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RichardKennaway comments on Say More, Justify Less - Less Wrong
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Aumann agreement requires knowing one's priors and posteriors. Actually knowing, i.e. being able to state the actual numbers. But no-one can do this.
Noone can do this exactly, but why isn't some approximation effective? To update in a Bayesian way we need to know our priors too, and not being able to state the numbers precisely isn't seen as a reason for not using Bayesian updating in a wide class of practical situations.
I would guess the problem isn't approximation, its the common knowledge no one has. You can't approximate this, and if anyone suspects it may not be completely true (which they should, since it isn't) the result completely falls apart.
I forgot the other requirement, and the more onerous one, for Aumann agreement: the two people's priors must already agree. This is absolutely unrealistic.
Strong Bayesians may say that there is a unique universal prior that every perfect Bayesian reasoner must have, but until that prior can be exhibited, Aumann agreement must remain a mirage. No-one has exhibited that prior.