Strategyproofness Versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match

Posted: 30 Jan 2007

See all articles by Atila Abdulkadiroglu

Atila Abdulkadiroglu

Duke University - Department of Economics

Parag A. Pathak

Massachusetts Institute of Technology (MIT) - Department of Economics

Alvin E. Roth

HBS Negotiations, Organizations and Markets Unit; National Bureau of Economic Research (NBER)

Abstract

The design of the New York City (NYC) High School match involved tradeoffs between incentives and efficiency, because some schools are strategic players that rank students in order of preference, while others order students based on large priority classes. Therefore it is desirable for a mechanism to produce stable matchings (to avoid giving the strategic players incentives to circumvent the match), but is also necessary to use tie-breaking for schools whose capacity is sufficient to accommodate some but not all students of a given priority class. We analyze a model that encompasses one-sided and two-sided matching models. We first observe that breaking indifferences the same way at every school is sufficient to produce the set of student optimal stable matchings. Our main theoretical result is that a student-proposing deferred acceptance mechanism that breaks indifferences the same way at every school is not dominated by any other mechanism that is strategyproof for students. Finally, using data from the recent redesign of the NYC High School match, which places approximately 90,000 students per year, we document that the extent of potential efficiency loss is substantial. Over 6,800 student applicants in the main round of assignment could have improved their assignment in a (non strategy-proof) student optimal mechanism, if the same student preferences would have been revealed.

Suggested Citation

Abdulkadiroglu, Atila and Pathak, Parag A. and Roth, Alvin E., Strategyproofness Versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match. Harvard PON Working Paper No. 959938. Available at SSRN: https://ssrn.com/abstract=959938

Atila Abdulkadiroglu

Duke University - Department of Economics ( email )

213 Social Sciences Building
Box 90097
Durham, NC 27708-0204
United States

Parag A. Pathak

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

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

Alvin E. Roth (Contact Author)

HBS Negotiations, Organizations and Markets Unit ( email )

Soldiers Field
Boston, MA 02163
United States
617-495-5447 (Phone)
617-496-7379 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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