The three most common school choice mechanisms are the Deferred Acceptancemechanism (DA), the classic Boston mechanism (BM), and a variant of the Bostonmechanism where students automatically skip exhausted schools, which we callthe adaptive Boston mechanism (ABM). Assuming truthful reporting, we comparestudent welfare under these mechanisms both from a conceptual and from aquantitative perspective: We first show that, BM rank dominates DA wheneverthey are comparable; and via limit arguments and simulations we show that ABMyields intermediate student welfare between BM and DA. Second, we performcomputational experiments with preference data from the high school match inMexico City. We find that student welfare (in terms of rank transitions) ishighest under BM, intermediate under ABM, and lowest under DA. BM, ABM, and DAcan thus be understood to form a hierarchy in terms of student welfare. Incontrast, in (Mennle and Seuken, 2017), we have found that the same mechanismsalso form a hierarchy in terms of incentives for truthtelling that points inthe opposite direction. A decision between them therefore involves an implicittrade-off between incentives and student welfare.
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