Can we make school choice more efficient?

A new paper by Eduardo Azevedo and Jacob Leshno addresses a recent puzzle in school choice: Can we make school choice more efficient? An Example

Here's their abstract:
"The deferred acceptance mechanism, currently used in the New York City and in the Boston public school systems, can produce Pareto-dominated assignments. When students are non-strategic a Pareto-dominating and efficient mechanism can be achieved by allowing some students to trade schools (e.g. Stable improvement Cycles, Erdil and Ergin 2008). We find that when students are strategic the equilibrium assignments of these mechanisms can be unstable with respect to the true preferences and can be Pareto inferior to the deferred acceptance equilibrium assignment."

The paper follows up on the Erdil and Ergin 2008 AER paper, and also on the paper by Atila Abudlkadiroglu, Parag Pathak and me which discusses the NYC high school match and shows that about a thousand NYC high school students could in principle be made better off
Abdulkadiroglu, Atila , Parag A. Pathak, and Alvin E. Roth, "Strategy-proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match,'' American Economic Review, 99, 5, Dec. 2009, pp1954-1978.

That paper sets the stage for Azevedo and Leshno by observing that about 1,000 of the approximately 90,000 new high school students each year could have been given better matches if strategy-proofness were not a desiderata, and if their true preferences could be recovered without strategy proofness. So that raises the open question of what kind of preferences would be submitted to a system that tried to get these apparent welfare gains, and whether welfare gains could be achieved at equilibrium:
"Nothing is yet known about what kinds of preferences one could expect to be strategically submitted to such a mechanism, or what their welfare consequences would be. Consequently, there is room for more work to further illuminate the tradeoff between efficiency and strategy-proofness."

Azevedo and Leshno show that there's at least a possibility that attempting to improve welfare while sacrificing strategy-proofness could, in equilibrium, reduce welfare.

One of the exciting things about the modern school choice literature is how it has given rise to questions about matching that didn't arise in other applications (like to labor market clearinghouses). The special feature of school choice is the importance of how ties are broken, between between students who have equal priority for a given school that doesn't have capacity for all of them.

Azevedo and Leshno advance the discussion of how we should evaluate school choice algorithms, in the complex settings in which we're asked to design them. Their paper shows how strategy-proofness and welfare can be intertwined in subtle ways at equilibrium. There's a lot more to learn about this, so their short paper answers one question and raises many others.