Intersubjective Consistency of Beliefs and the Logic of Common Belief

We characterize the class of n-person belief systems for which common belief has the properties of the strongest logic of belief, KD45. The characterizing condition states that individuals are not too mistaken in their beliefs about common beliefs. It is shown to be considerably weaker than the consistency condition on interpersonal beliefs implied by the common knowledge assumption: it allows individuals to ""agree to disagree"" and to be quite incorrect about others7 beliefs.