Agent-wise–replication invariance for random allocations

We study the problem of allocating objects via lotteries when agents report their strict preferences over the objects. In combination with standard axioms of efficiency, fairness, and incentive, we explore implications of agent-wise–replication invariance (Thomson, 2024), an axiom pertaining to variable populations through replication. We first show that the equal-division lower-bound and consistency jointly imply agent-wise–replication invariance. We also provide a characterization of the serial rule (Bogomolnaia and Moulin, 2001). It is the only rule satisfying efficiency, the equal-division lower-bound, bounded invariance, and agent-wise–replication invariance.