A minimal model of a social system

How do beliefs of society evolve? We typically see a pendulum swinging back and forth, maybe slowing down as it reaches equilibrium. Sometimes, beliefs appear driven, as when polarization on issues that are essentially either Republican or Democratic swing back and forth more and more violently between extremes. How can we, as a society, intervene so that we reach a desired equilibrium faster?

For example, let's take the case of an issue we all care about-- racism. There's racism, and there are people that claim that there is "reverse racism", which only makes sense if you ignore that racism requires a systemic oppression from society. But still, we could imagine that a college admissions process favors white applicants or black applicants. We seem to be swinging back and forth between those two extremes with court case and societal movement after court case and societal movement. Wouldn't it be nice if we could find an intervention or interventions on society that slows down the pendulum with just the right amount of drag so we reach color-blindness as fast as possible? Research is accumulating that shows that implicit bias training does little, as many people hate being told that they're actually racist, so is there an intervention that works?

For this, we would like to make a model of the system that describes the evolution of societal beliefs. This is a coarse-graining of the overall belief dynamics of everyone in society, which can get quite complicated and even show potentially chaotic behavior when you add in enough cognitive biases. However, if we do a Taylor expansion about an equilibrium point-- which may not be warranted-- we will find that there is a linear dynamical system with potentially weird Gaussian noise that describes how the state of society evolves. When the belief is binary, this will approximately take the form of a mass on a spring with damping hit by particles randomly. The key, then, is to relate interventions to the spring constant, the mass, the drag coefficient, and the temperature by correctly Taylor expanding. This is impossible except in a toy model, for now.

There is a critical damping that will get us to equilibrium as fast as possible. In theory, we merely need to solve for it.

What if things explode? We see this in some social systems, as the number of papers in a field for example (https://www.sciencedirect.com/science/article/pii/S0303264720301015) explodes. A simple linear model might explain a great deal of social science phenomena.