Mathematical measures reveal how groups interact and separate
Measuring Diversity and Segregation with Convex Functions
Social and Information Networks
Summary
Measuring segregation means figuring out how different groups of people mix or stay apart based on things like race or income. The authors explain a mathematical way to do this using convex functions, which help measure diversity more clearly. They describe how to compare local and global diversity to understand segregation, calling these comparisons Jensen informations. They also show how to include location or space when measuring segregation and suggest ways to explore this research further.
What this means in practice
- •For urban planners: Use refined mathematical measures to better analyze how neighborhoods separate or mix different population groups spatially.
- •For social policy analysts: Evaluate local and global diversity in organizations or regions to inform policies addressing segregation more precisely.
A survey. It maps existing work.
Authors
Philip S. Chodrow
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.