I'm going to try to summarize my quibbles with the article (all of which have probably been mentioned in one manner or another in this thread):

1)

If the amount paid for an object equals exactly what it's worth, no wealth changes hands.

The yard sale game is a bogus representation for how an economy works. An economy is not a zero-sum game. For the typewriter example used in the article, presumably the seller has more utilization for the $10, and the buyer more utilization for the typewriter (perhaps the seller has just retired and no longer needs a typewriter). In other words, both parties become wealthier in a rational economic transaction (not saying that all transactions are rational...).

2)

To understand how this happens, suppose you are in a casino and are invited to play a game. You must place some ante—say, $100—on a table, and a fair coin will be flipped. If the coin comes up heads, the house will pay you 20 percent of what you have on the table, resulting in $120 on the table. If the coin comes up tails, the house will take 17 percent of what you have on the table, resulting in $83 left on the table. You can keep your money on the table for as many flips of the coin as you would like (without ever adding to or subtracting from it). Each time you play, you will win 20 percent of what is on the table if the coin comes up heads, and you will lose 17 percent of it if the coin comes up tails. Should you agree to play this game?

I would more than likely play this game (ignoring any potential time suck), because $100 is de minimus to me (hence low risk) and the expected value is positive. The distribution of payouts would be very similar to a game like slots or the lottery, where most people lose money but there is the occasional big winner (with the difference being that the house always has the edge in the real world). Another analogy would be venture capitalism: sure, you're going to lose most of the time, but if you can minimize the risk through diversification then the payouts when you win more than offset the small losses.

Now if $100 was a significant amount of my net worth, I would not play, because then you get into utility functions.

What if I stay for 10 flips of the coin? A likely outcome is that five of them will come up heads and that the other five will come up tails.

Technically, this isn't likely; less than 25% of the time will you get five heads and five tails on ten flips. It would be accurate to state that it's likely one would lose money (~62%). This perhaps is nitpicky, but the author is presenting the illusion that this is a losing game, when it isn't necessarily.

3)

What should a single transaction between a pair of agents look like? People have a natural aversion to going broke, so we assume that the amount at stake, which we call Δω (Δω is pronounced “delta w”), is a mere fraction of the wealth of the poorer person, Shauna. That way, even if Shauna loses in a transaction with Eric, the richer person, the amount she loses is always less than her own total wealth. This is not an unreasonable assumption and in fact captures a self-imposed limitation that most people instinctively observe in their economic life. To begin with—just because these numbers are familiar to us—let us suppose Δω is 20 percent of Shauna's wealth, ω, if she wins and –17 percent of ω if she loses. (Our actual model assumes that the win and loss percentages are equal, but the general outcome still holds. Moreover, increasing or decreasing Δω will just extend the time scale so that more transactions will be required before we can see the ultimate result, which will remain unaltered.)

As others have noted, these are peculiar percentages that are almost (but not quite) reciprocals of each other. Now what if we change the -17% to -16%? Then the attractor is income equality (rather than inequality), and his final statement (in parenthesis) is an outright lie (coming from the expert). I can send an Excel spreadsheet if anyone wants to play with the scenarios.

If one exactly balances the percentages (using reciprocals), one gets a lognormal distribution as I had mentioned in my previous comment.

4)

We found that this simple modification stabilized the wealth distribution so that oligarchy no longer resulted. And astonishingly, it enabled our model to match empirical data on U.S. and European wealth distribution between 1989 and 2016 to better than 2 percent. The single parameter χ seems to subsume a host of real-world taxes and subsidies that would be too messy to include separately in a skeletal model such as this one.

The three-parameter (χ, ζ, κ) model thus obtained, called the affine wealth model, can match empirical data on U.S. wealth distribution to less than a sixth of a percent over a span of three decades.

The affine wealth model has been applied to empirical data from many countries and epochs. To the best of our knowledge, it describes wealth-distribution data more accurately than any other existing model.

Wow, he really loves his 3-parameter best fit model, doesn't he? Not to berate his outcome, but it is a simple law of mathematics that the more parameters one adds to a model, the better the fit must be. (For example, let's say one collects data from a known second-order process with 10 data points. Would a second-order fit give the best results? Absolutely not; the third-order would be better, and fourth-order better, etc., until we achieved a perfect fit with a ninth-order model.

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Now that those nitpicks are out of the way, I'll conclude with I generally agree with his model and the need to redistribute wealth to some extent in order to 1) promote the ability for the gifted to get ahead and 2) provide basic sustenance and skills for an overall wealthier economy.