Abstract
In school choice contexts, we compare stable mechanisms under a dozen measures of coalitional manipulability degree. Although no stable mechanism is group strategy-proof for all school choice contexts, we show that the student-optimal stable mechanism is the least manipulable by coalitions, whereas the school-optimal stable mechanism is the most coalitionally manipulable. These results still hold when students can only report truncated preferences, when the set of coalitions is limited, or when schools cannot be declared unacceptable as long as there are more available seats than students. In contrast, if there is a shortage of seats and students have no outside options, the school-optimal stable mechanism can be less manipulable by coalitions than the student-optimal stable mechanism. Furthermore, the presence of externalities compromise the existence of a stable mechanism that minimizes coalitional/individual manipulability, even when students are primarily concerned with their assignments.