Pursuing Randomness

Ruminating some more on Nassim Nicholas Taleb's The Black Swan . . .

Say the income of Americans approximates a normal distribution (i.e., is Gaussian), as Taleb suggests most people, including economists and Wall Street, tend to assume, if only for simplification. Say the average American income is $50,000, and that the standard deviation in income is $10,000. Then about 16% of the population should be making more than $60,000 (and 16% less than $40,000). 2.3% of Americans should be making more than $70,000, and 0.2% more than $80,000. Only 0.003% of Americans should be making more than $90,000 a year (or less than $10,000). But it's a big country--0.003% of 300,000,000 is still 10,000 people! But for $100,000 or more, only 86 Americans should be found in the income bracket, and I think we can safely say there are more than that in this country. And for $110,000, the chances would only be one in three that any American would achieve that level of wealth.

Ok, but let's say that I grossly underestimated both the average American wealth (which I didn't), and the standard deviation thereof (which I to some extent just pulled out of my ass). Let's say instead that the average American makes $500,000, with a standard deviation of $250,000. In that case, the odds of any one person having an income of $2,000,000 are one in a billion--so we'd have about a one-in-three chance of seeing a twice millionaire in the US--again, I think we can safely say that we've got more than that.

In fact, if the least-earning American made $20,000,000 a year, and if the standard deviation in incomes was $20,000,000, the odds of seeing even one Bill Gates in the entire country would be one in 220,000,000,000,000.

As Taleb points out, book, music, and movie sales; incomes; fame; internet success; financial booms and busts; deaths in war; all these types of phenomena are non-Gaussian: The chances of the next one being unimaginably orders of magnitude larger than the last are far (far, far, far, far) greater than could be justified in the tail of a Gaussian curve.

I'm going to go stuff my money in my mattress (half of it--the other half I'm investing as venture capital in my future blogging empire). Thanks a lot, Taleb!