Lies, damned lies, and statistics
Or, “we’re winning! We’re winning!”
March 21, 2011.
A mathematical model of social group competition with application to the growth of religious non-affiliation, a paper from Cornell by Daniel M. Abrams, Haley A. Yaple, and Richard J. Wiener.
When groups compete for members, the resulting dynamics of human social activity may be understandable with simple mathematical models. Here, we apply techniques from dynamical systems and perturbation theory to analyze a theoretical framework for the growth and decline of competing social groups. We present a new treatment of the competition for adherents between religious and irreligious segments of modern secular societies and compile a new international data set tracking the growth of religious non-affiliation. Data suggest a particular case of our general growth law, leading to clear predictions about possible future trends in society.
full PDF (5 pages).
From the PDF:
What we have shown by the generalization of the model to include network structure is surprising: even if conformity to a local majority influences group membership, the existence of some out-group connections is enough to drive one group to dominance and the other to extinction. […]
We found that a particular case of the solution fits census data on competition between religious and irreligious segments of modern secular societies in 85 regious around the world. The model indicates that in these societies the perceived utility of religious non-affiliation is greater than that of adhering to a religion, and therefore predicts continued growth towards non-affiliation, tending towards the disappearance of religion. According to our calculations, the steady-state predictions should remain valid under small perturbations to the all-to-all network structure that the model assumes, and, in fact, the all-to-all analysis remains applicable to networks very different from all-to-all. Even an idealized highly polarized society with a two-clique network structure follows the dynamics of our all-to-all model closely, albeit with the introduction of a time delay. This perturbation analysis suggests why the simple all-to-all model fits data from societies which undoubtedly have more complex network structures. […]
Emphasis mine. Citation: http://arxiv.org/abs/1012.1375v2