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- Aumanns_agreement_theorem abstract "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. More specifically, if two people are genuine Bayesian rationalists with common priors, and if they each have common knowledge of their individual posteriors, then their posteriors must be equal.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. Scott Aaronson has shown that this is indeed the case.Of course, the assumption of common priors is a rather strong one and may not hold in practice. However, Robin Hanson has presented an argument that Bayesians who agree about the processes that gave rise to their priors (e.g., genetic and environmental influences) should, if they adhere to a certain pre-rationality condition, have common priors.Studying the same issue from a different perspective, a research paper by Ziv Hellman considers what happens if priors are not common. The paper presents a way to measure how distant priors are from being common. If this distance is ε then, under common knowledge, disagreement on events is always bounded from above by ε. When ε goes to zero, Aumann's original agreement theorem is recapitulated.In a 2013 paper, Joseph Halpern and Willemien Kets argued that "players can agree to disagree in the presence of ambiguity, even if there is a common prior, but that allowing for ambiguity is more restrictive than assuming heterogeneous priors."".
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- Aumanns_agreement_theorem wikiPageRevisionID "671153158".
- Aumanns_agreement_theorem wikiPageWikiLink Agree_to_disagree.
- Aumanns_agreement_theorem wikiPageWikiLink Bayesian_probability.
- Aumanns_agreement_theorem wikiPageWikiLink Bayesian_theory.
- Aumanns_agreement_theorem wikiPageWikiLink Category:Bayesian_statistics.
- Aumanns_agreement_theorem wikiPageWikiLink Category:Game_theory.
- Aumanns_agreement_theorem wikiPageWikiLink Category:Probability_theorems.
- Aumanns_agreement_theorem wikiPageWikiLink Category:Statistical_theorems.
- Aumanns_agreement_theorem wikiPageWikiLink Common_knowledge_(logic).
- Aumanns_agreement_theorem wikiPageWikiLink Joseph_Halpern.
- Aumanns_agreement_theorem wikiPageWikiLink Posterior_probability.
- Aumanns_agreement_theorem wikiPageWikiLink Prior_probability.
- Aumanns_agreement_theorem wikiPageWikiLink Rational_choice_theory.
- Aumanns_agreement_theorem wikiPageWikiLink Robert_Aumann.
- Aumanns_agreement_theorem wikiPageWikiLink Robin_Hanson.
- Aumanns_agreement_theorem wikiPageWikiLink Scott_Aaronson.
- Aumanns_agreement_theorem wikiPageWikiLink Willemien_Kets.
- Aumanns_agreement_theorem wikiPageWikiLinkText "Aumann's agreement theorem".
- Aumanns_agreement_theorem wikiPageWikiLinkText "agreement theorem".
- Aumanns_agreement_theorem hasPhotoCollection Aumanns_agreement_theorem.
- Aumanns_agreement_theorem wikiPageUsesTemplate Template:Reflist.
- Aumanns_agreement_theorem subject Category:Bayesian_statistics.
- Aumanns_agreement_theorem subject Category:Game_theory.
- Aumanns_agreement_theorem subject Category:Probability_theorems.
- Aumanns_agreement_theorem subject Category:Statistical_theorems.
- Aumanns_agreement_theorem comment "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.".
- Aumanns_agreement_theorem label "Aumann's agreement theorem".
- Aumanns_agreement_theorem sameAs Teorema_de_Aumann.
- Aumanns_agreement_theorem sameAs m.051vvcb.
- Aumanns_agreement_theorem sameAs Теорема_Ауманна_о_согласии.
- Aumanns_agreement_theorem sameAs Q4454919.
- Aumanns_agreement_theorem sameAs Q4454919.
- Aumanns_agreement_theorem wasDerivedFrom Aumanns_agreement_theoremoldid=671153158.
- Aumanns_agreement_theorem isPrimaryTopicOf Aumanns_agreement_theorem.