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Lotteries in Student Assignment: An Equivalence Result

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  • 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.

Suggested Citation

  • Parag A. Pathak & Jay Sethuraman, 2010. "Lotteries in Student Assignment: An Equivalence Result," NBER Working Papers 16140, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:16140
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    1. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth, 2005. "The New York City High School Match," American Economic Review, American Economic Association, vol. 95(2), pages 364-367, May.
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    JEL classification:

    • D45 - Microeconomics - - Market Structure, Pricing, and Design - - - Rationing; Licensing
    • D6 - Microeconomics - - Welfare Economics

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