will be developed in what follows.