Uncertainty, Vagueness, and Rational Decision

Abstract Nicholas J.J. Smith (2014) has argued that there are different kinds of degrees of belief, but that they must be fused into one ‘all kinds considered’ degree of belief. We provide an example which shows that different kinds of degrees of belief can have diverging impacts on the rationality of a decision: there are cases in which two rational subjects with identical preferences and the same ‘all kinds considered’ degree of belief make different decisions. Thus, different kinds of degrees of belief should not be merged into a single degree-of-belief function.