Affinity and Hostility in Divided Communities: A Mathematical Model

Abstract

We propose, develop, and analyze a mathematical model of the probability distribution of intergroup attitudes (measured on a linear scale) in a community that is divided between two distinct social groups (which may be distinguished by religion, ethnicity, or some other socially distinguishing factor). The model is based on very simple premises that are both intuitive and justified by sociological research. Under certain assumptions, we derive analytical equations to approximate the evolution of the probability distribution of affinities. We investigate the behavior of the model in various special cases, for various model configurations. We conclude that the analytical approximations do substantially capture the behavior of the system. According to the model, social pressures cause individuals in each group to tend towards extremes of hostility or affinity towards the other group. Under some conditions, groups can have stable extremist and moderate factions; but a very small change in system parameters can upset the stability, and the entire group is driven to unanimous extremism or moderation. Groups with intermediate affinity may end up unanimously extremist or unanimously moderate, depending on model parameters and random factors; a small change in parameters can have a huge effect on the likely outcome. Interpersonal cohesion (the degree to which individuals influence each other ’s opinions) plays a significant role in controlling within-group polarization. We show that programs to improve intergroup relations that target subpopulations of each group have greatly reduced effectiveness when cohesion is low. There is a narrow changeover range in which a small reduction in cohesion produces a much larger tendency towards within-group polarization.