Theoretical Economics, Volume 6, Number 1 (January 2011)

Theoretical Economics 6 (2011), 1–17


Lotteries in student assignment: An equivalence result

Parag A. Pathak, Jay Sethuraman

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.

Keywords: Matching, random assignment

JEL classification: C78, D63

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