Allocation and exchange of discrete resources such as kidneys, school seats, and many other resources for which agents have single-unit demand is conducted via direct mechanisms without monetary transfers. Incentive compatibility and efficiency are primary concerns in designing such mechanisms....

Ordinal random mechanisms have been used in real-life situations for reasons such as sustaining fairness or preventing collusion. Two examples of such domains are voting and matching. We investigate whether desirable properties of a random mechanism survive decomposition as a lottery over...