Phase Transition in the Social Impact Model of Opinion Formation in Log-Normal Networks

Fattaneh Taghiyareh,Alireza Mansouri

doi:10.52547/jist.9.33.1

Abstract

People may change their opinions as a consequence of interacting with others. In the literature, this phenomenon is expressed as opinion formation and has a wide range of applications, including predicting social movements, predicting political voting results, and marketing. The interactions could be face-to-face or via online social networks. The social opinion phases are categorized into consensus, majority, and non-majority. In this research, we study phase transitions due to interactions between connected people with various noise levels using agent-based modeling and a computational social science approach. Two essential factors affect opinion formations: the opinion formation model and the network topology. We assumed the social impact model of opinion formation, a discrete binary opinion model, appropriate for both face-to-face and online interactions for opinion formation. For the network topology, scale-free networks have been widely used in many studies to model real social networks, while recent studies have revealed that most social networks fit log-normal distributions, which we considered in this study. Therefore, the main contribution of this study is to consider the log-normal distribution network topology in phase transitions in the social impact model of opinion formation. The results reveal that two parameters affect the phase transition: noise level and segregation. A non-majority phase happens in equilibrium in high enough noise level, regardless of the network topology, and a majority phase happens in equilibrium in lower noise levels. However, the segregation, which depends on the network topology, affects opinion groups’ population. A comparison with the scale-free network topology shows that in the scale-free network, which have a more segregated topology, resistance of segregated opinion groups against opinion change causes a slightly different phase transition at low noise levels. EI (External-Internal) index has been used to measure segregations, which is based on the difference between between-group (External) links and within-group (Internal) links.

Highlights

Analytical sociology has emerged as an approach for understanding the social world, concerning important social facts such as network structures, patterns of residential segregation, typical beliefs, cultural tastes, and common ways of acting [1]
Since some recent studies have revealed that the log-normal networks are more realistic models for real world social networks, we considered the log-normal network in this study on phase transition in the social impact model of opinion formation
The results show that the segregation phenomenon is a main parameter affecting the phase transition for different noise levels, the level of the stochastic behavior of the social system

Summary

Introduction

Analytical sociology has emerged as an approach for understanding the social world, concerning important social facts such as network structures, patterns of residential segregation, typical beliefs, cultural tastes, and common ways of acting [1]. We used the social impact model of opinion formation [7], based on the psychological theory of social impact, formulated by Bibb Latané [8]. This model is a discrete opinion model, assuming opinion as binary values, e.g., agree/disagree. As a traditional discipline of social sciences, sociology studies all forms of human and social dynamics and organization at all levels of analysis, including cognition, decision making, behavior, groups, organizations, societies, and the world system [20]. The number of papers on using agent-based models to describe how opinions emerge in a group of people has grown at an overall annual rate of 16%, though not continually [3]

Methods

Results

Discussion

Conclusion