I'm going to offer three arguments for a conclusion I found quite counterintuitive when I got to it, and which I still find counterintuitive, but I can't get out of the arguments for it.
Argument 1. There is a game being played in my sight. The player chooses some value (e.g., a number, a pair of numbers, etc.) and gets a payoff that is a function of the value she chose and some facts that I have no information whatsoever about. Moreover, the payoff function is the same for each player, and the facts don't change between players. I see Jones playing and choosing some value v. I don't get to see what payoff Jones gets. What value should I choose? I think there is a very good case that I should choose v, just as Jones did. After all, I know that I have no information about the unknown facts, but for all I know, Jones knows something more about them than I do (if that's not true, then I do know something about the unknown facts, namely that Jones doesn't know anything about them).
Now, suppose that the game is the game of assigning credences (whether these be point values, intervals, fuzzy intervals, etc.) to a proposition p, and that the payoff function is the right epistemic utility function measuring how close one's credence is to the actual truth value of p. If I should maximize epistemic utility, I get the conclusion that if I know nothing about p other than that you assign to it a credence r, then I should assign to it credence r. Note: I will assume throughout this post that the credences we are talking about are neither 0 or nor 1—there are some exceptional edge effects in the case of those extreme credences, such as that Bayesian information won't shift us out of them (we might have special worries about irreversible decisions, which may trump the above argument).
I find this result quite counterintuitive. My own intuition is that when I know nothing about p other than the credence you assign to p, I should assign to p a downgrade of your credence—I should shift your credence closer to 1/2. But contradicts the conclusion I draw from the above argument.
I can get to the more intuitive result if I have reason to think Jones is less risk averse than I am. In the case of many reasonable epistemic utility measures, risk averseness will push one towards 1/2. So perhaps my intuition that you should downgrade the other's credence, that you should not epistemically trust the other as you trust yourself, comes from an intuition that I am more epistemically risk averse than others. But, really, I have little reason to think that I am more epistemically risk averse than others (though I do have reason to think that I am more non-epistemically risk averse than others).
Argument 2: Suppose I have no information about some quantity Q (say, the number of hairs you've got, the gravitational constant, etc.) other than that Jones' best estimate for Q is r. What should my best estimate for Q be? Surely r. But now suppose I have no information about a proposition p, except that Jones' best estimate for how well p is supported by her evidence is r. Then my best estimate for how well p is supported by Jones' evidence is r. And since I have no evidence to add to the pot, and since my credence should match evidential support (barring some additional moral or pragmatic considerations, which I don't have reason to think apply, since I have no additional information about p), I should have credence r. (Again, it doesn't matter if credences are points or intervals vel caetera.)
Let me make a part of my thinking more explicit. If I have no further information on Q, which Jones estimates to be r, it is equally likely that Jones is under-estimating Q as that Jones is over-estimating Q, so even if I don't trust Jones very much, unless I have specific information that Jones is likely to over-estimate or under-estimate, I should take Q as my best estimate. If Q is the degree to which p is supported by Jones' evidence, then the thought is that Jones might over-estimate this (epistemic incautiousness) or Jones might under-estimate it (undue epistemic caution). Here the assumption that we're not working with extreme credences comes in, since, say, if Jones assigns 1, she can't be under-estimating.
Argument 3: This is the argument that got me started on this line of thought. Imagine two scenarios.
Scenario 1: I have partial amnesia—I forget all information relevant to the proposition p, including information as to how reliable I am in judgments of the p sort. And I don't gain any new evidence. But I do find a notebook where I wrote that I assign credence r to p. I am certain the notebook is accurate as to what credence I assigned. What credence should I assign?
Scenario 2: Same as Scenario 1, except that the notebook lists Jones' credence r for p, not my credence. And I have no information on Jones' reliability, etc.
In Scenario 1, I should assign credence r to p. After all, I shouldn't downgrade (I assume upgrading is out of the question) credences that are stored in my memory, or else all my credences will have an implausible downward slide absent new evidence, and it shouldn't matter whether the credence is stored in memory or on paper.
But I should do in Scenario 2 exactly what I would do in Scenario 1. After all, barring information about reliability, why take my past self to be any more reliable than Jones? So, in Scenario 2, I should assign credence r, too. But the partial amnesia is doing no work in Scenario 2 other than ensuring I have no other information about p. So, given no other information about p, I should assign the same credence as Jones.
Final off-the-cuff remark: I am inclined to take this as a way of loving one's neighbor as oneself.[note 1]