Astounding mathematical law of inequality

But yeah I don’t need a bunch of maths nerds to tell me that the rich suck. I’m in.

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I’m inclined to agree with you.

After skimming a few of the papers I have a slightly different take. They’re claiming that chance and chance alone (under various types of stochastic processes and conditions) can produce the Pareto-like distributions of wealth that we observe in reality. So, play along with me for a second and assume they are correct and have identified a superior model for economic transactions. In the most meta case of the model, they could be agnostic about the various forces of rigging and unrigging at micro levels (e.g., regulatory capture versus redistribution) and simply tune some parameter(s) to account for it.

Yes. They are arguing that redistribution has to be part of the response because no amount of corruption fighting or trust busting will be sufficient to counter the anti-gravity of wealth.

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I’m struggling to get the intuition behind the result that the oligarch gets all the money, even when the oligarch has negative EV on the flips. If the flips are fixed in size, then gambler’s ruin would say that one person has to end up with all the money, because everyone else ends up at zero. That doesn’t happen here, but it could be that as the oligarch soaks up more and more wealth, the wager sizes get smaller and smaller (because they are tied to the wealth of the counterparty), so you just asymptotically have less and less money changing hands even if you run infinite trials. But I’m not at all confident that’s what’s going on, and it could be something else entirely.

I pulled up one of the underlying papers (here), which is honestly pretty shocking for a post-replication crisis published social science paper. At a high level:

  • Their preferred model has three free parameters that can be tuned to make their model output look like the empirical Lorenz curve. And then they explicitly go through the process of picking a variant of the model that’s easiest to fit to the data, so there’s a fourth degree of freedom. It’s not especially impressive that you can take a function of 4 variables and match it to a particular curve. The Pareto distribution only has 2 parameters.
  • Comically, they retune the model for each year in the data set, so the “model” admittedly has no external validity or ability to predict anything. If you want to know what the Lorenz curve will look like in 2022, you need to know what Xopt and some other Greek letters will be. To find those out, you need to get the 2022 Lorenz curve and reverse engineer them.
  • The capstone, though, is that even after all this fine-tuning, the model consistently predicts that approximately 30% of aggregate wealth is held by the oligarch, a single individual! In reality, total household wealth in the US is around $100 trillion (per naive Google search), and Jeff Bezos has $100 billion, so the empirical value is actually 0.1%, so they are off by a factor of 300. The Lorenz curves cover up this striking disparity by zooming out so far that you can’t clearly see the shape of the critical portion of the curve. But the absolute central result of the model is that a single individual (not a small fraction of agents–exactly one) end up with a very large proportion of the wealth, and the result is not consistent with reality.

It’s strange that anyone would take this seriously. If you want theoretical underpinnings for progressive redistribution policies, the Piketty/Saez/Zucman crew are there, and have the economic training to make their models withstand some level of scrutiny. There’s also not much theoretical appeal in modelling the economy as a sequence of coin-flip bets for a fraction of your net worth, since that is not actually what people do in the economy.

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They should have titled the article, “WAAF” and left the math out of it. Now that I could get behind.

Edit: that’s a generic response, not directed at you, Bobman

I found the story and the paper pretty interesting. The crux is that if the effects of redistribution are smaller than the advantage of wealth, a system tends inexorably to oligarchy. Which everybody has already pretty much known for thousands of years. This model suggests there can be a level of redistribution that keeps a society in a steady state rather than in a state of runaway inequality. I’m not sure we have ever seen that in history. In the 200 years for which we have good enough records we (Europe and US) have tended to go increasing inequality - > social instability - > war (which destroys wealth, decreasing inequality) - > repeat. Perhaps identifying a level of redistribution that can instead provide a sustainable level of inequality is possible.

To be fair, I don’t think anyone is taking it that seriously judging by the journals and number of citations.

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As far as I understand, “the oligarch” is really “the oligarch class”, not necessarily a single individual. In the long run, the system tends towards a steady state where the oligarch(y) obtains a fraction of the money. How big of a fraction is based on a couple of variables, such as the rate of redistribution.

I see the relationship between this and how the economy works as similar to the relationship between the AKQ game and no-limit hold em.

My earlier post mostly explains it but I realize now their simulation actually does put the richer partner at an EV disadvantage (I thought previously they turned it into a fair game but I misread). So a few adjustments:

The poor partner placing +EV bets still tends to lose over infinite trials because of the reverse Martingaling and the bet sizing as fixed percentages which are just in the narrow range where (% change if win)*(% change if loss)<1 (0.996 to be specific). In this range the variance is constantly increasing so that although you earn +1.5% of your wealth in Sklansky bucks for every transaction it becomes less likely your actual results end up positive over many trials.

The richer partner is making -EV bets but the sizing forced by the poorer partner changes the variance equation. Expecting an equal number of wins and losses the result of the richer partner’s bets will be (1+.17/k)*(1-.20/k), where k = a factor correlating the wealth difference between the two participants. This approaches 1 at high wealth discrepancies but also a critical number occurs when the richer person has 8.5x the wealth of the poorer person (the result of k=8.5 is 0.996, the same most likely return of the other player). Any player that maintains 8.5x the wealth of their partner will be the more likely winner in a simulation of infinite trials, even though they’re taking the -EV bet every time.

It’s essentially a finely tuned management between Sklansky bucks and real bucks. Obviously there’s a very narrow range where it’s possible to drive variance to the point where you’re unlikely to realize + earnings while making infinite +EV bets and vice versa. It also requires constant feedback for bet sizes based on bankroll size. To claim that this model might be the basis for any complex economy is ridiculous.

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Thank you! I get it now.

haha some of you need to read theory of poker again

Frontline from Nov 5 on the rise of AI puts it simply- when the gains in productivity are substantially from CAPITAL (automation/AI) then the gains will move toward capital holders and away from Labor.

This fits the general idea. For the “90%” they risk a high fraction of their worth (labor) while those on the other side risk capital which is a small fraction of their worth.

Here’s a cool math trick: Some anonymous trust bought the condo I was renting after my landlord did a panic sell. Then a liaison for the trust offers to rent the same condo back to me for a 50% price increase. Somebody out there been reading a lot of Ricardo.

There was a letter to editor of Sci Amer on this article and I finally got an intuitive grasp of the dynamic.

Say on coin flip you either win 100% or lose 75% of your $100. If you win first flip, great. but if you lose and drop to $25, it takes two wins in a row to get back to $100.

So the big difference between the winning side of the equation and the losing is who is closer to zero. If you start out losing, it gets extremely difficult to climb out. You could easily drop into the pennies. But if you get lucky early, the sky’s the limit. So big money in the vicinity of small banks are at a huge advantage and unless pennies can be divided indefinitely, the small banks always get zeroed out.

It’s definitely counterintuitive that despite every trial having positive expectation your worth converges to zero almost surely.

Also, here is a script simulating this yard sale model. I made it when this thread first appeared but never uploaded it:

Red curve is wealth distribution and blue curve is the Gini curve.

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Marx himself already said this, in Capital, only with a much more convincing identification of the specific mechanism of imbalance (labor markets).

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Awesome stuff. Not be a pain, but is there a way to have this animation run more slowly?

So red is showing all the money getting concentrated, and blue shows the number of fund holders declining?

Here it is slowed down:

It would probably be best to have a user interface where you can enter your own values.

The red curve is the wealth distribution. It’s sorted on along the x-axis from poorest to richest. For each person on the x-axis, the height of the curve gives you the wealth of that person. The y-axis scale isn’t fixed, it scales dynamically so the richest person takes up the total height of the graph.

The black line is the median wealth.

The blue line is the Lorentz curve which is the cumulative wealth function. If you pick a point on the x-axis, it is the sum of the wealth of everyone to the left (poorer) divided by the sum wealth of everyone. For the blue curve, the y-axis ranges from 0 to 1.

In a perfectly equally distributed wealth, the blue curve is a straight line starting from 0 on the left side to 1 on the right side. As wealth inequality increases, the blue curve sinks below this line. The wikipedia article shows how to calculate the Gini coefficient from this curve:

The Gini coefficent ranges from 0 to 1, where 0 is perfect wealth equality and 1 (or about 1) is when one person has all the wealth. The US is around 0.85.

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