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arXiv · 1102.3931

Social consensus through the influence of committed minorities

J. Xie·S. Sreenivasan·G. Korniss·W. Zhang·C. Lim·B. K. Szymanski
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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 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.

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J. Xie, S. Sreenivasan, G. Korniss, W. Zhang, C. Lim, B. K. Szymanski. 2011-02-18. Social consensus through the influence of committed minorities. https://doi.org/10.1103/physreve.84.011130

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