A Rank-Based Assignment Lottery for an Assignment Problem

For a traditional assignment problem with the same number of objects and agents, we introduce a new assignment lottery based on the notion of rank and analyze some of its properties. In particular, we prove that, like the Random Serial Dictatorship, it is ex post efficient and guarantees positive probability to each Pareto optimal deterministic assignment; moreover, the expected rank of this new assignment lottery, which is a measure of the social welfare, cannot be greater than the Random Serial Dictatorship’s one and there exist assignment problems where it is strictly lower.