Behavioral and Topological Heterogeneities in Network Versions of Schelling's Segregation Model
Will Deter, Hiroki Sayama
TL;DR
The paper addresses how concurrent heterogeneity in agent tolerances and network topology shapes residential segregation in Schelling-like network models. It combines a baseline $32 \times 32$ lattice with a densification procedure to generate topological heterogeneity and employs empirically grounded tolerance distributions (including a rank-ordered logit for nonconforming cases) to induce behavioral heterogeneity, measuring outcomes with the assortativity coefficient $r$ and entropy $H$. The main finding is that while tolerance heterogeneity or topology heterogeneity alone can have limited or opposite effects, their combination reduces segregation and yields novel dynamics such as ordered migration and tolerance repelling intolerance, especially in denser networks. These results suggest that comprising both dimensions of heterogeneity can alter core segregation mechanisms and have implications for housing policy and cultural diffusion in urban and organizational settings, guiding future work on incorporating random movements and economic factors.
Abstract
Agent-based models of residential segregation have been of persistent interest to various research communities since their origin with James Sakoda and popularization by Thomas Schelling. Frequently, these models have sought to elucidate the extent to which the collective dynamics of individual preferences may cause segregation to emerge. This open question has sustained relevance in U.S. jurisprudence. Previous investigation of heterogeneity of behaviors (preferences) has shown reductions in segregation. Meanwhile, previous investigation of heterogeneity of social network topologies has shown no significant impact to observed segregation levels. In the present study, we examined the effects of the concurrent presence of both behavioral and topological heterogeneities in network segregation models. Simulations were conducted using both homogeneous and heterogeneous preference models on 2D lattices with varied levels of densification to create topological heterogeneities (i.e., clusters, hubs). Results show a richer variety of outcomes, including novel differences in resultant segregation levels and hub composition. Notably, with concurrent increased representations of heterogeneous preferences and heterogeneous topologies, reduced levels of segregation emerge. Simultaneously, we observe a novel dynamic of segregation between tolerance levels as highly tolerant nodes take residence in dense areas and push intolerant nodes to sparse areas mimicking the urban-rural divide.