Polarization and Non-Positive Social Influence: A Hopfield Model of Emergent Structure

Introduction

Almost all social interactions are, at least in part, shaped by opinions. Some opinions are ultimately evolved into acceptable behaviors such as what we deem as social norms. They not only affect our daily lives but also shape our political participation and attitudes. Towards a specific object or event, human collective opinions display different patterns, e.g. consensus, polarization and diversity with a variety of factors, such as mutual influence, the external intervention etc, which had been long studied by sociologists and become an important research field among multiple disciplines. As a matter of fact, opinion dynamics has been widely studied in management science (Simon, 1954), social psychology (French, 1956; Latane, 1981; Friedkin, 1998), economics (Blume & Durlauf, 2004), sociophysics (Stauffer, 2005; Galam, 2007), systems science (Hummel, 1996), statistic physics (Sznajd-Weron & Sznajd, 2000), etc. Recently, with the booming of Internet and advances in information technologies, the topic is maturing into the spotlight in computer science (Leskovec, Huttenlocher, & Kleinberg, 2010; Conover, Ratkiewicz et al., 2010), etc.

In this paper, we focus on the impacts of social influence toward group opinion, investigate to what extend that social influence can affect group opinion formation. We make a clear classification about three types of social influence as positive, neutral and negative based on social identity theory. Furthermore, we study the relation of polarization and non-positive influence through Hopfield network model simulation.

The rest of the paper is organized as follows: according to social identity, we discuss three kinds of social influence implications and make a clear classification. Structure balance theory and 16 types of triadic structure are referred. First, we extend Hopfield model implication and assign three types of discrete social influence weights into the model. By adding three types of social influence into Hopfield model, we study the relationship between opinion bi-polarization and non-positive social influence. Moreover, we analyze the local triad distribution before and after group opinions polarization, and discuss some interesting social-psychological implications about local level signed social structure balance and global pattern emergence. Finally we discuss our concluding remarks.