Local and global deference

A norm of local expert deference says that your credence in an arbitrary proposition A, given that the expert’s probability for A is n, should be n. A norm of global expert deference says that your credence in A, given that the expert’s entire probability function is E, should be E(A). Gaifman taught us that these two norms are not equivalent. Stalnaker conjectures that Gaifman’s example is “a loophole”. Here, I substantiate Stalnaker’s suspicions by providing characterisation theorems which tell us precisely when the two norms come apart. They tell us that, in a good sense, Gaifman’s example is the only case where the two norms differ. I suggest that the lesson of the theorems is that Bayesian epistemologists need not concern themselves with the differences between these two kinds of norms. While they are not strictly speaking equivalent, they are equivalent for all philosophical purposes.