Credal imprecision and the value of evidence

This paper is about a tension between two theses. The first is Value of Evidence : roughly, the thesis that it is always rational for an agent to gather and use cost-free evidence for making decisions. The second is Rationality of Imprecision : the thesis that an agent can be rationally required to adopt doxastic states that are imprecise , i.e., not representable by a single credence function. While others have noticed this tension, I offer a new diagnosis of it. I show that it arises when an agent with an imprecise doxastic state engages in an unreflective inquiry , an inquiry where they revise their beliefs using an updating rule that doesn’t satisfy a weak reflection principle. In such an unreflective inquiry, certain synchronic norms of instrumental rationality can make it instrumentally irrational for an agent to gather and use cost-free evidence. I then go on to propose a diachronic norm of instrumental rationality that preserves Value of Evidence in unreflective inquiries. This, I suggest, may help us reconcile this thesis with Rationality of Imprecision . Consider this argument. The success of our actions depends on the way the world is. We can only find out how the world is by gathering more evidence and revising our beliefs in light of it. So, if a piece of evidence is available for gathering and use, it always makes sense to gather that evidence and use it for making decisions.