Strategy-Proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match

By Atila Abdulkadiroglu, Parag A. Pathak, Alvin E. Roth. 2009

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The design of the New York City (NYC) High School match involved tradeoffs among efficiency, stability and strategy-proofness that raise new theoretical questions. We analyze a model with indifferences--ties--in school preferences. Simulations with field data and the theory favor breaking indifferences the same way at every school --single tie breaking-- in a student-proposing deferred acceptance mechanism. Any inefficiency associated with a realized tie breaking cannot be removed without harming student incentives. Finally, we empirically document the extent of potential efficiency loss associated with strategy-proofness and stability, and direct attention to some open questions.

Subfields: Economics and Econometrics, Education, Gender Studies

View Paper: https://www.semanticscholar.org/paper/e02f2edb09a046243cf9578e6a560185e2f849d5

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Citations in the corpus

Constrained school choice (2009, neutral): “From (2) and (3), x ∈ V (Q, g)\Pg for each step g, p ≤ g < l.”
Expanding 'Choice' in School Choice (2015, background): “Furthermore, DA is strategy-proof, meaning that the students have a dominant strategy of revealing their preference rankings of schools truthfully (Dubins and Freedman, 1981; Roth, 1982).(4) Nevertheless, the DA does not respond to applicants’ cardinal preferences.”
Do Parents Value School Effectiveness? (2020, methodology): “Motivated in part by insights derived from the theory of market design, in 2003 the city adopted a coordinated single-offer assignment mechanism based on the student-proposing deferred acceptance (DA) algorithm (Gale and Shapley, 1962; Abdulkadiroğlu et al., 2005, 2009).”
Designing Matching Mechanisms under General Distributional Constraints (2015, result): “Because the assignment for every student in Sk is identical to the outcome of the DA under capacity profile qk, by a claim in the proof of Theorem 1 of Abdulkadiroğlu, Pathak, and Roth (2009), the subsets of students in Sk who are matched to some school in ϕ(≻S) and ψ(≻S) are identical.”
Assignment Mechanisms under Distributional Constraints (2018, background): “Some applications of SD (with some variations) include school choice (Abdulkadiroğlu et al. 2009, Pathak and Sönmez 2013), college admissions (Chen and Kesten 2017, Baswana et al. 2019), on-campus housing, and office allocation (Chen and Snmez 2002).”
An analysis of the German university admissions system (2013, methodology): “2Most public schools in Boston have to admit any student with an older sibling already attending the school (see Abdulkadiroglu et al 2006), while some public schools in New York City have to admit all students whose performance in a standardized English language exam is among the top 2 percent (see”