Posted October 28, 2008 By Presh Talwalkar. Read about me , or email me .



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"All will be well if you use your mind for your decisions, and mind only your decisions." Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon. .

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[update: welcome readers from The Club for Growth]

Update: Vi Hart and Nicky Case have created an interactive animation that explains the model using triangles and squares. Check it out: parable of the polygons.

Fidel Castro says America is “profoundly racist.” What do you think?

His statement made me think about segregation. I thought about racially divided neighborhoods in big cities. I thought about the “racial cliques” I observed among peers at Stanford. I thought about how few CEOs are of color. Is Castro right-do these things mean America is deeply racist?

The surprising answer is no. There is an alternate and perhaps more convincing explanation of why segregation happens.

During the 1960s the economist Thomas Schelling researched segregation and racial preferences. He suspected segregation was the result of a subtle interaction and he created a model to investigate. Not only did the model confirm his suspicion but it showed something very surprising: even very small preferences among otherwise civic individuals could lead to segregation.

I’ll cover the model and then explain its implications which affect everything from housing sales to company hiring policies.

Agent based models

Schelling analyzed racism by a technique called “agent based modeling.” It’s a computational idea that’s now being used to model everything from traffic flows to the spread of a disease.

The focus of such models is on creating autonomous “agents” who act according to relatively simple rules. Some rules of interaction might involve learning or randomness. The interesting part of these models is seeing how these simple agent rules can create complex global patterns or emergent behavior. (In Schelling’s language, the agents have “micro-motives” and the emergent pattern is a “macro-behavior”).

The Schelling Segregation Model (a.k.a. Schelling Tipping Model)

The model is easy to create if you have common household items. Here is how it is set up:

The game takes place on a checkerboard, which represents a city. The checkerboard is filled with dimes and nickels representing two different types of agents. The different types of agents can be thought of a different races, genders, etc. Each agent evaluates its current position based on a “happiness rule,” which depends on the adjacent squares. Unhappy agents are allowed to switch places with each other (there are various ways one can model this). The game continues until agents are happy, and this represents the equilibrium outcome.

The outcome primarily depends on the happiness rule. One example of a happiness rule would be “I want all my neighbors to be the same race.” Not surprisingly this rule leads to an outcome of complete segregation.

The interesting part is playing around with other rules. Schelling found even small preferences could result in complete segregation.

Try playing yourself

Schelling played the game during the 1960s and 1970s with nickels and dimes on a physical board. Now we can simulate them on computer. I highly encourage you to try a few simulations to get the feel for how things work.

Update: It seems NetLogo applets are not working. Vi Hart and Nicky Case have created an interactive animation that explains the model using triangles and squares. Check it out: parable of the polygons

NetLogo has a good model here with instructions. Here’s a link directly to the simulation (requires Java).

Here’s a simulation I ran with 2500 agents and a happiness rule of wanting 30 percent of neighbors to be of the same color (red or green). This is a mild preference of race.

The results are absolutely stunning-there appear to be neighborhoods that are completely segregated! Although each run is different because the initial setting is random, these results are typical. Try it for yourself.

What do these results mean in practical terms? I’ll rephrase an explanation from The Atlantic. A 30 percent happiness rule would mean the following:

[Notice that] these “people” would all be perfectly happy in an integrated neighborhood, half red, half [green]. If they were real, they might well swear that they valued diversity. The realization that their individual preferences lead to a collective outcome indistinguishable from thoroughgoing racism might surprise them no less than it surprised me and, many years ago, Thomas Schelling. (source)

Four implications of the model



The Schelling model is not perfect but it can give us good insight into racial and other segregation. Here are a few insights:

1. Don’t assume groups are deeply racist

I would imagine most people are not racist but have small preferences. Schelling’s model illustrates how these individual preferences can aggregate into complete segregation. It’s impossible to assign blame to any particular person, and it is not necessary that group members are deeply racist (though that is a possibility).

2. If you can, get it right the first time

In the Schelling model, initial conditions matter. If some neighborhood starts highly segregated, natural interaction would keep it that way.

The implication is that if you want diversity, you should try to get it right from the start. This applies for races as well as for other categories. For instance, teachers that want genders to interact in class should not leave it to chance. They should assign alternate boy-girl seating from the start. Who knows, the students might even like it.

3. Intervention may be necessary to maintain diversity

How can a neighborhood maintain integration? The issue is the integration may not be a stable: if one or a few families of one race moved out randomly, there might be a flight that could lead to complete segregation. This is the concept of “tipping.”

The book Thinking Strategically explains one city’s effort to maintain diversity:

The racially integrated Chicago suburb of Oak Park provides an ingenious example of policies that work. It uses two tools: first the town bans the use of “For Sale” signs in front yards, and secondly, the town offers insurance that guarantees homeowners that they will not lose the value of their house and property because of a change in the racial mix. (page 244)

Such policies seem to work but they have been criticized. Some point out the ban on “For Sale” signs is unconstitutional. Here is another good article (pdf) that analyzed and questions the practices.

4. Intervention may be needed to “fix” things

What should you do when a group has become segregated? In the NFL, head coaches are predominantly white and there was an investigation about why. The Schelling model implies it might not be deep racism but the consequence of mild racism.

The NFL changed its free-for-all hiring practices and adopted the Rooney rule. This rule stipulates that teams must interview at least one minority applicant when filling a head coaching position. This intervention has created much controversy and some question its effectiveness. But one thing is evident: since the rule, more minority coaches have been hired.

What is your take on segregation in America?