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α: calibrated so average coauthorship-adjusted count equals average raw count
Hafalir et al. (2022) introduce a model of interdistrict school choice. We show that any district's admission rule satisfying their assumptions is uniquely rationalized by a collection of schools' choice functions satisfying substitutability and acceptance. We then establish that all students weakly prefer the outcome of the cumulative offer process (COP) under the school-based admissions to the outcome under the district-based admissions. This has the implication that if students prefer the interdistrict outcome for the district-based admissions to the intradistrict outcome, then all students are weakly better off under the school-based admissions compared to either of these outcomes. Therefore, for student-optimal interdistrict school choice the introduction of district admission rules hurts students and it suffices to endow schools with usual choice priorities (if students' welfare is more important than districts' policy goals) and to (de)centralize district admissions by letting schools choose.