Efficient Major Transition Exchange under Distributional and Dual Priority-respecting Constraints

Many real matching markets encounter distributional and fairness constraints. Motivated by the Chinese Major Transition Program (CMT), this paper studies the design of exchange mechanisms within a fresh framework of both distributional and dual priority-respecting constraints. Specifically, each student has an initial assigned major and applies to transfer to a more desirable one. A student can successfully transfer majors only if they obtain eligibility from both their initial major and the applied major. Each major has a dual priority: a strict priority over current students who wish to transfer out and a strict priority over students from other majors who wish to transfer in. Additionally, each major faces a ceiling constraint and a floor constraint to regulate student distribution. We show that the existing mechanisms of CMT result in avoidable inefficiencies, and propose two mechanisms that can match students to majors in an efficient way as well as respecting each major's distributional and dual priority. The efficient mechanisms are based on a proposed solution concept: eligibility maximization (EM), and two processes for identifying improvement cycles--specifically, transfer-in exchangeable cycles and transfer-out exchangeable cycles.