Game theory and racism: the Schelling Segregation Model

[update: welcome readers from The Club for Growth]

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:

  1. The game takes place on a checkerboard, which represents a city.
  2. The checkerboard is filled with dimes and nickels representing two different types of agents.
  3. The different types of agents can be thought of a different races, genders, etc.
  4. Each agent evaluates its current position based on a “happiness rule,” which depends on the adjacent squares.
  5. Unhappy agents are allowed to switch places with each other (there are various ways one can model this).
  6. 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.

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?



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  • Glen Pearson

    As usual, a very intersting article. Thanks.

    America – as does any country if you look at it – has had its share of race problems, but I have long maintained that America is the least racist country that has ever existed. What other country in the world allows you to become a citizen, with all the same rights and privileges as natural born citizens, as easily as the U.S.?

    All people tend to associate themselves with groups, some inherent (skin color, heritage) and some by choice (sports affiliations, school choice, unions, fraternal organizations). Groups with differing goals tend to become antagonistic towards each other. It’s human nature, but one that can be controlled with thought and discipline.

    The work you presented shows the results of even small preferences. Can moderate to strong preferences ever be eliminated?

    The U.S. has come a long way from institutional racism, and still has some way to go towards eradicating all racist actions. If such a goal is even possible. Segregation is widely viewed as a negative, but where does one draw the line between unforced segregation and free association?

    I’m sure that some will take exception to my statement that the U.S. is the least racist country that ever existed, but that’s okay. The U.S. allows freedom of speech, too.

  • Paul

    I have noticed that people often divide socially amongst very trivial differences. It might be interesting to attempt to quantify these differences, but the parameters change, depending on the culture / zeitgeist. In times of war, people unite much easier, and overlook glaring differences for the “greater good”. In times of peace, the Macy’s shopper’s might easily snub the Target shoppers. Even family members may have stopped talking to each other for irritating social situations that occurred decades in the past.

    Religious wars are also interesting examples. Catholic /Protestant, Sunni/ Shite, etc. These can be confusing because its not clear if the differences are in any way worthwhile.

  • http://www.mawsoft.com/blog RohoMech

    Glen Pearson

    Curious, so you’re measuring racism in terms of first how the U.S. has laws against discrimination coupled with the social freedoms people have.

    So, compared to certain European countries where something like “hate speech” is not allowed, you’d argue the U.S. appears to be more permissive.

    I’m curious about your measure because, while I would agree that the U.S. is doing quite well in terms of squashing racism, I often wonder about subversive forms of racism, things like voluntary segregation or the “Bradley effect”, where people publicly try to appear unbiased but then in private actions do make a decision based off race.

    However, both those areas are hard to measure, and because of that I’d argue they’d be hard to prevent…

  • alfanje

    It seems to me that nature has designed the human being so that it tends to create groups that are antagonistic to other groups, and that we prefer the company of our alike. The color of our skin is just too evident, but indeed this also applies to which groups of colleagues have lunch together or to class or gender segregation.

    In general it cannot be said that the USA is a racist country, even if there is a racism problem as anywhere else. Many times other phenomena overlap or are mistakenly assumed to be racism (for instance, cultural differences or income inequality).

  • http://mgccl.com Mgccl

    What other country in the world allows you to become a citizen, with all the same rights and privileges as natural born citizens, as easily as the U.S.?

    Australia, thank you very much.

  • Mahesh

    Gary Becker, the 1992 Nobel Laureate in Economics wrote a book called “The economics of Discrimination” and he explained some of the economic effects when people express “preferences”.

    A link to an excerpt from the book can be found here.

    http://hispanicpundit.com/2005/08/30/gary-becker-on-affirmative-action/

    There is a basic human need of belonging which drives this behavior and it is just above survival. When survival is not an issue, preferences come into play.

    For e.g., a preference to pay a premium buy a house in a neighborhood where you believe people of your calling lives might not make sense from an economic rational man theory, but it is a premium one decides to pay for expressing that privilege.

    Another way of looking it is to take a look at Maslow’s hierarchy of needs. http://en.wikipedia.org/wiki/Hierarchy_of_needs

    Belonging is above survival and safety, but bbelow esteem and self actualization. As you move higher up the pyramid, belonging is not an issue.

    The US is definitely a meritocracy for the most part, but nobody is asking for perfection.

  • Glen Pearson

    Mgcci, my apologies. I looked it up and found that Australia (as far as I could determine) actually has a slightly easier immigration process than the U.S. As a fellow country founded by immigrants, it makes sense that Australia would also be liberal in that regards. I assume you are Australian, so are naturalized immigrants considered as Australian as people born there? That’s not a rhetorical question, I honestly don’t know. I have been to many countries, but not Australia (yet). It’s a shame that both our countries set limits on the number of immigrants they will accept.

    Rohomech, I wasn’t using a pure metric, merely making general statements and supporting them with selective evidence. It is my experience that both the U.S. and most European countries serve as great examplars of the Bradley Effect, though. Officially, the public supports outlawing “hate speech” and discrimination, but still have trouble dealing with any sizable minority or quelling racism in their populace. I will cherry pick a few examples with complete awareness that the same could be done about the U.S. English soccer fans shouting “monkey” and throwing bananas at opposing black players, unrest with and discrimination against Pakistanis in England, Muslims in France, Turks in Germany, Jews in Germany, anyone vs. anyone else in the former Yugoslavia are a few notable ones.

    It’s not that the U.S. is better in outlawing discrimination, merely about equal to most European countries. My point was that the “Melting Pot” mentality is what seperates the U.S. (and Canada and Australia!) from most other countries.

    There has been a lot of media coverage of European attitudes towards the U.S. election. The reports seem to be uniformly that the Europeans interviewed support Obama (partly based on race and partly based on hatred of Bush), but are shocked that he could be doing well in the “racist U.S.” (their words). A few brave interviewers then asked about the possibility of a national leader being elected from one of their countries larger minorities. Those asked did not indicate that the chances were good. Again, an indicator, but not a true measure.

    As I acknowledged, examples of poor race relations still exist in the U.S., too. Alfanje said it well that skin color is just too obvious a seperator for a species that likes to segregate itself into groups – and then get antagonistic against dissimilar groups. I don’t think that racism can ever be eliminated from every person everywhere. We can only publically condemn it and protect against discrimination. However, as the cited study indicates, voluntary segregation may not be related to true racism at all.

  • Kent Pearson

    You left out a fifth implication of the model.

    5. The model does not provide good insight into racial and other segregation.

    Yes the model does produce segregation. And yes human society often/usually produces segregation. But it is my belief that the method of segregation is fundamentally different and only partial based on visual census of neighbors’ characteristics (racial or otherwise).

    It has been my experience that in urban and suburban societies one may rarely see ones neighbors. At my several homes and apartments I have never seen all my neighbors. And this is especially true for decision making preceeding moving into a new home or apartment.

    So I would recommend that the model include some random factor for how many of the neighboring pieces each piece gets to see.

    Also, as far as I could tell the model did not include any economic factor for the cost of moving. As we all know, moving requires considerable time, effort and money.

    Including cost factors in the model, I believe would inhibit the segregation of pieces from their random starting positions.

    The author acknowledges that random starting position is non-real world state, so I won’t criticise the model for that.

    My guess is that social scientists have already thought of these points and either incorporated them into newer models (which would be interesting to see) or abandoned this model entirely. I’m not a social scientist, so I’m in no position to quote or comment on the state of the art of segregation modeling.

    To me this is a Rorschach computer model. It says more about us and the framing of the question that we see human segregation in the reshuffling of pieces based on these rules.
    —
    PS: yes related.

  • http://linuxdatabases.info/ Christopher Browne

    In the not-entirely-dissimilar issue of sexism, orchestras have evidently found that requiring that auditions be done with screens to hide the musicians from the eyes of the judges has fundamentally shifted the balance, there…

    http://www.princeton.edu/pr/pwb/01/0212/7b.shtml

    There are exceptions (e.g. – Abbie Conant, once of the Munich Philharmonic, who was *very* shabbily treated when the “screen” allowed her to “win” an audition), but I suspect that orchestras could very readily bias to “gender segregation” based on very mild sexist tendancies.

    Blind auditions have apparently been highly significant in improving fairness. I’m not sure what analagous mechanisms could be used to help address mild racism. (I don’t think that’s relevant when racism is deeply entrenched; in such cases, there’s likely a LOT of hatred, and you essentially get to choose between mighty intrusive remedies OR waiting for hateful people to be overcome by old age…)

  • http://hoenir.himinbi.org Will Holcomb

    To come up with a computer model that can create segregation based on mild preferences does not necessarily mean that the segregation in the US isn’t based on a more entrenched racism.

    One in three black men black men will be in prison at some point in their lives. One in ten white men will be. (http://www.pewcenteronthestates.org/report_detail.aspx?id=35904) This suggests strongly that there is more than a simple same-race neighbor preference at work.

  • http://www.mindyourdecisions.com/blog/ Presh Talwalkar

    Thanks all for the insightful and intelligent comments. Racism is an emotional subject, so its admirable that you guys kept the discussion classy.

    Glen Pearson:

    I have long maintained that America is the least racist country that has ever existed

    I don’t know if I completely agree but this is a useful perspective. Many of my friends tell me other countries are much more outwardly racist. Then they have a good laugh about how Americans are “politically correct” and people take things too seriously…

    You’re right to ask if complete integration is possible. People will always have other likings that might associate with race. How far should we force integration–some say Oak Park has gone too far.

    Paul:
    Great examples. Schelling’s model can be about any two types of people–genders, religions, etc.

    Alfanje:
    The book “Nonzero” touches on this subject of how antagonistic activities seemed to have helped us grow as societies. We developed weapons and organized under laws. But I wonder if we have done more good than harm in all of these efforts.

    Mahesh:
    Thanks for the reference to Becker. I think he makes an interesting point about how poeple view affirmative action:

    However, now, minority doctors and other professionals are greeted suspiciously by many patients and customers who fear they got where they are only because they were subject to lower standards.

    This is a sad state of affairs.

    Kent Pearson:

    It has been my experience that in urban and suburban societies one may rarely see ones neighbors. At my several homes and apartments I have never seen all my neighbors. And this is especially true for decision making preceeding moving into a new home or apartment.

    You’re right that Schelling’s model overemphasizes “seeing” one’s neighbor. But I would guess many people still make housing decisions on the racial makeup of a neighborhood. When you add in transaction costs, this makes it much harder for a segregated neighborhood to become integrated.

    And yes, there are probably more sophisticated models but I bet each of them suffers from a fatal flaw as well. There is something to be said for the simplicity in Schelling’s model, though yes it is unrealistic.

    PS–both you Pearson’s have quite interesting comments!

    Christopher Browne:
    This is an excellent related point! I read about the sexism issue in Gladwell’s book “Blink” and was amazed the blind audition made such a difference.

    Will Holcomb:
    Nice counter. The disparity in incarceration is troubling. I would like to know more about it since this is a big topic in racism.

  • Ibrahim

    Very nice piece, thank you.

    I wonder what the outcome would be like, if people actually had a preference for a diverse mix. As in, the agents dont want to be surrounded by 100% people of their own background.

    Would a theoretical preference for diversity end up with a non-segregated makeup?

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  • http://www.mindyourdecisions.com/blog/ Presh Talwalkar

    Ibrahim:
    Good point. But the interesting part is the model does look at cases where people would be happy with a mix! A preference of 30 percent similar means someone is happy with being in the minority, and would be happy with a 50/50 mix, they just don’t and don’t want to be “alone.” This nevertheless ends up in segregation, and it would seem to mimic real life beliefs.

    I suspect if one put in a preference only for a mix (and could model that precisely), then the model would result in a diverse outcome. That sort of thinking might be similar to a school that places strict quotas on student admissions–it is an expected but forced outcome.

  • Joon

    The intelligence of your readers has skyrocketed. I no longer feel like I have anything valuable to contribute. Very impressed.

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  • shiv

    A game that allows he existence of racism AND causes segregation as a stable strategy is called “Harm Everyone”. It could also fall into he pattern of the game “chicken”

    You can find a description of these games on the Wiki page:
    http://en.wikipedia.org/wiki/Evolutionarily_stable_strategy

    Segregation is a simple evolutionary fallout of a game in which the existence of racism results in a lower score for a mixed interaction and a higher score for interaction with a person of the same color.

    I believe that this same type of game caused segregation of caste in Indian society and is equally applicable to segregation of Muslims into pockets of Muslim dominated areas from which non Muslims are squeezed out.

  • http://www.mindyourdecisions.com/blog/ Presh Talwalkar

    Good connection with India…segregation is a really interesting phenomenon to study. Thanks for the comment.

  • http://www.positiveparty.blogspot.com andrew wainwright

    The big thing that a lot of people leave out in this issue is that of metaphysics. People will talk of sex and race, but not of materialism and mentalism. Put simply materialists believe mind is a product of matter and mentalists believe matter is a product of mind.

    those of a mentalistic outlook generally pay little attention to physical appearance, fashion, clothing , gait , voice (excluding emotional tone), accent etc. words and symbols are far more important. the NT sums this up best : “In the beginning was the word” – a word is a unit of information

    Crucial to this is the difference between similar and compatable.

    A lot of the strongest marriages and friendships are not actually between the genetically , circumstantially or intellectually similar. It is between “saw partners” – the phrase comes from the timber industry and means a person who will “push” when the other “pulls”

    Ironically, genetics tends to support this very much – the more diverse the individuals of the same species (and there is only one human species) the healthier the offspring is likely to be, as a faulty gene must be carried by both parents in most cases to be passed on..

    Something worth mentioning is the issue of IQ. IQ does not necessarily measure “spritual” intelligence. Whilst I’m quite academic myself I much prefered comprehensive to selective eduction as I found the comprehensive group to be more concerned about friendship rather than objects and looks. Since the 11-plus , A-Levels (uk quals) etc are essentially IQ tests , you would think that those scoring higher would be more “intelligent”. I have not found this to be the case- more they are better able to cope with petty social mores and rules – sadly essential for manipulative behaviour – but not actually “smarter”.

    An interesting difference between the mentalistic and materialistic outlook is the concept of love and fear. Materialists are more likely to be influenced by threats or bribes than mentalists, on the ground that long term this is futile – why do materialists have no trouble with newtons law of reaction but not karma which is the identical principle applied to human nature. And happiness is not actually about confomation but about being true to yourself. The materialist elite sadly don’t like this because – they can’t control us!!!

    It’s not a left/right thing either. Consider competion. It could be argued that the scores in any sport are actually completely irrelavent. Why do we compete? To learn , to raise human standards , to have fun , to make friends – this is win / win competition , whereas the “dog eat dog” variety is lose / lose

    Let Love Lead The Way – and love is the natural attraction between opposites!!

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