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

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

Constrained School Choice: An Experimental Study

The literature on school choice assumes that families can submit a preference list over all the schools they want to be assigned to. However, in many real-life instances families are only allowed to submit a list containing a limited number of schools. Subjects' incentives are drastically affected, as more individuals manipulate their preferences. Including a safety school in the constrained list explains most manipulations. Competitiveness across schools play an important role. Constraining choices increases segregation and affects the stability and efficiency of the final allocation. Remarkably, the constraint reduces significantly the proportion of subjects playing a dominated strategy.school choice, matching, experiment

Constrained School Choice: An Experimental Study

The literature on school choice assumes that families can submit a preference list over all the schools they want to be assigned to. However, in many real-life instances families are only allowed to submit a list containing a limited number of schools. Subjects' incentives are drastically affected, as more individuals manipulate their preferentes. Including a safety school in the constrained list explains most manipulations. Competitiveness across schools plays an important role. Constraining choices increases segregation and affects the stability and efficiency of the final allocation. Remarkably, the constraint reduces significantly the proportion of subjects playing a dominated strategy.School Choice, Matching, Experiment, Gale-Shapley, Top Trading Cycles, Boston Mechanism, Efficiency, Stability, Truncation, Truthtelling, Safety School

Constrained school choice : an experimental study

The literature on school choice assumes that families can submit a preference list over all the schools they want to be assigned to. However, in many real-life instances families are only allowed to submit a list containing a limited number of schools. Subjects' incentives are drastically affected, as more individuals manipulate their preferences. Including a safety school in the constrained list explains most manipulations. Competitiveness across schools play an important role. Constraining choices increases segregation and affects the stability and efficiency of the final allocation. Remarkably, the constraint reduces significantly the proportion of subjects playing a dominated strategy

School Choice with Control

Controlled choice over public schools is a common policy of school boards in the United States. It attempts giving choice to parents while maintaining racial and ethnic balance at schools. This paper provides a foundation for controlled school choice programs. We develop a natural notion of fairness and show that assignments, which are fair for same type students and constrained non-wasteful, always exist in controlled choice problems; a "controlled" version of the student proposing deferred acceptance algorithm (CDAA) always finds such an assignment which is also weakly Pareto-optimal. CDAA provides a practical solution for controlled school choice programs

Welfare theorems for random assignments with priorities

Motivated by the application of designing fair and efficient school choice lotteries, we consider constrained efficiency notions for random assignments under priorities. We provide a constrained (priority respecting) version of the ordinal efficiency welfare theorem for random assignments. Moreover, we show that a constrained version of a cardinal second welfare theorem fails to hold

School Choice with Transferable Students Characteristics

We consider a school choice problem where schools' priorities depend on transferable students' characteristics. A school choice algorithm selects for each profile of students' preferences over schools an assignment of students to schools and a final allocation of characteristics (an extended matching). We define the Student Exchange with Transferable Characteristics (SETC) class of algorithms. Each SETC always selects a constrained efficient extended matching. That is an extended matching that i) is stable according to the priorities generated by the final allocation of characteristics and ii) is not Pareto dominated by another stable extended matching. Every constrained efficient extended matching that Pareto improves upon a stable extended matching can be obtained via an algorithm in the SETC class. When students' characteristics are fully transferable, a specific algorithm in the SETC family is equivalent to the application of the Top Trade Cycle Algorithm starting from the Student Optimal Stable Matching