10% Rule

Interesting paper via Freakonomics:

"What does it take for an idea to spread from one to many? For a minority opinion to become the majority belief? According to a new study by scientists at the Rensselaer Polytechnic Institute, the answer is 10%. Once 10% of a population is committed to an idea, it’s inevitable that it will eventually become the prevailing opinion of the entire group. The key is to remain committed.

The research was done by scientists at RPI’s Social Cognitive Networks Academic Research Center (SCNARC), and published in the journal Physical Review E. Here’s the 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 ppc, Tc~lnN. We conclude with simulation results for Erdos-Rényi random graphs and scale-free networks which show qualitatively similar behavior."