Continuous Opinion Dynamics with Anti-conformity Behavior

Abstract

We propose an appropriate updating rule of continuous opinions for modeling anti-conformity behavior, defined according to the repelling function, which gives the shift of the opinion based on the current opinion and the reference opinion for an agent. Two models of continuous opinion dynamics (with opinion value on a continuous scale [0,1]) are studied in undirected networks, by introducing the heterogeneity in the sense of conformity and anti-conformity behavior either in nodes or in links. In the first one, the society is composed of both conformist and anti-conformist agents. Conformist agents update their opinions following the DeGroot rule with equal weights. However, anti-conformist agents would like to repel from others, and the repelling level is negatively related to the opinion distance between the anti-conformist and her reference point. No consensus will be reached for any connected network in the presence of anti-conformist agents. Instead, opinions converge to a disagreement or oscillate over time. In the second part, by supposing a signed graph where agents have positive links (+1) with their friends and negative links (-1) with their enemies, agents update their opinion as the sum of the averaged opinion of their friends and repelling value from their enemies. When the network is balanced, i.e., there are two communitarian groups, and each sub-network corresponding to each group is connected and the initial opinion ranges of the two groups are disjoint, the consensus within each group is guaranteed. Both synchronous and asynchronous updating models are discussed in these two parts.