Many centralized matching schemes incorporate a mix of random lottery and non-lottery tie-breaking. A leading example is the New York City public school district, which uses criteria like test scores and interviews to generate applicant rankings for some schools, combined with lottery...

The design of the New York City (NYC) High School match involved tradeoffs among efficiency, stability and strategy-proofness that raise new theoretical questions. We analyze a model with indifferences--ties--in school preferences. Simulations with field data and the theory favor breaking...