Examples often help. I don't know if you have a misconception - but a common misconception is that A and B need to share their evidence pertaining to the temperature rise before they can reach agreement.
What Aumann says - counterintuitively - is that no, they just need to share their estimates of the temperature rise with each other repeatedly - so each can update on the other's updates - and that is all. As the Cowen quote from earlier says:
"In essence his opinion serves as a 'sufficient statistic' for all of his evidence".
(nods) Examples do indeed help.
Suppose agent A has access to observations X1..X10, on the basis of which A concludes a 1-degree temperature rise.
Suppose agent B has access to observations X1..X9, on the basis of which A concludes a 2-degree temperature rise, and A and B are both perfect rationalists whose relevant priors are otherwise completely shared and whose posterior probabilities are perfectly calibrated to the evidence they have access to.
It follows that if B had access to X10, B would update and conclude a 2-degree rise. But neither A nor B know t...
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