Democratic Distributions

Gaussian, Poisson, and other bell-shaped distributions are some times called “democratic.” This colloquial term is intended to indicate an important feature: an average value is a typical value.

Compare this to heavy-tailed distributions which follow generally the so-called 80/20 rule: 80% of your business comes from 20% of your clients, 80% of the wealth is controlled by 20% of the population. Indeed, this principle was originally illustrated by Italian economist Vilfredo Pareto when he demonstrated that 80% of the land in Italy was owned by 20% of the population.

In these distributions, an average value is not typical: the average household income doesn’t mean much when a small group of people are vastly more wealthy than the rest. This skew can be shown mathematically: in a bell curve, the variance – which measures the spread of a distribution – is well defined, while it diverges for a heavy-tailed distribution.

Yet while heavy-tailed distributions are clearly not democratic, I’m still struck by the use of the term for normal distributions. I’m not sure I’d call those distributions democratic either.

I’m particularly intrigued by the use of the word “democratic” to nod to the idea of things being the same. Indeed, such bell-shaped distributions are known primarily for being statistically homogeneous.

That’s starting to border on some Harrison Bergeron imagery, with a Handicapper General tasked with making sure that no outliers are too intelligent or too pretty.

That’s not democratic at all. Not really.

This, of course, leads me to the question: what would a “democratic” distribution really look like?

I don’t have a good answer for that, but this does raise an broader point about democracy: most real-world systems are heavy-tailed. Properties like hight and weight follow normal distributions, but power, money, and fame are heavy-tailed.

So the real question isn’t what a democratic distribution looks like; it is how do we design a democratic system in a complex system that is inherently undemocratic?


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