Working Paper: NBER ID: w16140
Authors: 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: student assignment; lottery mechanisms; equivalence results
JEL Codes: D45; D61
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Single lottery mechanism (H27) | Distribution of student assignments (D30) |
| Multiple lottery mechanism (H27) | Distribution of student assignments (D30) |
| Single lottery mechanism (H27) | Multiple lottery mechanism (H27) |
| Partitioned random priority (PRP) mechanism (D72) | Distribution of student assignments (D30) |
| Partitioned random endowment (PRE) mechanism (D51) | Distribution of student assignments (D30) |
| PRP mechanism (E65) | PRE mechanism (Y20) |
| Distribution of student assignments (D30) | Fairness of assignment process (C78) |