https://en.wikipedia.org/wiki/Aumann%27s_agreement_theorem https://en.wikipedia.org/wiki/Aumann%27s_agreement_theorem Aumann's agreement theorem says that two

https://en.wikipedia.org/wiki/Aumann%27s_agreement_theorem https://en.wikipedia.org/wiki/Aumann%27s_agreement_theorem 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 posterior probabilities, then their posteriors must be equal. This theorem holds even if the people's individual posteriors are based on different observed information about the world. Simply knowing that another agent observed some information and came to their respective conclusion will force each to revise their beliefs, resulting eventually in total agreement on the correct posterior. Thus, two rational Bayesian agents with the same priors and who know each other's posteriors will have to agree.