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https://www.youtube.com/watch?v=ocilCO2u_kM
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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 pc≈10%, 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.
https://journals.aps.org/pre/abstract/10.1103/PhysRevE.84.011130