Resolving Conflicting Preferences in School Choice
The Boston mechanism is among the most popular school choice procedures in use. Yet, the mechanism has been criticized for its poor incentive and welfare performances, which led the Boston Public Schools to recently replace it with Gale and Shapley's deferred acceptance algorithm (henceforth, DA). The DA elicits truthful revelation of "ordinal" preferences whereas the Boston mechanism does not; but the latter induces participants to reveal their "cardinal" preferences (i.e., their relative preference intensities) whereas the former does not. We show that cardinal preferences matter more when families have similar ordinal preferences and schools have coarse priorities, two common features of many school choice environments. Specifically, when students have the same ordinal preferences and schools have no priorities, the Boston mechanism Pareto dominates the DA in ex ante welfare. The Boston mechanism may not harm but rather benefit participants who may not strategize well. In the presence of school priorities, the Boston mechanism also tends to facilitate a greater access than the DA to good schools by those lacking priorities at those schools. These results contrast with the standard view, and cautions against a hasty rejection of the Boston mechanism in favor of mechanisms such as the DA.
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