["International Economic Review, EarlyView. ", "\nABSTRACT\nMany countries around the world use centralized admission systems to assign thousands of students to university programs every year. However, the impact of admission policy changes on students' welfare remains largely unknown. To address this, we propose a novel methodology that recovers students' true preferences in a mechanism where students hold private information and face constraints on the number of options they can submit as preferences. This methodology involves two steps: first, the nonparametric recovery of ordinal preferences using a revealed preference approach based on a concatenation algorithm; and, second, the recovery of cardinal preferences using either a Gibbs sampler estimator or a calibration method. Applying our methodology to administrative data from the University of Costa Rica, we evaluate counterfactual policies and suggest two alternate mechanisms based on an ascending auction and competitive equilibrium prices."]