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New Swiss algorithm to desegregate schools, one block at a time

Two researchers from Zurich University created an algorithm that helps desegregate schools by slightly changing the boundaries of each school’s catchment area.

Ever since authorities decided to open public schools to children of all backgrounds in the course of the 20th century, elite families regrouped in select schools. The resulting segregation has been shown in multiple studies to decrease the performance of pupils across the board. In schools where underprivileged pupils are over-represented, the grades of all children, irrespective of background, tend to suffer. But when an elite school enrolls more underprivileged students, their performance improves while the grades of privileged children remains unchanged.

Because everyone has to gain from desegregation, many countries have mandatory programs to make schools more diverse. The most well-known of these, where Black students were “bussed” into white-majority schools in the United States, has been under fire from proponents of segregation to the point that schools in the United States are back to the segregation levels of the 1970s, according to a data analysis by Vox.

Low-key approach

Oliver Dlabac and Adina Amrhein of the Centre for Democracy Studies Aarau at the University of Zurich developed an algorithm that reduces segregation in a much subtler way than “bussing”.

In a pilot study released on November 18, they modeled each block of the city of Zurich according to the proportion of households where German was not spoken at home and where both parents did not attend school beyond compulsory education, a standard measure of an underprivileged background. They called this measure the “concentration index”, or K-index.

They reconstituted the catchment area of 77 of the city’s primary schools, block by block. As was to be expected, they found an almost perfect correlation between the concentration index of a school’s surroundings and that of a school’s catchment area. In other words, school segregation reflected existing segregation.

The algorithm they developed runs like a board game. At each turn, a school swaps up to four blocks with neighboring schools, provided the exchange brings the concentration index of that school closer to the city average without harming a more segregated school. When no school can proceed to such an exchange anymore, the game stops. There are rules: The catchment area of each school must remain contiguous, school capacity must remain constant, children may not have a longer walk to their schools, they may not walk in front of another school on their way and may not cross a large street. (Such parameters are commonly used when designing a school’s catchment area.)

Effective desegregation

After playing 1094 turns, the algorithm proposed new catchment areas for Zürich’s primary schools. At first sight, the map changes little. Indeed, for schools that are in remote areas, swapping blocks while following the rules is impossible. But for others, in denser neighborhoods, the changes are remarkable.

In one of the most segregated schools, Zurlinden, the algorithm could bring the K-index from over 70% to 44% (still 16 percentage points over the city average). Overall, the algorithm could bring the number of pupils attending schools where the K-index was 15 percentage points above or below the city-wide average from 2,600 to 2,100 (from a total of about 7,000 pupils).

The changes might be modest, but are colossal considering that the method used is unobtrusive to schools, children and parents alike. In Zurich, catchment areas are stored in a massive Excel-sheet which is updated every year. Block-swaps between schools from year to year is not uncommon. It would be easy to insert the algorithm in this updating process.

Applicable in most cities

In an e-mail interview to AlgorithmWatch, Mr Dlabac and Ms Amrhein wrote that their algorithm could be adapted to any city, provided the schools’ catchment areas are defined by a territory. “What is needed is a complete footway network of a city ([available freely on] OpenStreetMap), geo-coded data on traffic density and/or estimated safety of street crossing (e.g., according to school instruction by local police), a comprehensive data set on pupils to be assigned, and attributes allowing to characterize street blocks in terms of their contribution to some concentration measure K,” they wrote.

They estimate that the project required 950 person-hours, or about 2.5 months of work for a 2-person team.

While there is no definitive plan to implement the algorithm yet, several school districts in Zurich and in other cities have already expressed interest in the tool, Mr Dlabac wrote. He and Ms Amrhein plan a follow-up project in four other large cities in Switzerland.


Published: November 26, 2019
Category: story
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