Now, one Parfit-style objection to expressivism about single-case probabilities is as follows:
Bramsey suggests that betting dispositions might be mistaken in the sense that we would not have these dispositions if our standpoint were improved in certain ways. But to explain the sense in which this standpoint would be improved, Bramsey would have to claim that, if we had this standpoint, our betting dispositions would be less likely to be mistaken. This explanation would fail because it would have to use the word ‘mistaken’ in the sense that Bramsey is trying to explain.
Blackburn responds, "Comment should be unnecessary: Bramsey already explained why Bill is a better bookmaker than Kevin" -- namely, "Bill has, in thought or talk, a discursive practice of improving and refining his sensitivity to evidence, and thence his dispositions to buy and sell bets, and to make the judgments that are the propositional reflection of those dispositions. Kevin, of course, does the same, but is not nearly as good at it as Bill."
This strikes me as unsatisfying. For simplicity of exposition, let's focus in on a particular piece of evidence E: the fact that the horse Eclipse has a broken leg. And consider hypothesis H: that Eclipse will win the race. Now the question is: can the expressivist explain why it would be to the advantage of a book-keeper (selling bets on H) to learn E?
Here's a realist explanation: there's a metaphysical probability distribution over the possible worlds, corresponding to the antecedent objective chance of each world's being actualized. Now, the balance of probabilities more favours H in worlds where E is false than in worlds where E is true. So upon learning E, a book-keeper who takes this to lessen the chance of H is responding in a way that matches the real propensities of possible outcomes. Simply put: H is objectively less likely given E, and so it's no surprise that it's in the interests of a bookie to learn E, if he is disposed to respond by reducing his credence in H.
Now, the problem for the expressivist is that their view implies that there's no objective sense in which it's "more correct" to respond to E by lowering rather than raising one's credence in H. Of course, our epistemic practices favour this response. But we can imagine someone with wacky priors who instead takes the conditional probability of H given E to be greater than H given not-E. And it's an implication of expressivism that it's in some sense arbitrary which priors, or epistemic standards, we adopt. (Of course, from within their own practice, even expressivists will insist on first order claims about the other guy being "mistaken", and so on, but you know what I mean: it's arbitrary from an outside, objective perspective. The other guy can say all the same things about us, and there's nothing in the world that makes one of us right and the other wrong.)
So consider two bookies. Bill responds to E by lowering his credence in H. Bob responds to E by raising his credence in H. Objectively speaking, it's completely arbitrary which epistemic practice one happens to adopt. So in what sense is it to the advantage of both to learn E? Each might expect the new evidence to have positive utility for himself, insofar as their credence in H conditional on E differs from their credence in H. But each will likewise expect that the new evidence has negative utility for the other bookie, insofar as he's disposed to adjust his credence in H, upon learning E, in the opposite direction from them. Objectively speaking, it looks like a wash. Learning new "evidence" may cause changes in people's credences, which may either conform to our violate our epistemic norms; but if expressivism is true there's no further sense in which the changes could qualify as "improvements". (At least, assuming both agents are at least internally consistent, and so not susceptible to Dutch Books or the like.)
Am I missing something?