Representing and Aggregating Conflicting Beliefs

We consider the two-fold problem of representing collective beliefs and aggregating these beliefs. We propose a novel representation for collective beliefs that uses modular, transitive relations over possible worlds. They allow us to represent conflicting opinions and they have a clear semantics, thus improving upon the quasi-transitive relations often used in social choice. We then 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 by accounting for the explicitly encoded conflicts. 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. Finally, we e...

• Type: Conference
• Year: 2000
• Where: KR
• Authors: Pedrito Maynard-Reid II, Daniel J. Lehmann
• Keywords: Arrow's Impossibility Theorem, Automated Reasoning, Belief State, Collective Beliefs, KR 2000