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Few clear-cut fixes exist in education. When it comes to school enrollment, however, a specific centralized process exists that is both simple for families to navigate and efficient for schools and districts.

Traditionally, school districts have assigned families to their neighborhood school by default. Yet over the past two decades, access to a variety of public school options has increased dramatically, especially in large urban areas. According to a 2017 analysis by the Brookings Institution, the proportion of large school districts that offered school choice doubled from 2000 through 2016.¹ As a result, of the more than 50.1 million students nationwide who attended public schools over the 2015-16 school year, more than 2.8 million students attended public charter schools, and more than 2.6 million students attended magnet schools. Additional students attended other types of public schools of choice, such as those with specialty or thematic programs.²

While the expansion of school choice has allowed parents or guardians to select schools that best meet their children’s needs, some application and enrollment processes can present barriers to families with less time or familiarity with the system. In decentralized systems, for example, students must apply separately to each school. Some students may get multiple offers and hold onto seats they do not intend to accept, while others may not receive any offers at all. Families without the information or time to strategize are often left with the least in-demand schools, which often have worse academic outcomes. Meanwhile, schools and districts find it difficult to forecast enrollment as students constantly shift across their rosters and waitlists.

A centralized system can simplify enrollment for both families and schools. Students apply through a single application, ranking a list of schools that they would like to attend and receiving a single offer to one of their preferred schools. However, system design matters when it comes to centralized enrollment. Depending on how a district assigns an offer for each student, some families can unfairly manipulate the system to make it more likely that their child secures a seat at a more in-demand, usually better-performing school.

To reduce this risk of strategic manipulation in centralized enrollment systems, Atila Abdulkadiroglu, Parag Pathak, Alvin E. Roth and Tayfun Sönmez—economists with expertise in game theory and market design—proposed a solution. They designed two fair and efficient matching algorithms—or a set of rules and calculations—to ensure that, given the preferences of all other students and schools in the system, each student receives a single offer with his or her best possible school match. Specifically, the economists designed two matching algorithms suitable for centralized assignment: deferred acceptance (DA) and top trading cycles (TTC).³

The economists first introduced this method in New York City in 2003, which helped streamline admissions to the city’s nonselective high schools. Since 2003, additional cities—including New Orleans; Denver; Washington, D.C.; Newark and Camden, New Jersey; Boston; and Indianapolis—have adopted similar algorithms to level the school choice playing field. After New York City adopted the DA algorithm, allowing students to apply to more schools, the number of students who did not receive an offer from one of their chosen schools fell drastically—from 30,000 students in 2003 to 3,000 students in 2004.⁴

Notably, there are many contentious policy issues related to public school choice that are beyond the scope of these algorithms. For instance, communities debate which types of schools should exist and how the city and state should allocate public dollars to those schools. Families also tend to demand more seats in the most desirable schools. There should be no debate, however, that all families should have fair and equal access to the public schooling options that do exist. Carefully designed assignment systems, based on the most efficient and effective algorithms, help ensure that all families have such access.

This report provides an overview of two more fair, efficient, and transparent school matching algorithms: DA and TTC. The authors review the background of DA and TTC and how each functions, discuss how they can be implemented, and highlight how these algorithms have been used to operate enrollment systems in New Orleans, Indianapolis, and Denver. The goal is to improve the efficiency of enrollment systems, while also ensuring that every student has a fair shot at the school he or she wants to attend—something that can, in the long run, improve academic outcomes.⁵

When districts allow students to attend schools outside their neighborhoods, disconnected application and enrollment processes can be difficult for families to navigate. Decentralized systems benefit families who have more time or knowledge to game the system. While a centralized enrollment system may help reduce these inequities to some extent, it must also use fair and efficient matching algorithms to further level the playing field.

Decentralized systems are difficult to navigate

Some cities require families and students to apply to each school separately, because there is no centralized system to coordinate application and enrollment across schools. Decentralized systems require families to devote time and resources to the selection process: They have to learn about and perhaps visit each school, keep track of various application timelines, and submit applications to each school. This can be particularly difficult for economically disadvantaged families, families who do not speak English at home, and single-parent families.

In decentralized systems, one student may receive an offer from multiple schools, while another student may not receive a single offer. The student with multiple offers may be placed on rosters at multiple schools and hold seats at schools that are in high demand, while the student with no offers has to enroll in a less desirable school. Less desirable schools tend to have lower test scores and graduation rates.⁶

Centralized enrollment simplifies the process but does not eliminate inequities

Centralized enrollment creates a single application and assignment process for participating schools. Students submit one application ranking their desired schools. A coordinating organization—usually either a school district or an independent nonprofit—manages the application process and uses a computerized set-of-rules program, or algorithm, that aims to match students to a school on their list. Each matched student receives a single school offer.

Unified enrollment is a centralized enrollment system in which all or most schools in the city, including traditional public and charter schools, participate. Unified enrollment simplifies the application experience for families and is more efficient for school districts, because it coordinates enrollment across sectors.

First, the entity that manages the enrollment process places students in priority groups. Districts may choose to determine priorities such as increased school diversity, neighborhood cohesion, lower transportation costs, or expanded access to high-quality schools for economically disadvantaged students. If a district priority is to minimize transportation costs, students who live near a school might receive priority over students who live in other parts of the city. Depending on the enrollment entity’s priorities, students may also receive higher priority at a particular school if they have siblings attending that school; if they are applying to continue at a combined middle and high school; or if they are eligible for free or reduced price lunch.

Centralized enrollment with a gameable assignment algorithm perpetuates inequities

While centralized enrollment simplifies the application process by creating a single access point for families, not all centralized enrollment systems are created equal. Though it may seem like a technical detail, the design of the algorithm that matches students to schools significantly affects students’ chances of being placed at their preferred school.

Traditionally, some districts with centralized enrollment have used simple algorithms that try to assign as many students as possible to the school they rank as their top choice. These algorithms have a so-called first preference first mechanism, wherein students are given priority at each school according to how high they ranked that school among their choices.

Under these systems, informed applicants may know that many other students are likely to rank the desirable School A at the top of their list. They may then choose to rank the slightly less desirable, but nonetheless preferred, School B as their own top choice, avoiding the risk of being denied admission to School A and maximizing their chances at School B. Applicants without information about schools’ relative popularity or with less understanding of various trade-offs would likely rank School A as their top choice, thereby increasing their likelihood of losing out on a seat not only in School A, but also in their second choice, School B.

Systems driven by a first preference first mechanism incentivize applicants with more information to manipulate the system. As a result, applicants with more information are more likely to get a seat in one of their desired schools. Applicants without this knowledge may rank long-shot, in-demand schools first, causing them to get locked out of placement in not only their first-choice school, but also in other schools that they ranked second or lower.

In fact, some districts explicitly recommend that parents choose schools that are not highly competitive. Before New York City implemented its new system in 2003, its high school directory instructed applicants to “determine what your competition is for a seat in this program.”⁷ In Boston, the 2004 school brochure recommended that “for a better chance of your ‘first choice’ school … consider choosing less popular schools.”⁸

It is challenging for applicants to accurately assess the odds of being accepted to a certain school and strategize their school rankings accordingly. However, it can be especially difficult for economically disadvantaged or disconnected families who may lack the time and information to play the game. Furthermore, experience and social networks increase understanding of the application process, putting newcomers at a disadvantage.

In addition to being unfair, these systems are inefficient, leaving many students without a match to any of their chosen schools. Unassigned students are either placed at a school they did not choose or asked to participate in additional rounds of matching, in which they can only select from a smaller pool of less in-demand schools that have seats remaining. These less desirable schools tend to have worse educational outcomes, such as lower test scores and graduation rates.⁹ 

Atila Abdulkadiroglu, Parag Pathak, Alvin Roth, and Tayfun Sönmez, economists specializing in game theory and market design, crafted school choice matching algorithms that are resilient to gaming and produce better matches for all students. Two algorithms—DA and TTC—do not penalize students for ranking high-demand schools at the top of their lists, and districts can customize the DA or TTC algorithms to reflect their policy goals. Policymakers should consider the trade-offs of each to determine which algorithm best suits their context.

As previously noted, districts can customize both DA and TTC. Overall, the two algorithms are more similar than different. However, districts and policymakers should consider the trade-offs of each to determine which is best for them.

The deferred acceptance algorithm

DA algorithms create stable matches between schools and students and allow both to set preferences for their desired match. The underlying research to develop DA formed the basis of the 2012 Nobel Memorial Prize in Economic Sciences¹⁰ and is also the same process used to match medical students to residency programs in the United States.¹¹

DA is unique in the way it matches students to schools. It loops through a series of tentative matches between schools and students; no decision is final, and each acceptance is deferred until the entire process ends. Each student applies to his or her first-choice school, which either tentatively accepts or rejects the student based on its priorities. Each student who is not yet matched to a school applies to their next choice. Each school tentatively accepts or declines the student and can release a student who was tentatively accepted in a previous round if a new applicant with higher priority emerges in a later round. The process continues until all students are matched or until students exhaust all their preferences. If students do not receive any of their preferences, the entity that is managing the enrollment process will assign them to a school.

Because assignments are not finalized until the end of the DA process, each applicant has a fair chance of being considered by a school on her or his list, regardless of how high she or he ranked the school compared with other applicants. Applicants gain nothing from misrepresenting their true preferences or ranking fewer schools. Because DA cannot be gamed, it levels the playing field for families regardless of the time and resources they possess.

In contrast to conventional algorithms, DA ensures that matches strictly adhere to enrollment priorities and student preferences. A student will never lose his or her spot at a preferred program to a student with a lower priority. Therefore, no student and school pair should prefer each other over their assigned matches. However, after DA has finished running, there may be pairs of students who would rather have the other’s assigned school—but these instances are exceedingly rare. It is not possible to have a system that strictly adheres to enrollment priorities and student preferences and also never results in an instance where a pair of students may want to trade their assignments, in violation of a school’s priority.

New York City’s nonselective high schools have been using DA since 2003 to match about 70,000 students to approximately 400 schools each year.¹² Other cities—including New Orleans; Denver; Washington, D.C.; Camden; Boston; and Indianapolis—have also adopted DA.¹³

The top trading cycle algorithm

Like DA, TTC cannot be manipulated by applicants who strategically rank schools. However, unlike DA, TTC seeks to swap assignments between students to ensure that they receive their more preferred choice, even if their preference does not match the enrollment priorities of each school. In other words, TTC does not strictly adhere to enrollment priorities but rather favors the goal of trying to maximize student choices.

Both DA and TTC require schools to participate in centralized assignment, where all students apply using one application and are assigned to one school. Implementing centralized assignment requires a standardized, transparent set of assignment rules across participating schools. Unified enrollment requires an additional step: All public schools in a city or region, including traditional public schools, magnet schools, and public charter schools, must participate and buy into the centralized enrollment system.

To unify enrollment, the district must work with other sectors or entities that run schools, such as local charter management organizations, local charter authorizing boards, or regional magnet programs. Some districts, such as Denver Public Schools, directly manage the common enrollment process across sectors,¹⁵ while others develop an independent entity to manage the matching process. For instance, Enroll Indy—an independent nonprofit organization in Indianapolis—manages unified enrollment for Indianapolis Public Schools (IPS) and most of the city’s public charter schools.¹⁶ Washington, D.C. uses a slightly different model to manage its unified enrollment system: My School DC is housed within the Office of the State Superintendent of Education (OSSE) and is independently supervised by the Common Lottery Board. The Common Lottery Board comprises representatives from both D.C. Public Schools and public charter schools.¹⁷

Participating schools and the managing entity must consider a few components that are critical to the effective implementation of both DA and TTC enrollment systems:

• How many schools can a student rank? The managing entity may wish to designate a maximum number of schools that a student applicant can rank. However, for DA and TTC to be fully resilient to manipulation, applicants must be allowed to list as many options as they would like. Students who can rank an unlimited number of schools on their application are less likely to prefer more options than they can rank, which would require them to strategize about which options to include.¹⁸
  Some districts may be concerned that letting students rank an unlimited number of schools could encourage students to apply to schools in which they do not seriously intend to enroll. In reality, the rate at which students enroll in their assigned school has been shown not to vary, regardless of how many options they are allowed to rank.¹⁹

• What are the enrollment priorities? Districts must decide on the policy objectives governing enrollment priorities in the matching process. These objectives often require community buy-in. Many centralized enrollment systems include enrollment priorities for siblings, students who live near a school, or students who previously attended a feeder school—schools that send the majority of their graduates to a particular school that may have a similar theme or instructional program. Systems may also give priority to students who qualify for free or reduced price lunch.

• Who will audit the system? An outside individual or entity should audit the system to ensure that rules are coded correctly and outcomes are consistent with enrollment priorities. A number of districts with centralized enrollment systems publish audit reports for the sake of transparency, accountability, and learning.²⁰

• How will policies be communicated to students and families? The managing entity should provide informational tools for families to understand the goals and operation of the enrollment system and its benefits; learn about the available school options; and receive instructions for applying to schools and checking results. Most entities that manage the enrollment process offer these resources online. Some hire community liaisons to partner with community-based organizations to share the information in community centers or even from door to door.

• What technology systems need to be put in place? Computerized systems can help ease the burden of collecting application forms, linking applications to existing registration data, and running the assignment algorithm.

Cost

The cost of switching to DA or TTC varies significantly across districts. If a city or district already has a centralized enrollment system, switching the algorithm may only require coding changes and communication to stakeholders. If a city or district does not have a centralized enrollment system, switching to DA or TTC requires integrating existing applications and matching processes into one system. In Chicago, for example, students were still submitting paper applications only a few years before the city switched to using the DA algorithm. Before implementing the algorithm, the district needed to transition to computerized collection of student applications and tracking of open school seats.²¹

The considerations listed above are critical to any centralized matching process, and the associated costs are not specific to only DA or TTC. 

This section describes three districts that are currently using DA within a unified enrollment system: New Orleans, one of the oldest adopters of the algorithm; Indianapolis, which launched its OneMatch system in 2017; and Denver, which adopted unified enrollment using DA in 2012. Each matching process looks different to reflect the districts’ unique political and education contexts, but the use of the algorithm ensures fair access to public schools of choice and efficient matching.

To collect information for these case studies, the authors interviewed individuals who developed or managed enrollment systems in New Orleans, Indianapolis, and Denver.

EnrollNOLA, New Orleans: Encouraging school participation, educating the community

New Orleans is unique in that the vast majority of its public schools—all but two—are charter schools. Following Hurricane Katrina in 2005, the Recovery School District (RSD)—a statewide school district that assumes oversight of underperforming schools across the state—took control of most public schools in New Orleans and converted them to charter schools.²² Citywide enrollment was decentralized for most public schools, which required families to travel around the city and individually apply to each school they considered.

EnrollNOLA—managed by the RSD at the time—launched the OneApp unified enrollment system in 2012 to simplify the application process for families and increase school match efficiency. Today, EnrollNOLA is housed under the Orleans Parish School Board (OPSB), the school district in New Orleans that now operates more as a charter authorizer than a traditional school district. EnrollNOLA manages the admissions and transfers for all but three of the city’s public schools, as well as private schools that participate in the Louisiana Scholarship Program—a voucher program that provides families with a fixed amount of public funding to put toward private school tuition. As part of this work, EnrollNOLA implements OneApp—the annual lottery and admissions process for all participating schools.²³

Building community understanding of the system

Ray Cwiertniewicz, the former executive director of student enrollment at OPSB who was responsible for supervising OneApp, notes that one of EnrollNOLA’s biggest ongoing challenges is helping fa