Power Laws

Picture all measurable variables divided into two worlds: Mediocristan and Extremistan.

Nassim Taleb uses these two “worlds” to illustrate the differences between variables that follow Gaussian distributions and those that don’t. We’ll return to this in a moment.

I’m always fighting the urge to think linearly. Sometimes (most of the time) we have to think exponentially.

For various reasons, we’re terrible at this. Our brains are wired to think linearly. 

Take this famous problem: how many people do you need to have in a room for there to be a 50% chance that there is a shared birthday?

I remember the first time I came across this problem. I was sitting in a college math class, and in my head I’m thinking to myself “what’s the trick? It can’t be 182.5 people (half the days in a year). Is it possible that the answer is a really low number?”

The answer is 23 people. With that amount, there’s a 50% chance of a shared birthday. For a great explanation why, read this Twitter thread.

It’s our inability to think exponentially that prevents us from solving these problems. 

It’s also the reason why we’re unable to see just how many situations follow power laws.

Getting back to Mediocristan and Extremistan. 

Picture a football stadium full of people. We’re going to measure the crowd in attendance according to two variables: height, and wealth.

Height’s an easy one. If you had to guess the average height of the crowd, you’re likely to be very close to the true value. 

Let’s throw a wrinkle in. Imagine I had the ability to replace one person in the crowd with another person of my choosing. Would your guess change?

No, it wouldn’t.

I could substitute Shaquille O’Neal in for anyone, and across 60,000 people, there’s a negligible difference in average height. 

Now, let’s do the same exercise again. This time with the average wealth of people in attendance. I’m sure there are many ways of attacking this problem, but that’s not what we’re interested in. 

I can guarantee you that your guess is going to be way off if Elon Musk is in the crowd. Or, if he’s not, he could be substituted in. 

When measuring variables like wealth, book sales, and podcast downloads, they all follow power laws. 

Another way to view it is in differences among people within the same crowd. No matter who is in that stadium, the difference between the tallest and shortest person can’t be more than about 6 feet. And the difference between the tallest person and the fifth tallest person is likely to be less than a foot.

However, there’s likely a substantial difference between the wealthiest and fifth wealthiest person in the crowd. 

With height, we’re in Mediocristan. One value won’t change much.

With wealth, sales, web traffic, etc we’re in Extremistan, and one value can change everything.

We must always remember which world we’re in.