Lotteries in Student Assignment: An Equivalence Result
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.
Pathak's research was supported by the National Science Foundation under grant SES-0924555 and Sethuraman's research was supported by the National Science Foundation under grant CMMI-0916453. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.
Pathak, Parag A. & Jay Sethuraman. "Lotteries in student assignment: An equivalence result." Theoretical Economics 6, 1 (2011): 1-17. citation courtesy of