Quételyte's Average Monster
Taleb criticizes Adolphe Quételet’s use of the average person as a norm and his tendency to see bell curves throughout nature and society. The criticism concerns both imposing an ideal average and using a distribution that may not fit the evidence.
THE IDEA
QUÉTELET’S AVERAGE MONSTER
This monstrosity called the Gaussian bell curve is not Gauss’s doing. Although he worked on it, he was a mathematician dealing with a theoretical point, not making claims about the structure of reality like statistical-minded scientists. G. H. Hardy wrote in “A Mathematician’s Apology”:
The “real” mathematics of the “real” mathematicians, the mathematics of Fermat and Euler and Gauss and Abel and Riemann, is almost wholly “useless” (and this is as true of “applied” as of “pure” mathematics).
The bell curve was mainly the concoction of a gambler, Abraham de Moivre (1667–1754), a French Calvinist refugee who spent much of his life in London, though speaking heavily accented English. But it is Quételet, not Gauss, who counts as one of the most destructive fellows in the history of thought.
Adolphe Quételet (1796–1874) came up with the notion of a physically average human, l’homme moyen. There was nothing moyen about Quételet, “a man of great creative passions, a creative man full of energy.” He wrote poetry and even coauthored an opera. The basic problem with Quételet was that he was a mathematician, not an empirical scientist, but he did not know it. He found harmony in the bell curve.
The problem exists at two levels. Primo, Quételet had a normative idea, to make the world fit his average, in the sense that the average, to him, was the “normal.” It would be wonderful to be able to ignore the contribution of the unusual, the “nonnormal,” the Black Swan, to the total. But let us leave that dream for utopia.
Secondo, there was a serious associated empirical problem. Quételet saw bell curves everywhere. He was blinded by bell curves and, I have learned, again, once you get a bell curve in your head it is hard to get it out. Later, Frank Ysidro Edgeworth would refer to Quételesmus as the grave mistake of seeing bell curves everywhere.
When to use it
Evaluating social science research that uses averages to define 'normal' behaviors, potentially marginalizing minorities.
Risk management: relying solely on standard deviation and bell curves can underestimate extreme events (Black Swans).
Designing products or services: basing designs on average user metrics may exclude a large portion of users who are not average.
Education: using standardized tests that assume a bell curve can label many students as 'below average' and neglect individual learning needs.
FROM THEORY TO EVERYDAY LIFE
In practice
Average Height Fallacy
A city planner assumes the 'average person' height (e.g., 5'9") and designs all public facilities for that height, ignoring the needs of shorter and taller individuals, leading to discomfort for a significant portion of the population.
Educational Testing
A school district judges every class against the same expected average score, without considering differences in the students entering each class. A teacher’s apparent performance can then reflect the choice of benchmark as much as the teaching. The problem is treating the average as an adequate standard for every group.
A MOMENT TO REFLECT
Put it to work.
In what areas of your life do you assume that the average represents the ideal or normal? How might this assumption mislead you?
Think of a decision you made based on 'normal' statistics. Did you consider the impact of outliers (Black Swans) on the outcome?
How can the 'Average Monster' bias affect public policy, such as healthcare or education, when defining 'normal' behavior or traits?
References
- A Mathematician's Apology — G. H. Hardy (1940)
CONTINUE THE CONVERSATION
Source texts
- The Black Swan The Impact of the Highly Improbable With a new section On Robustness and Fragility (Nassim Nicholas Taleb)