We introduce (strict) favoring upper ranks, which is an extension of favoring higher ranks for random assignments. We demonstrate that ex-post favoring ranks implies (strict) favoring upper ranks, and envy-freeness implies favoring upper ranks. Moreover, for at least four agents, no mechanism...

We introduce a new notion of ex-post efficiency for random assignment problems, namely ex-post rank efficiency that gives a maximal number of agents their favored objects. An ex-post rank efficient random assignment is a lottery over rank efficient deterministic assignments, in the sense of...