The obvious position is that we should proportion our credences in P to the probability of P given our evidence. The hard work is all in working out what this amounts to. You have to say where your prior probability distribution should come from, what counts as evidence, how to deal with apparently non-propositional evidence, and so on. There is also an issue about actively seeking out evidence. Maybe we should make exceptions when not proportioning our credences to the evidence will enable us to get more evidence, so our beliefs will better approximate the truth in the long run. A stock example is when the fount of all knowledge can only be reached by jumping a chasm which you’re more likely to clear if you believe you will. But it seems that the action in epistemic virtue theory is in finding out how to emulate Sherlock when it comes to gathering evidence and making proper inferences from it. We don’t expect to have to emulate his sociopathy.
Lately that’s what I’ve questioning. When a friend, spouse or what have you tells you something, you are in many circumstances supposed to believe what they say. Suppose your wife tells you she was stuck at the office until 3am and slipped in a large puddle of beer on her way home. You could add that she has said this and that she came home stinking of beer when it was already getting light to the rest of your evidence and update like a good Bayesian, but perhaps this is one thought too many. Sometimes there are conflicts between being a good husband and a good Bayesian, and skill at resolving such conflicts is one of the things distinguishing the epistemically virtuous from the rest of us.
I don’t know what people whose day job it is to think about this sort of thing have thought about it, but I can see three natural responses. One is to say that belief isn’t voluntary and all this talk about epistemic virtues is wrongheaded. I’ll put that to one side. Another response is that the epistemic virtues and the virtues of personal concern aren’t the same and can conflict. I’m quite sympathetic towards that, but if it’s true then parity of reasoning would suggest that favouring our friends isn’t any more morally virtuous than believing our wives is epistemically virtuous. The last natural response is to say we’re called upon to practise a kind of doublethink, where we separate our credences as rational inquirers from the credences which rationalise our behaviour and which we profess to have. We can’t do this with the conflicts between morality and friendship because we have only one set of actions, but with credences it seems almost feasible.