title: Social consensus through the influence of committed minorities.
abstract: We show how the prevailing majority opinion in a population can be rapidly reversed by a small fraction p of randomly distributed committed agents who consistently proselytize the opposing opinion and are immune to influence. Specifically, we show that when the committed fraction grows beyond a critical value p(c) ≈ 10%, there is a dramatic decrease in the time T(c) taken for the entire population to adopt the committed opinion. In particular, for complete graphs we show that when p < pc, T(c) ~ exp [α(p)N], whereas for p>p(c), T(c) ~ ln N. We conclude with simulation results for Erdős-Rényi random graphs and scale-free networks which show qualitatively similar behavior.
authors.affiliation: Department of Computer Science, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180, USA.
authors.forename: J
authors.initials: J
authors.lastname: Xie
authors.forename: S
authors.initials: S
authors.lastname: Sreenivasan
authors.forename: G
authors.initials: G
authors.lastname: Korniss
authors.forename: W
authors.initials: W
authors.lastname: Zhang
authors.forename: C
authors.initials: C
authors.lastname: Lim
authors.forename: B K
authors.initials: BK
authors.lastname: Szymanski
mesh_terms: D000465:Algorithms; D001519:Behavior; D001703:Biophysics / Q000379:methods*; D003198:Computer Simulation; D032921:Consensus; D004059:Diffusion of Innovation; D006801:Humans; D008913:Minority Groups; D015233:Models, Statistical; D008962:Models, Theoretical; D012944:Social Support