Dynamics of Social Group Competition: Modeling the Decline of Religious Affiliation

When social groups compete for members, the resulting dynamics may be understandable with mathematical models. We demonstrate that a simple ordinary differential equation (ODE) model is a good fit for religious shift by comparing it to a new international data set tracking religious nonaffiliation. We then generalize the model to include the possibility of nontrivial social interaction networks and examine the limiting case of a continuous system. Analytical and numerical predictions of this generalized system, which is robust to polarizing perturbations, match those of the original ODE model and justify its agreement with real-world data. The resulting predictions highlight possible causes of social shift and suggest future lines of research in both physics and sociology.

Figure 1

Fraction of population religiously unaffiliated versus time for (a) Schwyz Canton in Switzerland, (b) the autonomous Aland islands region of Finland, (c) the Netherlands, and (d) all 85 data sets. Dots indicate data points from census surveys; light gray (red) dots correspond to regions within countries and dark gray (blue) dots to entire countries. Black lines indicate model fits. For (a)–(c), relative utilities for the religiously unaffiliated populations as determined by model fits were $u_x=0.70,0.63,0.56$. In (c) we extend the model’s projection to show the expected change in concavity around 2025. For (d) time has been rescaled so data sets lie on top of one another and the solution curve with $u_x=0.65$. Representative data sets were chosen to show varied current rates of nonaffiliation (low, medium, and high).

Figure 2

Results of simulation of the discrete stochastic model Eq. (2) on a network with two initial clusters weakly coupled to one another. The ratio $p$ of out-group coupling strength to in-group coupling strength is (a) $p=0.01$, (b) $p=0.40$, (c) $p=0.80$ ($N=500$). Steady states are nearly identical to the predictions of the all-to-all model Eq. (1).

Figure 3

Variation in the behavior of Eq. (3) with increasing perturbation off of all-to-all ($N=500$, $x_0=0.1$, $u=0.6$). Equivalent values of the perturbation parameter $\delta$ in order of decreasing $p$ are $\delta =0$, $\delta =0.11$, $\delta =0.43$, and $\delta =0.98$.