We consider the egalitarian welfare aspects of random assignment mechanisms when agents have unrestricted cardinal utilities over the objects. We give bounds on how well different random assignment mechanisms approximate the optimal egalitarian value and investigate the effect that different well-known properties like ordinality, envy-freeness, and truthfulness have on the achievable egalitarian value. Finally, we conduct detailed experiments analyzing the tradeoffs between efficiency with envy-freeness or truthfulness using two prominent random assignment mechanisms --- random serial dictatorship and the probabilistic serial mechanism --- for different classes of utility functions and distributions.
In a variety of contexts, individuals must be allocated to positions with limited capacities. Legislators must be assigned to committees, college students to dormitories, and urban homesteaders to dwellings. (A general class of fair division problems would have the positions represent goods.) This paper examines the general problem of achieving efficient allocations when individuals' preferences are unknown and where (as with a growing number of nonmarket allocation schemes) there is no facilitating external medium of exchange such as money. An implicit market procedure is developed that elicits honest preferences, that assigns individuals efficiently, and that is adaptable to a variety of distributional objectives.