RSD attempts to insert fairness into this situation in the following way.
RSD always yields an ex-post Pareto efficient (PE) outcome.
As an example, suppose there are three agents, three items and the VNM utilities are: RSD gives a 1/3 chance of every object to each agent (because their preferences over sure objects coincide), and a profile of expected utility vector (0.6, 0.4, 0.4).
Moreover, when agents have ordinal rankings, RSD fails even the weaker property of sd-efficiency.
[1]: Sec.2 When the rankings of the agents over the objects are drawn uniformly at random, the probability that the allocation given by RSD is ex-ante PE approaches zero as the number of agents grows.
Each agent has large equivalence classes in his preference, since he is indifferent between all the allocations in which he gets the same item.
[5] When agents can have weak preferences, however, no procedure that extends RD (which includes RSD) satisfies both efficiency and strategyproofness.