Increasing Peer Pressure on any Connected Graph Leads to Consensus

Abstract

In this paper, we propose a novel generic model of opinion dynamics over a social network, in the presence of communication among the users leading to interpersonal influence i.e., peer pressure. Each individual in the social network has a distinct objective function representing a weighted sum of internal and external pressures. We prove conditions under which a connected group of users converges to a fixed opinion distribution, and under which conditions the group reaches consensus. Through simulation, we study the rate of convergence on large scale-free networks as well as the impact of user stubbornness on convergence in a simple political model.