Models, Computational/Agent-Based

All models of politics are models in the colloquial sense of being simplified “miniature” artifacts that their creators believe represent some important aspect of the real world. The hope is that manipulating moving parts of the model gives useful intuitions about how the real world works. “Useful” in this sense means something that is a valid inference from the model, nonobvious, and, at least a priori, empirically plausible. Theoretical models are constructed from abstract statements about the real world. Useful general propositions about the real world may be derived analytically by “solving” the model using some form of logical manipulation. For example, if one knows the radius r of a circle and wants to know its area, A, he or she can make use of an ancient analytical result: A = π r2. This result derives from a formal mathematical proof and is always and forever true in a Euclidean space.

The same result could be derived from a well-designed computational experiment:

• 1.
  Scatter p dots at random on a Euclidean plane, in a uniform distribution; every locus on the plane is equally likely to have a dot on it.
• 2.
  Randomly select a locus (x, y) on the plane; draw a circle with radius r centered on (x, y), picking values of x, y, and r at random; count n, the number of scattered dots inside the circle; n is a computed estimate of A, the area of the circle.
• 3.
  Iterate (1) and (2) above m times.

Careful analysis of observations from this experiment would reveal, among other things, that n is completely uncorrelated to the values of x and y, the coordinates of the center of the circle; the best-fit prediction of n is n = π r2. The precision of this estimate will depend on the number of dots scattered, d, and the number of times the scattering is done, m. In other words, it depends on the amount of computational resources deployed on the problem—the more the better. All this computation would be an utterly pointless waste of resources. It is known analytically that n ≈ A = π r2.

Very often, however, empirically plausible models of real-world processes that actually interest researchers are analytically “difficult” or “intractable,” leaving them unable to generate the formal proofs that they would very much like, because they cannot solve the model analytically. An intractable model is one that researchers know cannot be solved analytically. A difficult model is one that researchers do not know cannot be solved analytically, but they do know that it has not yet been solved, and they do not yet know how to solve. There are two basic solutions to this very common intellectual problem. The first is to make the model tractable by simplifying its representation of the real world. The resulting model looks less like the real world, but at least it can be solved analytically. The second solution is to use computational methods to investigate and in some sense “solve” difficult or intractable models. In this entry, the strengths and limitations of computational modeling and its possible applications in political science are discussed.

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