Incontestable Assignments

In school districts where assignments are exclusively determined by a clearinghouse students can only appeal their assignment with a valid reason. An assignment is incontestable if it is appeal-proof. We study incontestability when students do not observe the other students' preferences and assignments. Incontestability is shown to be equivalent to individual rationality, non-wastefulness, and respect for top-priority sets (a weakening of justified envy). Stable mechanisms and those Pareto dominating them are incontestable, as well as the Top-Trading Cycle mechanism (but Boston is not). Under a mild consistency property, incontestable mechanisms are i-indinstiguishable (Li, 2017), and share similar incentive properties.