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Schelling's Segregation Model: Parameters, scaling, and aggregation


  • Abhinav Singh

    (Georgia Institute of Technology)

  • Dmitri Vainchtein

    (Georgia Institute of Technology)

  • Howard Weiss

    (Georgia Institute of Technology)


Thomas Schelling proposed a simple spatial model to illustrate how, even with relatively mild assumptions on each individual's nearest neighbor preferences, an integrated city would likely unravel to a segregated city, even if all individuals prefer integration. This agent based lattice model has become quite influential amongst social scientists, demographers, and economists. Aggregation relates to individuals coming together to form groups and Schelling equated global aggregation with segregation. Many authors assumed that the segregation which Schelling observed in simulations on very small cities persists for larger, realistic size cities. We describe how different measures could be used to quantify the segregation and unlock its dependence on city size, disparate neighbor comfortability threshold, and population density. We identify distinct scales of global aggregation, and show that the striking global aggregation Schelling observed is strictly a small city phenomenon. We also discover several scaling laws for the aggregation measures. Along the way we prove that as the Schelling model evolves, the total perimeter of the interface between the different agents decreases, which provides a useful analytical tool to study the evolution.

Suggested Citation

  • Abhinav Singh & Dmitri Vainchtein & Howard Weiss, 2009. "Schelling's Segregation Model: Parameters, scaling, and aggregation," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 21(12), pages 341-366, September.
  • Handle: RePEc:dem:demres:v:21:y:2009:i:12

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    References listed on IDEAS

    1. Zhang, Junfu, 2004. "Residential segregation in an all-integrationist world," Journal of Economic Behavior & Organization, Elsevier, vol. 54(4), pages 533-550, August.
    2. W. Clark, 1991. "Residential preferences and neighborhood racial segregation: A test of the schelling segregation model," Demography, Springer;Population Association of America (PAA), vol. 28(1), pages 1-19, February.
    3. Schelling, Thomas C, 1969. "Models of Segregation," American Economic Review, American Economic Association, vol. 59(2), pages 488-493, May.
    4. William Clark, 1992. "Residential preferences and residential choices in a multiethnic context," Demography, Springer;Population Association of America (PAA), vol. 29(3), pages 451-466, August.
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    Cited by:

    1. Vinicius M. Netto & MaĆ­ra Soares Pinheiro & Roberto Paschoalino, 2015. "Segregated Networks in the City," International Journal of Urban and Regional Research, Wiley Blackwell, vol. 39(6), pages 1084-1102, November.
    2. Collet, Jacques Henri & Fanchon, Jean, 2015. "Crystallization and tile separation in the multi-agent systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 405-417.

    More about this item


    clusters; segregation; simulation; statistics;

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • Z0 - Other Special Topics - - General


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