Phase Transitions in Schelling Model Variants: Foundations for Exploring Positional Choice Models.

Simulating simplified models of social interactions with agent-based models (ABMs) fills a special role in the study of social phenomena, where it is often impossible to design controlled experiments. Schelling's model of segregation is one of the best-known ABMs, notable for being among the first and simplest to demonstrate how societal outcomes can collectively fail to match individual preferences. This link between microscopic rules and macroscopic social behavior, has established it as a valuable bridge between the physical, computational, and social sciences. This has yielded a proliferation of model variants and a disjointed state of the literature. In this work, a comprehensive analysis of Schelling model rule variants is achieved by classification of the space of macroscopic outcomes via phase diagrams. Among 54 rule variants, only 3 phase diagram classes are found, characterized by the number of phase transitions. The statistical and dynamic drivers of these transitions are elucidated by analyzing the roles of agent vision, movement criteria, vacancies, the initial state, and rivalry. This comprehensive classification gives new insight into the drivers of transitions in the Schelling model and creates a basis for studying model extensions. We report progress on how sloped, curved, and peaked satisfaction functions, along with a stochastic move rule, affect the system's phase space.