Researchers in Belgium have developed a model to attempt to explain how opinions change within a population, but I'm not sure their assumptions are valid. My masters thesis was in a very similar vein, but used a more complex model.
The key, say European researchers, is how strongly the groups communicate with each other. The work could explain how language differences persist across geographic boundaries and how political thought can quickly become polarized. ...
To model the evolution of opinions, researchers led by physicist Renaud Lambiotte of the University of Liege in Belgium imagined two groups, initially isolated, whose members gradually begin to talk to members of the other group.
They supposed for simplicity that individuals hold one of two opinions, assigned randomly at the start. People then change their views by a â€œmajority ruleâ€ â€“ each person tends to adopt the opinion that is held by a majority of those with whom they are linked in the social network.
Because of the majority rule system, it's perfectly logical that increasing connections between groups would lead to equilibrium (agreement) across the population. However, no opinion space is really binary and very few people make up their minds based purely on what the majority of their friends think. It seems that these assumptions might be so simplifying that they miss the essence of the problem at hand, but I reached a similar conclusion in my masters research.