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Exercise 3. Extending the Social Influence Model.

Exercise 3. Extending the Social Influence Model. To gain practice in extending an existing model, here is an exercise based on the model of social influence described in Chapter 7. The model is simple enough that even adding an extension keeps it quite manageable. The purpose of this exercise is to implement a particular extension of the model to see what insights can be gleaned.

A dozen suggestions are briefly outlined in the section of Chapter 7 on "Extensions of the Model." Here are some more details about two of these possibilities.

a. Early Geographic Differences. The initial values of cultural features are assigned at random in the basic model. A wide variety of interesting experiments could be conducted by having some or all of the features given particular values. For example, suppose one wanted to study the effects of the seemingly universal phenomena that "things are different in the south." An easy way to do this would be to give one or two of the cultural features one value in the northern sites, and a different value in the southern sites. Would regions tend to form based on these small initial differences? If so would the eventual boundary between the regions closely correspond to the initial line between the north and the south? Another example of an interesting experiment would be to see how easy or hard it is for an initial advantage in numbers to take over the entire space. A simple way to study this is by giving a slight bias in the original assignment of values to features throughout the space, and seeing how much bias it takes to overcome the tendency to get swamped by random variations, and eventually to dominate the entire space.

b. Cultural Attractiveness. Some cultural features might be favored in the adoption process over others. For example, Arabic numbers are more likely to be adopted by people using Roman numerals than the other way around. This differential attractiveness of cultural features might be due to superior technology (as in this case of number systems), or it might be due to seemingly arbitrary preferences. One way to model this process would be to favor higher values of a given cultural feature over lower values. Presumably, features that are culturally attractive would tend to drive out less attractive features. Just how attractive does a feature have to be to dominate? Does the process of differential attractiveness lead to larger (and thus fewer) regions?

Incidentally, I do not have good answers to the questions raised by these two suggested extensions or any of the others mentioned in Chapter 7. These are open research topics.

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University of Michigan Center for the Study of Complex Systems
Revised November 4, 1996.