Agreeing to Disagree. STOR. Robert J. Aumann. The Annals of Statistics, Vol. 4, No. 6 (Nov., ), Stable URL. In “Agreeing to Disagree” Robert Aumann proves that a group of current probabilities are common knowledge must still agree, even if those. “Agreeing to Disagree,” R. Aumann (). Recently I was discussing with a fellow student mathematical ideas in social science which are 1).

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Aumann’s agreement theorem [1] is the result of Robert Aumann’s, winner of the Swedish National Bank’s Prize in Economic Sciences in Memory of Alfred Nobelgroundbreaking discovery that a sufficiently respected game theorist can get anything into a peer-reviewed journal.

The one-sentence summary is “you can’t actually agree to disagree”: For such careful definitions of “perfectly rational” and “common knowledge” this is equivalent to saying that two functioning calculators will not give different answers on the same input.

Consider two agents tasked with performing Bayesian analysis this is “perfectly rational”. Both are given the same prior probability of the world being in a certain state, and separate sets of further information.

Both sets of information include the posterior probability arrived at by the other, as well as the fact that their prior probabilities are the same, the fact that the other knows its posterior probability, dixagree-aumann set of events that might affect probability, the fact that the other knows these things, the fact that the other knows it knows these things, the fact that the other knows it knows the other knows it knows, ad infinitum this is “common knowledge”. Their posterior probabilities must then be the disagre-eaumann.


Essentially, the proof goes that if they were not, it would mean that they did not dizagree-aumann the accuracy of one another’s information, or did not trust the other’s computation, since a different probability being found by ayreeing rational agent is itself evidence of further evidence, and a rational agent should recognize this, and also recognize that one would, and that this would also be recognized, and so on.

Scott Aaronson [3] sharpens this theorem by removing the common prior and limiting the number of messages communicated.

Aumann’s agreement theorem – Wikipedia

This theorem is almost as much a favorite of LessWrong as the “Sword of Bayes” [4] itself, because of its popular phrasing along the lines of “two agents acting rationally Unlike many questionable applications of theorems, this one appears to have been the intention of the paper itself, which itself cites a paper defending the application of such techniques to the real world.

For an illustration, how often do two mathematicians disagree on the invalidity of the proof within an agreed-upon framework, once one’s objections are known to the other? Or the paper’s own example, the fairness of a coin — such a simple example having been chosen for accessibility, it demonstrates the problem with applying such an oversimplified concept of information to real-world situations. Scott Aaronson believes that Aumanns’s therorem can act as a corrective to overconfidence, and a guide as to what disagreements should look like.


Yudkowsky ‘s mentor Robin Hanson tries to handwave this with something about genetics and environment, [9] but to have sufficient common knowledge of genetics and environment for this to work practically would require a few calls to Laplace’s demon.

It may be worth noting that Yudkowsky has said he wouldn’t agree to try to reach an Aumann agreement with Hanson. The Annals of Statistics 4 6 Polemarchakis, We can’t disagree forever, Journal of Economic Theory 28′: Theory and Decision 61 4 — Retrieved from ” https: Views Read Edit Fossil record.

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