Blog: Mathematical Model Shows How Groups Split Into Factions

Mathematical Model Shows How Groups Split Into Factions
Cornell Chronicle (01/03/11) Bill Steele

A mathematical model of how social networks evolve into opposing factions under strain has been developed by Cornell researchers. Earlier models of structural balance demonstrate that under suitable conditions, a group conflict will facilitate a split into just two factions, while the new model indicates how friendships and rivalries change over time and who ends up on each side. The model consists of a simple differential equation applied to a grid of numbers that can stand for relationships between persons, countries, or corporations. Cornell's Seth Marvel says people may forge alliances based on shared values, or may consider the social effects of allying with a specific individual. "The model shows that the latter is sufficient to divide a group into two factions," Marvel says. The model traces the division of groups to unbalanced relationship triangles that trigger changes that spread throughout the entire network. All too frequently the final state is comprised of two factions, each with all favorable links among themselves and all negative connections with members of the opposing faction. The model shows that if the average strength of ties across the entire system is positive, then it evolves into a single, all-positive network.

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