Opinion formation and distribution in a bounded confidence model on various networks

In the social, behavioral, and economic sciences, it is an important problem to predict which individual opinions will eventually dominate in a large population, if there will be a consensus, and how long it takes a consensus to form. This idea has been studied heavily both in physics and in other disciplines, and the answer depends strongly on both the model for opinions and for the network structure on which the opinions evolve. One model that was created to study consensus formation quantitatively is the Deffuant model, in which the opinion distribution of a population evolves via sequential random pairwise encounters. To consider the heterogeneity of interactions in a population due to social influence, we study the Deffuant model on various network structures (deterministic synthetic networks, random synthetic networks, and social networks constructed from Facebook data) using several interaction mechanisms. We numerically simulate the Deffuant model and conduct regression analyses to investigate the dependence of the convergence time to equilibrium on parameters, including a confidence bound for opinion updates, the number of participating entities, and their willingness to compromise. We find that network structure and parameter values both have an effect on the convergence time, and for some network topologies, the convergence time undergoes a transition at a critical value of the confidence bound. We discuss the number of opinion groups that form at equilibrium in terms of a confidence-bound threshold for a transition from consensus to multiple-opinion equilibria.