Characterizing Consensuses in Belief Flow Networks

Nicolas Schwind, Gauvain Bourgne, Katsumi Inoue

Keywords: Belief Flow Networks, Consensus formation, Epistemic states, Iterated belief change, Improvement operators

TL;DR: We characterize which beliefs can emerge as consensuses in Belief Flow Networks, where agents with epistemic states (capturing beliefs and conditional beliefs) communicate asynchronously.

Abstract: The BeliefFlow framework models how logical beliefs spread in networks of interacting agents. In a Belief Flow Network (BFN), agents hold epistemic states capturing current and conditional beliefs and revise them asynchronously, taking into account the beliefs of those that influence them as specified by an acquaintance graph, using an improvement operator, a rational form of iterated belief change. Earlier work showed that in strongly connected BFNs, all agents always converge to a global consensus, regardless of initial beliefs, revision policies, or the stochastic order of communications. This paper examines the nature of such consensuses. While past results proved that consensus is reached, we characterize which formulas may emerge. Given a BFN scheme defined by its acquaintance graph and the agents’ initial beliefs, we provide necessary and sufficient conditions for a formula to be realizable as a consensus outcome. A key outcome of our study is that deciding whether a formula is a possible consensus for a given scheme can be done in polynomial time with polynomially many calls to an $\mathsf{NP}$ oracle. This matches the complexity of inference for single iterated belief change operators, showing that consensus characterization in BFNs is no harder than reasoning about belief change itself.

Area: Representation and Reasoning (RR)

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Submission Number: 1513