Group Pressure Leads to Consensus of Hegselmann-Krause Opinion Dynamics

A typical assumption concluded from the existing opinion formation models is that two individuals (agents) can communicate with each other only if the distance between their opinions is less than a threshold which is called confidence bound. However, in the real world, formation of opinion and expression may be different, for the reason that agent feels pressured to express opinion that is similar to the dominant opinion in the group. In this paper, a modified Hegselmann-Krause (H-K) model is introduced by integrating the opinion dynamics with confidence bound and group pressure, which describes the evolution of an individual's opinion that conform to the dominant opinion under group pressure. We find that, when there is only one agent hold dominant opinion, the system can always achieve a consensus in a finite time regardless of the confidence bound value. In generalized case, we further establish a sufficient condition for multiple agents with dominant opinions, we prove that in this condition the whole group could also reach a consensus.