  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.
