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Creutzer comments on Personal Evidence - Superstitions as Rational Beliefs - Less Wrong
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In practice, though, how are they going to attain knowledge of each other's posteriors without communicating?
Actually, to agree on a proposition, they only need to have common knowledge of their posteriors for that proposition. (At least this is how Aumann describes his result.) And they can communicate those posteriors without communicating their evidence.
You're right, of course. It was wrong of me to confuse communicating their posterior with communicating their evidence.