Representing and Aggregating Conflicting Beliefs

We consider the two-fold problem of rep resenting collective beliefs and aggregating these beliefs. We propose modular, transitive relations for collective beliefs. They allow us to represent conflicting opinions and they have a clear semantics. We compare them with the quasi-transitive relations often used in Social Choice. Then, we describe a way to construct the belief state of an agent in formed by a set of sources of varying degrees of reliability. This construction circumvents Arrow's Impossibility Theorem in a satisfac tory manner. Finally, we give a simple set-theory-based operator for combining the in formation of multiple agents. We show that this operator satisfies the desirable invariants of idempotence, commutativity, and associa tivity, and, thus, is well-behaved when iter ated, and we describe a computationally ef fective way of computing the resulting belief state.