Social consensus through the influence of committed minorities

DSA ADS Course - 2021

Social consensus through the influence of committed minorities

Psychology, Psychological Science, Social Consensus, Social and Information Networks, Statistical Mechanics

Scientists at Rensselaer Polytechnic Institute have found that when just 10 percent of the population holds an unshakable belief, their belief will always be adopted by the majority of the society. The scientists, who are members of the Social Cognitive Networks Academic Research Center (SCNARC) at Rensselaer, used computational and analytical methods to discover the tipping point where a minority belief becomes the majority opinion. The finding has implications for the study and influence of societal interactions ranging from the spread of innovations to the movement of political ideals.

"When the number of committed opinion holders is below 10 percent, there is no visible progress in the spread of ideas. It would literally take the amount of time comparable to the age of the universe for this size group to reach the majority," said SCNARC Director Boleslaw Szymanski, the Claire and Roland Schmitt Distinguished Professor at Rensselaer. "Once that number grows above 10 percent, the idea spreads like flame."

February, 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 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 Erdős-Rényi random graphs and scale-free networks which show qualitatively similar behavior.

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