  We consider the two-fold problem of representing 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 informed by a set of sources of varying degrees of
reliability. This construction circumvents Arrow's Impossibility Theorem in a
satisfactory manner. Finally, we give a simple set-theory-based operator for
combining the information of multiple agents. We show that this operator
satisfies the desirable invariants of idempotence, commutativity, and
associativity, and, thus, is well-behaved when iterated, and we describe a
computationally effective way of computing the resulting belief state.
