Нассим Талеб - The Black Swan. The Impact of the Highly Improbable

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.

Fractal Wealth Distribution with Large Inequalities

People with a net worth higher than €1 million: 1 in 63

Higher than €2 million: 1 in 125

Higher than €4 million: 1 in 250

Higher than €8 million: 1 in 500

Higher than €16 million: 1 in 1,000

Higher than €32 million: 1 in 2,000

Higher than €320 million: 1 in 20,000

Higher than €640 million: 1 in 40,000

If wealth were Gaussian, we would observe the following divergence away from €1 million.

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.

What to Remember

Remember this: the Gaussian–bell curve variations face a headwind that makes probabilities drop at a faster and faster rate as you move away from the mean, while “scalables,” or Mandelbrotian variations, do not have such a restriction. That’s pretty much most of what you need to know. *

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.

Extremistan and the 80/20 Rule

Have you ever heard of the 80/20 rule? It is the common signature of a power law—actually it is how it all started, when Vilfredo Pareto made the observation that 80 percent of the land in Italy was owned by 20 percent of the people. Some use the rule to imply that 80 percent of the work is done by 20 percent of the people. Or that 80 percent worth of effort contributes to only 20 percent of results, and vice versa.

As far as axioms go, this one wasn’t phrased to impress you the most: it could easily be called the 50/01 rule, that is, 50 percent of the work comes from 1 percent of the workers. This formulation makes the world look even more unfair, yet the two formulae are exactly the same. How? Well, if there is inequality, then those who constitute the 20 percent in the 80/20 rule also contribute unequally—only a few of them deliver the lion’s share of the results. This trickles down to about one in a hundred contributing a little more than half the total.

The 80/20 rule is only metaphorical; it is not a rule, even less a rigid law. In the U.S. book business, the proportions are more like 97/20 (i.e., 97 percent of book sales are made by 20 percent of the authors); it’s even worse if you focus on literary nonfiction (twenty books of close to eight thousand represent half the sales).

Note here that it is not all uncertainty. In some situations you may have a concentration, of the 80/20 type, with very predictable and tractable properties, which enables clear decision making, because you can identify beforehand where the meaningful 20 percent are. These situations are very easy to control. For instance, Malcolm Gladwell wrote in an article in The New Yorker that most abuse of prisoners is attributable to a very small number of vicious guards. Filter those guards out and your rate of prisoner abuse drops dramatically. (In publishing, on the other hand, you do not know beforehand which book will bring home the bacon. The same with wars, as you do not know beforehand which conflict will kill a portion of the planet’s residents.)

Grass and Trees

I’ll summarize here and repeat the arguments previously made throughout the book. Measures of uncertainty that are based on the bell curve simply disregard the possibility, and the impact, of sharp jumps or discontinuities and are, therefore, inapplicable in Extremistan. Using them is like focusing on the grass and missing out on the (gigantic) trees. Although unpredictable large deviations are rare, they cannot be dismissed as outliers because, cumulatively, their impact is so dramatic.

The traditional Gaussian way of looking at the world begins by focusing on the ordinary, and then deals with exceptions or so-called outliers as ancillaries. But there is a second way, which takes the exceptional as a starting point and treats the ordinary as subordinate.

I have emphasized that there are two varieties of randomness, qualitatively different, like air and water. One does not care about extremes; the other is severely impacted by them. One does not generate Black Swans; the other does. We cannot use the same techniques to discuss a gas as we would use with a liquid. And if we could, we wouldn’t call the approach “an approximation.” A gas does not “approximate” a liquid.

We can make good use of the Gaussian approach in variables for which there is a rational reason for the largest not to be too far away from the average. If there is gravity pulling numbers down, or if there are physical limitations preventing very large observations, we end up in Mediocristan. If there are strong forces of equilibrium bringing things back rather rapidly after conditions diverge from equilibrium, then again you can use the Gaussian approach. Otherwise, fuhgedaboudit. This is why much of economics is based on the notion of equilibrium: among other benefits, it allows you to treat economic phenomena as Gaussian.