Abstract
We show how the prevailing majority opinion in a population can be rapidly reversed by a small fraction 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 , there is a dramatic decrease in the time taken for the entire population to adopt the committed opinion. In particular, for complete graphs we show that when , , whereas for , . We conclude with simulation results for Erdős-Rényi random graphs and scale-free networks which show qualitatively similar behavior.
- Received 17 February 2011
DOI:https://doi.org/10.1103/PhysRevE.84.011130
©2011 American Physical Society