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My model has ‘the average borrower’. Nobody is the average borrower. What am I talking about?

Wanjiru Njenga Fellow
· 5 replies
Philosophy of mathematicsAfrican & AfricanaAnalyticH. L. A. HartMilton Friedman#averages#fictionalism#legal-fiction#statistics
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I build credit-scoring models for a mobile-money company in Nairobi. Every week I write sentences like "the average borrower in this segment repays within 23 days" or "the typical applicant has 2.4 active SIM cards". Everyone understands them. No borrower repays in exactly 23 days, and nobody has 2.4 SIM cards.

Philosophers apparently use the same example: "the average family has 1.8 children" is true, but it is not about any family. So what is it about? The easy answer is that it's shorthand for "the total number of children divided by the number of families is 1.8". Fine. But then I'm talking about a number, and I'm told whether numbers exist is its own fight.

Here is what actually bothers me. These fictional people make real decisions. "The average borrower" sets the threshold that decides whether a real woman in Kisumu with a vegetable stall gets a loan. If she is unusual in a way the model doesn't see, the fiction wins. I read about "fictionalism" in mathematics, the idea that talk of numbers is a useful fiction like a story, and I wonder whether that framing helps me or just makes me feel more clever about a problem I already had.

People who work with fictions in law, economics or data, how do you think about this?

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5 replies

  1. Nur Aisyah Rahman

    Fellow

    This is my daily life too. In fairness work we call it the problem of "the statistical person". The average is a fine description of a group, and a terrible description of anyone in it. What has helped me is to treat every model output as a claim about the group, and then require a separate step, often a human one, before it becomes a decision about a person. Al-Ghazālī has nothing to say about logistic regression, but he did insist that each soul is judged individually, and I think of that more often than I admit.

    Helpful · 2
  2. Javier Ferrandis

    Fellow

    Economists have argued about this since Milton Friedman's 1953 essay on methodology, where he said that a theory's assumptions do not need to be realistic as long as its predictions are good: firms behave "as if" they maximise profit. That's fictionalism with a business card. It works well for predictions about aggregates. It works badly as soon as you use the "as if" agent to decide what is owed to real ones, which is your case exactly.

    Helpful · 3
  3. Hamza Qureshi

    Fellow

    The law lives with this. The "reasonable person" is a fiction nobody has met, and courts use it to decide whether real defendants were negligent. Hart's lesson was that such terms should be understood by how they work in reasoning, not by asking what thing they name. The reasonable person works because judges can ask, in each case, what someone careful in this position would have done. Perhaps your model needs a version of "in this position".

  4. Oskar Nyberg

    Fellow

    On the philosophy: the average family sentence is the easy case, because the paraphrase is simple and only costs you numbers, not ghostly families. Fictionalists about mathematics face much harder paraphrases in physics. But your worry is not really about ontology. You know the average borrower doesn't exist. Your worry is moral: the fiction is being used as if it described a person. That is a misuse of a true sentence, not a false one.

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    1. Wanjiru Njenga

      Fellow

      Oskar, that's the distinction I needed: the sentence is true, and the misuse is the problem. Hamza's "in this position" is going into our next model review. I can't make the woman with the vegetable stall average, but I can stop treating her as if she were.

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