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Dorikka comments on Alan Carter on the Complexity of Value - Less Wrong
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I'm pretty sure they do need to have the same priors.
My intuition is that AAT is basically saying that the perfect epistemic rationalists involved can essentially transfer all of the evidence that they have to the other, so that each one effectively has the same evidence and so should have the same posteriors...except that they'll still have different posteriors unless they began with the same priors.
If they found that they had different priors, I think that they could just communicate the evidence which led them to form those priors from previous priors and so forth, but I think that if they trace their priors as far back as possible and find that they have different ones, AAT doesn't work.
I'm not actually super-familiar with it, so update accordingly if I seem to have said something dumb.
Nope, I was wrong. It is the case that agents require equal priors for ATT to hold. AAT is like proving that mixing the same two colors of paint will always result in the same shade or that two equal numbers multiplied by another number will still be equal.
What a worthless theorem!
I guess when I read that AAT required "common priors" I assumed Aumann must mean known priors or knowledge of each others' priors, since equal priors would constitute both 1) an asinine assumption and, 2) a result not worth reporting. Hanson's assumption that humans should have a shared prior by virtue of being evolved together is interesting, but more creative than informative.
Good thing I don't rely on ATT for anything. It's obvious that disagreeing with most people is rational so updating on people's posteriors without evidence would be pretty unreasonable. I'm not surprised that ATT would turn out to be so meaningless.