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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Community Saloon bar To do list What is going on? Articles with short description. Scott Aaronson has shown that this is indeed the case.
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.
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: 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. It may be worth noting that Yudkowsky has said he wouldn’t agree to try to reach an Aumann agreement with Hanson. 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.
The paper presents a way to measure how distant priors are from being common. Unless explicitly noted otherwise, all content licensed as indicated by RationalWiki: 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.
International Journal of Game Theory. Views Read Edit Fossil record.
Aumann’s agreement theorem
Their posterior probabilities must then be the same. This page was last modified on 12 Septemberat The one-sentence summary is “you can’t actually agree to disagree”: All-pay auction Alpha—beta pruning Bertrand paradox Bounded rationality Combinatorial game theory Confrontation analysis Coopetition First-move advantage in chess Game mechanics Glossary of game theory List of game theorists List of games in game theory No-win situation Solving chess Topological game Tragedy of the commons Tyranny of small decisions.
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. External links Twitter Facebook Discord. Both are given the same prior probability of the world being in a certain state, and separate sets of further information.
Consider two agents tasked with performing Bayesian analysis this is “perfectly rational”.
“Agreeing to Disagree,” R. Aumann () | A Fine Theorem
Studying the same issue from a different perspective, a research paper by Ziv Hellman considers what happens if priors are not common. 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 agreelng it knows, ad infinitum this is “common knowledge”.
Arrow’s impossibility theorem Aumann’s agreement theorem Folk theorem Minimax theorem Nash’s theorem Purification theorem Revelation principle Zermelo’s theorem. This page was last edited on 6 Octoberat From Wikipedia, the free encyclopedia.
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 Annals of Statistics.
Views Read Edit View history. Retrieved from ” https: Topics in game theory. 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 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? The Annals of Statistics 4 6 Scott Aaronson believes that Aumanns’s therorem can act as a corrective to overconfidence, and a guide as to what disagreements should look like.
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.
However, Robin Hanson has presented an argument that Bayesians who agree about the processes that gave rise to their priors e.
Thus, two rational Bayesian agents with the same priors and who know each other’s posteriors will have to agree. Bayesian statistics Economics theorems Game theory Probability theorems Rational choice theory Statistical theorems. 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.
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.
Business and economics portal Statistics portal Mathematics portal. Aumann’s agreement theorem says that two disagrde-aumann acting rationally in a certain precise sense and with common knowledge of each other’s beliefs cannot agree to disagree.
Scott Aaronson  sharpens this theorem by removing the common prior and limiting the number of messages communicated. More specifically, if two people are genuine Bayesian rationalists with common priorsagreeeing if they each have common knowledge of their individual posterior probabilitiesthen their posteriors must be equal.