On two kinds of manipulation for school choice problems

Many school districts in the US. employ centralized clearing houses to assign students to public schools. An important potential threat against any school choice mechanism is the tendency of schools to circumvent the procedure via two kinds of strategic manipulation: manipulation via capacities and manipulation via pre-arranged matches. This paper studies the extent of the vulnerability of three prominent school choice mechanisms that have been adopted (or, considered for adoption) by some school districts in the US. We find that the highly debated Boston mechanism as well as the top trading cycles mechanism are immune to manipulation via capacities, unlike the student-optimal stable mechanism (SOSM). We show that SOSM is immune to manipulation via capacities if and only if the priority structure satisfies an acyclicity condition proposed by Ergin (Econometrica 70:2489—2497, 2002). On the other hand, we show that essentially no mechanism is immune to manipulation via pre-arranged matches.