Vol. 8, No. 5, 2015

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Coalitions and cliques in the school choice problem

Sinan Aksoy, Adam Azzam, Chaya Coppersmith, Julie Glass, Gizem Karaali, Xueying Zhao and Xinjing Zhu

Vol. 8 (2015), No. 5, 801–823

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.

mechanism design, assignment, matching, school choice
Mathematical Subject Classification 2010
Primary: 91B68, 90B80, 91B14
Received: 9 April 2014
Revised: 22 September 2014
Accepted: 15 October 2014
Published: 28 September 2015

Communicated by Kenneth S. Berenhaut
Sinan Aksoy
Department of Mathematics
University of California, San Diego
9500 Gilman Drive # 0112
La Jolla, CA 92093
United States
Adam Azzam
University of California, Los Angeles
Los Angeles, CA 95155
United States
Chaya Coppersmith
Bryn Mawr College
Bryn Mawr, PA 19010
United States
Julie Glass
Department of Mathematics and Computer Science
California State University, East Bay
RO 232
Hayward, CA 94542
United States
Gizem Karaali
Department of Mathematics
Pomona College
610 North College Avenue
Claremont, CA 91711
United States
Xueying Zhao
Northwestern University
Evanston, IL 60201
United States
Xinjing Zhu
Mount Holyoke College
South Hadley, MA 01075
United States