Lotteries in Student Assignment: An Equivalence Result

Abstract

This paper formally examines two competing methods of conducting a lottery to assign students to schools, motivated by the design of the centralized high school student assignment system in New York City. The main result of the paper is that single and multiple lottery mechanisms are equivalent for the problem of allocating students to schools in which students have strict preferences and the schools are indifferent. In proving this result, a new approach is introduced that simplifies and unifies all the known equivalence results in the house allocation literature. Along the way, two new mechanisms—Partitioned Random Priority and Partitioned Random Endowment—are introduced for the house allocation problem. These mechanisms generalize widely studied mechanisms for the house allocation problem and may be appropriate for the many-to-one setting such as the school choice problem.