= 27d567bc2d48d9f40e9ccc20ea370b15)
Psy-Kosh comments on The Aumann's agreement theorem game (guess 2/3 of the average) - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (149)
The Aumann agreement theorem, as I understand it, has to do with what happens when rational agents share all their data with each other.
But still, sending my guess.
I assume that the point is to test the assumption of common knowledge of rationality (which is crucial to Aumann agreement) rather than testing Aumann agreement directly.
The Aumann agreement theorem has to do with what happens when rational agents share a single probability estimate with each other. They need not share their evidence.
Ah, okay, thanks.
...and to whoever voted me and Robin Hanson down (not that they're necessarily the same person), if you think that we're wrong, please say so, so that our disagreement will be resolved through reasoning, not through brute force.
It wasn't me, but I think that your response is much better than Robin's, because instead of an unsupported flat out contradiction, you described what the theorem is actually about.
As near as I can tell, what the theorem says is that, provided two people have common knowledge (meaning not only that they know, but also that they know the other one knows, and that the other one knows they know, ad infinitum) that they are Bayesian rationalists with the same priors, that if they both give each other probability estimates for an event, and they don't then change their estimates, then their estimates must have been equal. It doesn't actually say how they should come to an agreement if their initial estimates differ, or even that they will.
Indeed, Aumann's original proof was not constructive. However, it has since been proved that the protocol "state your current posterior, update on the other agent's statement, repeat" will converge to agreement.
No, that is not what the agreement theorem is about.