Asymptotic ordinal inefficiency of random serial dictatorship
证明，在物品类型很多时，随机序列独裁机制产生的分配在序数意义上有效的偏好剖面比例趋近于零；即使考虑偏好相似性，该概率也随物品类型增加而趋于零。
We establish that the fraction of preference profiles for which the random serial dictatorship allocation is ordinally efficient vanishes for allocation problems with many object types. We consider also a probabilistic setting where in expectation agents have moderately similar preferences reflecting varying popularity across objects. In this setting we show that the probability that the random serial dictatorship mechanism is ordinally efficient converges to zero as the number of object types becomes large. We provide results with similarly negative content for allocation problems with many objects of each type. One corollary is that ordinal efficiency is a strict refinement of ex-post efficiency at most preference profiles.