Freedom and the power law

Readers of this blog know that I have long been fascinated and troubled by the power law, which imposes a massive inequality in the distribution of anything – from volunteer hours to blog links – in a complex society.

Power law distributions make a mockery of most social and economic analyses.  The human brain seems to take the law of averages for granted, so we speak in terms of “quintiles” in the distribution of income, and of broad “classes” in the organization of society.

In fact, for every distribution in a complex system – say, of income or wealth – a handful of the top-ranked stand at an increasingly greater distance from each other, while the vast majority languish in the long tail of the chart.  Every distribution is inequality on steroids.

Possibly because we think in terms of averages, few attempts have been made to explain, or even describe, the general effects of the power law on social life.  The ever-perceptive Clay Shirky has explored the subject – I’m not aware of anyone else who has tried.

For this reason, I’m happy to see that, in a wonderful series of posts, Sophistpundit has  reflected on the power law and added to our understanding of its implications.

The first three posts deal with the “anatomy of power laws,” beginning with the basic structure.  This is, as noted, both discontinuous and enormously unequal.  There are no “classes.”  There is no “A list.”  Sophistpundit cites Shirky on the subject of blog link rankings:

[T]here is no real A-list, because there is no discontinuity. Though explanations of power laws (including the ones here) often focus on numbers like “12% of blogs account for 50% of the links”, these are arbitrary markers. The largest step function in a power law is between the #1 and #2 positions, by definition. There is no A-list that is qualitatively different from their nearest neighbors, so any line separating more and less trafficked blogs is arbitrary.

The posts then deal with the known reasons for power law behavior, and with one segregator of success – quality.  Sophistpundit concludes with a significant observation:  the dynamism of power law distributions depends on the freedom or unfreedom of the transactional environment.

In what Adam Smith would call a condition of perfect liberty, a power law distribution represents a dynamic structure where people rise and fall in relative prominence all the time. Liberty is the key–and, with this analysis of power laws concluded, I hope to apply them to a particular aspect of liberty in the near future.

This raises an interesting line of inquiry.  I had always viewed the power law distribution as a problem in inequality.  How (I wondered) can highly skewed human arrangements be consistent with liberal democracy’s ideal of moral and political equality?  But to my surprise, the implications of the power law for freedom are even more powerful.

The fourth post in Sophistpundit’s series, “The power law in a free society,” connects power law distributions to human progress and freedom.  Progress depends on early-adopter elites who open the path to mass participation:  think of idle socialites who developed the game of tennis, now a sport to millions.  Such individuals stand at the top of the spike in the power law chart.

One important question from the perspective of liberal democracy is the degree of “churn” at the top.  Some churn will always exist, even in the most ossified societies:  competition among elites will guarantee this.  But to the degree that we approximate Smith’s condition of perfect liberty, the dynamism of the power law will be accelerated in every direction.  Vastly more items will be produced to seek distribution.  Proportionately more individuals or groups will seek to ride those items to the top of the chart.

Speeding up the rate of churn at the top of the chart becomes crucial when a  winning outcome has been undesirable – a corrupt or incompetent ruler, for example.  Under conditions of unfreedom, such an outcome will linger.  Under conditions of freedom, elections and impeachment will sweep new people to the top, minimizing the damage.

Sophistpundit, following Hayek, looks at this process in terms of dynamism among good or bad practices.  I prefer to consider good or bad outcomes – events, people, and products as well as the behaviors which determine their ranking in the distribution.  Still, the point is the same.

The power law exists whether we are free or unfree, but only under conditions of freedom to we have recourse to a change in outcomes.  Paradoxically, this turns the highly skewed inequality of the power law into a potent argument on behalf of political and economic freedom.

Sophistpundit believes that power law relations scale down, all the way to the ground.  “The larger the scale,” he writes, “the more compressed the power law. But there is a power law at every scale–it is simply more dramatic at a larger scale than it is at a smaller one.”

This may well be the case.  Another possibility is that, at the small-world, hunter-gatherer band level, the law of averages really does trump the power law.  That would explain why we have evolved minds so fixated on the former and so blind to the latter.

Read this series by Sophistpundit – first post to last.  It’s important.


One Response to Freedom and the power law

  1. Adam says:

    I settled on the word “practices” only after struggling to think of a word that would describe anything from a new product on the market to a sport to an idea; admittedly, “practices” doesn’t do this very well. Outcomes is probably a better word.

    My (undoubtedly untestable) theory is that power law relationships dominated even in hunter-gatherer settings. Even there a subset probably had more sway, status, influence, whatever you want to call it, than everyone else. And even if food was distributed more or less evenly, it’s possible that the amount of food caught/gathered broke down to a power law by individual.

    But this could just be case of attempting to impose on reality a theory that has the allure of elegance when it is unlikely to be accurate.

    Thanks for the endorsement!

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