Binary Opinion Models of Influence and Opinion Dynamics in Social Networks

The process of influence and opinion dynamics is predominant in many kinds of real-life situations involving agents' interactions. This phenomenon is extensively analyzed in different fields and with the help of various methods and tools. Network analysis is particularly suitable for the study of influence and opinion formation. The aim of this paper is to provide an overview of selected results on models of influence and opinion dynamics in social networks with non-strategic updating of binary opinions. We start with presenting some results on the relation between a static binary opinion model of influence with influence indices, follower and influence functions, and a framework of simple games called command games. Then, we focus on binary opinion dynamics with non-strategic agents embedded in a social network. In this overview, a special attention is paid to models based on aggregation functions which can be seen as a generalization of the threshold model. In particular, we present some of themain results of the convergence analysis concerning anonymous social influence, conformism and anti-conformism in social networks. Also the phenomenon of diffusion in large networks with the diffusion mechanism represented by an aggregation function is briefly presented. Finally, we conclude this overview paper by indicating some possible directions for future research on the discrete opinion dynamics in social networks.