Schelling's Segregation Model: Parameters, scaling, and aggregation

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.

Examining the Schelling Model Simulation through an Estimation of Its Entropy

“…From the concise set of equations for the dynamics of the Schelling model iterations it is seen that there is a resemblance with that of the Ising model [15] which is also noted in previous research [15][16][17][18]25]. This similarity rests predominantly upon the premise that both models utilize a lattice for the placement of cell occupants whose state depends exclusively upon the states of the occupants in the adjacent/neighboring cells.…”

“…The examination of cell values outside of the lattice bounds are treated as m empty making no contribution to the residential satisfaction as this function is not called on behalf of empty cells. This state determination for each cell based upon the adjacency of the grid is the main motivation for the comparison to the Ising model in the previous research [25,26].…”

“…The value for threshold is set to h = 6 in this work (as in [25]), and it is typical for this to be adjusted to examine the sensitivity with the final {m group1 , m group2 } (non-empty residents) spatial arrangements. This binary value represents the state for each of the non-empty occupants for which the movement is conditioned upon.…”

A unified framework for Schelling’s model of segregation

“…Schelling himself produced several iterations of his first model [1,2,3]; a consequence of which is that there is no definitive "Schelling model". As computing power increased many researchers have simulated model variants related to their particular interests [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21], finding segregation everywhere from the suburbs of Tel-Aviv [15] to the Sierpinski fractal [20].…”

Monte Carlo Analysis in Academic Research

“…A sharp separation of races can develop over time even if the families are relatively tolerant of each other (Schelling, 1971(Schelling, , 1978. This publication gave rise to a steady succession of studies of segregation (for example, Singh et al, 2009;Zhang, 2004;Aydinonat, 2007) and the "tipping models" of social behavior (Granovetter & Soong, 1988).…”