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

Abstract We compare the three most common school choice mechanisms: the Deferred Acceptance mechanism (DA), the classic näıve Boston mechanism (NBM), and a variant of the Boston mechanism where students automatically skip exhausted schools, which we call the adaptive Boston mechanism (ABM). When priorities are random we show that the three mechanisms form two hierarchies, one in terms of incentives and the other in terms of student welfare. Regarding incentives: while DA is strategyproof, we show that ABM satisfies the intermediate partial strategyproof concept but NBM does not. Regarding student welfare the hierarchy is exactly inverted: we first show that, given truthful preference information, NBM rank dominates DA whenever they are comparable; and via limit arguments and simulations we show that ABM yields intermediate student welfare between NBM 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 NBM, intermediate under ABM, and lowest under DA. Our results show that a decision between these three common mechanisms involves an implicit trade-off between incentives and student welfare.