I think this is a little different. It's not the whole methodology that's the problem. It's the non-standard bin-sizes. If he wants to do log or exponential sizes, then it's 90.1, 9, .9 or you could round it off to 90, 9, and 1. By making it 90, 9.9 and .1, then he's artificially inflated the middle bin size while simultaneously exclaiming that this bin has more wealth in it than expected.

It's like having a y-axis on a graph that reads: 10 100 5000 10000 (with equally spaced points) and then talking about how there's more action between 100 and 5000 than there is between 5000 and 10000.

9.9 is the top ten percent minus the .1 percent - he agrees the .1% are a problem, but wants to address his own class, the rest of the top 10% = 9.9%. That bin has the size it has, and the measured effects he points to presumably deduct the stats for the .1%. There's no trickery, just a stat or two to conjure with.

If you think he's skewed the measure by using mean instead of median or mode and not subtracting the contributions of the .1% that's an interesting argument but you have to make it - show evidence of that, plus make the calculation to demonstrate that the effect is large. If that's the argument I might suggest dropping "bin size" and employing the term "skew."

There are ways to estimate right bin locations and sizes given a relatively known distribution - maximising information. He's done none of them. (As opposed to disinformation.)

Even simple PCA would figure it out.

You want the hair split more finely - but doing so changes nothing. Not to mention that ya need two possibly correlated variables for a PCA not one, wealth: so unless you doubt that wealth yields social power in the U.S., there doesn't seem to be any work for a PCA to do.

A standard density function would do fine, and not have a wholly artificial dependence on bucket width.

What's a topological map?

Got it - you won't draw any line; that way nobody in particular is responsible or has to do anything. This sort of maneuver is surely just what the author means when he says a central tactic of the 9.9% is: "the pretense of being part of the middle as one of our strategies for remaining on top."

The OP argument in a nutshell: "In the United States, it’s the children of the bottom decile and, above all, the top decile—the 9.9 percent—who settle down nearest to their starting point."

So how would using just a function, so as not to embarrass any one class, fix that?