Scoring rules measures the inaccuracy of one's credences. Roughly, when p is true, and one assigns credence r to p, then a scoring rule measures the distance between r and 1, while when p is true, the scoring rule measures the distance between r and 0. The smaller the score, the better.
Some scoring rules are better than others. Let's suppose some scoring rules are right. Then this thesis seems to be implicit in some applications of scoring rules (e.g., here):
- If S is the right scoring rule, then a credence-assignment policy is epistemically rational only if following the policy minimizes expected total or average S-scores.
But (1) is false. Here's a simple counterexample that works for most reasonable scoring rules. Consider a situation like this: A fair coin is flipped. If you assign credence 0.51 to heads, a mindreader who knows your credence assignments will immediately reveal to you how the coin landed. Otherwise, you will never have any information on how the coin landed.
Obviously, the epistemically rational thing to do is to assign 0.5 to heads. But this leads to higher expected total and average scores on most reasonable scoring rules. For if you assign 0.51, then once the mindreader tells you how the coin landed, you will update your credence to be very close to 0 or 1, and your score will be very low. And the only cost of this scenario is the slight inoptimality from briefly having score 0.51 instead of the optimal score of 0.5. So the epistemically rational policy for dealing with situations like this, namely assigning 0.5, does less well in expected scores than the epistemically irrational policy of assigning 0.51.
The case may seem farfetched. But there are real-life cases that may be similar. It may be that for psychological reasons when you are a bit more sure, or a bit less sure (depending on your character and the thesis), of a thesis than rationality calls for, you will be better able to investigate whether the thesis is true. Thus it may be better for your long term epistemic score that you do what is epistemically irrational.