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Social consensus through the influence of committed minorities

By J. Xie, S. Sreenivasan, G. Korniss, W. Zhang, C. Lim and B. K. Szymanski

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 \approx 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 < p_c, T_c \sim \exp(\alpha(p)N), while for p > p_c, T_c \sim \ln N. We conclude with simulation results for Erd\H{o}s-R\'enyi random graphs and scale-free networks which show qualitatively similar behavior.Comment: 9 pages, 5 figure

Topics: Physics - Physics and Society, Condensed Matter - Statistical Mechanics, Computer Science - Social and Information Networks
Year: 2011
DOI identifier: 10.1103/PhysRevE.84.011130
OAI identifier: oai:arXiv.org:1102.3931
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