Unambiguous Efficiency of Random Allocations

In the problem of allocating indivisible objects via lottery, a social planner often knows only agents' ordinal preferences over objects, but not their complete preferences over lotteries. Such an informationally constrained planner cannot distinguish between different utility profiles that induce the same rankings over the objects. In this context, we ask what it means to adjudge an allocation as efficient. We introduce the concept of unambiguous efficiency, which guarantees no further Pareto improvement regardless of how agents' ordinal preferences extend to lotteries. We compare this concept with the predominant formulation of efficiency in the random allocation literature and explore some structural properties. As an application to mechanism design, we characterize the class of efficient and strategy-proof ordinal mechanisms that satisfy certain regularity conditions.