Power Laws and Inequality

One of my favorite passages in Here Comes Everybody is the discussion of power law distributions that begins on page 122. Power law distributions are ubiquitous in social systems. For example, we can see power law distributions at work in the blogosphere. The most popular bloggers get millions of readers, while there are millions of bloggers who get hardly any traffic at all. You will find power law distributions in almost any complex social system: the popularity of books or music, the number of contributions to Wikipedia or free software, the popularity of programming languages, university endowments, and so forth. Shirky makes a really interesting observation about the imbalances inherent in a power law distribution:
The imbalance drives large social systems rather than damaging them. Fewer than two percent of Wikipedia users ever contribute, yet that is enough to create profound value for millions of users. And among those contributors, no effort is made to even out their contributions. The spontaneous division of labor driving Wikipedia wouldn't be possible if there were concern for reducing inequality. On the contrary, most large social experiments are engines for harnessing inequality rather than limiting it...
The most salient characteristic of a power law is that the imbalance becomes more extreme the higher the ranking. The operative math is simple—a power law describes data in which the nth position has 1/nth of the first position's rank. In a pure power law distribution, the gap between the first and second position is larger than the gap between second and third, and so on. In Wikipedia article edits, for example, you would expect the second most active user to have committed only half as many edits as the most active user, and the tenth most active to have committed one-tenth as many. This is the shape behind the so-called 80/20 rule, where, for example, 20 percent of a store's inventory accounts for 80 percent of its revenues, and it has been part of social science literature since Vilfredo Pareto, an Italian economist working in the early 1900s, found a power law distribution of wealth in every country he studied; the pattern was so common that he called it "a predictable imbalance."
Presumably because this is a book about the Internet, not political philosophy, Shirky doesn't dwell on this latter point. But I think it's worth pondering its implications for America's perennial debate over income inequality. The New York Times regularly runs hand-wringing articles on the growth of income inequality, suggesting that the growing gap between rich and poor is a sign of deep flaws with the American economy. While it's rarely stated explicitly, people seem to have an intuition that dramatic wealth disparities are signs of inequities in the American economy. That wealth is somehow being unjustly "redistributed upward."
But I think Shirky's discussion suggests another explanation: that power law distributions are simply a natural characteristic of complex social systems, and that distributions naturally become more unequal as the size and complexity of the overall system increases. This is certainly the pattern we've seen online, with the most popular websites gaining a disproportionate share of the eyeballs, and in many cases widening their lead over time. While we've seen a bit of hand-wringing over this process, most people accept that this is just the way the world works. The fact that Cory Doctorow and Josh Marshall get several orders of magnitude more traffic than I do isn't a sign that there's something wrong with the blogosphere, there just happen to be a lot more people interested in their work than in mine.
Moreover, the inequality of blog traffic is in many ways socially beneficial. If every blogger got exactly the same traffic, none of them would be able to earn enough to make a living at it, and the quality of blogospheric discussion would almost certainly suffer. Instead, because the best bloggers have orders of magnitude more traffic than the average blogger, the Doctorows and Marshalls of the world can afford to not only write full-time, but also to hire like-minded writers to further expand their sites' content. And of course, the possibility of becoming the next Josh Marshall drives many a blogger to produce valuable content for the rest of us. Not only is there no practical way to affect an equal distribution of blog traffic, but it pretty clearly wouldn't be helpful even if it were feasible.
For reasons that aren't clear to me, a lot of people seem to have a very different intuition when we're talking about the distribution of dollars rather than eyeballs or Wikipedia edits. The mere existence of growing income inequality is treated as a prima facie evidence of serious flaws in the American economic system. People seem to assume that such a distribution cannot arise absent systematic distortions redistributing income upwards. Therefore, even if we can't identify the specific mechanism that's robbing from the poor and giving to the rich, we can infer its operation from the skewed distribution of income.
But in fact, the processes that give rise to income inequality are roughly the same as the processes that give rise to inequality online. We should expect that even in a perfectly just economic system, some people would earn a lot more money than others, and that the gap would grow over time as technological progress increases the size of the market and the potential for division of labor.
This isn't to deny that our real-world economy includes economic distortions that unjustly exacerbate the gap between the rich and the poor. Such distortions do exist, and they should be eliminated. Nor is it to deny that there are good arguments for taxing the wealthy in order to provide government services to the non-wealthy. But it does mean that the bare fact of income inequality isn't evidence of injustice. If we reformed every regressive and unjust aspect of our economic system, we should still expect a high degree of inequality of pre-tax incomes. Power laws distributions are an inherent characteristic of complex social systems, and they're no more troubling when they appear in the distribution of income than in the distribution of website traffic.













I suggest that the problem is not "unequality of distribution" but rather the tendency, over time, for the inequitable distribution to become inflexible. As long as the power distribution is based on some sort of fundamental merit, we are OK: it is no big deal if Person X gets most of the eyballs as long as someone else who is better will eventually displace him (or her).
Income inequality is similarly problematic when the main (or perhaps even sole) predictor of a child's income is his (or her) parents' income, instead of some sort of merit. If the only way to be rich is to be born that way, ideas and improvements get stifled.
June 17, 2008 2:03 PM | Reply | Permalink
Or, to put it better: social and economic mobility are crucial.
June 17, 2008 2:15 PM | Reply | Permalink
I am always amazed reading libertarians. Mr. Lee you write
" We should expect that even in a perfectly just economic system, some people would earn a lot more money than others, and that the gap would grow over time as technological progress increases the size of the market and the potential for division of labor."
Then again in your next sentence you write:
"This isn't to deny that our real-world economy includes economic distortions that unjustly exacerbate the gap between the rich and the poor."
Then again in the next sentence you write:
"But it does mean that the bare fact of income inequality isn't evidence of injustice. If we reformed every regressive and unjust aspect of our economic system, we should still expect a high degree of inequality of pre-tax incomes."
Now you have written in the three excerpts above about economic justice and a just economic system. But what is a just economic system? Is it one that operates according to laws that guarantee fairness of operation? Is it a game where everyone starts out at birth with equal opportunity? Is it a system which taxes every person the same percentage of income? of wealth? None of these terms have been defined nor has even an inkling of meaning been given to them. It does differ you know. From person to person; from community to community, from economic system to economic system. It would be enormously helpful to me if you might indicate what constitutes "just" or "justice" or "fairness" in the context you are using. Thanks.
June 17, 2008 4:52 PM | Reply | Permalink
Finally, an intelligent article about inequality.
June 17, 2008 6:38 PM | Reply | Permalink