What is Schelling's model of segregation?

Schelling's model of segregation is an agent-based model developed by the economist Thomas Schelling. It shows that people with only a mild preference for living near their own group can still end up in a highly segregated society, even when no outside pressure forces them apart. Sources date it variously to 1969, 1971, or both, reflecting Schelling's papers from those years. [1] [2] [3]

In the original version, agents from two groups sit on a grid, one per cell, and each has up to eight neighbors. Each agent wants at least a certain fraction of its neighbors to belong to its own group, with empty cells ignored. An agent below that threshold moves to a vacant spot where it would be satisfied. Rounds continue until everyone is satisfied, though the original description notes that not every agent is guaranteed to reach satisfaction. [1] [4]

Other versions change the setup. Some teaching versions place agents as points on a unit square and judge happiness by the ten nearest neighbors, using Euclidean distance. In one such version an agent is happy unless more than six of those ten neighbors are of the other type, so agents are content in neighborhoods that are 60 percent mixed. [3] [5]

The striking result is that mixed neighborhoods tend to be unstable and collapse over time, leaving strongly divided areas. One published example sets the satisfaction level at 60 percent, meaning agents accept 40 percent of neighbors being different. The final average same-color ratio then exceeds 90 percent, far above what anyone required. [3] [6]

The mechanism is a chain reaction. Because agents start in random positions, someone is bound to be unhappy by chance. When that person moves, the composition changes both where they left and where they arrive, which can make previously satisfied neighbors want to move. A small initial imbalance can therefore grow into large-scale segregation, and the effect is reinforced when agents differ in their preferences. [4]

One account places the model in its historical setting. Public attitudes and laws changed sharply during the 1960s, and many observers expected housing segregation to decline quickly, but the decline was almost imperceptible. The model offered an explanation: small differences in tolerance or starting positions could produce high segregation without legal constraints, even at decent overall levels of tolerance. [4]

The model leaves out outside forces such as Jim Crow laws, so it does not say these played no part in real segregation. It also does not show that residents of a segregated area are hostile to one another. One summary notes that a divided neighborhood may not mean particularly hostile residents, though it may. [1] [6]