Aumann’s agreement theorem says that two people acting rationally (in a certain precise sense) and with common knowledge of each other’s beliefs cannot agree to disagree. More specifically, if two people are genuine Bayesian rationalists with common priors, and if they each have common knowledge of their individual posterior probabilities, then their posteriors must be equal.
With common priors.
This is what does all the work there! If the disagreeers have non-equal priors on one of the points, then of course they’ll have different posteriors.
Of course applying Bayes’ Theorem with the same inputs is going to give the same outputs, that’s not even a theorem, that’s an equals sign.
If the disagreeers find a different set of parameters to be relevant, and/or the parameters they both find relevant do not have the same values, the outputs will differ, and they will continue to disagree.
Aumann’s agreement theorem says that two people acting rationally (in a certain precise sense) and with common knowledge of each other’s beliefs cannot agree to disagree. More specifically, if two people are genuine Bayesian rationalists with common priors, and if they each have common knowledge of their individual posterior probabilities, then their posteriors must be equal.
With common priors.
This is what does all the work there! If the disagreeers have non-equal priors on one of the points, then of course they’ll have different posteriors.
Of course applying Bayes’ Theorem with the same inputs is going to give the same outputs, that’s not even a theorem, that’s an equals sign.
If the disagreeers find a different set of parameters to be relevant, and/or the parameters they both find relevant do not have the same values, the outputs will differ, and they will continue to disagree.
Relevant: Why Common Priors