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

Abstract

The design of the New York City (NYC) high school match involved trade-offs 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 tiebreaking—in a student-proposing deferred acceptance mechanism. Any inefficiency associated with a realized tiebreaking 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. (JEL C78, D82, I21)

The Welfare Effects of Coordinated Assignment: Evidence from the New York City High School Match

“…The coordinated scheme achieves 80 percent of this idealized benchmark. Next, we find relatively modest gains from relaxing the mechanism design constraints emphasized by a large theoretical market design literature (Erdil and Ergin 2008;Abdulkadiroglu, Pathak, and Roth 2009;Kesten 2010;Kesten and Kurino 2012). Had the mechanism produced a student-optimal stable matching, the average student welfare would improve by another 0.6 percent of this range.…”

“…The new mechanism was designed with input from economists (see Roth 2005 andRoth 2009). When publicizing the new mechanism, the DOE explained that its goals were to utilize school places more efficiently and reduce the gaming involved in obtaining school seats (Kerr 2003).…”

“…When priorities include ties, however, DA must include a tiebreaker. Tiebreaking opens the door to multiple student-optimal stable matchings and DA may fail to find a student-optimal stable matching (Erdil and Ergin 2008;Abdulkadiroglu, Pathak, and Roth 2009). …”

“…This mechanism is not strategy-proof, and in general, there is no strategy-proof mechanism that Pareto dominates the deferred acceptance or stable improvement cycles mechanism (Abdulkadiroglu, Pathak, and Roth 2009;Kesten 2010;Kesten and Kurino 2012). Table 8 shows that the difference in distance-equivalent utility between the neighborhood and utilitarian assignment is 18.96 miles.…”

“…When a student is interested in more than 12 schools, she has to carefully reduce the choice set down to 12 schools. If a student is only interested in 11 or fewer schools, this constraint in principle should not influence ranking behavior (Abdulkadiroglu, Pathak, and Roth 2009;Haeringer and Klijn 2009). It is a weakly dominant strategy to add an acceptable school to a rank-order list as long as there is room for additional schools on the application form.…”