Power Law Distributions
Power law distributions describe phenomena where extreme events are far more common than in a Gaussian distribution, making them scalable and prevalent in areas like wealth distribution, city sizes, and book sales.
THE IDEA
Wealth Distribution Assuming a Gaussian Law
People with a net worth higher than €1 million: 1 in 63
Higher than €2 million: 1 in 127,000
Higher than €3 million: 1 in 14,000,000,000
Higher than €4 million: 1 in 886,000,000,000,000,000
Higher than €8 million: 1 in 16,000,000,000,000,000,000,000,000,000,000,000
Higher than €16 million: 1 in … none of my computers is capable of handling the computation.
What I want to show with these lists is the qualitative difference in the paradigms. As I have said, the second paradigm is scalable; it has no headwind. Note that another term for the scalable is power laws.
Just knowing that we are in a power-law environment does not tell us much. Why? Because we have to measure the coefficients in real life, which is much harder than with a Gaussian framework. Only the Gaussian yields its properties rather rapidly. The method I propose is a general way of viewing the world rather than a precise solution.
When to use it
Analyzing income and wealth inequality in economics
Modeling the distribution of city sizes (Zipf's law)
Understanding the frequency of natural disasters like earthquakes
Predicting the success distribution of creative works (books, movies, music)
FROM THEORY TO EVERYDAY LIFE
In practice
Wealth under Gaussian assumption
Taleb’s illustrative Gaussian model assigns an extremely small probability to net worth over €16 million. His comparison shows how a Gaussian assumption can miss the large values in a heavy-tailed distribution; the illustration alone does not establish a specific power law for real-world wealth.
A MOMENT TO REFLECT
Put it to work.
Why does assuming a Gaussian distribution for wealth lead to absurd probabilities?
How would choosing a power-law rather than a Gaussian wealth model affect an economic policy analysis?
What other real-world phenomena are likely to follow power law rather than Gaussian distributions?
Often confused with
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Source texts
- The Black Swan The Impact of the Highly Improbable With a new section On Robustness and Fragility (Nassim Nicholas Taleb)