Trade-offs in School Choice: Comparing Deferred Acceptance, the Näıve and the Adaptive Boston Mechanism

So far, research on school choice mechanisms has focused primarily on two procedures: the Deferred Acceptance (DA) mechanism and the (näıve) Boston mechanism (NBM). A variant of the Boston mechanism, where students automatically skip exhausted schools in the application process, has been largely overlooked by researchers, but is nonetheless frequently used in practice. We formalize this adaptive Boston mechanism (ABM), and we study the three mechanisms DA, NBM, and ABM in the presence of coarse priorities and random tie-breaking. When priorities are determined by a single, uniform lottery, we find that the three mechanisms form two hierarchies: one with respect to strategyproofness, and one with respect to efficiency : DA is known to be strategyproof while NBM is not even weakly strategyproof, and we show in this paper that ABM satisfies the intermediate requirement of partial strategyproofness. Regarding efficiency, we show that NBM rank dominates DA whenever a comparison is possible. Furthermore, using new limit arguments and simulations, we establish that ABM has intermediate efficiency between NBM and DA. Our results reveal the inherent trade-off between strategyproofness and efficiency that market designers face when choosing between these three school choice mechanisms. While all of our results hold when priorities are determined by a single uniform lottery, we prove that many continue to hold for general priority structures and other tie-breakers as well.