Comparing school choice mechanisms by interim and ex-ante welfare
Recent work has highlighted welfare gains from the use of the Boston mechanism over deferred acceptance (DA) in school choice problems, in particular finding that when cardinal utility is taken into account, Boston interim Pareto dominates DA in certain incomplete information environments with no school priorities. We show that these previous interim results are not robust to the introduction of (weak) priorities. However, we partially restore the earlier results by showing that from an ex-ante utility perspective, the Boston mechanism Pareto dominates any strategyproof mechanism (including DA), even allowing for arbitrary priority structures. Thus, we suggest ex-ante Pareto dominance as a relevant criterion by which to compare school choice mechanisms. This criterion may be of particular interest to school districts, as they can be thought of as social planners whose goal is to maximize the overall ex-ante welfare of the students.
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