Achieving Balanced Representation in School Choice with Diversity Goals

TL;DR

This paper introduces a new approach to student placement under diversity constraints that ensures fair and balanced representation across types, using flow networks for improved efficiency over traditional bipartite graph methods.

Contribution

It proposes a novel property called balanced representation and a choice function satisfying key fairness and diversity criteria, utilizing flow networks for better computational performance.

Findings

The new choice function guarantees maximal diversity and fairness.

Flow network methods outperform bipartite graph algorithms in efficiency.

Balanced representation improves fairness in student placements.

Abstract

Student placements under diversity constraints are a common practice globally. This paper addresses the selection of students by a single school under a \emph{one-to-one convention}, where students can belong to multiple types but are counted only once based on one type. While existing algorithms in economics and computer science aim to help schools meet diversity goals and priorities, we demonstrate that these methods can result in significant imbalances among students with different type combinations. To address this issue, we introduce a new property called \emph{balanced representation}, which ensures fair representation across all types and type combinations. We propose a straightforward choice function that uniquely satisfies four fundamental properties: maximal diversity, non-wastefulness, justified envy-freeness, and balanced representation. While previous research has primarily focused on algorithms based on bipartite graphs, we take a different approach by utilizing flow networks. This method provides a more compact formalization of the problem and significantly improves computational efficiency. Additionally, we present efficient algorithms for implementing our choice function within both the bipartite graph and flow network frameworks.