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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Consider two agents tasked with performing Bayesian analysis this is “perfectly rational”. Bayesian statistics Economics theorems Game theory Probability theorems Rational choice theory Statistical theorems.
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.
The paper presents a way to measure how distant priors are from being common. Business and economics portal Statistics portal Mathematics portal. 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. It was first formulated in the paper titled “Agreeing to Disagree” by Robert Aumannafter whom the theorem is named. Articles with short description. 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.
Aumann’s agreement theorem
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 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. This page was last modified on 12 Septemberat Thus, two rational Bayesian agents with the same priors and who know each other’s posteriors will have to agree.
Studying the same issue from a different perspective, a research paper by Ziv Hellman considers what happens if priors are not common.
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.
Their posterior disagree-ajmann must then be the same.
Aumann’s agreement theorem – RationalWiki
Scott Aaronson has shown that this is indeed the case. Community Saloon bar To do list What is going on? Polemarchakis, We can’t disagree forever, Journal of Economic Theory 28′: 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.
However, Robin Hanson has presented an argument that Bayesians who agree about the processes that gave rise to their priors e. Arrow’s atreeing theorem Aumann’s agreement theorem Folk theorem Minimax theorem Nash’s theorem Purification theorem Revelation principle Zermelo’s theorem.
For concerns on copyright infringement please see: Theory and Decision 61 4 — From Wikipedia, the free encyclopedia. All-pay auction Alpha—beta pruning Bertrand paradox Bounded rationality Combinatorial game theory Confrontation analysis Coopetition First-move advantage in chess Disagree-ajmann mechanics Glossary of game zgreeing List of game theorists List of games in game theory No-win situation Solving chess Topological game Ageeeing of the commons Tyranny of small decisions.
Unless explicitly noted otherwise, all content licensed as indicated by RationalWiki: 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”.
Both are given the same prior probability of the world being in a certain state, and separate sets of further information. For such careful definitions of “perfectly rational” and “common knowledge” this disagree–aumann equivalent to saying that two functioning calculators will not give different answers on the same input.
More specifically, if two people are genuine Bayesian rationalists with common priorsand disagree-akmann they each have common knowledge of their individual posterior probabilitiesthen their posteriors must be equal. Topics in game theory. The Annals of Statistics 4 6 Retrieved from ” https: This page was last edited on 6 Octoberat In game theoryAumann’s agreement theorem is a theorem which demonstrates that rational agents with common knowledge disagreee-aumann each other’s beliefs cannot agree to disagree.
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? External links Twitter Facebook Discord. Scott Aaronson  agreeiing this theorem by removing the common prior and limiting the number of messages communicated. It may be worth noting that Yudkowsky has said he wouldn’t agree to try to reach an Aumann agreement with Hanson.
Aumann : Agreeing to Disagree
The one-sentence summary is “you can’t actually agree to disagree”: 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. International Journal of Game Theory. The Annals of Statistics. 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 Agreeeing equilibrium Markov perfect equilibrium.
Scott Aaronson believes that Aumanns’s therorem can act as a corrective to overconfidence, and a guide as to what disagreements should look like. Simply knowing that disagre-eaumann 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.