Robust fragmentation modeling of Hegselmann–Krause-type dynamics

Abstract

In opinion dynamics, how to model the enduring fragmentation phenomenon (especially the bipartite cleavage) of social opinions has long been a central problem. It is widely known that the confidence-based opinion dynamics provide an acceptable mechanism to produce fragmentation. In this study, taking the famous confidence-based Hegselmann–Krause (HK) model, we examine the robustness of the fragmentation coming from HK dynamics and its variations with prejudiced and stubborn agents against random noise. Prior to possible insightful explanations, the theoretical results in this paper explicitly reveal that the fragmentation of HK dynamics and its homogeneous variations finally vanishes in the presence of arbitrarily tiny noise, while only the HK model with heterogenous prejudices displays a solid cleavage in noisy environment. Moreover, it is found that noise could help regularize the group to form the innate bipartite cleavage.