Lotteries in Student Assignment: An Equivalence Result

Abstract

This paper formally examines two competing methods of conducting a lottery in assigning 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 a single and multiple lottery mechanism 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.

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