Aumann's agreement theorem

Aumann's agreement theorem states that two rational individuals with the same prior knowledge cannot agree to disagree about a specific proposition, assuming they are both fully aware of each other's beliefs. If they share the same information and update their beliefs correctly, they will eventually reach a consensus. This theorem highlights the importance of shared knowledge in discussions and suggests that if two people maintain conflicting opinions, either their knowledge or reasoning processes must differ. Thus, if both are rational and informed, they should find common ground on beliefs about uncertain matters.