We know that a strategyproof mechanism does not exist that is ordinally efficient and fair in the sense of equal division lower bound. We show that this impossibility for random assignments prevails even if agents have uniform preferences where a weakly decreasing utility function determines...

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 ex-ante Pareto efficiency, which is a slightly weaker notion of efficiency than ex-post Pareto efficiency. We strengthen the impossibility between ex-post Pareto efficiency, strategyproofness, and envy-freeness in the random assignment problem and show that it prevails if ex-post...

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...

We introduce ex-ante Pareto efficiency, which is a slightly weaker notion of efficiency than ex-post Pareto efficiency. We strengthen the impossibility between ex-post Pareto efficiency, strategyproofness, and envy-freeness in the random assignment problem and show that it prevails if ex-post...