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Mar22-11, 11:25 PM
P: 500

A mathematical model of social group competition with application to the growth of
religious non-affiliation

When groups compete for members, the resulting dynamics of human social activity may be un-
derstandable 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.
The model indicates that in these societies
the perceived utility of religious non-aliation is greater
than that of adhering to a religion, and therefore pre-
dicts continued growth of non-aliation, tending toward
the disappearance of religion. According to our calcu-
lations, the steady-state predictions should remain valid
under small perturbations to the all-to-all network struc-
ture that the model assumes, and, in fact, the all-to-
all analysis remains applicable to networks very di er-
ent 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.
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