When All Measures Fail the Same Way: Correcting Compositional Dependence in Segregation Indices

Boris Barron , Max Planck Institute for Demographic Research
Matthew Hall, Cornell University
Peter Rich, Cornell University
Itai Cohen, Cornell University
Tomas Arias, Cornell University

The comparability of segregation measures across time and space often relies on compositional invariance—the assumption that index values remain unchanged when only group proportions vary. Despite its central role in segregation research, this assumption has never been empirically verified. Using agent-based simulations and U.S. Census data, we show that all widely used evenness indices—including dissimilarity, Gini, Theil’s entropy, Hutchens’ R, and Fossett’s separation—exhibit a strong and nearly identical compositional dependence. We then introduce an information-theoretic correction based on information projection that isolates what segregation values would be if only composition changed, while holding neighborhood sorting dynamics constant, using only single-city data. This procedure provides the first empirically validated operationalization of compositional invariance, is computationally tractable, and aligns segregation indices with their intended interpretations. Applied to U.S. data, the correction reveals that the widely noted stability in White/Hispanic and White/Asian segregation since 1990 is an artifact of compositional dependence. More broadly, this work demonstrates how information-theoretic methods can formalize long-standing demographic assumptions in an empirically verifiable manner, offering a general template for methodological correction beyond segregation research.

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 Presented in Session 52. Flash Session Advances in Subnational and Small-Area Population Analysis