Bounded Confidence-based Opinion Formation for
Opinion Leaders and Opinion Followers on
Yiyi ZHAO1, Gang KOU2
1 School of Economics and Management, University of Electronic Science and Technology of China
Chengdu, 611731, China
2 School of Business Administration, Southwest University of Finance and Economics of China
Chengdu, 610074, China
Abstract: Opinion dynamics is a complex collective behavior in human societies. When individuals exchange opinions with others, they usually adopt a bounded confidence rule and only accept the opinions within the confidence range. Furthermore, individuals are heterogeneous in real social systems. Thus, they have distinct confidence levels, and also play different roles in the collective opinion formation. In this paper, a leader-follower bounded confidence model is proposed for a group of social agents, who have heterogeneous confidence levels, at the same time, come from two subgroups: opinion leaders and opinion followers. Simulation results are obtained for the collective opinion evolution influenced by three factors: the leader fraction, the group size and the trust degree. The results show that the roles of opinion leaders are remarkable when the opinion followers have high confidence levels and trust degrees.
Keywords: Bounded confidence; opinion formation; heterogeneous confidence levels; opinion leaders.
CITE THIS PAPER AS:
Yiyi ZHAO, Gang KOU, Bounded Confidence-based Opinion Formation for Opinion Leaders and Opinion Followers on Social Networks, Studies in Informatics and Control, ISSN 1220-1766, vol. 23 (2), pp. 153-162, 2014.
Recently great attention has been paid to social network science, which concerns the influence of the networking structure and the social behavior of individuals in the networks. The references [1-5] investigated some interesting social behaviors, such as patter searching, online recommendation, reputation formation, et al, on computer networks. The references [6-7] considered decision making clustering for social networks. Opinion formation is also an important kind of social behaviors in social networks, which is closely related with opinion dynamics modeling.
The modeling of a collective opinion evolution can be generally classified into two categories: discrete opinion dynamics and continuous opinion dynamics. The bounded confidence model is a representative model used to study continuous opinion dynamics. In a network of multiple agents, initially every agent is assigned randomly an opinion described by a real value within some intervals. A pair of agents begins to interact only if their opinion difference is smaller than a given threshold, which is referred to as bounded confidence level. The Deffuant model  and the Hegselmann-Krause (HK) model [9-10] are two common bounded confidence models.
In the original Deffeunt model and HK model, all agents are homogeneous and have an identical confidence level. However, in a real society, different agents should have different confidence levels due to diverse individual characteristics. Motivated by these facts, Lorenz et al. proposed an agent-based and a density-based bounded confidence model with heterogeneous confidence levels in  and , respectively. Kou, Zhao et al. built up a heterogeneous HK opinion dynamics with multi-level confidence level to analyze the impacts of confidence levels, initial opinions and group size on the evolution of the collective opinion systematically in .
Many studies on opinion leader mainly focused on election of a party and marketing science. According to different opinion update rules, a lot of opinion dynamics models have been built to analyze the function of opinion leaders. An collective invitation process to an event organized by facebook was considered in . Elihu Katz, et al. had a profound contribution on the theory of public opinion formation, because a “two-step flow” model describes the information influence “flows” from the media through opinion leaders to their respective followers with various decision-making scenarios. In a two-step flow model, compared with the rest of the population, opinion leaders were found to be considerably more exposed to the formal media of communication [15-16]. Since then, the idea of opinion leaders, or “influentials” as they are also called in , had occupied a central place in the literatures of the marketing , diffusion of innovations , and communication research .
It is clear that most literatures indicate that opinion leaders play an important role in information propagation. In many cases, opinion leaders may transfer the information to the neighboring agents unconsciously. However, in some other cases, opinion leaders hope to guide the neighbors to an expected opinion for a purpose, such as panic buying or social harmony. In this paper, we consider the collective opinion formation through the bounded confidence communication among opinion followers and opinion leaders, who want to actively guide the neighboring agents to an expected opinion.
Three main questions are left: can the guiding powers of the opinion leaders increase with the leader fraction in a fixed-size group, whether the group size has impact on the final opinion profile? And what is the influence of the opinion followers’ trust degrees on the final opinion distribution? We will answer the three questions one by one.
In this paper, the evolution of the collective opinion will be investigated under the framework of heterogeneous HK opinion dynamics for a group of social agents. One important extension is made on the HK model: divide the social agents into two subgroups, opinion leaders and opinion followers. The impacts of the opinion leaders on the evolution of the collective opinion will be investigated deeply and some practical measures will be provided for some related public departments to guild the collective human behaviors.
The rest of this paper is organized as follows. A leader-follower opinion formation model with heterogeneous confidence levels is proposed based on a Hegselmann and Krause (HK) bounded confidence rule in Section 2. Section 3 presents some computer simulation results to study the impacts of opinion leaders on the opinion propagation with the proposed heterogeneous opinion dynamics. Section 4 concludes the paper.
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