%0 Journal Article %1 Xie2011 %A Xie, J. %A Sreenivasan, S. %A Korniss, G. %A Zhang, W. %A Lim, C. %A Szymanski, B. K. %D 2011 %I American Physical Society %J Phys. Rev. E %K consensus-formation graphs networks opinion-formation naming-game zealots %N 1 %P 011130 %R 10.1103/PhysRevE.84.011130 %T Social consensus through the influence of committed minorities %V 84 %X 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\~expα(p)N, whereas for p>pc, Tc\~lnN. We conclude with simulation results for Erd\Hos-Rényi random graphs and scale-free networks which show qualitatively similar behavior.

@article{Xie2011, 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 {Erd\H{o}s-R\'{e}nyi} random graphs and scale-free networks which show qualitatively similar behavior.}, added-at = {2011-07-25T11:42:59.000+0200}, author = {Xie, J. and Sreenivasan, S. and Korniss, G. and Zhang, W. and Lim, C. and Szymanski, B. K.}, biburl = {https://www.bibsonomy.org/bibtex/283f71d369b106703a36e081487c0601f/rincedd}, doi = {10.1103/PhysRevE.84.011130}, file = {Xie2011 - Social consensus through the influence of committed minorities.pdf:Contact Processes/Xie2011 - Social consensus through the influence of committed minorities.pdf:PDF}, groups = {public}, interhash = {5300c742d46d8db25c171df395ed8ce2}, intrahash = {c0ca9432c693f55b957ca277c8cff29b}, journal = {Phys. Rev. E}, keywords = {consensus-formation graphs networks opinion-formation naming-game zealots}, number = 1, pages = 011130, publisher = {American Physical Society}, timestamp = {2011-07-25T11:52:21.000+0200}, title = {Social consensus through the influence of committed minorities}, username = {rincedd}, volume = 84, year = 2011 }