When open mindedness hinders consensus

Abstract

We perform a detailed study of the Hegselmann-Krause bounded confidence opinion dynamics model with heterogeneousconfidence εi drawn from uniform distributions in different intervals [ε1, εu]. The phase diagram reveals a highly complex andnon-monotonous behaviour, with a re-entrant consensus phase in the region where fragmentation into multiple distinct opinionsis expected for the homogeneous case. A careful exploration of the phase diagram, along with an extensive finite-size analysis,allows us to identify the mechanism leading to this counter-intuitive behaviour. This systematic study over system sizes whichgo well beyond those of previous works, is enabled by an efficient algorithm presented in this article.