Measuring Diversity and Segregation with Convex Functions
Abstract
The problem of segregation measurement is to quantitatively describe the interaction of a population's attributes (such as race, ethnicity, education level, or income) with a separating distinction (such as organizational rank, school district, or spatial location). This primarily expository article gives an opinionated tour of one mathematical approach to measuring segregation. We begin with some basic intuitions about diversity and unify these through the framework of convex functions on the probability simplex. Formalizing segregation as a local-to-global comparison of diversity measures, resulting in the general class of Jensen informations as segregation measurements. We describe and computationally illustrate three ways to incorporate spatial structure into segregation measurements: spatial smoothing, aggregation, and local Jensen information. We close with several suggestions for future work.
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BibTeX
@misc{chodrow2026measuring,
title = {{Measuring Diversity and Segregation with Convex Functions}},
author = {Philip S. Chodrow},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02446},
eprint = {2610.02446},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02446},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Measuring Diversity and Segregation with Convex Functions
AU - Philip S. Chodrow
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.02446
UR - https://arxiv.org/abs/2610.02446
AB - The problem of segregation measurement is to quantitatively describe the interaction of a population's attributes (such as race, ethnicity, education level, or income) with a separating distinction (such as organizational rank, school district, or spatial location). This primarily expository article gives an opinionated tour of one mathematical approach to measuring segregation. We begin with some basic intuitions about diversity and unify these through the framework of convex functions on the probability simplex. Formalizing segregation as a local-to-global comparison of diversity measures, resulting in the general class of Jensen informations as segregation measurements. We describe and computationally illustrate three ways to incorporate spatial structure into segregation measurements: spatial smoothing, aggregation, and local Jensen information. We close with several suggestions for future work.
ER -