With its decision in Brown vs. Board of Education, the Supreme Court ended systemic racial segregation in public education. Now, sixty years later, courts have released hundreds of school districts from enforced integration—with the result being an increase in “resegregation” of public schools.

Numerous media outlets have recently picked up on a story by the investigative journalism nonprofit ProPublica about schools in Tuscaloosa, Alabama. According to the report:

In recent years, a new term, apartheid schools—meaning schools whose white population is 1 percent or less, schools like Central—has entered the scholarly lexicon. While most of these schools are in the Northeast and Midwest, some 12 percent of black students in the South and nearly a quarter in Alabama now attend such schools—a figure likely to rise as court oversight continues to wane. In 1972, due to strong federal enforcement, only about 25 percent of black students in the South attended intensely segregated schools in which at least nine out of 10 students were racial minorities. In districts released from desegregation orders between 1990 and 2011, 53 percent of black students now attend such schools, according to an analysis by ProPublica.

Why has this resegregation occurred? A forty-year-old experiment on racial diversity might just hold the answer.

In the 1960’s, the Harvard economics professor Thomas C. Schelling devised a simple model to test his intuitions about segregated neighborhoods. Shelling found that most neighborhoods in America were mostly or prised of black or white families. Only a handful of neighborhoods where found where neither race made up more than three fourths of the total. Racism seemed to be the obvious culprit for the lack of diversity, but Schelling thought something else might be involved.

His model showed how even tolerant people can behave in ways that can lead to segregated neighborhoods. It consisted of a checkerboard with 64 squares representing places where people can live. Two types of actors (representing, for example, whites and blacks) are placed at random among the squares, with no more than one per square. Schelling provided a “rule” that an actor will be content if more than one-third of its immediate neighbors (those in adjacent squares) are of the same type as itself. For example, if all the eight adjacent squares were occupied, then the actor is content if at least three of them are the same type itself as itself. If an actor is content, it stays put. If it is not content it moves. In Schelling’s original model, it would move to one of the nearest squares where it would be content.

Not surprisingly, Schelling found that the board quickly evolved into a strongly segregated pattern if the agents’ “happiness rules” were specified so that segregation was heavily favored. What was unexpected, though, was that initially integrated boards tipped into full segregation even if the agents’ happiness rules expressed only a mild preference for having neighbors of their own type.

Figure 1 on the right shows four stages in a simulation run by The Atlantic in 2002. As they note in their article:

Schelling’s model implied that even the simplest of societies could produce es that were simultaneously orderly and unintended: es that were in no sense accidental, but also in no sense deliberate. “The interplay of individual choices, where unorganized segregation is concerned, is plex system with collective results that bear no close relation to the individual intent,” he wrote in 1969. In other words, even in this extremely crude little world, knowing individuals’ intent does not allow you to foresee the social e, and knowing the social e does not give you an accurate picture of individuals’ intent.

If Schelling’s model is correct, we should find similar racial groups clustered together in neighborhoods. Now take a look these maps of 21 highly segregated cities in America. Schelling’s model predicts almost perfectly the results we find.

You don’t need Jim Crow laws, or even racial animus, to cause racial segregation in housing. All it takes is for people to have a “mild preference” for neighbors who share their race or ethnicity. In the majority of school districts in America, children are sent to local schools based on their address. When neighborhoods are racially homogenous, we should expect to find the same lack of diversity in the schools.

Assuming it’s a problem, what’s the solution to this “resegregation” of public education? One answer may be to support school choice.

Attitudes toward racial diversity (whether for or against) doesn’t appear to be an important factor in parents choosing private schooling for their kids. Likewise, it is unlikely to be a significant factor in the decision to use a voucher program to send a child to another public school.

When parents are allowed to send their children to the school of their choice, they are more likely to base their decision on factors that are related to educational concerns. Because this reasoning is shared by parents of all races, the effect can be a mitigation of racial segregation. For example, a study on Louisiana schools found that vouchers programs improved racial integration in public schools in 34 districts under desegregation orders.

“Micromotives,” as Schelling calls them, can lead to strikingly peculiar “macrobehavior.” The micromotive of seeking a better education for one’s child may just have the macrobehavior of improving racial diversity in public schools—but only if parents are given the freedom to choose their child’s school.