I think LWers have been using "Aumann agreement" to refer to the whole literature spawned by Aumann's original paper, which includes explicit protocols for Bayesians to reach agreement. This usage seems reasonable, although I'm not sure if it's standard outside of our community.
This community already hopefully accepts that one can learn from knowing other people's opinions without knowing their arguments
I'm not sure this is right... Here's what I wrote in Probability Space & Aumann Agreement:
But in such methods, the agents aren't just moving closer to each other's beliefs. Rather, they go through convoluted chains of deduction to infer what information the other agent must have observed, given his declarations, and then update on that new information. The two agents essentially still have to communicate I(w) and J(w) to each other, except they do so by exchanging posterior probabilities and making logical inferences from them.
Is there a result in the literature that shows something closer to your "one can learn from knowing other people's opinions without knowing their arguments"?
I haven't read your post and my understanding is still hazy, but surely at least the theorems don't depend on the agents being able to fully reconstruct each other's evidence? If they do, then I don't see how it could be true that the probability the agents end up agreeing on is sometimes different from the one they would have had if they were able to share information. In this sort of setting I think I'm comfortable calling it "updating on each other's opinions".
Regardless of Aumann-like results, I don't see how:
...one can learn from knowing othe
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