Complexity

Foundations

It is said that Thomas Schelling proposed the first modern complex systems model in the social sciences. In research in the 1960s into the phenomenon of racial segregation in housing, he modeled a process where people (agents) decide where to live based on the racial mix of their neighborhood. Schelling randomly placed nickels and dimes on a checkerboard, with each coin resting on only one square and with fewer coins than available squares. He then randomly picked one of the coins, say a dime, and examined its neighborhood, meaning the squares that bordered the square on which the dime stood. There will be eight squares in the neighborhood (unless it rested on the edge of the board, which we shall ignore for this example). If the neighborhood consisted of fewer than 5 nickels, Schelling did nothing. Otherwise, he moved the dime to another place on the board where there were fewer than 5 nickels in the neighborhood. He then iteratively moved through each coin and either moved it somewhere else or kept it in place, using the 5/8ths rule for tolerance of neighbors of the other type. Schelling argued that 5/8ths was a pretty tolerant threshold, in that his coins (agents) would stay put even if half of their neighborhood consisted of the other type. He showed that even with this relatively tolerant threshold, the dimes and nickels segregated into homogeneous zones on the checkerboard. He then started over and examined what happened with other [Page 365]kinds of thresholds (1/2, 3/4, etc.) and how quickly, if at all, the agents segregated themselves incrementally.

Note what happens in the dynamics of the Schelling model. When a coin is moved to another area of the checkerboard, it changes its own neighborhood and the neighborhood to which it moves. A single move alters the diversity of the neighborhoods of multiple agents and thus potentially alters the decisions of multiple other agents. This is an example of the kind of feedback that occurs in complex systems. Further, it is difficult to predict simply from the decision rule of the agents how the system will behave. Schelling confessed that he could not predict in advance when and if the system would segregate into neighborhoods of all dimes and all nickels.

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