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.
Influence Enhancement in Opinion Dynamics Using Edge Modification: A Kron Reduction-Based Approach
Department of Electrical Engineering, Indian Institute of Technology Kanpur（坎普尔印度理工学院电气工程系）；Adobe Systems, Bangalore（Adobe系统公司班加罗尔分部）；School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm（斯德哥尔摩皇家理工学院电气与计算机工程学院）
This paper proposes a network model of opinion dynamics based on both the social network structure and network centralities. The conceptual novelty in this model is that the opinion of each individual is weighted by the associated network centrality in characterizing the opinion spread on social networks. Following a degree-centrality-weighted opinion dynamics model, we provide an algorithm to partition nodes of any graph into two and multiple clusters based on opinion disagreements. Furthermore, the partition algorithm is applied to real-world social networks including the Zachary karate club…
In this chapter, we derive and analyse models for consensus dynamics on hypergraphs. As we discuss, unless there are nonlinear node interaction functions, it is always possible to rewrite the system in terms of a new network of effective pairwise node interactions, regardless of the initially underlying multi-way interaction structure. We thus focus on dynamics based on a certain class of non-linear interaction functions, which can model different sociological phenomena such as peer pressure and stubbornness. Unlike for linear consensus dynamics on networks, we show how our nonlinear model dyn…
Dynamical models for distributed social power perception in Friedkin-Johnsen influence networks
Graduate School of Informatics, Kyoto University（京都大学情报大学院）；Division of Decision and Control Systems, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology（皇家理工学院电气计算机科学与决策控制系统系）；Digital Futures（数字未来中心）；Graduate School of Advanced Science and Engineering, Hiroshima University（广岛大学先进理工学研究科）；Department of Mechanical and Energy Engineering, Southern University of Science and Technology（南方科技大学机械能源工程系）
We introduce a new opinion dynamics model where a group of agents holds two kinds of opinions: inherent and declared. Each agent's inherent opinion is fixed and unobservable by the other agents. At each time step, agents broadcast their declared opinions on a social network, which are governed by the agents' inherent opinions and social pressure. In particular, we assume that agents may declare opinions that are not aligned with their inherent opinions to conform with their neighbors. This raises the natural question: Can we estimate the agents' inherent opinions from observations of declared …
Trust and distrust are common in the opinion interactions among agents in social networks, and they are described by the edges with positive and negative weights in the signed digraph, respectively. It has been shown in social psychology that although the opinions of most agents (followers) tend to prevail, sometimes one agent (leader) with a firm stand and strong influence can impact or even overthrow the preferences of followers. This paper aims to analyze how the leader influences the formation of followers' opinions in signed social networks. In addition, this paper considers an asynchrono…
Motivated by the literature on opinion dynamics and evolutionary game theory, we propose a novel mathematical framework to model the intertwined coevolution of opinions and decision-making in a complex social system. In the proposed framework, the members of a social community update their opinions and revise their actions as they learn of others' opinions shared on a communication channel, and observe of others' actions through an influence channel; these interactions determine a two-layer network structure. We offer an application of the proposed framework by tailoring it to study the adopti…
