Affinity and Hostility in Divided Communities: a Mathematical Model

TL;DR

This paper introduces a mathematical model to analyze intergroup attitudes in divided communities, exploring stability, behavior dependence on parameters, and implications for improving intergroup relations.

Contribution

It presents a novel, sociologically justified mathematical framework for understanding and potentially improving intergroup affinity and hostility.

Findings

Model exhibits both stable and unstable equilibria.

Behavior depends continuously or discontinuously on parameters.

Implications suggest strategies to enhance intergroup affinity.

Abstract

We propose, develop, and analyze a mathematical model of intergroup attitudes 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. We investigate the behavior of the model in various special cases, for various model configurations. We discuss the stability of the model, and the continuous or discontinuous dependence of model behavior on various parameters. Finally, we discuss possible implications for strategies to improve intergroup affinity, and to defuse tension and prevent deterioration of intergroup relationships.