Entropy profiles of Schelling’s segregation model from the Wang–Landau algorithm

Abstract

We evaluate Schelling’s segregation outcomes from the square lattice, regular random networks, and clustered regular random networks by situating them in the probability distribution of the entire outcome space of satisfaction and segregation. To do so, we employ the Wang–Landau algorithm and calculate the entropy and the number of states as a function of satisfaction and segregation. According to the results, satisfaction tends to increase with segregation, irrespective of the network structure. Moreover, segregation occurs almost surely when satisfaction is maximized, which we also algebraically derive and confirm on infinite-size networks. The average ratios of the neighbors of the same tag are about 67% for the square lattice and regular random networks and about 73% for clustered regular random networks with a clustering coefficient of 0.37(1). Thus, clustering increases segregation on regular random networks. Further, we find that Schelling’s path-dependent process generates sharper segregation than expected by random configurations, an outcome symptomatic of over-optimization from the social welfare perspective. Adopting an alternative rule restricting individuals’ choice set may reduce segregation without compromising on satisfaction.