Evolution of opinions under social pressure on random graphs

Opinion dynamics models study how the opinions of individuals evolve in social settings. An important aspect of this often is social pressure, in which an individual feels pressure to conform her expressed opinions to the opinions of those around her, even against her true beliefs. This work studies an interacting Pólya urn model for opinion dynamics under social pressure, originally proposed in [1]. In this paper, we consider the behavior of this model on random graphs. Previous work has shown conditions for when the agents on the network approach consensus [2], in which all the agents asymptotically express the same opinion over time, even if this opinion is contrary to some of their true beliefs; however these conditions are not interpreted as explicit graph properties or characteristics. In this work, we bridge this gap by examining what kinds of basic network properties determine whether the network approaches consensus. We show that when the agents' network structure is a random graph, homophily, the tendency for agents to be connected to those more similar to themselves, diminishes the likelihood of consensus to occur. This result gives insight on how network characteristics affect the possibility of consensus.