I assign a credence 0.75 to p and I find out that you assign credence 0.72 to it, despite us both having the same evidence and epistemic prowess. According to conciliationism, I should lower my credence and you should raise yours.
Here's an interesting case. When I assigned 0.75 to p, I reasoned as follows: my evidence prima facie supported p to a high degree, say 0.90, but I know that I could have made a mistake in my evaluation of the evidence, so to be safe I lowered my credence to 0.75. You, being my peer and hence equally intellectually humble, proceeded similarly. You evaluated the evidence at 0.87 and then lowered the credence to 0.72 to be safe. Now when I learn that your credence is 0.72, I assume you were likewise being humbly cautious. So I assume you had some initial higher evaluation, but then lowered your evaluation to be on the safe side. But now that I know that both you and I evaluated the evidence significantly in favor of p, there is no justification for as much caution. As a result, I raise my credence. And maybe you proceed similarly. And if we're both advocates of the equal weight view, thinking that we should treat each others' credences on par, we will both raise our credence to the same value, say 0.80. As a result, you revise in the direction conciliationism tells you to (but further than most conciliationists would allow) and I revise in the opposite direction to what conciliationism says.
The case appears to be a counterexample to conciliationism. Now, one might argue that I was unfair to conciliationists. It's not uncommon in the literature to define conciliationism as simply the view that both need to change credence rather than the view that they must each change in the direction of the other's credence. And in my example, both change their credence. I think this reading of conciliationism isn't fair to the motivating intuitions or the etymology. Someone who, upon finding out about a disagreement, always changes her credence in the opposite direction of the other's credence is surely far from being a conciliatory person! Be that as it may, I suspect that counterexamples like the above can be tweaked. For instance, I might reasonably reason as follows:
You assign a smaller credence than I, though it's pretty close to mine. Maybe you started with an initial estimate close to but lower than mine and then lowered it by the same amount as I did out of caution. Since your initial estimate was lower than mine, I will lower mine a little. But since it was close, I don't need to be as cautious.It seems easy to imagine a case like this where the two effects cancel out, and I'm left with the same credence I started with. The result is a counterexample to a conciliationism that merely says I shouldn't stay pat.