Schelling's Segregation Model: Parameters, Scaling, and Aggregation

Abhinav Singh, Georgia Institute of Technology
Howard Weiss, Georgia Institute of Technology
Dmitri Vainchtein, Georgia Institute of Technology

Thomas Schelling proposed a simple spatial model to illustrate how, even with relatively mild assumptions on each individual's nearest neighbor preferences, an integrated city would likely unravel to a segregated city, even if all individuals prefer integration. His model has become quite influential amongst social scientists, demographers, and economists. Many authors assumed that the global aggregation which Schelling observed in simulations on very small ``cities" persists for larger, realistic size cities. In this paper, we devise new measures to quantify the aggregation and we unlock its dependence on city size, disparate neighbor comfortability threshold, and population density. We identify distinct scales of global aggregation, and we show that the striking global aggregation Schelling observed is strictly a small city phenomenon. We also discover several remarkable scaling laws for disparate aggregation measures as functions of population density.