Sunday, August 7, 2011

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 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 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.


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