Consensus, Polarization and Clustering of Opinions in Social Networks

We consider a variation of the Deffuant-Weisbuch model introduced by Deffuant et al. in 2000, to provide new analytical insights on the opinion dynamics in a social group. We model the trust that may exist between like-minded agents through a trust function, which is a discontinuous (hard-interaction) non-increasing function of the opinion distance. In this model, agents exchange their opinions with their neighbors and move their opinions closer to each other if they are like-minded (that is, the distance between opinions is smaller than a threshold). We first study the dynamics of opinion formation under random interactions with a fixed rate of communication between pairs of agents. Our goal is to analyze the convergence properties of the opinion dynamics and explore the underlying characteristics that mark the phase transition from opinion polarization to consensus. Furthermore, we extend the hard-interaction model to a strategic interaction model by considering a time-varying rate of interaction. In this model, social agents themselves decide the time and energy that should be expended on interacting each of their neighbors, based on their utility functions. The aim is to understand how and under what conditions clustering patterns emerge in opinion space. Extensive simulations are provided to validate the analytical results of both the hard-interaction model and the strategic interaction model. We also offer evidence that suggests the validity of the proposed model, using the location and monthly survey data collected in the Social Evolution experiment over a period of nine months.