Activism

# Social consensus through the influence of committed minorities

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

Phys. Rev. E 84, 011130 – Published 22 July 2011

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 p<pc, Tc~exp[α(p)N], whereas for p>pc, Tc~lnN. We conclude with simulation results for Erdős-Rényi random graphs and scale-free networks which show qualitatively similar behavior.

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