Quota Adjustment Process

Author: Taro Kumano, Morimitsu Kurino
Date: 2022/11/22
No: DP2022-016
JEL Classification codes: C78, D47, D78, I21
Language: English
[ Abstract ]
In designing priority-based matching problems, such as school choice, the quota of each school is, to some extent, a design variable for a market designer. We define an ex-post student-optimal stable matching (ESOSM) as a matching that is stable at some implementable quota distribution, and is not Pareto dominated by any stable matching among all implementable quota distributions. A simple question is whether the total resources subject to several constraints are optimally distributed in the above sense. As optimal quota distributions vary depending on students’ preferences realized, no predetermined quota distribution is optimal for all of the students’ preferences. This requires a new matching mechanism design for the variable quota distributions. We propose the novel mechanism called quota adjustment process (QAP), which endogenously finds an ESOSM and the corresponding optimal quota distribution for any preferences and any initial quota distribution. To put this into practice, we proposed the QAP in the process of admission reform at the University of Tsukuba in Japan. Our proposal was officially approved and implemented at the University of Tsukuba in 2021.