Strategic Analysis of Fair Rank-Minimizing Mechanisms with Agent Refusal Option

This paper investigates the strategic implications of the uniform rank-minimizing mechanism (URM), an assignment rule that selects uniformly from the set of deterministic assignments minimizing the sum of agents' reported ranks. We focus on settings in which agents may refuse their assignment and instead receive an outside option. Without the refusal option, we show that truth-telling is not strictly dominated under any fair rank-minimizing mechanism; that is, one satisfying equal treatment of equals. However, introducing the refusal option significantly changes strategic incentives: specific manipulations, called outside option demotion strategies, 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 fundamental trade-off in the design of fair rank-minimizing mechanisms when agents can refuse their assignments.