AGREEMENT THEOREMS FOR SELF-LOCATING BELIEF

Abstract

AbstractIn this paper, I first outline Aumann’s famous “no agreeing to disagree” theorem, and a second related theorem. These results show that if two or more agents, who have epistemic and credal states that are defined over algebras that do not include any self-locating propositions, have certain information about one another’s epistemic and credal states, then such agents must assign the same credence to certain propositions. I show, however, that both of these theorems fail when we consider agents who have epistemic and credal states that are defined over algebras that do include self-locating propositions. Importantly, these theorems fail for such agents even when we restrict our attention to the credences that such agents have in non-self-locating propositions. Having established this negative result, I then outline and prove three agreement theorems that hold for such agents.