Compartmental Models in Social Dynamics

Abstract: The dynamics of many aspects of social behaviour, such as spread of fads and fashion, collective action, group decision-making, homophily and disagreement, have been captured by mathematical models. The power of these models is that they can provide novel insight into the emergent dynamics of groups, e.g. 'epidemics' of memes, tipping points for collective action, wisdom of crowds and leadership by small numbers of individuals, segregation and polarisation. A current weakness in the scientific models is their sheer number. 'New' models are continually 'discovered' by physicists, engineers and mathematicians. The models are analysed mathematically, but very seldom provide predictions that can be tested empirically. In this work, we provide a framework of simple models, based on Lotka's original idea of using chemical reactions to describe social interactions. We show how to formulate models for social epidemics, social recovery, cycles, collective action, group decision-making, segregation and polarisation, which we argue encompass the majority of social dynamics models. We present an open-access tool, written in Python, for specifying social interactions, studying them in terms of mass action, and creating spatial simulations of model dynamics. We argue that the models in this article provide a baseline of empirically testable predictions arising from social dynamics, and that before creating new and more complicated versions of the same idea, researchers should explain how their model differs substantially from our baseline models.