Living with the power law

Suppose a mathematical formula was discovered that explained the necessary outcomes for all complex systems — including human actions.  Suppose, further, these outcomes were found to be deeply unequal and apparently unfair.  Our ideals would collide with our understanding of reality.  How would we respond?

In fact, such a formula has been discovered, and we have responded by ignoring it.

It’s called the power law, and it accounts for the distribution of wealth, property, productivity, audiences, sales of competitive commodities, the movement of financial markets, scientific citations, contributions to wikipedia, frequency of appearance of words in English, rates of adaptability and experimental success, and many, many more outcomes of complex social systems — including, alas, the number of hits and links to blogs such as this one.

I have remarked on the power law before, when arguing against the idea of an Internet-driven “daily me” of cocooned, self-validating information.  But I just finished Clay Shirky’s Here Comes Everybody, a brilliant book about social networks in which the formula reappears constantly to describe a vast range of outcomes.  The Web is indeed  ruled by the power law, but so, it seems, is every other large-scale human interaction.

The key feature of the power law is disproportion.  The top best-selling book sells twice as many copies as the second, which sells twice again as many as the next, and so on down the list.  A few big sellers thus inhabit the head of the power law chart, which spikes dramatically upward.  Most books hardly sell at all, and are represented by the chart’s “long tail.”

Few winners, many losers.  And according to Shirky, the larger the system, the greater the disproportion:  the rich get richer, blockbusters sell more, Instapundit receives a larger share of the Internet audience than Vulgar Morality.  Power law outcomes trample on our sense of normality.

In a liberal democracy, we tend to assume that people are roughly equal, which means no individual can fall too far from the average.  The bell curve, we imagine, applies to every significant description of human affairs.  This is true of human height — the tallest person won’t be 1,000 times taller than the average.  Also true of human intelligence.  But complex social systems, Shirky writes, achieve highly skewed imbalances, and “cannot be understood as a simple aggregation of some nonexistent ‘average’ user.”

Any system described by a power law . . . has several curious effects.  The first is that, by definition, most participants are below average.  This sounds strange to many ears, as we are used to a world in where average means middle, which is to say where the average is the same as the median.  You can see this “below average” phenomenon at work in the economist’s joke:  Bill Gates walks into a bar, and suddenly everyone inside becomes a millionaire, on average.  The corollary is that everyone else in the bar also acquires a below-average income.

What accounts for the general disproportion in outcomes?  In an earlier article, Shirky makes this extraordinary statement:  “Diversity plus freedom of choice creates inequality, and the greater the diversity, the more extreme the inequality.”  He adds:  “The very act of choosing, spread widely enough and freely enough, creates a power law distribution.”

Diversity and choice are core liberal democratic ideals.  Yet, if Shirky is correct, their consequences appear disastrous for liberal democracy:  massive structural inequality in every aspect of social life.  Few writers seem interested in taking on this paradox.  One who did is the author of the Econophysics blog, who worries about “potential misuse of the power law” leading to an “unhealthy concentration of political and social power.”  He continues:

If the power law is misapplied in this way — so as to reinforce unmeritocratic privilege — then society could suffer dire consequences. We will have leaders — in what are suppose to be democratic societies — that will be out of touch with their people. Rather than being public servants, politicians and policy makers will become callous and self-serving. Entrepreneurs that are from the ‘long tail’ rather than at the top of the power law may find themselves unable to find suitable business opportunities regardless of the merit and objective worth of their ideas. Otherwise intelligent and deserving people may be shut out of educational opportunities largely because they ‘chose’ the wrong parents.

More insidious than even those worrisome scenarios is the possibility that those who have the most power and influence in society will have too much in common with each other and too little in common with the masses down the long tail. This sort of cookie-cutter conformity will lead to a tacit lack of diversity and may even create an atmosphere of thinly disguised discrimination and bigotry.

On the face of it, these are reasonable concerns.  The power law seems superficially to describe an aristocracy ruling over a human herd.  However, pursuing this line of thought raises more questions than it answers.  One might invoke conspiracies by blue-bloods, capitalists, or Jews to account for inequalities in wealth or property.  But how to explain the disproportion in contributions to wikipedia — or blog links — or productivity — or scientific citations?  Skew relations rule inputs to social systems, not just outcomes.

To decry a “tacit lack of diversity” in outcomes ignores the troubling paradox that, according to Shirky, diversity is a necessary condition to power law arrays.  To equate the long tail with impotence disregards the findings of Chris Anderson and of Shirky himself.

More fundamentally, to fear like the Econophysics blogger does a “tyranny of the power law” makes no more sense than to condemn our involuntary servitude to gravity or the monopoly of atomic structure.  The power law is a description of reality.  It isn’t a moral or political principle.  If I were an absolute monarch and decided that the people should only read the 100 best books, each published in equal numbers, the human behaviors described by the power law would still assert themselves.  A few books would be hugely popular, and thus in short supply, while most would go unread.  That, in a nutshell, was the fate of the Soviet Union.

If the power law accurately describes large system interactions, it is incumbent on advocates of liberal democracy to reflect on the meaning and impact of these interactions:  to square reality, as best we can, with our ideals.  Other than the work of authors on social networks, like Shirky and Yochai Benkler, I’ve seen little in the way of such reflection.  The debate on inequality, for example, generally fixates on disparities among income “quintiles” — even though in a highly skewed distribution, this category carries little in the way of descriptive or analytical punch.

What follows, then, is a brief attempt to understand some of the the moral and political implications of the power law, written in the hope that brighter minds will follow.

For a start, a power law distribution is one description of reality.  It shouldn’t be confused with reality itself.  People aren’t isolated points on a chart.  Rather, we cluster in relatively small communities of interest — where, Benkler has found, an individual voice is more likely to be heard.  Those communities often represent our wishes to the larger population.  If I belong to the local chapter of the Democratic Party, I may feel personally validated by Barrack Obama’s victory, even though my own part in it was negligible.

In terms of outcomes, if we are doomed to power law distributions a key requirement of liberal democracy becomes the dynamism of the head of the chart, and the conditions of the long tail.

Free markets ensure dynamism in the creation and loss of wealth.  That’s the idea behind Schumpeter’s “creative destruction.”  Winners win big, but nobody wins for long.  In The New Industrial State, John Galbraith argued that the government needed to become a sort of referee between a monolithic Big Labor and a monopolistic Big Industry.  Most of the companies he thought too big to allow meaningful competition have gone the way of the dodo.  Creative destruction also applies to household income, which oscillates significantly even within a lifetime.

In politics, the power law may be a persuasive argument for term limits such as we have imposed on the presidency.

By definition, most of us live in the long tail, and the conditions there will determine the possibility of freedom for the nation as a whole.  Let me offer three examples of the right conditions.  First, the flip side of the dynamism of great wealth and power is their accessibility to those with less of either.  Second, the difference between head and tail must be of quantity, not of kind.  The rich aren’t really different — in education, information, leisure, travel, manners — they’re just richer.  Third, the floor of affluence must be high:  the long tail must represent a good life, not an impoverished or marginal existence.  From the perspective of freedom, it matters less that a few are wildly rich if most are financially independent.

There remains the question of fairness.  The answer may depend on the domain.  Shirky, for example, argues that the disproportion of traffic in the blogosphere is the result of a fair and equitable process.  Less can be said with certainty about imbalances of wealth and power.  With regard to inputs, fairness becomes undesirable.  The few who contribute disproportionately “drive” social systems.  The great saints and benefactors, the ultimate achievers in morality, politics, science, and industry — they push the human race upward without asking for fairness or help, while the rest of us ride their wake.

From this perspective, the skewed spike of the chart’s head may well stand for the progress of human genius.

COMMENT: Interesting observations from Peter V:

From an amoral analysis the distribution is and will always be the norm as you said.

From a moral analysis, I think anyone who finds themselves in the top 10% because of just actions (not a position of eminence achieved by force or arbitrary privilege) is entitled to that position. This is essentially Robert Nozick’s entitlement theory.

Trouble is, if you find yourself in that 10% and wish to avoid the destruction in Schumpeter’s “creative destruction” you may turn to coercive force or arbitrary favor to maintain your eminence. There are myriad examples of this throughout history. A once successful but now struggling industry that lobbies the government for help (or for harm to their competitors) is a prime example from our times.

Not only does this put an end to the Nozickian morality described earlier, it also puts a stop to what you called the dynamism of the top, because the efforts of the entity are being utilized to lobby a second coercive entity (or to become that coercive entity itself) rather than being utilized to legitimately maintain power in a market. In this sense the opportunity cost of privilege is utility. The more common way of describing this unfortunate situation is “moral hazard.”

If we could imagine a world without coercive entities and with low or no transaction costs (not so ridiculous actually, the world of the internet is essentially that world) we would see at any given moment 10% of the individuals with 90% of the influence. But, because the landscape is fluid and volatile the turn over from that group is fast (people in that 10% are not golden gods…they’re just enjoying their fifteen minutes of fame). I suspect then that the power law does weaken for samples taken from a wider time dimension. This is merely my suspicion. A good question to ask would be: How many top websites from 1999 are still top websites in 2009?

Trouble is that (outside of fantasy internet-land) coercion offers a nefarious way of staying on top well past your fifteen minutes. This is why we still have GM even while they can’t turn a profit and make desirable products. This is why there were dynasties in china that lasted centuries even while they destroyed the societies they ruled.

This is, I imagine, the tyranny that the Econophysics blogger fears. He’s wrong however to claim that the nature of the power law is the cause of said tyranny. It is caused by the use of coercive force to artificially maintain power. In our modern world (GM again) it is caused by liberal democracy. The power law is freedom. Liberal democracy is tyranny.

THE VULGAR MORALIST RESPONDS:  Wow, Peter, I think we almost agree.  But  liberal democracy is political jiujitsu:  it uses one power law distribution against another.  Executive against legislative, judicial against both, state versus federal, local versus both, economic power against political influence, regulation versus free markets, law on top of custom, high producers slugging it out with silver-tongued salesmen, fine quality against big volume, tree huggers against tree cutters, big media against loud blogosphere, and so on, in a system so complex I doubt anyone’s smart enough to manipulate it systemically (but bits and pieces of it — sure).

I am confident the result of this chaos is still another power law distribution.  I think, with far less confidence, that the head of the chart remains a dynamic place.  I am utterly uncertain about the moral disposition of this power law of power laws.

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One Response to Living with the power law

  1. […] That true vanguards exist, however, can be deduced from the shape of all complex human interactions:  the power law. […]

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