Asymptotic Equivalence of Probabilistic Serial and Random Priority Mechanisms

The random priority (random serial dictatorship) mechanism is a common method for assigning objects to individuals. The mechanism is easy to implement and strategy-proof. However this mechanism is inefficient, as the agents may be made all better off by another mechanism that increases their chances of obtaining more preferred objects. Such an inefficiency is eliminated by the recent mechanism called probabilistic serial, but this mechanism is not strategy-proof. Thus, which mechanism to employ in practical applications has been an open question. This paper shows that these mechanisms become equivalent when the market becomes large. More specifically, given a set of object types, the random assignments in these mechanisms converge to each other as the number of copies of each object type approaches infinity. Thus, the inefficiency of the random priority mechanism becomes small in large markets. Our result gives some rationale for the common use of the random priority mechanism in practical problems such as student placement in public schools.