Why the ultra-rich are inevitable

Why do the super wealthy exist in society?

Many of us think it's because some people are making better financial decisions. But what if this is not true? What happens if the economy does – our economy – Designed to create a small number of ultra-rich people?

That's what mathematicians claim in something called the yard sale model, and I promise it has something to do with my stupid watch purchase. But first…

Let's think for a moment about what just happened.

• I lost the first match.
• We won the second game.
• That means you won 50% of your matches.
• but you have I don't have much money than the first.

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

This is the core of the yard sale model. In a free market, one person ends up with all the wealth, completely by chance.

This is completely counterintuitive. If everyone wins half the games, everyone should end up winning the starting amount, which is about $1,000.

But when you put yourself in the shoes of a bad player, everything starts to make sense. The stake depends on how much you can afford.

• when you lose, the maximum amount you can bet will be lowered. In other words, you can't get back what you lost by tossing a single coin.
• when you win, the maximum amount you can bet increases. Therefore, you can lose more than you won in the first game.

This is still confusing. Now let's play against a wealthy opponent to see how this plays out.

If you play enough rounds, both players will win about half of the games. However, poor players will lose most of their money.

On the other hand, richer players win money. That's because, from their perspective, every game they lose means they have a chance to get it back on the next coin toss. Every game they win means they remain net positive no matter what happens on the next coin toss.

If you repeat this process millions of times with millions of people, only one person will remain who is extremely wealthy.

What can we learn from the yard sale model?

Decades ago, physicists began studying inequality. They typically study the physical world, such as how two balls interact when they collide. However, they began using their methods to study economics, a field now called econophysics. They say that instead of looking at how two balls interact, in a transaction he looks at how two humans interact and how that plays out on a large scale. was modeled. This helped model the distribution of wealth.

In 2002, physicist Anirban Chakraborty published a paper describing the yard sale model (the simulation we did in the introduction). You can play again here.

To be clear, econophysics has received its fair share of criticism. However, the yard sale model is not intended to accurately model the real world.

I emailed Gabriel Zachman, an economist at the University of California, Berkeley. He advised Sen. Elizabeth Warren on her 2021 wealth tax proposal. Zakman said the yard sale model is a more generalized model than those often used by economists, but it's still useful.

[The Yard-sale model] It seems appropriate as a simple statistical model of the distribution of wealth.

—Gabriel Zucman

Bruce M. Bogosian, a mathematics professor at Tufts University, echoed that sentiment when he compared the yard sale model to an “X-ray” in Scientific American.

We believe that this purely analytical approach is similar to We believe that it provides deep insight into the forces that act on growth. Poverty and inequality today.

—Bruce M. Bogosian

In other words, the yard sale model does not capture the complex variables of the economy and therefore cannot really influence concrete policy decisions.

But it is a useful way to think about the general “trickle-up” nature of free markets. That's contrary to what many conservative politicians have been saying for decades: wealth trickles down. They argue that the government should let the wealthy create jobs for the rest of the population. This ideology has led to massive tax cuts for the wealthy, from the 1981 Ronald Reagan tax cuts to the 2017 Donald Trump tax cuts.

What if we redistributed wealth?

In a 2002 paper on this model, Chakraborty wrote:[Wealth concentration] For example, it can be prevented by government intervention through taxes. ”

So what if we ran the game again, taking a certain percentage of money from everyone each turn and redistributing it evenly? After all, Americans pay a lot of taxes, and usually the wealthy are taxed more than the poor. And most of that money goes to government programs that typically help the poor more than the rich.

It also adds the ability for people to bet more or less of their money.

Maximum bet: What is the maximum percentage of the property that each person can bet in each round?

Redistribution: How much of each player's wealth should be redistributed to everyone else after each round?

This time players will be willing to bet 20% A portion of their wealth per game.Tax all players after each round 0.5% and distribute it evenly to all players.

Track how people are playing Can be redistributed Rates compared to people playing No redistribution.

We find that even a small amount of redistribution prevents the emergence of a single super-rich class.

This is similar to what Boghossian and his colleagues did in their 2017 paper, where they modeled real-world redistribution much more accurately than my version. They were able to match the wealth distributions of the United States and Europe to within 2 percent.

Currently in the United States, the richest 20% of families own about 70% of wealth. However, this does not capture the true wealth disparity in the United States. If the population of the United States is represented by 1,000 people in one room, then the richest one has four times as much money as the poorest 500 people.

Another thing to note about this simulation is that even with redistribution, the richest people in the game are exponentially better off than the poorest people. And this was born out of sheer luck. But imagine what would happen if you played this game with real people. Some wealthy players will inevitably claim that they deserve to be rich because they are good at guessing the outcome of a coin toss.

So the clock

I actually bought a vintage Omega watch a few years ago and actually overpaid by $50.

After getting burned once, I didn't want to risk that much money. So my next purchase was a $100 vintage Seiko watch, which I bought for $20 less than the market price. Although I won the trade, I was unable to recover my losses. In fact, I've been collecting vintage watches for years, only to lose money.

I blame the yard sale model.

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• Anirban Chakraborti's original paper on the yard sale model can be found here.
• Brian Hayes, Senior Editor american scientist, he was actually the one who named it the yard sale model. His work also contains strong criticism of this model.
• For a more detailed and easy-to-understand explanation of this model, read Bruce M. Boghosian, professor of mathematics at Tufts University, in Scientific American.