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A Model of Chaos

Researchers develop a mathematical model that could help us make sense of how conflicts get messy.
January 27, 2011

It’s a familiar situation: A couple goes through a bitter breakup and their mutual friends have to choose sides. Sociologists have studied this type of situation, but in recent years, some researchers have looked at ways to model it mathematically.

That’s because such models could prove useful in many ways—from helping predict key players in a political or business conflict to refining the way online social networks display information.

In a paper published recently in the Proceedings of the National Academy of Sciences, researchers from Cornell University describe a model for predicting how a social group will break apart during a turbulent split. Jon Kleinberg, a professor of computer science at Cornell, who led the work, says researchers have traditionally focused on predicting how a group will look once the conflict has shaken out. He says this work proposes a way of looking at the process of the split itself.

Kleinberg notes that his group’s model doesn’t apply to every situation. Instead, it portrays extremely polarizing conflicts. A sociological theory called “structural balance” describes the decisions that group members are forced to make when a group splits completely apart. The model best fits ” situations where the logic starts to become, ‘If you’re not with me, you’re against me,’” Kleinberg says.

The researchers tested their model on data documenting the split of a university karate club, as well as to the division between the Axis and the Allies in World War II. They modeled the stages of the karate club’s split correctly, except for one error. For World War II, the model correctly predicted the side chosen by every country except Denmark and Portugal.

Kleinberg says the models have not been thoroughly tested on other situations, but it’s easy to watch a simulation and imagine the interpersonal relationships playing out. For example, in one model he ran, one side coalesced quickly, while the other group seemed to form only after each of its members was isolated from the first group.

Sidney Redner, a professor of physics at Boston University who has also worked on modeling how groups split apart, says the researchers’ work is very sophisticated, but there’s a long way to go before we have a clean understanding of the process. He adds that it’s notoriously hard to apply models like this to the real world. For example, he says, efforts to use theories like this to predict violence between Los Angeles street gangs have not been successful so far.

Others are even more skeptical. Stanley Wasserman, a professor of statistics, psychology, and sociology at Indiana University, says the model is too simplistic to lead to much insight about human behavior. He’s also skeptical about whether any model based purely on abstract mathematical principles—like this one—can accurately portray how people behave. He says predictive models built from experiential data are more reliable.

“The impact [of this work] depends on the general level of acceptance of math in the social sciences by sociologists,” says Krzysztof Kulakowski, a professor of physics and applied computer science at Akademia Gorniczo-Hutnicza University of Science and Technology. Kulakowski has also worked on the problem.

Kleinberg admits that it isn’t certain how mathematical models could prove practical. But he thinks the work suggests some interesting directions. For example, he notes that the new model could help identify key players in a worsening conflict. There were moments during the conflicts the researchers modeled when social subgroups floated between the two main rivals; certain people in these groups could be pivotal. A model like this might call attention to those people in a real conflict and give negotiators a chance to influence them.

Models like the one developed at Cornell could also help improve online social networks. Kleinberg notes that sometimes peoples’ positive or negative sentiments—when rating a product, for example—reflect their social connections rather than their genuine opinions. Social networks could use a model like this to catch this effect and test methods of filtering it out. Social networks might also use a model like this to be more sensitive after members of a group have fallen out with each other. In other words, they might finally know not to recommend that you become friends with your hostile ex-partner’s sister.

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