Extremistan and Mediocristan
Taleb uses Mediocristan for quantities whose extremes have limited influence on the total, and Extremistan for quantities where a single observation can dominate it. In Extremistan, a sample average may change sharply when a rare extreme value appears.
THE IDEA
Extremistan and Knowledge
While this distinction (between Mediocristan and Extremistan) has severe ramifications for both social fairness and the dynamics of events, let us see its application to knowledge, which is where most of its value lies. If a Martian came to earth and engaged in the business of measuring the heights of the denizens of this happy planet, he could safely stop at a hundred humans to get a good picture of the average height. If you live in Mediocristan, you can be comfortable with what you have measured—provided that you know for sure that it comes from Mediocristan. You can also be comfortable with what you have learned from the data. The epistemological consequence is that with Mediocristan-style randomness it is not possible* to have a Black Swan surprise such that a single event can dominate a phenomenon. Primo, the first hundred days should reveal all you need to know about the data. Secondo, even if you do have a surprise, as we saw in the case of the heaviest human, it would not be consequential.
If you are dealing with quantities from Extremistan, you will have trouble figuring out the average from any sample since it can depend so much on one single observation. The idea is not more difficult than that. In Extremistan, one unit can easily affect the total in a disproportionate way. In this world, you should always be suspicious of the knowledge you derive from data. This is a very simple test of uncertainty that allows you to distinguish between the two kinds of randomness. Capish?
What you can know from data in Mediocristan augments very rapidly with the supply of information. But knowledge in Extremistan grows slowly and erratically with the addition of data, some of it extreme, possibly at an unknown rate.
When to use it
Risk management in finance: markets are in Extremistan, so portfolio models must account for rare but catastrophic events.
Data collection planning: consider how much extreme observations could affect an estimate and whether the sample is likely to capture them.
Policy making for income inequality: understanding that wealth distribution is in Extremistan helps design progressive taxation or social safety nets.
Scientific research: when estimating earthquake losses, consider how a few exceptionally destructive events could dominate the total.
FROM THEORY TO EVERYDAY LIFE
In practice
Measuring Heights
Taleb imagines a Martian measuring human heights and uses a sample of 100 to illustrate a quantity with limited extremes. The example contrasts height with quantities such as wealth; it is not a universal rule for choosing a sample size.
Wealth Distribution
A small sample of personal wealth can have a modest average until it includes a billionaire. Taleb uses this kind of disproportionate influence to illustrate Extremistan: the sample may miss observations that matter greatly to the total.
A MOMENT TO REFLECT
Put it to work.
Can you identify a real-world dataset that is likely from Extremistan? How would you adjust your analysis to account for this?
Why is it dangerous to apply statistical methods designed for Mediocristan (e.g., Gaussian assumptions) to Extremistan?
How might you test whether a given phenomenon belongs to Mediocristan or Extremistan before drawing conclusions from data?
Often confused with
References
- The Black Swan — Nassim Nicholas Taleb (2007)
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)