Representing and Aggregating Conflicting Beliefs
<|reference_start|>Representing and Aggregating Conflicting Beliefs: 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.<|reference_end|>
@article{maynard-reid2002representing,
    title={Representing and Aggregating Conflicting Beliefs},
    author={Pedrito Maynard-Reid II (Miami University), Daniel Lehmann (Hebrew
  University)},
    journal={Proceedings of the Seventh International Conference on Principles
  of Knowledge Representation and Reasoning (KR 2000), April 2000, pp. 153-164},
    year={2002},
    archivePrefix={arXiv},
    eprint={cs/0203013},
    primaryClass={cs.AI cs.LO}
}