The Boston Public School Match
01 May 2005-The American Economic Review (American Economic Association)-Vol. 95, Iss: 2, pp 368-371
TL;DR: The Boston Public Schools (BPS) system for assigning students to schools is described in this paper, where the authors describe some of the difficulties with the current assignment mechanism and some elements of the design and evaluation of possible replacement mechanisms.
Abstract: 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.
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TL;DR: In this article, the authors developed a model of matching with contracts which incorporates, as special cases, the college admissions problem, the Kelso-Crawford labor market matching model, and ascending package auctions.
Abstract: We develop a model of matching with contracts which incorporates, as special cases, the college admissions problem, the Kelso-Crawford labor market matching model, and ascending package auctions. We introduce a new "law of aggregate demand" for the case of discrete heterogeneous workers and show that, when workers are substitutes, this law is satisfied by profit-maximizing firms. When workers are substitutes and the law is satisfied, truthful reporting is a dominant strategy for workers in a worker-offering auction/matching algorithm. We also parameterize a large class of preferences satisfying the two conditions.,
792 citations
Cites methods from "The Boston Public School Match"
...…and Tayfun Sönmez (2003) advocated a variation of the same algorithm for use by school choice programs, a similar centralized match was adopted by the New York City schools (Abdulkadiroğlu et al., 2005b) and another is being evaluated by the Boston schools (Abdulkadiroğlu et al., 2005a)....
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TL;DR: 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 as mentioned in this paper.
Abstract: 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
676 citations
TL;DR: This paper proposed a combinatorial assignment mechanism based on an approximation to competitive equilibrium from equal incomes (CEEI) in which incomes are unequal but arbitrarily close together, and the mechanism is approximately efficient, satisfies two new criteria of outcome fairness, and is strategyproof in large markets.
Abstract: This paper proposes a new mechanism for combinatorial assignment—for example, assigning schedules of courses to students—based on an approximation to competitive equilibrium from equal incomes (CEEI) in which incomes are unequal but arbitrarily close together. The main technical result is an existence theorem for approximate CEEI. The mechanism is approximately efficient, satisfies two new criteria of outcome fairness, and is strategyproof in large markets. Its performance is explored on real data, and it is compared to alternatives from theory and practice: all other known mechanisms are either unfair ex post or manipulable even in large markets, and most are both manipulable and unfair.
531 citations
Cites background from "The Boston Public School Match"
...5 See Sönmez and Ünver (2011) for a survey treatment and Chen and Sönmez (2002), Abdulkadiroğlu, Pathak, and Roth (2005), and Abdulkadiroğlu et al. (2005) on applications to housing markets and school choice....
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...…in the large and that have been shown to have important incentive problems in practice include nonstable matching algorithms (cf. Roth 2002), the Boston mechanism for school choice (Abdulkadiroğlu, Pathak, and Roth 2005), and discriminatory price multiunit auctions (e.g., Friedman 1991)....
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Posted Content•
TL;DR: In this paper, the design of the New York City (NYC) High School match involved tradeoffs among efficiency, stability and strategy-proofness that raise new theoretical questions.
Abstract: 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.
442 citations
Cites background from "The Boston Public School Match"
...In contrast, a primary feature of school choice in NYC and in other cities including Boston (in which a new design was implemented in 2006, see Abdulkadiro ̆ glu et al. 2005, 2006) is that there are indifferences—ties—in how students are ordered by at least some schools....
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TL;DR: In this article, the authors show that, although this constraint eliminates some potential exchanges, there is a wide class of constrained-efficient mechanisms that are strategy-proof when patient-donor pairs and surgeons have 0-1 preferences.
435 citations
References
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TL;DR: In this article, the authors studied the relationship between college admission and the stability of marriage in the United States, and found that college admission is correlated with the number of stable marriages.
Abstract: (2013). College Admissions and the Stability of Marriage. The American Mathematical Monthly: Vol. 120, No. 5, pp. 386-391.
5,655 citations
TL;DR: In this article, the authors 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, and offer two alternative mechanisms each of which may provide a practical solution to some critical school choice issues.
Abstract: 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.
1,446 citations
TL;DR: In this paper, an economic model of trading in commodities that are inherently indivisible, like houses, is investigated from a game-theoretic point of view, and the concepts of balanced game and core are developed, and a general theorem of Scarf's is applied to prove that the market in question has a nonempty core, that is, at least one outcome that no subset of traders can improve upon.
1,232 citations
"The Boston Public School Match" refers background in this paper
...Many properties of TTC carry over to school choice, including Pareto efficiency (Shapley and Scarf, 1974) and dominant-strategy incentive compatibility (Roth, 1982b)....
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TL;DR: In this article, the authors make the case that experimental and computational economics are natural complements to game theory in the work of design, and that some of the challenges facing both markets involve related kinds of complementarities.
Abstract: Economists have lately been called upon not only to analyze markets, but to design them. Market design involves a responsibility for detail, a need to deal with all of a market's complications, not just its principle features. Designers therefore cannot work only with the simple conceptual models used for theoretical insights into the general working of markets. Instead, market design calls for an engineering approach. Drawing primarily on the design of the entry level labor market for American doctors (the National Resident Matching Program), and of the auctions of radio spectrum conducted by the Federal Communications Commission, this paper makes the case that experimental and computational economics are natural complements to game theory in the work of design. The paper also argues that some of the challenges facing both markets involve dealing with related kinds of complementarities, and that this suggests an agenda for future theoretical research.
968 citations
"The Boston Public School Match" refers background in this paper
...York City high schools (Abdulkadiroğlu et al., 2005) and elsewhere (Roth, 2002): Step 1....
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TL;DR: The main focus of this paper is on determining the extent to which matching procedures can be designed which give agents the incentive to honestly reveal their preferences, and which produce stable matches.
Abstract: This paper considers some game-theoretic aspects of matching problems and procedures, of the sort which involve matching the members of one group of agents with one or more members of a second, disjoint group of agents, ail of whom have preferences over the possible resulting matches. The main focus of this paper is on determining the extent to which matching procedures can be designed which give agents the incentive to honestly reveal their preferences, and which produce stable matches. Two principal results are demonstrated. The first is that no matching procedure exists which always yields a stable outcome and gives players the incentive to reveal their true preferences, even though procedures exist which accomplish either of these goals separately. The second result is that matching procedures do exist, however, which always yield a stable outcome and which always give all the agents in one of the two disjoint sets of agents the incentive to reveal their true preferences.
908 citations
"The Boston Public School Match" refers background in this paper
...However, if welfare considerations apply only to students, there is tension between stability and Pareto optimality (Roth, 1982a)....
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...Moreover all students prefer their outcome to any other stable matching (Gale and Shapley, 1962), and the induced student-optimal stable mechanism is dominantstrategy incentive-compatible (Roth, 1982a)....
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...Many properties of TTC carry over to school choice, including Pareto efficiency (Shapley and Scarf, 1974) and dominant-strategy incentive compatibility (Roth, 1982b)....
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