Abdulkadiroglu, Atila

Pathak, Parag A.

Roth, Alvin

Sönmez, Tayfun

The American Economic Review

Harvard University - DASH

The Boston Public School MatchBy ATI ˙LA ABDULKADI ˙ROG ˘LU,P ARAG A. PATHAK,A LVIN E. ROTH, AND TAYFUN SO ¨NMEZ*After the publication of “School Choice: AMechanism Design Approach” by Abdulkadiro-g ˘lu and So ¨nmez (2003), a Boston Globe re-porter contacted us about the Boston PublicSchools (BPS) system for assigning students toschools. The Globe article highlighted the dif-ﬁculties that Boston’s system may give parentsin strategizing about applying to schools.Brieﬂy, Boston tries to give students their ﬁrst-choice school. But a student who fails to get herﬁrst choice may ﬁnd her later choices ﬁlled bystudents who chose them ﬁrst. So there is a riskin ranking a school ﬁrst if there is a chance ofnot being admitted; other schools that wouldhave been possible had they been listed ﬁrstmay also be ﬁlled.Valerie Edwards, then Strategic PlanningManager at BPS, and her colleague CarletonJones invited us to a meeting in October 2003.BPS agreed to a study of their assignment sys-tem and provided us with micro-level data setson choices and characteristics of students in thegrades at which school choices are made (K, 1,6, and 9), and school characteristics. Based onthe pending results of this study, the Superin-tendent has asked for our advice on the designof a new assignment mechanism. This paperdescribes some of the difﬁculties with the cur-rent mechanism and some elements of the de-sign and evaluation of possible replacementmechanisms.School choice in Boston has been partly shapedby desegregation. In 1974, Judge W. ArthurGarrity ordered busing for racial balance. In1987, the U.S. Court of Appeals freed BPS toadopt a new, choice-based assignment plan. In1999 BPS eliminated racial preferences in as-signment and adopted the current mechanism.I. The Current Boston MechanismBPS has over 60,000 students from gradesK–12 in almost 140 schools in three zones:East, West, and North. During the ﬁrst registra-tion period in January, students who will beentering a new school in grades K, 1, 6, and 9are asked to rank at least three schools in orderof preference. Although most assignments aremade in the ﬁrst registration period, Boston hasother registration periods in February, March,and April.For elementary and middle school, parentsare asked to consider schools in their zone plusﬁve schools open to all neighborhoods. Highschool admissions are city-wide for 18 schools.There are also 13 high schools that requirespecial admissions and three special-educationprograms that are not part of the centralizedallocation process.In 2004, at the end of the ﬁrst registrationperiod, there were about 4,800 students enteringkindergarten, 4,000 entering grade 1, over 4,300students entering grade 6, and about 4,000 en-tering grade 9.Boston assigns students if possible to theirﬁrst-choice school, allocating over-demandedseats by a system of priorities. First, a youngersibling has priority to attend the same school asan older sib. Next in priority for half of eachprogram’s seats are students from the school’swalk zone. Not every residential location in thecity has a school for which they obtain walk-zone preference. Students who live in theselocations are then given priority for assignmentto their ﬁrst- and second-choice schools. Addi-tional priorities are assigned by random num-bers generated once for each student. After theﬁrst registration period there is no longer awalk-zone priority.* Abdulkadirog ˘lu: Department of Economics, ColumbiaUniversity, New York, NY 10027; Pathak and Roth:Harvard Business School and Department of Economics,Harvard University, Cambridge, MA 02138; So ¨nmez: De-partment of Economics, Koc ¸ University, Istanbul, Turkey,and Harvard University.368Within each priority class, students’ randomnumbers determine a strict priority order. Eachschool has a maximum capacity determined byBPS. The Boston mechanism assigns studentsas follows:Step 1.—For each school, consider the studentswho have listed it as their ﬁrst choice andassign seats to these students in priority orderuntil either no seats remain or no studentremains who has listed it as ﬁrst choice.Step k.—For each school with seats still avail-able, consider the students who have listed itas their kth choice and assign seats to thesestudents in priority order until either no seatsremain or no student remains who has listedit as kth choice.The procedure terminates when each student isassigned a seat (or all submitted choices areconsidered).If a student does not get her top choice, shemay be added to a school’s waiting list. Stu-dents who get their second choice go on thewait-list for their ﬁrst choice. Students who getneither their ﬁrst nor second choice are placedon wait-lists for both. Students who do not getany of their choices go on wait-lists for up tothree choices. The priority on the wait-list isbased on sibling preference, round of applica-tion, and random number. When the school yearstarts, if a student leaves the public-school sys-tem, the student may no longer stay on a wait-list. All wait-lists expire in January of the nextschool year.During the 2002–2003 assignment process,about 11 percent of students were on wait-lists.In 2004, two major changes were introduced:caps to the size of the wait-list and active con-ﬁrmation of interest in a wait-list. This year,students may go on wait-lists only until thewait-list contains 25 percent of the number ofseats at the grade level in the school. Also,students already on the number of wait-liststhey are entitled to according to the schoolchoice they received must leave one list beforebeing added to another.At the end of the assignment process, if astudent is not given any of his choices, or didnot return an application, BPS assigns the stu-dent to the school closest to home that hasspace.The Boston mechanism is a priority matchingmechanism (Roth, 1991). Priority mechanismshave been used to match medical graduates tointernships in several regions of the UnitedKingdom, starting in the 1960s. Each of thesemechanisms was abandoned after being gamedby the participants. Yan Chen and So ¨nmez(2005) experimentally examine preference ma-nipulation under the Boston mechanism andobserve the associated welfare loss.Priority mechanisms are common in schoolchoice. The largest district we know of with apriority mechanism is Hillsborough CountySchool District in Tampa-St. Petersburg, the11th largest school district in the United States,with about 170,000 students.1 Cambridge, Den-ver, Minneapolis, and Seattle also have prioritymechanisms.The idea that students and parents should becautious in choosing their ﬁrst choice is in-cluded in the reference material provided tostudents and parents. BPS states “for a betterchance of getting your ‘ﬁrst choice’ school... consider choosing less popular schools” (In-troducing Boston Public Schools, 2004, p. 3[quotation marks in original]). In Seattle andTampa-St. Petersburg, the incentives for suchpreference manipulation are advocated in thelocal press (see Haluk Ergin and So ¨nmez,2005). Note that when students rank less com-petitive programs ﬁrst, many get their statedﬁrst choice. Approximately 80 percent of stu-dents who submit preferences in the ﬁrst regis-tration period get their stated ﬁrst choice inBoston. Of course, this is not necessarily theirmost preferred school.II. Two Alternative Matching MechanismsIt is costly in the Boston mechanism to list aﬁrst-choice that you do not succeed in gettingbecause, once other students are assigned theirﬁrst-choice places, they cannot be displacedeven by a student with higher priority. A classof mechanisms that avoid this are deferred-acceptance algorithms (David Gale and LloydShapley, 1962) of the kind adopted by New1 Often, the precise allocation rules are not publiclyspeciﬁed by the school districts.369 VOL. 95 NO. 2 PRACTICAL MARKET DESIGNYork City high schools (Abdulkadirog ˘lu et al.,2005) and elsewhere (Roth, 2002):Step 1.—Each student “proposes” to her ﬁrstchoice. Each school tentatively assigns itsseats to its proposers one at a time in theirpriority order. Any remaining proposers arerejected.Step k.—Each student who was rejected in theprevious step proposes to her next choice ifone remains. Each school considers the stu-dents it has been holding together with itsnew proposers and tentatively assigns itsseats to these students one at a time in priorityorder. Any remaining proposers are rejected.The algorithm terminates when no student pro-posal is rejected, and each student is assignedher ﬁnal tentative assignment.In contrast with the Boston algorithm, thedeferred-acceptance algorithm assigns seatsonly tentatively at each step, so students withhigher priorities may be considered in subse-quent steps. Consequently it is stable in thesense that there is no student who loses a seat toa lower-priority student and receives a less-preferred assignment. Moreover all studentsprefer their outcome to any other stable match-ing (Gale and Shapley, 1962), and the inducedstudent-optimal stable mechanism is dominant-strategy incentive-compatible (Roth, 1982a).(Unlike in New York City, the schools are notstrategic players in Boston, as the priorities areset centrally.) If the intention of the schoolboard is that priorities be “strictly enforced,”this mechanism is a leading candidate.However, if welfare considerations applyonly to students, there is tension between sta-bility and Pareto optimality (Roth, 1982a). Ifpriorities are merely a device for allocatingscarce spaces, it might be possible to assignstudents to schools they prefer by allowing themto trade their priority at one school with a stu-dent who has priority at a school they prefer.The following top trading cycles (TTC) mech-anism creates a virtual exchange for priorities:Step 1.—Assign counters for each school totrack how many seats remain available. Eachstudent points to her favorite school, and eachschool points to the student with the highestpriority. There must be at least one cycle. (Acycle is an ordered list of distinct schools andstudents (student 1 - school 1 - student 2 - ... -student k - school k) with student 1 pointingto school 1, school 1 to student 2, ... , studentk to school k, and school k pointing to student1.) Each student is part of at most one cycle.Every student in a cycle is assigned a seat atthe school she points to and is removed. Thecounter of each school is reduced by 1, and ifit reaches zero, the school is removed.Step k.—Each remaining student points to herfavorite school among the remaining schools,and each remaining school points to the stu-dent with highest priority among the remain-ing students. There is at least one cycle.Every student in a cycle is assigned a seat atthe school she points to and is removed. Thecounter of each school in a cycle is reducedby 1, and if it reaches zero, the school isremoved.The procedure terminates when each student isassigned a seat (or all submitted choices areconsidered).This version of the TTC mechanism was in-troduced by Abdulkadirog ˘lu and So ¨nmez(2003) and is an extension of Gale’s “top trad-ing cycles mechanism” described in Shapleyand Herbert Scarf (1974). Many properties ofTTC carry over to school choice, including Pa-reto efﬁciency (Shapley and Scarf, 1974) anddominant-strategy incentive compatibility (Roth,1982b). Variations of this procedure can also beconsidered which may reduce instability (e.g.,Onur Kesten, 2005). See also the recent designof a kidney exchange clearinghouse (Roth et al.,2004, 2005).III. Design ConsiderationsUnlike in New York (Abdulkadirog ˘lu et al.,2005), students’ priorities at schools are not setby schools, but by the central administration.There does not seem to be any issue of individ-ual schools gaming the system in Boston.Therefore, it is natural to ask whether the ben-eﬁts that “stable” matching produces in NewYork have parallel beneﬁts in the different sit-uation in Boston, and if not, whether the welfareimprovements that might be available from aTTC-like mechanism should be considered.At a public meeting of the Boston School370 AEA PAPERS AND PROCEEDINGS MAY 2005Committee in October 2004 we were asked foradvice about how to think about this. We re-plied with the question “Would anyone mind iftwo students who each preferred the school inthe other student’s walk zone were to trade theirpriorities and enroll in those schools?” If this isnot desirable (e.g., because of transportationcosts, or because walk-zone priorities reﬂect apublic good that results when parents walk chil-dren to school, or because lawsuits might followif a child is excluded from a school while an-other with lower priority is admitted), then sta-ble matchings would efﬁciently combinestudent preferences with priorities. But if help-ing the students this way is worth whatevertransportation and other costs might be in-curred, then only the students’ preferences needto be taken into account and a TTC-like mech-anism might be more appropriate.IV. Recent DevelopmentsIn December 2003, the Boston School Com-mittee initiated an evaluation of all aspects ofstudent assignment. The ﬁnal task-force reportrecommends changing the student assignmentalgorithm. The task force observed that, eventhough students can select three schools, manychildren do not get any of their picks because, ifa parent and student choose three popularschools and do not get their ﬁrst choice, theymay also miss their second and third choice.A memorandum from Superintendent Payzantin December 2004 states that BPS plans tochange the computerized process used to assignstudents to schools. Although the task-force re-port recommended that BPS adopt the TTCassignment algorithm, the School Committee isinterested in simulations of both mechanismsand in understanding the extent of preferencemanipulation under the Boston mechanism.They are also thinking through their philosoph-ical position on the trade-off between stabilityand efﬁciency.REFERENCESAbdulkadirog ˘lu, Atila; Pathak, Parag A. andRoth, Alvin E. “The New York City HighSchool Match.” American Economic Review,2005 (Papers and Proceedings), 95(2), pp.364–67.Abdulkadirog ˘lu, Atila and So ¨nmez, Tayfun.“School Choice: A Mechanism Design Ap-proach.” American Economic Review, 2003,93(3), pp. 729–47.Chen, Yan and So ¨nmez, Tayfun. “School Choice:An Experimental Study.” Journal of Eco-nomic Theory, 2005 (forthcoming).Ergin, Haluk and So ¨nmez, Tayfun. “Games ofSchool Choice under the Boston Mecha-nism.” Journal of Public Economics, 2005(forthcoming).Gale, David and Shapley, Lloyd. “College Ad-missions and the Stability of Marriage.”American Mathematical Monthly, 1962,69(1), pp. 9–15.Kesten, Onur. “Student Placement to PublicSchools in the US: Two New Solutions.”Mimeo, University of Rochester, 2005.Roth, Alvin E. “The Economics of Matching:Stability and Incentives.” Mathematics ofOperations Research, 1982, 7(4), pp. 617–28.Roth, Alvin E. “Incentive Compatibility in aMarket with Indivisible Goods.” EconomicsLetters, 1982b, 9(2), pp. 127–32.Roth, Alvin E. “A Natural Experiment in theOrganization of Entry-Level Labor Markets:Regional Markets for New Physicians andSurgeons in the United Kingdom.” AmericanEconomic Review, 1991, 81(3), pp. 414–40.Roth, Alvin E. “The Economist as Engineer:Game Theory, Experimental Economics andComputation as Tools of Design Econom-ics.” Econometrica, 2002, 70(4), pp. 1341–78.Roth, Alvin E.; So ¨nmez, Tayfun and U ¨nver, M.Utku. “Kidney Exchange.” Quarterly Journalof Economics, 2004, 119(2), pp. 457–88.Roth, Alvin E.; So ¨nmez, Tayfun and U ¨nver, M.Utku. “A Kidney Exchange Clearinghouse inNew England.” American Economic Review,2005 (Papers and Proceedings), 95(2), pp.376–80.Shapley, Lloyd and Scarf, Herbert. “On Coresand Indivisibility.” Journal of MathematicalEconomics, 1974, 1(1), pp. 23–28.371 VOL. 95 NO. 2 PRACTICAL MARKET DESIGN

The Boston Public School Match

http://dash.harvard.edu/bitstream/handle/1/2562764/Roth_bostonpublic.pdf?sequence=2

The Boston Public School Match

Abstract

Similar works

Full text

Available Versions

Harvard University - DASH