How an Algorithm Can Make School Choice Fairer

September 03, 2019


In 2003 Neil Dorosin, admissions director for New York City public schools, called up Al Roth, then a Harvard professor, for advice on designing a better school admissions system. Roth had just developed a new system for assigning medical students to hospitals and Dorosin thought that this could work in schools too. Roth and colleagues Parag Pathak and Atila Abdulkadiroglu set about designing the theoretically optimal application and admissions system.

In the old system, students in New York City listed their top five schools. This list was passed to schools, who could see if a student had listed them as a top choice or not. This would lead to strategic applications by students, who wouldn’t necessarily put their real top choice first, but the top choice that they thought they might get into. Many students wouldn’t get any of the top five choices and would be assigned a totally different school. Many schools would lie about the number of places available, holding some back in reserve for students they weren’t matched with through the official process.

In work for which Roth was later awarded the Nobel Prize, the team came up with a new algorithm that is completely strategy-proof. No one has an incentive to play games. Students can put down their best choice in the knowledge that they will always get their highest possible choice. Schools have no incentive to hold back places in reserve, as they always get their most preferred candidates through the system.

In each of the first three years of the new system’s operation, more students were assigned to their first-choice school than had been in the old system. Before the new system was put in place, there were 30,000 students who didn’t get into any of their five choices and had to be assigned to schools by administrators. In the first year of the new system, only 3,000 students didn’t get into a school on their list (which now included up to 12 choices). This system is stable, meaning that after it has finished all students have been allocated their best possible choice, and all schools have received their best possible picks.

Why is any of this relevant for Africa?

Just 43 percent of students in sub-Saharan Africa are enrolled in secondary school (using the gross enrollment ratio), but that is changing fast. Getting more children into secondary school is a high priority for many governments, and achieving universal access by 2030 is one of the Sustainable Development Goals. And this expansion in secondary is already happening.

Centralized secondary school admissions are common in Africa. Most countries have a national standardized exam that all students sit for at the end of primary school, which determines who gets to go to secondary school at all and to which school. The students with the best test scores typically get into the best schools. But systems are inefficient, much like the New York City system was in 2003. For example last year in Rwanda, 7,000 students complained to the education board about their assignment. In Uganda, thousands of headteachers from across the country have traditionally come together to a large hall in Kampala to select their students from paper forms. World Bank economist Kehinde Ajayi has documented a host of weaknesses in Ghana, including that low-income students underestimate their own ability and apply to worse schools than they could get into. Some simple tweaks to the existing allocation system, such as how many schools children list on their form, could improve outcomes.

At the tertiary level, centralised application and assignment systems have been steadily growing over the past 50 years and are now used by 46 countries around the world (shown in the map below), according to a new paper by Princeton economist Christopher Neilson.

Neilson, “The Rise of Centralized Choice and Assignment Mechanisms in Education Markets around the World.”

Spreading the word

Dorosin later set up the Institute for Innovation in Public School Choice to help school systems in the US understand and adopt their own modern algorithms. The Institute has worked in New Orleans, Denver, and Washington, DC. Internationally, Christopher Neilson has advised governments in Chile and Peru to design and implement similar systems. But overall the global education community has failed to disseminate this now decades-old technology. In a scathing criticism of the global education architecture, Nicholas Burnett (Chair of the Board of UNESCO’s IIEP) wrote recently, “It is astonishing both how little we know about what works in education and how poorly we disseminate what we do know ... if the situation is bad regarding generating knowledge, it is even worse regarding promoting innovation in education.” The lack of any real effort from any multilateral agency to disseminate modern school choice algorithms seem like a pretty clear illustration of this failure.

Which teachers teach where?

The initial idea for the New York school choice algorithm came from Al Roth’s prior work improving the allocation of trainee doctors to hospitals. Another potential application could be in improving teacher allocation. Many countries struggle to incentivise teachers to take remote rural postings. For example, Sonja Fagernas and Panu Pelkonnen show systematic differences in preferences of Indian teachers, with urban women being much less willing to take remote jobs than men. A system which encouraged teachers to reveal their true preferences about location could increase efficiency in this domain. The Government of Punjab is currently attempting just this—building a new app to handle requests from teachers for transfers to new schools.   

The bottom line: Not a big win, but an easy one

As Roth writes in his book Who Gets What—And Why, “school choice systems, even if they are efficient, simple, and safe, don’t solve the problems created by not having enough good schools. They are at best a band-aid applied to those persistent problems, by letting existing schools be used more efficiently.” Neither do school choice systems fix the equity issue. New York City schools are some of the most segregated in the US. And in some cases selective, elite, schools aren’t actually significantly better than less prestigious schools, as found in Kenya by Adrienne Lucas and Isaac Mbiti (expect more on this in a follow-up blog).

So if school choice only helps a little, is it a distraction from what really matters? That is one argument. But we know that school improvement is difficult and expensive. Where (relatively) quick, cheap, and easy wins exist, we should grasp them. It may even be that enough marginal gains added up can lead to substantive change. Better school choice won’t create better schools, but it can save time for everyone involved and make a system fairer that is critical for the life chances of millions. That’s a choice worth making.

This post is the first in a two-part series looking at secondary schools in developing countries. Look out for the second part, which will go into more detail on elite, selective government schools. Thanks to Justin Sandefur and Susannah Hares for comments on this post.


CGD blog posts reflect the views of the authors, drawing on prior research and experience in their areas of expertise. CGD is a nonpartisan, independent organization and does not take institutional positions.