Lotteries in Student Assignment: An Equivalence Result

23 Pages Posted: 29 Jun 2010 Last revised: 8 Aug 2024

See all articles by Parag A. Pathak

Parag A. Pathak

Massachusetts Institute of Technology (MIT) - Department of Economics

Jay Sethuraman

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Date Written: June 2010

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.

Suggested Citation

Pathak, Parag A. and Sethuraman, Jay, Lotteries in Student Assignment: An Equivalence Result (June 2010). NBER Working Paper No. w16140, Available at SSRN: https://ssrn.com/abstract=1630145

Parag A. Pathak (Contact Author)

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

50 Memorial Drive
E52-391
Cambridge, MA 02142
United States

Jay Sethuraman

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

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