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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. |
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.