# Readings in Game Theory and Political Behavior

## Excerpt

The role of mathematics in any study is to provide a language by means of which investigation of phenomena can be carried further than would be possible without the introduction of symbols. Mathematical formulations enable us to deduce the forms which action will take in highly complex social systems once some initial theory of action of the individual, or aggregates of individuals, has been postulated.

The Nature of Mathematical Analysis

A mathematical analysis of a field of applied science involves the study of properties of systems. For instance, a model to predict the number of automobile fatalities on a road network distinguishes certain features which are relevant and worth measuring. These may be the variation of the individual's driving ability with his age, physical condition, fatigue, and the amount of alcohol he has consumed. The type and age of the automobile, road conditions, and the type of road may be introduced as the other major factors. Given this information, it is possible (if the initial laws were correct) to construct models for any road system with any population make-up and, from these, to predict the number of fatalities. Without the use of mathematics we could not carry through this analysis without running into considerable difficulty. The verbal discussion of, say, the effect of a change in the distribution of different automobiles would become so complex as to be almost unmanageable. Once the problem has been mathematically formulated, little trouble will be encountered in recomputing for the altered conditions.

We often hear that no two human beings are alike, and, hence, mathematical methods cannot be applied to the social sciences. In the example above, classes of individuals were sufficiently alike in certain aspects which were of interest to permit us to construct a useful model of action. It may also be possible to construct models of mob action and more complicated political phenomena if we are in a position to make statements about the major features governing such behavior.

In some situations we are at the stage where the validity of a model can be verified empirically. Thus, we may examine traffic-death forecasts, forecasts for consumer demand, and election forecasts. If there is little correlation between our predictions and the events, we are in a position to reject our model . . .

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