Difference between revisions of "Aumann's agreement theorem"

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'''Aumann's agreement theorem''', informally stated, 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]]s, share common [[priors]], and have common knowledge of each other's current probability assignments, then they must have equal probability assignments.
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'''Aumann's agreement theorem''', roughly speaking, says that two agents 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]]s, share common [[priors]], and have common knowledge of each other's current probability assignments, then they must have equal probability assignments.
  
Outside of well-functioning [[prediction market]]s, Aumann's conditions can probably only be reached by careful [[deliberation|deliberative discourse]]: whether deliberation tends to resolve disagreements in practice is an empirical question.
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==Blog posts==
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*[http://lesswrong.com/lw/gr/the_modesty_argument/ The Modesty Argument]
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*[http://www.overcomingbias.com/2006/12/agreeing_to_agr.html Agreeing to Agree] by [[Wikipedia:Hal Finney (cypherpunk)|Hal Finney]]
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*[http://www.overcomingbias.com/2007/01/the_coin_guessi.html The Coin Guessing Game] by Hal Finney
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*[http://lesswrong.com/lw/gq/the_proper_use_of_humility/ The Proper Use of Humility]
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*[http://www.overcomingbias.com/2006/12/meme_lineages_a.html Meme Lineages and Expert Consensus] by [[Carl Shulman]] (OB)
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*[http://lesswrong.com/lw/1il/probability_space_aumann_agreement/ Probability Space & Aumann Agreement] by [http://weidai.com/ Wei Dai]
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*[http://lesswrong.com/lw/i5/bayesian_judo/ Bayesian Judo]
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==External Links==
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*[http://dl.dropbox.com/u/34639481/Aumann_agreement_theorem.pdf A write-up of the proof of Aumann's agreement theorem] (pdf) by Tyrrell McAllister
  
 
==See also==
 
==See also==
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*[[Disagreement]]
 
*[[Disagreement]]
 
*[[Modesty argument]]
 
*[[Modesty argument]]
 
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*[[Aumann agreement]]
==Blog posts==
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*[[The Aumann Game]]
 
 
*[http://www.overcomingbias.com/2006/12/agreeing_to_agr.html Agreeing to Agree] by [[Hal Finney]]
 
*[http://lesswrong.com/lw/gq/the_proper_use_of_humility/ The Proper Use of Humility] by [[Eliezer Yudkowsky]]
 
  
 
==References==
 
==References==
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| year = 2004
 
| year = 2004
 
}} ([http://hanson.gmu.edu/deceive.pdf PDF], [http://www.newmedia.ufm.edu/gsm/index.php?title=Are_Disagreements_Honest%3F Talk video])
 
}} ([http://hanson.gmu.edu/deceive.pdf PDF], [http://www.newmedia.ufm.edu/gsm/index.php?title=Are_Disagreements_Honest%3F Talk video])
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==Tags==
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*{{lesswrongtag|aumann|majoritarianism|disagreement|modesty}}
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*[http://www.overcomingbias.com/tag/disagreement Overcoming Bias posts on "Disagreement"]
  
 
[[Category:Theorems]]
 
[[Category:Theorems]]

Latest revision as of 03:04, 11 March 2012

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Aumann's agreement theorem, roughly speaking, says that two agents 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 Bayesians, share common priors, and have common knowledge of each other's current probability assignments, then they must have equal probability assignments.

Blog posts

External Links

See also

References

  • Robert J. Aumann (1976). "Agreeing to Disagree". The Annals of Statistics 4 (6): 1236-1239. ISSN 00905364.  (PDF)
  • Tyler Cowen and Robin Hanson (2004). Are Disagreements Honest?.  (PDF, Talk video)

Tags