  The three most common school choice mechanisms are the Deferred Acceptance
mechanism (DA), the classic Boston mechanism (BM), and a variant of the Boston
mechanism where students automatically skip exhausted schools, which we call
the adaptive Boston mechanism (ABM). Assuming truthful reporting, we compare
student welfare under these mechanisms both from a conceptual and from a
quantitative perspective: We first show that, BM rank dominates DA whenever
they are comparable; and via limit arguments and simulations we show that ABM
yields intermediate student welfare between BM and DA. Second, we perform
computational experiments with preference data from the high school match in
Mexico City. We find that student welfare (in terms of rank transitions) is
highest under BM, intermediate under ABM, and lowest under DA. BM, ABM, and DA
can thus be understood to form a hierarchy in terms of student welfare. In
contrast, in (Mennle and Seuken, 2017), we have found that the same mechanisms
also form a hierarchy in terms of incentives for truthtelling that points in
the opposite direction. A decision between them therefore involves an implicit
trade-off between incentives and student welfare.
