Improving the Chilean college admissions system

In this paper we present the design and implementation of a new system to solve the Chilean college admissions problem. We develop an algorithm that obtains all applicant/program pairs that can be part of a stable allocation when preferences are not strict and when all students tied in the last seat of a program (if any) must be allocated. We use this algorithm to identify which mechanism was used in the past to perform the allocation, and we propose a new method to incorporate the affirmative action that is part of the system to correct the inefficiencies that arise from having double-assigned students. By unifying the regular admission with the affirmative action, we have improved the allocation of approximately 2.5% of students assigned every year since 2016. From a theoretical standpoint, we show that some desired properties, such as strategy-proofness and monotonicity, cannot be guaranteed under flexible quotas.