Opinion Dynamics of Modified Hegselmann-Krause Model with Group-based Bounded Confidence

Abstract

The continuous opinion dynamics with group-based heterogeneous bounded confidences is considered in this paper. Firstly, a slightly modified Hegselmann-Krause model is proposed, and the agents are divided into open-minded-, moderate-minded-, and close-minded-subgroups according to the corresponding confidence intervals. Then numerical simulations are carried out to analyze the influence of the close-minded and open-minded agents, as well as the population size, on the opinion dynamics. It is observed that (1) for the fixed population size, the larger proportion of close-minded agents, the more opinion clusters; (2) open-minded agents cannot contribute to forging different opinions, instead, the existence of them maybe diversify final opinions; also interestingly the relative size of the largest cluster varies along concave-parabola-like curve as the proportion of open-minded agents increases; (3) for the same proportion of the three subgroups, as population size increases, the number of final opinion clusters will increase at the beginning and then reach a stable level, which is quite different from the previous studies.