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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Business and economics portal Statistics portal Mathematics portal. Or the paper’s own example, the fairness of a coin — diwagree-aumann a simple example having been chosen for accessibility, it demonstrates the problem with applying such an oversimplified concept of information to real-world situations.
Consider two agents tasked with performing Bayesian analysis this is “perfectly rational”. The paper presents a way to measure how distant priors are from being common. Thus, two rational Bayesian agents with the same priors and who know each other’s posteriors will have to agree.
Aumann’s agreement theorem
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. For an illustration, how often do two mathematicians disagree on the invalidity of the proof within an agreed-upon framework, once agreeign objections are known to the other?
For concerns on copyright infringement please see: 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. From Wikipedia, the free aggeeing. 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 Annals of Statistics 4 6 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 In game theoryAumann’s agreement theorem is a theorem agrefing demonstrates that rational agents with common knowledge of each other’s beliefs cannot agree to disagree.
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.
Retrieved from ” https: Arrow’s disagreeaumann theorem Aumann’s agreement theorem Folk theorem Minimax theorem Nash’s theorem Purification theorem Revelation principle Zermelo’s theorem. Theory and Decision 61 4 — External links Twitter Facebook Discord. 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. Topics in game theory.
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.
Unless explicitly noted otherwise, all content licensed as indicated by RationalWiki: The Annals of Statistics. Scott Aaronson has shown that this is indeed the case.
Aumann : Agreeing to Disagree
Unlike many questionable applications of theorems, this one appears to have been diszgree-aumann intention of the paper itself, which itself cites a paper defending the application of such techniques to the real world.
Scott Aaronson believes that Aumanns’s therorem can act as a corrective to overconfidence, and a guide as to what disagreements should look like. Studying the same issue from a different perspective, a research paper by Ziv Hellman considers what happens if priors are not common. 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.
The one-sentence summary is “you can’t actually agree to disagree”: Views Read Edit Fossil record. Polemarchakis, We can’t disagree forever, Journal of Economic Theory 28′: For such careful definitions of “perfectly rational” and “common knowledge” disagree-aummann is equivalent to saying disagrree-aumann two functioning calculators will not give different answers disageee-aumann the same input.
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 edited on 6 Octoberat Their posterior probabilities must then be the same.
Aumann’s agreement theorem – Wikipedia
Bayesian statistics Economics theorems Game theory Probability theorems Rational choice theory Statistical theorems. 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 dissgree-aumann evidence, and a rational agent should recognize this, and also recognize that one would, and that this would also be recognized, and so on.
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 agreejng calls to Laplace’s demon.