Opinion Dynamics in the Presence of Increasing Agreement Pressure

Abstract

In this paper, we study a model of agent consensus in a social network in the presence increasing interagent influence, i.e., increasing peer pressure. Each agent in the social network has a distinct social stress function given by a weighted sum of internal and external behavioral pressures. We assume a weighted average update rule consistent with the classic DeGroot model and prove conditions under which a connected group of agents converge to a fixed opinion distribution, and under which conditions the group reaches consensus. We show that the update rule converges to gradient descent and explain its transient and asymptotic convergence properties. Through simulation, we study the rate of convergence on a scale-free network.

Opinion Dynamics With Competitive Relationship and Switching Topologies

“…|a ij | indicates the degree of impact and n j=1 |a ij (σ(k))| = 1 is assumed for all i = 1, 2, ..., n [17]. Similar to [7], [14], [17], a ij > 0 represents the cooperative relationship and a ij < 0 corresponds to confrontation and competition.…”

“…Remark 2. Different from the most works about opinion dynamics on the signed graph [14], [17], [39]- [43], [47], in our model the signed graph is allowed to be structurally unbalanced. Furthermore, as far as the authors know, in the investigation about the signed graph, it was implied that the diagonal entries of the adjacency matrix are nonnegative.…”

“…For general directed network topologies with self-loop, the sufficient conditions for consensus were closely related to the uniform quasi-strong connectivity of the graphs [23]. VOLUME 4, 2016 In the past few decades, various deformations of the De-Groot model have also been extensively studied [9], [14]- [16], [24], [25]. Combining the updated rules of the DeGroot model with the idea of "homophily" [26] which means that agents readily adopt opinions of like-minded individuals but accept the more deviant opinions with discretion, bounded confidence (BC) models [26], [27] were proposed to investigate the opinion evolution.…”

“…In fact, agents often form multiple clusters in F-J models [33], [34], [36], [38]. But if peer pressure between individuals was considered in FJ model, the modified FJ model can obtain consensus if peer pressure is increasing and unbounded [14].…”

“…These phenomena are usually modeled by repulsive couplings or negative ties [41] among the agents, i.e., the signed graph, where the positive edges represent friendly and cooperative interactions and negative edges correspond to antagonistic counterpart. Recently, opinion dynamics with antagonism or competition has attracted significant attention [14], [17], [41]- [47]. As shown in [44], the evolution of opinions on signed graphs may be more complicated due to the antagonistic interaction.…”