Academic journal article Demographic Research

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

Academic journal article Demographic Research

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

Article excerpt

Abstract

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. This agent based lattice model has become quite influential amongst social scientists, demographers, and economists. Aggregation relates to individuals coming together to form groups and Schelling equated global aggregation with segregation. Many authors assumed that the segregation which Schelling observed in simulations on very small cities persists for larger, realistic sized cities. We describe how different measures can be used to quantify the segregation and unlock its dependence on city size, disparate neighbor comfortability threshold, and population density. We develop highly efficient simulation algorithms and quantify aggregation in large cities based on thousands of trials. We identify distinct scales of global aggregation. In particular, we show that for the values of disparate neighbor comfortability threshold used by Schelling, the striking global aggregation Schelling observed is strictly a small city phenomenon. We also discover several scaling laws for the aggregation measures. Along the way we prove that in the Schelling model, in the process of evolution, the total perimeter of the interface between the different agents always decreases, which provides a useful analytical tool to study the evolution.

(ProQuest: ... denotes formula omitted.)

1. Introduction

In the 1970s, the eminent economic modeler Thomas Schelling proposed a simple spacetime population model to illustrate how, even with relatively minimal assumptions concerning every individual's nearest neighbor preferences, an integrated city would likely unravel to a segregated city, even if all individuals prefer integration (Schelling 1969; Schelling 1971a; Schelling 1971b; Schelling 2006). His agent-based lattice model has become quite influential amongst social scientists, demographers, and economists. Currently, there is a spirited discussion on the validity of Schelling-type models to describe actual segregation, with arguments both for (e.g., Young 1998; Fossett 2006), and against (e.g., Massey 1990; Laurie and Jaggi 2003), and a few authors have used and extended the Schelling model to address actual population data (Clark 1991; Bruch and Mare 2006; Benenson et al. 2006; Sander, Schreiber, and Doherty 2000; Clark and Fossett 2008). The few examples of quantitative analyses of such models are (Pollicott andWeiss 2001; Fossett 2006; Gerhold et al. 2008). Recently, Zhang (2004) proved analytically that, for certain wedge-like utility functions and with additional random noise, the equilibrium states possess a high degree of segregation.

Aggregation relates to individuals coming together to form groups or clusters, and Schelling equated global aggregation with segregation. Many authors assume that the striking global aggregation observed in simulations on very small ideal "cities" persists for large, realistic size cities. A recent paper (Vinkovic and Kirman 2006) exhibits final states for a small number of model simulations of a large city, and some final states that do not exhibit significant global aggregation. However, quantification of this important phenomenon is lacking in the literature, presumably due in part to the huge computational costs required to run simulations using existing algorithms. We develop highly efficient and fast algorithms that allow us to carry out many simulations for many sets of parameters and to compute meaningful statistics of the measures of aggregation.

The objective of this paper is to quantify the aggregation and unlock its dependence on city size, disparate neighbor comfort threshold, and population density. One of the measures is the total perimeter of a configuration: the total number of contacts between the agents of different kind, adjusted to the presence of empty spaces. …

Search by... Author
Show... All Results Primary Sources Peer-reviewed

Oops!

An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.