Comparing School Choice Mechanisms by Interim and Ex-Ante Welfare

The Boston mechanism and deferred acceptance (DA) are two competing mechanisms widely used in school choice problems across the United States. Recent work has highlighted welfare gains from the use of the Boston mechanism, 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 nontrivial (weak) priorities. However, we partially restore the earlier results by showing that from an ex-ante utility perspective, the Boston mechanism once again Pareto dominates any strategyproof mechanism (including DA), even allowing for arbitrary priority structures. Thus, we suggest ex-ante Pareto dominance as a criterion by which to compare school choice mechanisms. This criterion may be of interest to school district leaders, as they can be thought of as social planners whose goal is to maximize the overall ex-ante welfare of the students. From a policy perspective, school districts may have justification for the use the Boston mechanism over a strategyproof alternative, even with nontrivial priority structures.school choice, Boston mechanism, deferred acceptance, market design, weak priorities

Fictitious students creation incentives in school choice problems

We address the question of whether schools can manipulate the student-optimal stable mechanism by creating fictitious students in school choice problems. To this end, we introduce two different manipulation concepts, where one of them is stronger. We first demonstrate that the student-optimal stable mechanism is not even weakly fictitious student-proof under general priority structures. Then, we investigate the same question under acyclic priority structures. We prove that, while the student-optimal stable mechanism is not strongly fictitious student-proof even under the acyclicity condition, weak fictitious student-proofness is achieved under acyclicity. This paper, hence, shows a way to avoid the welfare detrimental fictitious students creation (in the weak sense) in terms of priority structures

Alternative characterizations of Boston mechanism

Kojima and Ünver (2011) are the first to characterize the class of mechanisms coinciding with the Boston mechanism for some priority order. By mildly strengthening their central axiom, we are able to pin down the Boston mechanism outcome for every priority order. Our main result shows that a mechanism is outcome equivalent to the Boston mechanism at every priority if and only if it respects both preference rankings and priorities and satisfies individual rationality for schools. In environments where each student is acceptable to every school, respecting both preference rankings and priorities is enough to characterize the Boston mechanism

Constrained School Choice

Recently, several school districts in the US have adopted or consider adopting the Student-Optimal Stable mechanism or the Top Trading Cycles mechanism to assign children to public schools. There is evidence that for school districts that employ (variants of) the so-called Boston mechanism the transition would lead to efficiency gains. The first two mechanisms are strategy-proof, but in practice student assignment procedures typically impede a student to submit a preference list that contains all his acceptable schools. We study the preference revelation game where students can only declare up to a fixed number of schools to be acceptable. We focus on the stability and efficiency of the Nash equilibrium outcomes. Our main results identify rather stringent necessary and sufficient conditions on the priorities to guarantee stability or efficiency of either of the two mechanisms. This stands in sharp contrast with the Boston mechanism which has been abandoned in many US school districts but nevertheless yields stable Nash equilibrium outcomes.school choice, matching, stability, Gale-Shapley deferred acceptance algorithm, top trading cycles, Boston mechanism, acyclic priority structure, truncation

Filling position incentives in matching markets

One of the main problems in the hospital-doctor matching is the maldistribution of doctor assignments across hospitals. Namely, many hospitals in rural areas are matched with far fewer doctors than what they need. The so called "Rural Hospital Theorem" (Roth (1984)) reveals that it is unavoidable under stable assignments. On the other hand, the counterpart of the problem in the school choice context|low enrollments at schools| has important consequences for schools as well. In the current study, we approach the problem from a different point of view and investigate whether hospitals can increase their filled positions by misreporting their preferences under well-known Boston, Top Trading Cycles, and stable rules. It turns out that while it is impossible under Boston and stable mechanisms, Top Trading Cycles rule is manipulable in that sense

Constrained school choice

Recently, several school districts in the US have adopted or consider adopting the Student-Optimal Stable Mechanism or the Top Trading Cycles Mechanism to assign children to public schools. There is clear evidence that for school districts that employ (variants of) the so-called Boston Mechanism the transition would lead to efficiency gains. The first two mechanisms are strategy-proof, but in practice student assignment procedures impede students to submit a preference list that contains all their acceptable schools. Therefore, any desirable property of the mechanisms is likely toget distorted. We study the non trivial preference revelation game where students can only declare up to a fixed number (quota) of schools to be acceptable. We focus on the stability of the Nash equilibrium outcomes. Our main results identify rather stringent necessary and sufficient conditions on the priorities to guaranteestability. This stands in sharp contrast with the Boston Mechanism which yields stable Nash equilibrium outcomes, independently of the quota. Hence, the transition to any of the two mechanisms is likely to come with a higher risk that students seek legal actionas lower priority students may occupy more preferred schools

Coalitions and Cliques in the School Choice Problem

The school choice mechanism design problem focuses on assignment mechanisms matching students to public schools in a given school district. The well-known Gale Shapley Student Optimal Stable Matching Mechanism (SOSM) is the most efficient stable mechanism proposed so far as a solution to this problem. However its inefficiency is well-documented, and recently the Efficiency Adjusted Deferred Acceptance Mechanism (EADAM) was proposed as a remedy for this weakness. In this note we describe two related adjustments to SOSM with the intention to address the same inefficiency issue. In one we create possibly artificial coalitions among students where some students modify their preference profiles in order to improve the outcome for some other students. Our second approach involves trading cliques among students where those involved improve their assignments by waiving some of their priorities. The coalition method yields the EADAM outcome among other Pareto dominations of the SOSM outcome, while the clique method yields all possible Pareto optimal Pareto dominations of SOSM. The clique method furthermore incorporates a natural solution to the problem of breaking possible ties within preference and priority profiles. We discuss the practical implications and limitations of our approach in the final section of the article

Strategic schools under the Boston mechanism revisited

We show that Ergin & Sönmez's (2006) results which show that for schools it is a dominant strategy to truthfully rank the students under the Boston mechanism, and that the Nash equilibrium outcomes in undominated strategies of the induced game are stable, rely crucially on two assumptions. First, (a) that schools need to be restricted to find all students acceptable, and (b) that students cannot observe the priorities set by the schools before submitting their preferences. We show that relaxing either assumption eliminates the strategy dominance, and that Nash equilibrium outcomes in undominated strategies for the simultaneous induced game in case (a) and subgame perfect Nash equilibria in case (b) may contain unstable matchings. We also show that when able to manipulate capacities, schools may only have an incentive to do so if students submit their preferences after observing the reported capacities