A Note on “Agreeing to Disagree”
According to the Aumann's agreement theorem, disagreement might seem irrational. On the other hand, if we use a system of expressing “what your personal analysis says while simultaneously adjusting your private opinions (which might be revealed in your actions) closer to the opinions of the majority,” then disagreements are more apparent than real. In such a system, “agreeing to disagree” can turn into “You look for evidence for X and I'll look for evidence for Y,” which makes sense if one person knows more about X (for example, if it was the religion he was raised in) and the other more about Y. This even makes “confirmation bias” look more rational.
On the other hand, this makes refusal to listen to a dissenter far less rational. It should be reserved for persons who are not arguing in good faith.