# Difference between revisions of "Aumann's agreement theorem"

From Lesswrongwiki

m (→External references) |
Steven0461 (talk | contribs) m |
||

Line 1: | Line 1: | ||

{{wikilink}} | {{wikilink}} | ||

− | '''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 | + | '''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. |

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. | 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. |

## Revision as of 22:41, 28 August 2009

**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 Bayesians, 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 markets, Aumann's conditions can probably only be reached by careful deliberative discourse: whether deliberation tends to resolve disagreements in practice is an empirical question.

## See also

## Blog posts

## 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)