Some quotes from Aumann's Agreement Theorem
I should not be able to predict the direction in which you're next going to disagree with me.
And that sort of rapid switching of the direction of disagreement. That's exactly what sort of an aumanian conversation should look like … If we could reach the point where I am expressed arguing for a more liberal position, and then five minutes later, I've switched, and I'm now arguing for the more conservative position, and then I switch back and so forth, that is actually a good sign.
Why should I just believe my opinion just because it's mine?