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Recommendation: The Pudding on the Yard-Sale Model and Wealth Tax

Yard Sale Model showing results of repeated trades between two partners of differing wealth.
Results of my round of the Yard Sale game – I wasn’t supposed to win.

In a free market [with only win-or-lose transactions, the outcomes of transactions decided by a coin flip], one person ends up with all of the wealth – completely by chance.

This is completely counterintuitive. If everyone wins half their games, everyone should end up approximately where they started, around $1,000.

But it all starts to make sense when you’re in the position of the poorer player. Your wager changes based on how much you can afford, so…

  • When you lose, the maximum amount you can wager goes down. So you can’t win back what you lost in one coin flip.
  • When you win, the maximum amount you can wager goes up. So you could potentially lose more than what you won in the first game.

This is still confusing. So let’s play a rich opponent to see how this plays out…

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

Meanwhile, the richer player will gain money. That’s because, from their perspective, every game they lose means they have an opportunity to win it back – and then some – in the next coin flip. Every game they win means, no matter what happens in the next coin flip, they’ll still be at a net-plus.

Repeat this process millions of times with millions of people, and you’re left with one very rich person.

The Pudding – Why the super rich are inevitable

This is a really interesting and well produced article (as are other pages on The Pudding), and I highly recommend it. There’s a version you can play that shows the results of the game at a population level with and without wealth redistribution to see the difference it makes (a lot).

Some thoughts:

  • The model rules out the possibility of win-win transactions – each game is zero-sum.
  • Real world transactions aren’t random – certain people are much more likely to get a better deal than others in any given transaction….
  • … and some people are very prudent in mostly choosing transactions at which they are more likely to win (going to work) than lose (going to a casino).
  • Wealth taxes: (a) seem unfair to those who save rather than spend; (b) are very difficult to calculate fairly (c.f. Elon Musk ‘losing’ US$200bn of his wealth since 2021)…
  • … but do seem like they might help us avoid the worst extremes of inequality.
  • We should recognise that inequality is inevitable, and work out how much is desirable / tolerable. (Probably a lot more than most of the left thinks, and a lot less than much of the right does. Good luck us.)

See also:

The Grasshopper and the Ants (Disney)
Thought experiment: poverty and inequality without injustice (and all the links at the bottom of it)
On inequality
Astonishing wealth inequality graphic


I'd love to hear your thoughts and recommended resources...