Good Books and Imprecise Probability

This paper explores the related questions of (i) whether there is a pragmatic presumption against imprecise probabilities and (ii) how imprecise probabilities should be integrated into a normative theory of rational choice. Elga (2008) argues that one rather natural way of effecting this integration allows an agent to reject each of a series of bets that promises a positive payout. A number of possible solutions to the case are argued to bear commitments in tension with basic assumptions of normative decision theory. Though we propose and tentatively defend a “higher-order” decision rule that seems to yield the right result in Elga’s case, it is far from obvious that it can avoid the problems attributed to other proposed solutions. The upshot: the champion of imprecise probabilities in Bayesian formal epistemology has a rather deep problem on her hands, and it behooves her to come up with some better solutions.