Schellings Model

Our demo of generative social science is based on a model of how two or more different groups become extremely segregated from one another even though they have very mild preferences to live amongst their own kind. The model was first worked out using pencil and paper in 1969 by the economist Thomas Schelling. It has become the leitmotiv of ABM and is the classic example of ‘emergence’.

It works as follows. Imagine a landscape of locations – arranged as a square grid of cells where each cell is occupied by one or other of two distinct types of object or group or individual, with some cells empty. The occupied cells may be classified black or white, red or green, zero or one. Imagine too that each object has a very mild preference to exist in a location where there are at least the same or more objects of the same type located in the cells which form the 8 cell neighbourhood around the object in question. If an object has more neighbours around it than it prefers, in this case 5 or more, it will shift its location to any empty cell. It still may not be satisfied with its neighbours but the process can be repeated a second, third time and so on.

If the process is operated synchronously for a few steps, what will happen is that the objects will begin to cluster around their own type and as the process continues, the landscape will ultimately become highly segregated. What is surprising is that with such mild preferences, extreme segregation can take place. Applications of this process are clearly relevant to residential segregation in cities but the generic model is applicable to any kind of binary divide which emerges through time from the adoption of a technology to segregation in a social network. The models can easily be generalised to more than two types of object.

Here is what the landscape looks like after the objects are first distributed amongst the cells randomly(figure on the left) and the process is operated for 20 times periods until a ‘steady state’ is generated (figure on the right).

You can try the model by running the following Netlogo program which is embedded in this web page. You may need Java to run the program but you machine should prompt you.

Click to Run Model

There are many, many examples of Schelling’s model on the web as much because it is so simple a demonstration of a surprising property in a system which is unexpected. We have provide a link here to Leigh Tesfatsion pages of demos where you can read more about the model.