Coalitions and Cliques in the School Choice Problem

TL;DR

This paper introduces two new adjustments to the Gale Shapley SOSM mechanism for school choice, using coalitions and cliques among students to improve efficiency and Pareto optimality, addressing known limitations.

Contribution

It proposes coalition and clique-based modifications to SOSM that enhance efficiency and Pareto optimality, extending the EADAM mechanism and providing tie-breaking solutions.

Findings

Coalition method achieves EADAM outcome and Pareto improvements.

Clique method yields all Pareto optimal outcomes of SOSM.

Clique approach offers a natural tie-breaking mechanism.

Abstract

The school choice mechanism design problem focuses on assignment mechanisms matching students to public schools in a given school district. The well-known Gale Shapley Student Optimal Stable Matching Mechanism (SOSM) is the most efficient stable mechanism proposed so far as a solution to this problem. However its inefficiency is well-documented, and recently the Efficiency Adjusted Deferred Acceptance Mechanism (EADAM) was proposed as a remedy for this weakness. In this note we describe two related adjustments to SOSM with the intention to address the same inefficiency issue. In one we create possibly artificial coalitions among students where some students modify their preference profiles in order to improve the outcome for some other students. Our second approach involves trading cliques among students where those involved improve their assignments by waiving some of their priorities. The coalition method yields the EADAM outcome among other Pareto dominations of the SOSM outcome, while the clique method yields all possible Pareto optimal Pareto dominations of SOSM. The clique method furthermore incorporates a natural solution to the problem of breaking possible ties within preference and priority profiles. We discuss the practical implications and limitations of our approach in the final section of the article.