This is a linkpost for http://www.scottaaronson.com/blog/?p=2410
It includes a great test of whether a given discussion is Aumann-rational:
what rational disagreements should look like: they should follow unbiased random walks, until sooner or later they terminate in common knowledge of complete agreement.
as opposed to
suppose your friend tells you a liberal opinion, then you take it into account, but reply with a more conservative opinion. The friend takes your opinion into account, and replies with a revised opinion. Question: is your friend’s new opinion likelier to be more liberal than yours, or more conservative?
Obviously, more liberal! Yes, maybe your friend now sees some of your points and vice versa, maybe you’ve now drawn a bit closer (ideally!), but you’re not going to suddenly switch sides because of one conversation.
Yet, if you and your friend are Bayesians with common priors, one can prove that that’s not what should happen at all.
The excellent Scott Aaronson has posted on his blog a version of a talk he recently gave at SPARC, about Aumann's agreement theorem and related topics. I think a substantial fraction of LW readers would enjoy it. As well as stating Aumann's theorem and explaining why it's true, the article discusses other instances where the idea of "common knowledge" (the assumption that does a lot of the work in the AAT) is important, and offers some interesting thoughts on the practical applicability (if any) of the AAT.
(Possibly relevant: an earlier LW discussion of AAT.)