Complex systems series · № 1

The Schelling segregation model

Nobody here is a bigot. The city segregates anyway.

In 1971 the economist Thomas Schelling drew a grid on paper, scattered coins on it, and moved them by one rule: a coin is content as long as at least some fraction of its neighbors match it. Discontent coins move to an empty square. That's the whole model — no history, no institutions, no hate.

Below is his city. Two populations, a few empty homes, and one dial: how many same-colored neighbors a household wants before it feels at home. Start at 30% — every household is happy living as a two-to-one minority on its own block. Then press Run and watch what these mild people build.

They asked for 30. They got 75.

Run the default and the city converges on neighborhoods where the average household is surrounded by three-quarters its own color — two and a half times the similarity anyone asked for. No household in this city objects to being a minority. The macro-pattern looks like the work of committed segregationists, and the micro-preferences are almost embarrassingly tolerant.

The gap has a mechanism: when one mildly discontent household leaves, it tips the block's ratio for the neighbors it abandons, who then leave, and each move that relieves one block nudges another past someone's threshold. Integration isn't impossible in this city — it's just unstable. The mixed map is a pencil balanced on its tip.

Now try the dial in both directions. Wind it down to 20% and almost nothing happens — the mixed city is stable when demands are that mild, so the cliff lives somewhere between one-in-five and one-in-three. Wind it up and it gets grim fast: at 60% — "a bare majority like me" — the city ends 98% separated, and at 70% it grinds through thousands of moves into perfect separation. Then at 80%, something stranger: demands that strong can't all be satisfied at once, so the city never settles — households churn forever, chasing a composition their own movement keeps destroying.

What the model actually proves

Schelling's point was never that real segregation is innocent — American cities had redlining, racial covenants, and steering, which are exactly the committed segregationists this model omits. The point is narrower and sharper: you cannot read individual intent off an aggregate pattern. A segregated map is consistent with a city of bigots, and with a city of people who'd each happily be a minority. The macro-outcome underdetermines the micro-motive — so the pattern alone convicts no one, and acquits no one.

It also breaks the comfortable inverse: if segregation doesn't require bigots, then removing bigotry doesn't automatically remove segregation. An equilibrium this stable doesn't unwind because attitudes soften; every individual is already content, so no individual move undoes it. That is the general signature of a complex system — the arrow from micro to macro only points one way, and good intentions at the bottom don't sum to the outcome you wanted at the top.