Tayfun Sönmez

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.

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.

Core in a simple coalition formation game

Abstract. We analyze the core of a class of coalition formation game in which every players payoff depends only on the members of her coalition. We first consider anonymous games and additively separable games. Neither of these strong properties guarantee the existence of a core allocation, even if additional strong properties are imposed. We then introduce two top-coalition properties each of which guarantee the existence. We show that these properties are independent of the Scarf-balancedness condition. Finally we give several economic applications.

School choice: an experimental study

We present an experimental study of three school choice mechanisms. The Boston mechanism is influential in practice, while the two alternative mechanisms, the Gale-Shapley and Top Trading Cycles mechanisms, have superior theoretical properties in terms of incentives and efficiency. Consistent with theory, this study indicates a high preference manipulation rate under the Boston mechanism. As a result, efficiency under Boston is significantly lower than that of the two competing mechanisms in the designed environment. However, contrary to theory, Gale-Shapley outperforms the Top Trading Cycles mechanism and generates the highest efficiency. Our results suggest that replacing the Boston mechanism with either Gale-Shapley or Top Trading Cycles mechanism might significantly improve efficiency, however, the efficiency gains are likely to be more profound when parents are educated about the incentive compatibility of these mechanisms.

A Kidney Exchange Clearinghouse in New England

In 2003 there were 8,665 transplants of deceased donor kidneys for the approximately 60,000 patients waiting for such transplants in the United States. While waiting, 3,436 patients died. There were also 6,464 kidney transplants from living donors (Scientific Registry of Transplant Recipients web site). Live donation is an option for kidneys, since healthy people have two and can remain healthy with one. While it is illegal to buy or sell organs, there have started to be kidney exchanges involving two donor–patient pairs such that each (living) donor cannot give a kidney to the intended recipient because of blood type or immunological incompatibility, but each patient can receive a kidney from the other donor. So far these have been rare: as of December 2004, only five exchanges had been performed in the 14 transplant centers in New England. One reason there have been so few kidney exchanges is that there have not been databases of incompatible patient–donor pairs. Incompatible donors were simply sent home. (Databases are now being assembled not only in New England, but also in Ohio and Baltimore.) Lainie Friedman Ross et al. (1997) discussed the possibility of exchange between incompatible patient–donor pairs. Not only have a few such two-way exchanges been performed, but two three-way exchanges (in which the donor kidney from one pair is transplanted into the patient in a second pair, whose donor kidney goes to a third pair, whose donor kidney goes to the first pair) have been performed at Johns Hopkins. There have also been a number of “list exchanges” in which an incompatible patient– donor pair makes a donation to someone on the waiting list for a cadaver kidney, in return for the patient in the pair receiving high priority for a cadaver kidney when one becomes available.

Matching, Allocation, and Exchange of Discrete Resources

A survey of the literature on matching market design regarding house allocation, kidney exchange, and school choice problems.

Utilizing List Exchange and Nondirected Donation through ‘Chain’ Paired Kidney Donations

In a list exchange (LE), the intended recipient in an incompatible pair receives priority on the deceased donor waitlist (DD‐waitlist) after the paired incompatible donor donates a kidney to a DD‐waitlist candidate. A nondirected donors (ND‐D) kidney is usually transplanted directly to a DD‐waitlist candidate. These two established practices would help even more transplant candidates if they were integrated with kidney paired donation (KPD).

Strategy-proofness and Essentially Single-valued Cores

IN THIS PAPER WE SEARCH for solutions to various classes of allocation problems. We hand results pertaining to housing markets are much more encouraging. Roth 1982b shows that in the context of housing markets the core correspondence, which is shown to Ž. Ž . be single-valued by Roth and Postlewaite 1977 , is strategy-proof. Moreover Ma 1994 shows that it is the only solution that is Pareto efficient, individually rational, and strategy-proof.

Matching With (Branch‐of‐Choice) Contracts at the United States Military Academy

Branch selection is a key decision in a cadets military career. Cadets at USMA can increase their branch priorities at a fraction of slots by extending their service agreement. This real-life matching problem fills an important gap in market design literature. Although priorities fail a key substitutes condition, the agent-optimal stable mechanism is well-defined, and in contrast to the current USMA mechanism it is fair, stable, and strategy-proof. Adoption of this mechanism benefits cadets and the Army. This new application shows that matching with contracts model is practically relevant beyond traditional domains that satisfy the substitutes condition.