Aumann's agreement theorem
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.
- Agreeing to Agree by Hal Finney
- The Proper Use of Humility by Eliezer Yudkowsky
- The Coin Guessing Game by Hal Finney, a toy problem illustrating the mechanics of Aumann agreement