SUBJECTIVE PROBABILITIES NEED NOT BE SHARP (forthcoming in Erkenntnis)

Abstract It is well known that classical, aka ‘sharp’, Bayesian deci-sion theory, which models belief states as single probability functions, faces a number of serious difficulties with respect to its handling of ag-nosticism. These difficulties have led to the increasing popularity of so-called ‘imprecise ’ models of decision-making, which represent be-lief states as sets of probability functions. In a recent paper, however, Adam Elga has argued in favour of a putative normative principle of sequential choice that he claims to be borne out by the sharp model but not by any promising incarnation of its imprecise counterpart. After first pointing out that Elga has fallen short of establishing that his prin-ciple is indeed uniquely borne out by the sharp model, I cast aspersions on its plausibility. I show that a slight weakening of the principle is satisfied by at least one, but interestingly not all, varieties of the impre-cise model and point out that Elga has failed to motivate his stronger commitment.