Wednesday, March 21, 2007

Percolation and social movements

Oh goody! I found one. The paper, "An application of percolation theory to political science" by two professors in Tokyo:

Kazuyuki Ikko Takahashi (Meiji University, Tokyo)
Ryosuke Murai (University of Electronics and Communication, Tokyo)

Unfortunately I couldn't understand their model very well, partly due to my ignorance of percolation theory and partly to difficult-to-read English. Basically what they look at is how a social model can spread in a society.

They break society into three kinds of actors: regular people, supporters and activists. The regular people, it seems are just sitting there waiting to be converted. Supporters ascribe to a social movement but they don't recruit anyone. Activists recruit.

How they got to their results, I don't understand very well, yet (it'd help if I could run my own simulations of innovation-spread in a social network, but i haven't found anything to let me do that. :( )* But what they found was that a social movement can create an infinite cluster (one that reaches throughout the network) with just 50% of the population. And there can be far fewer supporters if there are also a few activists.

However their model doesn't adequately deal with the topology of the network. Each actor in their model can only make 3 connections, and my impression is that those connections were limited to a lattice - that is if all actors/nodes made all three connections, you'd have a lattice of little triangles. There'd be no small-world effect or scale-free network effect.

What I'd like to do is look at percolation in a bi-partite graph where one layer is the graph of people and the other is the graph of groups they belong to.

(Note: future models should also examine how different groups bestow different levels of influence on their members. i.e. family and school influences are stronger than political party)

*How often to I end a parenthetical remark with an emoticon? I really want to find some way around that awkward double-parenthese thing.

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