Arrovian Efficiency and Auditability in the Allocation of Discrete Resources

In environments where heterogeneous indivisible resources are being allocated without monetary transfers and each agent has a unit demand, we show that an allocation mechanism is individually strategy-proof and Arrovian efficient, i.e., it always selects the best outcome with respect to some Arrovian social welfare function if, and only if, the mechanism is group strategy-proof and Pareto efficient. Re-interpreting Arrow's Independence of Irrelevant Alternatives in terms of auditability of the mechanism, we further show that these are precisely the mechanisms that are strategy-proof, Pareto efficient, and auditable.