Coalitions and cliques in the school choice problem

Abstract

The school choice problem (SCP) looks at assignment mechanisms matching students in a public school district to seats in district schools. The Gale–Shapley deferred acceptance mechanism applied to the SCP, known as the student optimal stable matching (SOSM), is the most efficient among stable mechanisms yielding a solution to the SCP. A more recent mechanism, the efficiency adjusted deferred acceptance mechanism (EADAM), aims to address the well-documented tension between efficiency and stability illustrated by SOSM. We introduce two alternative efficiency adjustments to SOSM, both of which necessarily sacrifice stability. Our discussion focuses on the mathematical novelty of new efficiency modifications rather than any practical superiority of implementation or outcome. That is, our contribution lies in process rather than outcome. Yet we argue that the demonstration of multiple processes yielding common outcomes is, in itself, a measure of the quality of that outcome. More specifically the consistency of outcome from different processes strengthens the argument that Pareto dominations of SOSM can be supported as “fair” despite the resulting priority violations.