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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Theory and Decision 61 4 — However, Robin Hanson has presented an argument that Bayesians who agree about the processes that gave rise to their priors e. In game theoryAumann’s agreement theorem is a theorem which demonstrates that rational agents with common knowledge of each other’s beliefs cannot agree to disagree.
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. The paper presents a way to measure how distant priors are from being common.
Aumann’s agreement theorem – Wikipedia
Yudkowsky ‘s mentor Robin Hanson tries to handwave this with something about genetics and environment,  but to have sufficient common knowledge of genetics and environment for this to work practically would require a few calls to Laplace’s demon. More specifically, if two people are genuine Bayesian rationalists with common priorsand if they each have common knowledge of their individual posterior probabilitiesthen their posteriors must be equal.
Simply knowing that another agent ayreeing some information and came to their respective conclusion will force each to revise their beliefs, resulting eventually in total agreement on the correct posterior.
From Wikipedia, the free encyclopedia. Or the paper’s own example, the disagree-auann of a coin — such a simple example having been chosen for accessibility, it demonstrates the problem agreelng applying such an oversimplified concept of information to real-world situations.
Thus, two rational Bayesian agents with the same priors and who know each other’s posteriors will have to agree. Arrow’s impossibility theorem Aumann’s agreement theorem Folk theorem Minimax theorem Nash’s theorem Purification theorem Disagree-aujann principle Zermelo’s theorem.
It may be worth noting that Yudkowsky has said he wouldn’t agree to try to reach an Aumann agreement with Hanson. Both sets of information include the posterior sisagree-aumann arrived at by the other, as well as the fact that their prior probabilities are the same, the fact that the other knows agrering posterior probability, the 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”.
For disagrse-aumann 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? Nash equilibrium Subgame perfection Mertens-stable equilibrium Bayesian Nash equilibrium Perfect Bayesian equilibrium Trembling hand Proper equilibrium Epsilon-equilibrium Correlated equilibrium Sequential equilibrium Quasi-perfect equilibrium Evolutionarily stable strategy Risk dominance Core Shapley value Pareto efficiency Gibbs equilibrium Quantal response equilibrium Self-confirming equilibrium Strong Nash equilibrium Markov perfect equilibrium.
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Aumann’s agreement theorem
Bayesian statistics Economics theorems Game theory Probability theorems Rational choice theory Statistical theorems. Studying the same issue agrering a different perspective, a research paper by Ziv Hellman considers what happens if priors are not common.
Business and economics portal Statistics portal Mathematics portal. This theorem is disagre-eaumann as much a favorite of LessWrong as the “Sword of Bayes”  itself, because of its popular phrasing along the lines of “two agents acting rationally The one-sentence summary is “you can’t actually agree to disagree”: A question arises whether such an agreement can be reached in a reasonable time and, from a mathematical perspective, whether this can be done efficiently.
Essentially, the proof goes that if they were not, it would mean that they did not trust the accuracy of one another’s information, or did not trust the other’s computation, since a different probability being found by a 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.
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Their posterior probabilities must then be the same. Views Read Edit View history.
The Annals of Statistics. Scott Aaronson has shown that this is indeed the case. Views Read Edit Fossil record. Polemarchakis, We can’t disagree forever, Journal of Economic Theory 28′: Retrieved from ” https: Aumann’s agreement theorem  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.
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