A Hybrid Model of Opinion Dynamics with Limited Confidence

Abstract

This paper proposes a novel model of opinion dynamics with limited confidence. As opposed to other models, the onset of reciprocal influences between individuals is not defined by absolute thresholds, but by a notion of relative relevance for each link. The proposed dynamics takes the form of a hybrid dynamical system, where topology and opinions are coupled but as distinct variables. We prove converge to opinion distributions where disconnected clusters of individuals agree locally, while each cluster holds a different opinion. We also illustrate the dynamics via simulations.