Fair and Efficient Lotteries over Indivisible Goods

We study the problem of assigning indivisible goods to individuals where each is to receive one object. To guarantee fairness in the absence of monetary compensation, we consider random assignments and analyse various equity criteria for such lotteries. In particular, we find that sd-no-envy (as championed by the Probabilistic Serial) is incompatible with the sd-core from equal division. As an alternative, we present a Walrasian mechanism, whose outcomes are sd-efficient, group sd-envy-free, lie in the sd-core from equal division and satisfy the sd-equal-division-lower-bound.