Schelling’s Model of Segregation - Mathematical Insights into Society
Written By: Vidya Sinha
Rampant political polarization is characteristic of our era, and it is difficult to overstate the self-sustaining nature of segregation. Alarmingly, we often fail to acknowledge the role of voluntary segregation in constraining our social landscapes; we find ourselves exclusively surrounded by those who echo our sentiments and operate under the faulty assumption that our ideologies and life trajectories are the default. The resulting ignorance that emerges between groups can lay the groundwork for heightened hostilities and in turn exacerbate geopolitical segregation, generating a vicious positive feedback loop.
The Schelling model of segregation employs mathematical algorithms to illustrate the evolution of a geopolitical landscape in the presence of tension between groups. It is a frequently cited example of an agent-based model, which in the context of the humanities, simulates aspects of society by representing individuals as “agents'' with a predetermined set of incentives and potential decisions. Agent-based modeling is often used in conjunction with decision theory to understand the implications of human behavior on a large scale.
In essence, the Schelling model is a mathematical framework for grasping the consequences of human behavior and illuminating the potential of groupism to shape society. In the Schelling model, each agent is placed on a cell in a rectangular grid, where each cell is most commonly interpreted as a neighborhood. The agents can be one of two different groups, which can represent ethnic, political, or other forms of divisions. Additionally, the simulation takes the “critical tolerance threshold” as a parameter. This is the fraction of neighboring cells that need to be inhabited by “friends”, or part of the same group as an agent, for the agent to migrate to or remain in that cell. This number effectively represents an agent’s resistance to having neighbors of an external group.
Each round of the simulation consists of each agent completing their next ideal step. Once the agent reaches a cell where it is no longer optimal to move, i.e. it is surrounded by a sufficiently high proportion of friends, it is said to be “happy.” The simulation runs until a state of equilibrium where all agents are happy and have no further incentive to relocate. A standard implementation of the simulation uses color-coding to signify the two different groups, so the rapidly changing geopolitical landscape is visually apparent, and the results are striking.
Initially a fairly heterogeneous grid, as the rounds progress, the grid becomes increasingly split into multiple factions. Depending on the tolerance threshold, the simulation outcome can range from several dispersed enclaves of group-members to two entirely polarized regions of the grid. You can experiment with varying tolerance thresholds here.
Crucially, this model cannot capture the complete nuance of an evolving distribution of people. The number of groups is restricted to two, and the simulation fails to incorporate external factors that may impede individuals in the process of movement, such as political or economic barriers. Nevertheless, the Schelling model of segregation provides crucial insight into the nature of our societies. I urge readers to experiment with the simulation and acknowledge the surprise it may evoke; even reasonably high tolerance levels can yield stark disparities in the final grid. This is a reflection of the tendency of communities to become increasingly segregated until we rarely interact with those dissimilar to us, a result of the butterfly effect that individual biases can engender on a societal level. The Schelling Model mathematically characterizes vague qualms about our world in a way that is easy to parse, offering an elegant bottom-up approach to understanding the trials and tribulations of mankind.
Works Cited:
JASSS. (n.d.). The schelling model of ethnic residential dynamics. https://www.jasss.org/15/1/6.html
Mingarelli, L. (2022, January 5). Schelling’s model of Racial Segregation - towards Data science. Medium. https://towardsdatascience.com/schellings-model-of-racial-segre gation-4852fad06c13
Schelling’s model of segregation. (n.d.). http://nifty.stanford.edu/2014/mccown-schelling-model-segregation/
