All Models Are Wrong. When Are They Useful?

In my career as a researcher I have heard the phrase “all models are wrong, but some are useful” on more than a few occasions.1 The first half is easy enough to motivate. All scientific models are simple approximations of complex realities. By their nature, they strip away a great amount of detail to make legible and tractable certain relationships at the expense of others. They depend on quantifiable measurements which themselves act to smother complex qualitative differences into numeric forms usable within models.

All models, then, are wrong. That isn’t the part of the phrase that particularly needs motivating. The part that does is the second part: that some are useful. Because it really begs a few questions:

  1. Useful as defined by what? Prediction, explanation, intervention?
  2. Given a definition of usefulness, how do we assess and measure that usefulness? How do we discriminate between more and less useful models?
  3. Relatedly, what properties are required for a model to be useful under these definitions of usefulness?

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Footnotes

  1. The phrase was coined by the British statistician George Box. Interestingly enough, he added the second half only later on in 1987, in the following passage: “The fact that the polynomial is an approximation does not necessarily detract from its usefulness because all models are approximations. Essentially, all models are wrong, but some are useful”. ↩