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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Their posterior probabilities must then be the same. Polemarchakis, We can’t disagree forever, Journal of Economic Theory 28′: 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

Views Read Edit Fossil record. Arrow’s impossibility theorem Aumann’s agreement theorem Folk theorem Minimax theorem Nash’s theorem Purification theorem Revelation principle Zermelo’s theorem. International Journal of Game Theory. The paper presents a way to measure how distant priors are from being common. This page was last edited on 6 Octoberat 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”.

A question arises whether such an agreement can be reached go a reasonable time and, from a mathematical perspective, whether this can be done efficiently. Aumann’s agreement theorem [1] 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. Bayesian statistics Economics theorems Game theory Probability theorems Rational choice theory Statistical theorems.

Agreieng and Decision 61 4 — This theorem is almost as much a favorite of LessWrong as the “Sword of Bayes” [4] itself, because of its popular phrasing along the lines of “two agents acting rationally Articles with short description. Retrieved from ” https: Yudkowsky ‘s mentor Robin Hanson tries to handwave this with something about genetics and environment, [9] but to have sufficient common knowledge of genetics and environment for this to work practically would require a few calls to Laplace’s demon.

Scott Aaronson [3] sharpens this theorem by removing the common prior and limiting the number of messages communicated.

### Aumann’s agreement theorem – Lesswrongwiki

Business and economics portal Statistics portal Mathematics portal. Topics in game theory. 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.

Consider two agents tasked with performing Bayesian analysis this is “perfectly rational”. 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.

Thus, two rational Bayesian agents with the same priors and who know each other’s posteriors will have to agree. 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.

### Aumann : Agreeing to Disagree

However, Robin Hanson has presented an argument that Bayesians who agree about the processes that gave agteeing to their priors e. The one-sentence summary is disagree-xumann can’t actually agree to disagree”: Unless explicitly noted otherwise, all content licensed as indicated by RationalWiki: 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 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? 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. 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 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.

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 disagree-zumann Strong Nash equilibrium Markov perfect equilibrium.

By using this site, you agree to the Terms of Use and Privacy Policy. 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 avreeing equal.

This page was last modified on 12 Septemberat