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 pc≈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∼lnN. We conclude with simulation results for Erdos-Rényi random graphs and scale-free networks which show qualitatively similar behavior. © 2011 American Physical Society.