The equivalence between random priority and probabilistic serial rule on restricted preference domains

Abstract

We study the outcome equivalence between the random priority (RP) rule and the probabilistic serial (PS) rule on restricted preference domains. For random assignment problems defined on restricted tier domains, the following three statements are equivalent: $\left(i\right)$ The RP rule is outcome equivalent to the PS rule; $\left(ii\right)$ On each tier consisting of two objects all agents except one have the same preferences over objects in such tier; $\left(iii\right)$ The RP rule is ordinally efficient. For problems defined on the universal domain, we provide a sufficient condition for the outcome equivalence of the RP rule and the PS rule.