Consensus on Social Influence Network Model

Many studies show that opinions formation displays multiple patterns, from consensus to polarization. Under the framework of the social influence network by Friedkin and Johnsen (1999) and based on random walk on graph, we rigorously prove that for a social group influence system, with static social influence structure, the group consensus is almost a quite certain result. In addition, we prove the lower bounds on the convergence time m for random walk \(P^{m}\) to be close to its final average consensus (wisdom group decision making) state, given an arbitrary initial opinions profile vector and one small positive error \(\epsilon \). Although our explanations are purely based on mathematic deduction, it shows that the latent social influence structure is the key factor for the persistence of disagreement and formation of opinions convergence or consensus in the real world social group.