Opinion dynamics in social networks with stubborn agents: an issue-based perspective

TL;DR

This paper studies opinion consensus in social networks with stubborn agents over sequences of issues, providing conditions for convergence and consensus, and analyzing the influence of network structure and bounded confidence.

Contribution

It introduces new necessary and sufficient conditions for opinion consensus in the Friedkin-Johnsen model over issue sequences, including bounded confidence scenarios.

Findings

Convergence conditions for the F-J model over single issues.

Criteria for opinion consensus over issue sequences.

Connectivity preservation in bounded confidence settings.

Abstract

Classic models on opinion dynamics usually focus on a group of agents forming their opinions interactively over single issue. Yet generally consensus can not be achieved over single issue when agents are not completely open to interpersonal influence. In this paper, opinion consensus in social networks with stubborn agents is considered over issue sequences. The social network with stubborn agents is described by the Friedkin-Johnsen (F-J) model where agents are stubborn to their initial opinions. Firstly, we propose some sufficient and necessary conditions both in terms of network topology and system matrix for convergence of the F-J model over single issue. Secondly, opinion consensus of the F-J model is investigated over issue sequences. Our analysis establishes connections between the interpersonal influence network and the network describing the relationship of agents' initial opinions for successive issues. Taking advantage of these connections, we derive the sufficient and necessary condition for the F-J model to achieve opinion consensus over issue sequences. Finally, we consider a more general scenario where each agent has bounded confidence in forming its initial opinion for every issue. By analyzing the evolution of agents' ultimate opinions for each issue over issue sequences, we prove that the connectivity of the state-dependent network is preserved in this setting. Then the conditions for agents to achieve opinion consensus over issue sequences are proposed. Simulation examples are provided to illustrate the effectiveness of our theoretical results.