(Non-)obvious manipulability of rank-minimizing mechanisms

In assignment problems, the rank distribution of assigned objects is often used to evaluate match quality. Rank-minimizing (RM) mechanisms directly optimize for average rank. While appealing, a drawback is RM mechanisms are not strategyproof. This paper investigates whether RM satisfies the weaker incentive notion of non-obvious manipulability (NOM, Troyan and Morrill, 2020). I show any RM mechanism with full support — placing positive probability on all rank-minimizing allocations — is NOM. In particular, uniform randomization satisfies this condition. Without full support, whether an RM mechanism is NOM or not depends on the details of the selection rule.