Characterizing segregation in the Schelling–Voter model

Abstract

In this work we analyze several aspects related with segregation patterns appearing in the Schelling–Voter model in which an unhappy agent can change her location or her state in order to live in a neighborhood where she is happy. Briefly, agents may be in two possible states, each one represents an individually-chosen feature, such as the language she speaks or the opinion she supports; and an individual is happy in a neighborhood if she has, at least, some proportion of agents of her own type, defined in terms of a fixed parameter T. We study the model in a regular two dimensional lattice. The parameters of the model are ρ, the density of empty sites, and p, the probability of changing locations. The stationary states reached in a system of N agents as a function of the model parameters entail the extinction of one of the states, the coexistence of both, segregated patterns with conglomerated clusters of agents of the same state, and a diluted region. Using indicators as the energy and perimeter of the populations of agents in the same state, the inner radius of their locations (i.e., the side of the maximum square which could fit with empty spaces or agents of only one type), and the Shannon Information of the empty sites, we measure the segregation phenomena. We have found that there is a region within the coexistence phase where both populations take advantage of space in an equitable way, which is sustained by the role of the empty sites.