Inequality in Mediocristan vs Extremistan
Taleb contrasts Gaussian distributions with scalable, heavy-tailed ones. In his examples, a very large combined total is more plausibly dominated by one contributor under a heavy-tailed model; the particular split depends on the distribution assumed.
THE IDEA
Inequality
Let us look more closely at the nature of inequality. In the Gaussian framework, inequality decreases as the deviations get larger—caused by the increase in the rate of decrease. Not so with the scalable: inequality stays the same throughout. The inequality among the superrich is the same as the inequality among the simply rich—it does not slow down.†
Consider this effect. Take a random sample of any two people from the U.S. population who jointly earn $1 million per annum. What is the most likely breakdown of their respective incomes? In Mediocristan, the most likely combination is half a million each. In Extremistan, it would be $50,000 and $950,000.
The situation is even more lopsided with book sales. If I told you that two authors sold a total of a million copies of their books, the most likely combination is 993,000 copies sold for one and 7,000 for the other. This is far more likely than that the books each sold 500,000 copies. For any large total, the breakdown will be more and more asymmetric.
Why is this so? The height problem provides a comparison. If I told you that the total height of two people is fourteen feet, you would identify the most likely breakdown as seven feet each, not two feet and twelve feet; not even eight feet and six feet! Persons taller than eight feet are so rare that such a combination would be impossible.
When to use it
Understanding and modeling income or wealth distribution in economics
Predicting sales figures for books, movies, or other cultural products
Assessing risk in financial markets where extreme events are more frequent than a Gaussian model would suggest
Analyzing web traffic, social media influence, or citation counts where a small minority dominates
FROM THEORY TO EVERYDAY LIFE
In practice
Income breakdown among two high earners
Taleb illustrates the contrast with two people earning a combined $1 million per year. He gives $500,000 each for Mediocristan and $50,000 and $950,000 for Extremistan. These are model illustrations, not estimates for every pair of high earners.
Book sales asymmetry
For two authors selling 1 million copies together, Taleb illustrates an asymmetric split of 993,000 and 7,000, compared with 500,000 each. The point is that a heavy-tailed model can make one dominant seller more plausible.
A MOMENT TO REFLECT
Put it to work.
Can you think of a phenomenon in your field that likely follows a scalable distribution rather than a Gaussian one? How would the inequality pattern differ?
What are the practical consequences of assuming a Gaussian distribution when the underlying reality is scalable?
How would your policy analysis change if inequality persisted far into the upper tail? What evidence would you need to support that model?
Often confused with
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)