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.[1]
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.[2]
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.[3]