 The assumptions of the DBA are significant. It is the agent’s system of credences together with the way they are involved in evaluating options that is implicated by the Dutch Book. To conclude that simply having incoherent credences is irrational, a further argument is needed showing that rationality demands that credences be linked to evaluations of bets as in the DBA, but there is little to suggest that graded degrees of belief must be so connected. Indeed, the DBA assumes not only that there is some connection between an agent’s credences and the evaluation of options, but that one should evaluate a bet as fair if it has an expected value of zero, using one’s credences with the standard expectation rule. This builds in that an agent’s credences are related such that for each \(H\),