PEOPLE WITH COMMON PRIORS CAN AGREE TO DISAGREE

Abstract

Abstract Robert Aumann presents hisAgreement Theoremas thekey conditional: “if two people have the same priors and their posteriors for an eventAare common knowledge, then these posteriors are equal” (Aumann, 1976, p. 1236). This paper focuses on four assumptions which are used in Aumann’s proof but are not explicit in the key conditional: (1) that agents commonly know, of some priorμ, that it is the common prior; (2) that agents commonly know that each of them updates on the prior by conditionalization; (3) that agents commonly know that if an agent knows a proposition, she knows that she knows that proposition (the “KK” principle); (4) that agents commonly know that they each update only on true propositions. It is shown that natural weakenings of any one of these strong assumptions can lead to countermodels to Aumann’s key conditional. Examples are given in which agents who have a common prior and commonly know what probability they each assign to a proposition nevertheless assign that proposition unequal probabilities. To alter Aumann’s famous slogan: peoplecan“agree to disagree”, even if they share a common prior. The epistemological significance of these examples is presented in terms of their role in a defense of theUniqueness Thesis: If an agent whose total evidence isEis fully rational in taking doxastic attitudeDtoP, then necessarily, any subject with total evidenceEwho takes a different attitude toPis less than fully rational.

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