A 10% Tipping Point Threshold

Scientists at Rensselaer Polytechnic Institute have recently published research into social networks which indicates  that when just 10 percent of a network steadfastly holds a given belief, then that belief will eventually be adopted by the majority of the society. These group of 10% “believers” are referred to as a committed minority.

Even though the research has produced quite a bit of press (see here and here for example) it is a little difficult to say how the result was arrived at. The abstract of the paper states that

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≈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~exp[α(p)N], whereas for p>p_c, T_c~lnN. We conclude with simulation results for Erdős-Rényi random graphs and scale-free networks which show qualitatively similar behavior.

It seems that they are using a model for the spread of opinion overlayed on various network topologies, starting with the complete graph (everyone knows everyone), then scale free, and a simulation of a random graph process. The results are strengthened by finding the 10% threshold present in each topology. Even so, the following graph was not that informative for me.

I think I will have to wait get a copy of the paper to make full sense of the result. Reported in Freakanomics.