Improving Matching under Information Constraint: Chinese College Admission Reconsidered (joint with Yuanju Fang)
College admissions in China have a distinct feature: the assignment is determined by test scores, students' preferences, and colleges' preferences. To examine this situation, we extend a standard many-to-one matching model by assuming that colleges have two different ordinal rankings over students, i.e., a common score order and individual preferences. Since it takes time and cost for colleges to review each student's application material, colleges have an information constraint; they can only partially figure out their true preferences over students. To alleviate the information problem, the current admission system, called the Chinese parallel (CP) mechanism, implements a so-called ``dummy quota policy'', allowing each college to receive more applications than its actual quota and choose the preferred students among the applicants. While the CP mechanism is a variant of the serial dictatorship mechanism, we show that it has various drawbacks. Depending on whether the dummy quota policy is maintained or abandoned, we propose two different modified mechanisms that outperform the CP mechanism.