Strategic analysis of fair rank-minimizing mechanisms with agent refusal option

This paper investigates the strategic implications of the uniform rank-minimizing mechanism (URM), which selects uniformly from the set of deterministic assignments minimizing the total reported rank. We focus on settings in which agents may refuse their assigned object and instead receive an outside option. Without the refusal option, we show that truth-telling is not strategically dominated under any rank-minimizing mechanism satisfying equal treatment of equals and independence of irrelevant rankings. However, introducing the refusal option significantly changes strategic incentives: specific manipulations, called outside option demotion strategies, strategically dominate truth-telling under the URM. Moreover, such manipulations can lead to inefficient outcomes, as desirable objects may be refused by misreporting agents and consequently remain unassigned. To address this issue, we propose a modification of the URM that restores undominated truth-telling, although it introduces incentives to underreport acceptable objects. Our results highlight a trade-off in the design of fair rank-minimizing mechanisms when agents can refuse their assigned objects.