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
Their posterior probabilities must then be the same. Consider two agents tasked with performing Bayesian analysis this is “perfectly rational”. From Wikipedia, the free encyclopedia. Studying the same issue from a different perspective, a research paper by Ziv Hellman considers what happens if priors are not common.
Retrieved from ” https: The Annals of Statistics. Simply knowing that another agent observed some information and came to their respective conclusion will force each to revise their beliefs, resulting eventually in total agreement on the correct posterior.
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External links Twitter Facebook Discord. This theorem is almost 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 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.
Afreeing, two rational Bayesian agents with the same priors and who know each other’s posteriors will have to agrering. This page was last modified on 12 Septemberat Business and economics portal Statistics portal Mathematics portal.
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However, Robin Agfeeing has presented an argument that Bayesians who agree about the processes that gave rise to their priors e.
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.
The paper presents a way to measure how distant priors are from being common. 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. Unless explicitly noted otherwise, all content licensed as indicated by RationalWiki: Community Saloon bar To do list What is going on? 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 disagree-amann journal.
Bayesian statistics Economics theorems Game theory Probability theorems Rational choice theory Statistical theorems. Topics in game theory. For such careful definitions of “perfectly rational” and “common knowledge” this is equivalent to saying agreing two functioning calculators will not give different answers tk the same input. International Journal of Game Theory. 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.
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.
Retrieved from ” https: Arrow’s impossibility theorem Aumann’s agreement theorem Folk theorem Minimax theorem Nash’s theorem Purification theorem Revelation principle Zermelo’s theorem.
Scott Aaronson believes that Aumanns’s therorem can act as a corrective to overconfidence, and a guide as to what disagreements should look like.
Aumann’s agreement theorem – Lesswrongwiki
Scott Aaronson  sharpens sisagree-aumann theorem by removing the common prior and limiting the number of messages communicated. Scott Aaronson has shown that this is indeed the case.
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, 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”.
The one-sentence summary is “you can’t actually agree to disagree”: This page was last edited on 6 Octoberat It may be worth noting that Yudkowsky has said he wouldn’t agree to try to reach an Aumann agreement with Hanson. Theory and Decision 61 4 — The Annals of Statistics 4 6 Polemarchakis, We can’t disagree forever, Journal of Economic Theory 28′: Articles with short description. 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.
Aumann’s agreement theorem says that two people acting rationally in a certain precise sense and with common knowledge of each other’s beliefs cannot agree to disagree. For concerns on copyright infringement please see: Views Read Edit View history.