NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

Lotteries in Student Assignment: An Equivalence Result

Parag A. Pathak, Jay Sethuraman

NBER Working Paper No. 16140
Issued in June 2010
NBER Program(s):   ED

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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Document Object Identifier (DOI): 10.3386/w16140

Published: Pathak, Parag A. & Jay Sethuraman. "Lotteries in student assignment: An equivalence result." Theoretical Economics 6, 1 (2011): 1-17.

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