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## 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 \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