Atila Abdulkadiroglu

School Choice: A Mechanism Design Approach

A central issue in school choice is the design of a student assignment mechanism. Education literature provides guidance for the design of such mechanisms but does not offer specific mechanisms. The flaws in the existing school choice plans result in appeals by unsatisfied parents. We formulate the school choice problem as a mechanism design problem and analyze some of the existing school choice plans including those in Boston, Columbus, Minneapolis, and Seattle. We show that these existing plans have serious shortcomings, and offer two alternative mechanisms each of which may provide a practical solution to some critical school choice issues.

The New York City High School Match

We assisted the New York City Department of Education (NYCDOE) in designing a mechanism to match over 90,000 entering students to public high schools each year. This paper makes a very preliminary report on the design process and the first year of operation, in academic year 2003–2004, for students entering high school in fall 2004. In the first year, only about 3,000 students had to be assigned to a school for which they had not indicated a preference, which is only 10 percent of the number of such assignments the previous year. New York City has the largest public school system in the country, with over a million students. In 1969 the system was decentralized into over 30 community school districts. In the 1990s, the city began to take more centralized control (Mark Schneider et al., 2000), and in 2002, a newly reorganized NYCDOE began to reform many aspects of the school system. In May 2003, Jeremy Lack, then the NYCDOE Director of Strategic Planning, contacted one of us for advice on designing a new high-school matching process. The NYCDOE was aware of the matching process for American physicians, the National Resident Matching Program (Roth, 1984; Roth and E. Peranson, 1999). They wanted to know if it could be appropriately adapted to the city’s schools. The three authors of the present paper (and, at several crucial junctures, also Tayfun Sonmez) advised (and often convinced) Lack, his colleagues (particularly Elizabeth Sciabarra and Neil Dorosin), and the DOE’s software vendor, about the design of the match. I. The Prior (2002–2003) New York City Matching Procedure

Random Serial Dictatorship and the Core from Random Endowments in House Allocation Problems

Random serial dictatorship and the core from random endowments in house allocation problems

The Boston Public School Match

After the publication of “School Choice: A Mechanism Design Approach” by Abdulkadiroglu and Sonmez (2003), a Boston Globe reporter contacted us about the Boston Public Schools (BPS) system for assigning students to schools. The Globe article highlighted the difficulties that Boston’s system may give parents in strategizing about applying to schools. Briefly, Boston tries to give students their firstchoice school. But a student who fails to get her first choice may find her later choices filled by students who chose them first. So there is a risk in ranking a school first if there is a chance of not being admitted; other schools that would have been possible had they been listed first may also be filled. Valerie Edwards, then Strategic Planning Manager at BPS, and her colleague Carleton Jones invited us to a meeting in October 2003. BPS agreed to a study of their assignment system and provided us with micro-level data sets on choices and characteristics of students in the grades at which school choices are made (K, 1, 6, and 9), and school characteristics. Based on the pending results of this study, the Superintendent has asked for our advice on the design of a new assignment mechanism. This paper describes some of the difficulties with the current mechanism and some elements of the design and evaluation of possible replacement mechanisms. School choice in Boston has been partly shaped by desegregation. In 1974, Judge W. Arthur Garrity ordered busing for racial balance. In 1987, the U.S. Court of Appeals freed BPS to adopt a new, choice-based assignment plan. In 1999 BPS eliminated racial preferences in assignment and adopted the current mechanism.

Accountability and Flexibility in Public Schools: Evidence from Boston's Charters And Pilots

Charter schools are publicly funded but operate outside the regulatory framework and collective bargaining agreements characteristic of traditional public schools. In return for this freedom, charter schools are subject to heightened accountability. This paper estimates the impact of charter school attendance on student achievement using data from Boston, where charter schools enroll a growing share of students. We also evaluate an alternative to the charter model, Bostons pilot schools. These schools have some of the independence of charter schools, but operate within the school district, face little risk of closure, and are covered by many of same collective bargaining provisions as traditional public schools. Estimates using student assignment lotteries show large and significant test score gains for charter lottery winners in middle and high school. In contrast, lottery-based estimates for pilot schools are small and mostly insignificant. The large positive lottery-based estimates for charter schools are similar to estimates constructed using statistical controls in the same sample, but larger than those using statistical controls in a wider sample of schools. The latter are still substantial, however. The estimates for pilot schools are smaller and more variable than those for charters, with some significant negative effects.

Resolving Conflicting Preferences in School Choice: The "Boston Mechanism" Reconsidered

Despite its widespread use, the Boston mechanism has been criticized for its poor incentive and welfare performances compared to the Gale-Shapley deferred acceptance algorithm (DA). By contrast, when students have the same ordinal preferences and schools have no priorities, we find that the Boston mechanism Pareto dominates the DA in ex ante welfare, that it may not harm but rather benefit participants who may not strategize well, and that, in the presence of school priorities, the Boston mechanism also tends to facilitate greater access than the DA to good schools for those lacking priorities at those schools. (JEL D82, I21, I28)

Expanding 'Choice' in School Choice

Truthful revelation of preferences has emerged as a desideratum in the design of school choice programs. Gale-Shapleys deferred acceptance mechanism is strategy-proof for students but limits their ability to communicate their preference intensities. This results in ex-ante inefficiency when ties at school preferences are broken randomly. We propose a variant of deferred acceptance mechanism which allows students to influence how they are treated in ties. It maintains truthful revelation of ordinal preferences and supports a greater scope of efficiency.

Ordinal efficiency and dominated sets of assignments

Abstract Using lotteries is a common tool for allocating indivisible goods. Since obtaining preferences over lotteries is often difficult, real-life mechanisms usually rely on ordinal preferences over deterministic outcomes. Bogomolnaia and Moulin (J. Econom. Theory 19 (2002) 623) show that the outcome of an ex post efficient mechanism may be stochastically dominated. They define a random assignment to be ordinally efficient if and only if it is not stochastically dominated. In this paper we investigate the relation between ex post efficiency and ordinal efficiency. We introduce a new notion of domination defined over sets of assignments and show that a lottery induces an ordinally efficient random assignment if and only if each subset of the full support of the lottery is undominated.

Advances in Economics and Econometrics: Matching Markets: Theory and Practice

Introduction It has been almost a half-century since David Gale and Lloyd Shapley (1962) published their pathbreaking paper, “College Admissions and the Stability of Marriage,” in American Mathematical Monthly . It is difficult to know whether Gale and Shapley expected the literature they initiated to be used to improve the lives of masses of people all around the world. We are fortunate to see that this is happening today. The model that Gale and Shapley presented is very simple. A number of boys and girls have preferences for one another and would like to be matched. The question Gale and Shapley were interested in especially was whether there is a “stable” way to match each boy with a girl so that no unmatched pair can find out later that they can both do better by matching each other. Gale and Shapley found that indeed there is such a stable matching, and they presented a deferred-acceptance algorithm that achieves this objective. Versions of the algorithm are used today to match hospitals with medical residents and students with public schools in New York City and Boston. In 1974, Lloyd Shapley and Herbert Scarf published a related paper, “On Cores and Indivisibility,” in the first issue of the Journal of Mathematical Economics . Arguably, their model was the simplest exchange economy we could imagine. Each agent comes to the market with one indivisible good and seeks to trade it for more preferred goods that might be brought by other agents.

Mechanism design with tacit collusion

In the mechanism design literature, collusion is often modelled as agents signing side contracts. This modelling approach is in turn implicitly justified by some unspecified repeated-interaction story. In this paper, we first second-guess what kind of repeatedinteraction story these side-contract theorists (would admit that they) are having in mind. We then show that , within this repeated-interaction story, there is a big difference between communicative and tacit collusion. While communicative collusion hurts the mechanism designer, tacit collusion is exploitable *We are very grateful to Yeon-Koo Che, Jeffrey Ely, and Larry Samulson, whose many probing questions have forced us to rethink our original intuition. All errors are ours.