Thursday, April 13, 2023

The Super-Rich, Like The Poor, Will Always Be With Us (It's the yard-sale math)

From The Pudding, December 2022:

A few years ago I bought a vintage watch for $200.

Later I found out I overpaid by $50.

But I figured I would eventually even out this bad purchase with a good purchase.

And over time I would buy and sell more things...

....and my money would all even out. 

I was wrong. The money doesn't even out. In fact, these uneven trades actually lead to a horrifying end….

Oligarchy – a few rich people, and very little for everyone else.

Why the super rich are inevitable

Why do super rich people exist in a society?

Many of us assume it's because some people make better financial decisions. But what if this isn't true? What if the economy – our economy – is designed to create a few super rich people?

That's what mathematicians argue in something called the Yard-sale model, and I promise it has something to do with my dumb watch purchase. But first…

Imagine you're in a room with 99 other people/

Everyone gets paired up with a random person to play a coin flip game.

Everyone starts with $1,000.

And the maximum anyone wants to risk is 20%. So the wager is $200.

You call heads.

It's tails. You lose.

But if we play more, you should eventually win about half the coin flips. So your money should even out, right?

Let's play again. Each person finds another player.

Jon won his first game, so he has more money than you.

He's willing to risk 20% of his money, so $240.

But you have less money. You can only risk 20% of your money, so $160.

You call tails.

It's tails. You win.

But wait, why do you have less than the $1,000 you started with?

Let's take a second to appreciate what just happened.

  • You lost the first game.
  • You won the second game.
  • So you've won 50% of your games.
  • But you have less money than you started with.

This might not seem like a big deal. But let's keep playing…