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.


Movies Gallery 2011 said...

Thanks for the experiment. It was very informative and useful. I keep in mind. Thanks a lot for sharing such a awe-some information.
Vee Eee Technologies| Vee Eee Technologies

Sai Santosh said...

As this website majorly give importance to the private jobs as well as govt jobs related information we appreciate it for the quality of its content.