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Larks comments on In Defense of Objective Bayesianism: MaxEnt Puzzle. - Less Wrong Discussion
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There are a couple of others, all of which seem to rely on being told probabilities. You assign P(A) = 0.5, and then get told that P(A) = 0.7.
It seems that either P(A) = 0.7 is someone else's degree of belief, in which case Aumann comes into play, or a statement about what your degree of belief should be, given your evidence. But idealised Bayesian agents don't make that sort of mistake!