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RichardKennaway comments on Say More, Justify Less - Less Wrong
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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 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.