See also:Related: Double-Crux, Conversation
Considered of particular relevance to disagreement between people trying to be rational, Aumann's agreement theorem can be informally interpreted as suggesting that if two people are honest seekers of truth, and both believe each other to be honest, then they should update on each other's opinions and quickly reach agreement. The very fact that a person believes something is Rational evidence that that something is true, and so this fact should be taken into account when forming your belief.
Outside of well-functioning prediction markets, Aumann agreement can probably only be approximated by careful deliberative discourse. Interest in Aumann agreement has waned in recent years within the Rationalist community, perhaps out of a sense Aumann agreement cannot be practically achieved by humans – there is too much background information to be exchanged. Instead, people now focus on things more like Double-Crux
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Disagreement is when two people have different beliefs.
See also: Double-Crux, Conversation