Social consensus through the influence of committed minorities

doi:10.1103/PhysRevE.84.011130

Social consensus through the influence of committed minorities

by J Xie, S Sreenivasan, G Korniss, W Zhang, C Lim, B K Szymanski

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Physical Review E - Statistical, Nonlinear and Soft Matter Physics (2011)

Volume: 84, Issue: 1-1, Publisher: American Physical Society, Pages: 011130

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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 pc10%, there is a dramatic decrease in the time Tc taken for the entire population to adopt the committed opinion. In particular, for complete graphs we show that when ppc, Tc~lnN. We conclude with simulation results for Erdős-Rényi random graphs and scale-free networks which show qualitatively similar behavior.