Persistent Homology for Resource Coverage: A Case Study of Access to Polling Sites

TL;DR

This paper applies persistent homology, a topological data analysis tool, to evaluate and compare the geographical coverage of polling sites in various cities, providing a novel quantitative approach to assess resource equity.

Contribution

It introduces the use of persistent homology for analyzing resource coverage and demonstrates its effectiveness through case studies of polling site distributions in multiple cities.

Findings

Persistent homology reveals holes in polling site coverage.

Coverage analysis shows differences across cities.

Method is feasible for assessing resource distribution.

Abstract

It is important to choose the geographical distributions of public resources in a fair and equitable manner. However, it is complicated to quantify the equity of such a distribution; important factors include distances to resource sites, availability of transportation, and ease of travel. We use persistent homology, which is a tool from topological data analysis, to study the effective availability and coverage of polling sites. The information from persistent homology allows us to infer holes in the distribution of polling sites. We analyze and compare the coverage of polling sites in Los Angeles County and five cities (Atlanta, Chicago, Jacksonville, New York City, and Salt Lake City), and we conclude that computation of persistent homology appears to be a reasonable approach to analyzing resource coverage.