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In the social, behavioral, and economic sciences, it is an important problemto predict which individual opinions will eventually dominate in a largepopulation, if there will be a consensus, and how long it takes a consensus toform. This idea has been studied heavily both in physics and in otherdisciplines, and the answer depends strongly on both the model for opinions andfor the network structure on which the opinions evolve. One model that wascreated to study consensus formation quantitatively is the Deffuant model, inwhich the opinion distribution of a population evolves via sequential randompairwise encounters. To consider the heterogeneity of interactions in apopulation due to social influence, we study the Deffuant model on variousnetwork structures (deterministic synthetic networks, random syntheticnetworks, and social networks constructed from Facebook data) using severalinteraction mechanisms. We numerically simulate the Deffuant model and conductregression analyses to investigate the dependence of the convergence time toequilibrium on parameters, including a confidence bound for opinion updates,the number of participating entities, and their willingness to compromise. Wefind that network structure and parameter values both have an effect on theconvergence time, and for some network topologies, the convergence timeundergoes a transition at a critical value of the confidence bound. We discussthe number of opinion groups that form at equilibrium in terms of aconfidence-bound threshold for a transition from consensus to multiple-opinionequilibria.

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