Schelling's Model: Small Preferences, Big Segregation

A grid, two types, one rule

In 1971 the economist Thomas Schelling — who would later share the 2005 Nobel Memorial Prize in Economic Sciences — published one of the simplest and most influential models in social science. Place two types of agents on a grid, mostly at random, with some empty cells left over. Give each agent one rule: look at your occupied neighbouring cells, and if fewer than a threshold fraction k share your type, you are unhappy and move to the nearest cell where you would be happy. Repeat until every agent is satisfied, or the system stops changing.

The surprising outcome

Schelling's striking discovery was that this process reliably produces large, sharply segregated clusters even when the threshold k is set well below 50% — an agent who would be perfectly content in a genuinely 30%-similar, 70%-mixed neighbourhood still ends up, after everyone relocates simultaneously, living somewhere far more homogeneous than they ever asked for. No single agent in the simulation wants segregation; every agent is only ever seeking a mild, moderate level of similarity around themselves. The strongly clustered result emerges purely from the collective interaction of many individually reasonable choices.

Why mild preferences compound

The mechanism is a feedback loop. When one unhappy agent moves away from a mixed block, the block becomes slightly more homogeneous in composition — which can then push a neighbour of the other type just below their own happiness threshold, prompting them to move too. Each individual departure nudges local composition further toward one type, triggering the next departure, and clusters snowball outward from small random fluctuations in the initial mixed arrangement. This is a textbook case of emergence: macro-level structure — large segregated regions — arising from micro-level rules that say nothing at all about the macro pattern.

for each unhappy agent (similar neighbours < k):
    move to nearest empty cell that satisfies k
repeat until no unhappy agents remain
    (or a maximum number of rounds is reached)

low k  (~10-20%)  → mostly stays mixed, little movement needed
mid k  (~30-50%)  → strong segregation emerges from mild preference
high k (~70%+)    → near-total, near-instant separation by type

A lesson about aggregation, not attitudes

Schelling's central point was methodological as much as sociological: you cannot reliably infer individual motives from an aggregate pattern. Observing a segregated neighbourhood does not tell you whether the residents hold strong exclusionary preferences or only the mildest of in-group comfort — both can produce the same visible outcome. That distinction matters enormously for policy, because a segregation problem caused by mild, near-universal micro-preferences calls for very different interventions than one caused by overt discrimination, even though the two can look identical from the outside.

What the model leaves out

Real-world housing segregation is shaped by far more than in-group preference alone — discriminatory lending and zoning history, income disparities, and outright discrimination all play documented roles that Schelling's minimal model does not attempt to capture. The model's value is not as a complete explanation of any real city, but as a precise demonstration that segregation does not require prejudice to be sufficient — it only requires a mild preference and a large enough population interacting freely over time.

Frequently asked questions

Try it live

Everything above runs in your browser — open Happiness & Similar Neighbours and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.