Verifiable affirmative action in school admissions

When implementing affirmative action through reserve systems, to maintain social trust and demonstrate the absence of corruption, countries such as Brazil, China, and India aim for verifiable allocations of reserve quotas, allowing students to confirm their assignments using private information and publicly disclosed data such as school admission cutoffs. Motivated by this, we study verifiable mechanisms in the controlled school choice model. We first show that sequential mechanisms, which allocate reserved and open seats in separate stages, offer intuitive verifiability but suffer from strategic complexity and inefficiency. We then formalize verifiability for simultaneous mechanisms, which allocate all seats in a single stage. We prove that a mechanism is individually rational, strategy-proof, and verifiable if and only if it is a deferred acceptance mechanism using one of two choice rules we characterize. We recommend a specific rule and mechanism and discuss their practical relevance to China's high school admissions.