Are Simple Models Bad? No!

Here is a frustrating critique of formal/game theoretical modeling:

The model the author presents is way too simple and completely divorced from reality. Therefore, we ought to ignore its conclusions.

Such comments pop up frequently. They are frustrating because they are grounded in ignorance. There is an implicit belief that formal modelers are attempting to match reality. With that as the premise, models fall woefully short. Consequently, the critics reject them.

However, I know of no serious modeler claims to or even wants to match reality. Formal modeling acts as accounting standards that verify or reject theories of causation. That’s it. That’s all. There’s nothing more. And that’s perfectly okay.

For example, consider the following argument on why countries develop nuclear weapons:

  1. Countries with rivalrous relationships are in competition for scarce resources.
  2. All other things being equal, countries with nuclear weapons receive more of the scarce resources.
  3. If the cost of the nuclear weapons is worth less than the additional amount of resources they bring in, we should expect a country to proliferate.

I just gave you the conventional wisdom about nuclear proliferation. I doubt many would criticize this as being too simplistic to reflect reality. For some reason, informal arguments have a certain immunity to this type of criticism. Perhaps this is because they do not explicitly detail what any of these assumptions mean–that nuclear weapons cost exactly $k, that power is equal to p, that the costs of war are c, and so forth. Yet, implicitly, those types of assumptions are present in the informal argument. And our inability to grasp that without formalization puts us in deep trouble.

As it turns out, the conventional wisdom is wrong. There normally exist bargained settlements that leave both sides better off than had the potential proliferator obtained nuclear weapons. A simple model illustrates this, and you can find the proof in this paper.

Yes, this model is way too “simple” and is completely divorced from reality. But so is the informal explanation I gave above. The English words make it feel more comfortable than Greek letters. But the critical difference is that the Greek letters show that the English words are wrong. And that is why modeling is useful. (And awesome.)

Life is a gigantic tradeoff. When anyone crafts a theory–formal or informal–they are simplifying reality into digestible bits. There is no shame in doing this, since indigestible chunks are completely worthless. Formal modeling is just really good at identifying logical inconsistencies.

This allows us to take the informal logic a bit deeper. For example, if the three above assumptions do not imply proliferation, what does? Sometimes, the second question is more interesting than the first.

Whenever you look at a model, ask a simple question: does this model help me understand the world better? If the answer is yes, then accept the model for what it is–a much simplified (but useful!) version of reality. If the answer is no, then feel free to hate it with a passion.

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