Scalable Wealth Distribution
In this illustrative wealth distribution, each doubling of the threshold reduces the share above it by a factor of four. That constant ratio across scales is a power-law pattern.
THE IDEA
Consider an illustrative distribution, rather than a measured population estimate:
People with a net worth higher than €1 million: 1 in 62.5
Higher than €2 million: 1 in 250
Higher than €4 million: 1 in 1,000
Higher than €8 million: 1 in 4,000
Higher than €16 million: 1 in 16,000
Higher than €32 million: 1 in 64,000
Higher than €320 million: 1 in 6,400,000
The speed of the decrease here remains constant (or does not decline)! When you double the amount of money you cut the incidence by a factor of four, no matter the level, whether you are at €8 million or €16 million. This, in a nutshell, illustrates the difference between Mediocristan and Extremistan.
Recall the comparison between the scalable and the nonscalable in Chapter 3. Scalability means that there is no headwind to slow you down.
Of course, Mandelbrotian Extremistan can take many shapes. Consider wealth in an extremely concentrated version of Extremistan; there, if you double the wealth, you halve the incidence. The result is quantitatively different from the above example, but it obeys the same logic.
When to use it
Modeling income and wealth inequality for economic analysis
Understanding the distribution of extreme events in fields like finance or natural disasters
Designing portfolios that account for fat-tail risks
Evaluating the impact of taxation or redistribution policies on the extremes
FROM THEORY TO EVERYDAY LIFE
In practice
Wealth Thresholds and Incidences
In the illustrative distribution, 1 in 62.5 people have over €1 million, while 1 in 6,400,000 have over €320 million. These figures describe the example’s assumed pattern.
Comparison with Mediocristan
In an exponential distribution, equal additive increases in a threshold produce the same proportional decline in incidence. In the power-law example, equal multiplicative increases produce that constant ratio instead.
A MOMENT TO REFLECT
Put it to work.
How does the scalable nature of wealth distribution challenge common assumptions about averages and typical outcomes?
In what ways does this pattern manifest in other domains, such as book sales or city sizes?
What are the implications for risk management and policy when dealing with such extreme inequalities?
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)