[ctdonath]

The article is a great example of gross innumeracy. The author confuses linear distributions with exponential ones, comparing them as stacked bar graphs without suitable differentiation of axis.

Doesn't take much of a consistent percentage increase in income from one person to the next, spread across a large population, to result in that top 20% indeed dominating most wealth.

ETA (after playing with Excel for a few minutes): If each person in the USA makes just 0.000003% more than the next, the resulting "20%s" wealth distribution graph looks exactly like the "Actual" part of the Percent Wealth Owned graph.

I'd say a wealth inequality of three millionths of one percent between one person and the next is about as fair a wealth distribution as you could ask for. The author needs to educate himself about statistics before self-righteously educating others about the virtues of communism.

ETA2: reduce the differential to 0.000002% and the graph approximates the "Estimated" part of the graph in question. To achieve the alleged "Ideal" distribution, further reduce the differential to 0.000001%. Innumeracy indeed.

[rwl]

> ETA (after playing with Excel for a few minutes): If each person in the USA makes just 0.000003% more than the next, the resulting "20%s" wealth distribution graph looks exactly like the "Actual" part of the Percent Wealth Owned graph.

Not sure what you're saying here. Do you mean that, in an imaginary country where everyone but the top earner makes exactly 0.000003% less than the person above him, income will be distributed in that way?

I see how this would tell against the author's particular choice of representation, but I'm not sure that it tells us much about how income is actually distributed in the U.S., much less how it should be distributed. Just because the same distribution can be realized in a country where income seems to slide much more "fairly" (i.e., gradually) from the richest to the poorest doesn't mean that distribution can't be realized in a much less fair way here. (Moreover, I suspect that if you put it in absolute dollars, rather than percentage points, the incomes in your imaginary country would strike most people as decidedly less fair.)

[ctdonath]

Yes, I do mean that. I ran the numbers & graphs in a few minutes on Excel and came up with results that matched the article's graphs (right down to the automatic color choices - heh). I also mean that the real-world actual, estimated, and (alleged) ideal distributions are a near-perfect match for the mathematical theory. Ergo, it gives lie the selfish "should" part: we are living the reality of statistics, to wit a near-zero differential of income between one person and the next necessitates a huge fluctuation between the bottom & top wealth holdings.

The "innumeracy" comment comes from the fact that those decrying "unfair!" do not realize that a miniscule (two millionths of one percent is nigh unto zero) linear adjustment of percentages translates to exponential variations when applied across hundreds of millions of people. They're performing an equal linear division of the population (20% increments) and somehow expecting the wealth numbers to come out with a similar "fair" equal division of holdings; realizing that the rich should indeed have more than the poor (hence the semantic difference in terms), they resolve this cognitive dissonance by "allowing" the rich to hold some 3x the wealth of the poor - oblivious to the statistical fact that variations in wealth are a matter of exponential-accumulation percentages, not linear accumulations multipliers.

I don't see how income can slide much more "fairly" (i.e., gradually) from the richest to the poorest than a differential of a vanishingly small three millionths of one percent. To say that somehow it "should" (obvious moral arguments of "it's not yours to distribute" aside) be _one_ millionth of one percent instead is to wage class warfare, a very real and bloody process as history shows, because the dividing lines for the 20% groupings mean the guy at the bottom of the highest bracket is making $0.10 more than the guy at the top of the second-highest bracket, and the guy at the bottom of the second-lowest bracket is making $0.0003 more than the top person in the lowest bracket. Comparing between adjacent individuals, and even across entire brackets, with real numbers should strike most as decidedly fair. Is the 80% division hundreds of times wealthier than the 20% division? and the very top unto billions more than the very bottom? sure - and that's reality, folks: the wealth distribution curve is a natural consequence of miniscule percentages aggregated over hundreds of millions of people, and no amount of "should" and social-reengineering (to wit: "comply or die") can render viable change to a natural, social, statistical phenomenon.

But since many people cannot cope with exponential consequences of uniform miniscule percentages applied across a population of hundreds of millions, we will always be faced with those who cry "unfair!" and insist on forcing their notion of "fair" upon the population. The 20th Century suffered some 100,000,000 dead as a consequence, and the authors of TFA (and, it seems, you (rwl)) want to repeat that toll for want of the 0.000003% more their neighbor makes, when 0.000001% would somehow be OK.

[rwl]

Sorry, I still don't get it. Let's put the empirical question aside, and suppose that in fact, if you lined up every American in order of income, the difference between any given person's income and that of the person on his left or right would be no more than 0.000003%.

What does that show? Well, it shows exactly what you say: that income in absolute dollars would grow exponentially from one end of the line to the other. I'm not sure what comfort this is supposed to be. Can you say to the guy at the bottom that, just because there's no place on the line where incomes take a big leap (percentage-wise), he should be content to live in a society that's structured this way? that he is unjustified in thinking the global pattern is wrong, because there's no obvious local point where it goes wrong?

I agree that it sounds ludicrous to say a 0.000003% differential is unfair, while a 0.000001% differential would be okay. But it isn't clear that the issue should be framed in terms of a percentage differential at all. You say that this is a "natural, social, statistical" phenomenon -- but why is it more "natural" that wealth should grow exponentially from one end of the line to the other, rather than (say) linearly? (And why should we expect that making society more fair will consist in adjusting a uniform percentage differential in wealth, as opposed to, say, the normal non-uniform means of redistribution we use now, like progressive taxation?)

Moreover, if exponential growth from poorest to richest really is the natural structure of income in modern society, then the question of whether a 0.000003% or 0.000001% differential makes for the best society becomes quite important, for exactly the reasons you point out: such a tiny difference in percentage has enormous consequences when iterated over hundreds of millions of people. And surely, in doing our moral reasoning and in making policy, those global consequences should count for something. We need not be consigned to incredulity that such an apparently tiny difference could matter.

[ctdonath]

"I agree that it sounds ludicrous to say a 0.000003% differential is unfair, while a 0.000001% differential would be okay."

Good. It is. Even when taking into account my own innumeracy and screwing up the calculations so the difference is in fact between 0.000003% vs. 0.0000003%.

It is clear indeed that the issue should be framed in terms of a percentage differential. $100 is a big deal to the guy who sweeps your office, but not so much to the guy who owns it. When asking for a raise, the dollar amount you seek is based on a percentage of your income, not the amount independent of your income: you ask for a $1000 or $10,000 raise, not a $100 one. It makes sense because when you _are_ dealing with large orders of magnitude, you don't maintain the notion that values significant to small orders of magnitude are still relevant (you may waffle over the price of a single doorknob for your home, but not for your office building). I'm not sure how to present a persuasive argument that what is, is. If you're dealing with millions/billions of dollars, a hundred dollars isn't a concern - but if you're scraping by in poverty, it is. Maybe the best argument is that when I plugged in 0.0000003%, 0.0000017% and 0.0000033% as applied exponentially over a large population into Excel (to wit: applied percentages .01%, .05%, and .10% to a population of 100, then scaled to the US population), the resulting graph looked _exactly_ like the one in the article (save for perhaps some slight real-world distortions). The theory, with little effort, matches the reality.

Sure, the question of whether a 0.000003% or 0.0000003% differential makes for the best society becomes quite important, for exactly the reasons you agree to: such a tiny difference in percentage has enormous consequences when iterated over hundreds of millions of people. My concern is what you overlooked in my post: a century of trying to adjust that natural reality resulted in some 100,000,000 deaths under Communism.

[ckuehne]

"The author confuses linear distributions with exponential ones, comparing them as stacked bar graphs without suitable differentiation of axis."

Could you elaborate? By the way, the graph is taken from the original paper (click the details link below the graph).

[ctdonath]

The graph (and the article's conclusion) would be more sensible if the bottom bar were on a linear axis while the top was on a suitably scaled logarithmic axis. The author does not comprehend the consequential differences between percentages and absolute values.

[ctdonath]

Addressing my own innumeracy, reworking the numbers I find that all three bars are indeed exponential, expressing percentage increases of different orders of magnitude (the top is increasing wealth accumulation at 10x the percentage rate of the bottom). Mea culpa aside, the author is using a linear X axis instead of a far more suitable logarithmic scale, thus skewing the reader's perception of the graph (as exemplified by the fact that all the HN comments failed to notice this).