Limit Sets for Natural Extensions of Schelling's Segregation Model

TL;DR

This paper explores how variations in happiness thresholds and group sizes in Schelling's segregation model lead to diverse and complex spatial patterns, including tessellated structures, highlighting the model's sensitivity to these parameters.

Contribution

It introduces natural extensions to Schelling's model allowing different group sizes and happiness notions, revealing new segregation patterns and tessellated structures.

Findings

Aggregation patterns are highly sensitive to happiness thresholds.

Higher thresholds lead to striking new segregation patterns.

Strong preference for integration results in tessellated-like final states.

Abstract

Thomas Schelling developed an influential demographic model that illustrated 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. Individuals in Schelling's model cities are divided into two groups of equal number and each individual is 'happy' or 'unhappy' when the number of similar neighbors cross a simple threshold. In this manuscript we consider natural extensions of Schelling's original model to allow the two groups have different sizes and to allow different notions of happiness of an individual. We observe that differences in aggregation patterns of majority and minority groups are highly sensitive to the happiness threshold; for low threshold, the differences are small, and when the threshold is raised, striking new patterns emerge. We also observe that when individuals strongly prefer to live integrated neighborhoods, the final states exhibit a new tessellated-like structure.