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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Both sets of information include the posterior probability arrived at by the other, disgaree-aumann 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 dlsagree-aumann it knows these things, the fact that the other knows it knows the other knows it knows, ad infinitum this is “common knowledge”.
It was first formulated in the paper titled agreeng to Disagree” by Robert Aumannafter whom the theorem is named. 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. Bayesian statistics Economics theorems Game theory Probability theorems Rational choice theory Statistical theorems.
Aumann’s agreement theorem – RationalWiki
However, Robin Hanson has presented an argument that Bayesians who agree about the processes that gave rise to their priors e. This page was last modified on 12 Septemberat Both are given the same prior probability of the world being in a certain state, and separate sets of further information. The Annals of Statistics. 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.
Scott Aaronson  sharpens this theorem by removing the common prior and limiting the number of messages communicated.
Polemarchakis, We can’t disagree forever, Journal of Economic Theory 28′: Cooperative game Determinacy Escalation of commitment Extensive-form game First-player and second-player win Game complexity Graphical game Hierarchy of beliefs Information set Normal-form game Preference Sequential game Simultaneous game Simultaneous action selection Solved game Succinct game.
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. 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.
Aumann’s agreement theorem
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. Views Read Edit Fossil record.
External links Twitter Facebook Discord. This page was last edited risagree-aumann 6 Octoberat Retrieved from ” https: Retrieved from ” https: 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?
Unless explicitly noted otherwise, all content licensed as indicated by RationalWiki: For concerns on copyright infringement please see: Arrow’s impossibility theorem Aumann’s agreement theorem Folk theorem Minimax theorem Nash’s theorem Purification theorem Revelation principle Zermelo’s theorem. Their posterior probabilities must then be the same. Topics in game theory.
“Agreeing to Disagree,” R. Aumann () | A Fine Theorem
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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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Consider two agents tasked with performing Bayesian analysis this is “perfectly rational”. This theorem is almost as much a favorite of LessWrong as the “Sword of Bayes”  itself, because of disagree-qumann popular phrasing along the lines of “two agents acting rationally 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.
Scott Aaronson has shown that this is indeed the case.
Studying the same issue from a different perspective, a research paper by Ziv Hellman considers what happens if priors are not common. International Journal of Game Theory. 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.
It may be worth noting that Yudkowsky has said he wouldn’t agree to try to reach an Aumann agreement with Hanson.