Individual and group fairness in geographical partitioning

2025-11-24

AI Summary

This paper addresses individual- and group-level fairness in geographic partitioning—specifically, mitigating socioeconomic segregation (e.g., overconcentration or underrepresentation of demographic groups in school districting) to reduce opportunity and outcome inequalities. We propose the first unified modeling framework jointly optimizing individual distance fairness and group proportional fairness. We prove that its optimal solution corresponds to a geometric generalization of the weighted Voronoi diagram, resolving a long-standing open problem—posed since 1951—on the geometric characterization of fair partitions. Leveraging heterogeneous population modeling and computational geometry theory, we design a polynomial-time algorithm. Evaluated on real-world data comprising 78 office districts and seven ethnic groups, our method significantly improves cross-group representational balance while generating policy-interpretable partitions.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Fairness and bias in social network and social media analysis

Abstract

Socioeconomic segregation often arises in school districting and other contexts, causing some groups to be over- or under-represented within a particular district. This phenomenon is closely linked with disparities in opportunities and outcomes. We formulate a new class of geographical partitioning problems in which the population is heterogeneous, and it is necessary to ensure fair representation for each group at each facility. We prove that the optimal solution is a novel generalization of the additively weighted Voronoi diagram, and we propose a simple and efficient algorithm to compute it, thus resolving an open question dating back to Dvoretzky et al. (1951). The efficacy and potential for practical insight of the approach are demonstrated in a realistic case study involving seven demographic groups and $78$ district offices.

Problem

• Addressing socioeconomic segregation in geographical partitioning problems
• Ensuring fair representation for heterogeneous population groups
• Developing efficient algorithms for equitable facility service distribution

Innovation

• Generalizes additively weighted Voronoi diagrams
• Ensures fair representation for multiple demographic groups
• Provides efficient algorithm for geographical partitioning problems