Multi-Level Opinion Dynamics under Bounded Confidence

Opinion dynamics focuses on the opinion evolution in a social community. Recently, some models of continuous opinion dynamics under bounded confidence were proposed by Deffuant and Krause, et al. In the literature, agents were generally assumed to have a homogeneous confidence level. This paper proposes an extended model for a group of agents with heterogeneous confidence levels. First, a social differentiation theory is introduced and a social group is divided into opinion subgroups with distinct confidence levels. Second, a multi-level heterogeneous opinion formation model is formulated under the framework of bounded confidence. Finally, computer simulations are conducted to study the collective opinion evolution, focusing on three key factors: the fractions of heterogeneous agents, the initial opinions, and the group size. The simulation results demonstrate that the number of final opinions depends on the fraction of close-minded agents when the group size and the initial opinions are fixed; the final opinions converge more easily when the initial opinions are closer; and the number of final opinions can be approximately modeled by a linear increasing function of the group size and the increasing rate is the fraction of close-minded agents.