Abstract
We show that there is no consistent Pareto improvement over any stable mechanism. To overcome this impossibility, we introduce the following weak consistency requirement: Whenever a set of students, each of whom is assigned to a school that is under-demanded at the student-optimal stable matching, are removed with their assigned seats, then the assignments of the remaining students should not change. We show that EADA (Kesten, 2010) is the unique mechanism that is weakly consistent and Pareto improves over the student-optimal stable mechanism.
Highlights
The tradeoff between efficiency and stability has been a central question in the context of assigning students to schools following the pioneering work of Abdulkadiroglu and Sönmez (2003)
We introduce the following weakly consistent Pareto improvement requirement: whenever a set of students, each of whom is assigned to a school that is underdemanded at the student-optimal stable matching, is removed with their assigned seats, the assignments of the remaining students do not change
We introduce weak consistency and characterize efficiency-adjusted deferred acceptance mechanism (EADAM) as the unique weakly consistent Pareto improvement over deferred acceptance algorithm (DA)
Summary
The tradeoff between efficiency and stability has been a central question in the context of assigning students to schools following the pioneering work of Abdulkadiroglu and Sönmez (2003). A mechanism is consistent whenever a set of students take their assigned seats under φ and leave; the mechanism φ keeps the matchings the same for the reduced market with the remaining students and schools with reduced capacities (Thomson 1990).
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