Of power laws and random fools

Since reading Clay Shirky’s Here Comes Everybody, I have been puzzled by the moral implications of the power law — the highly skewed distribution that describes pretty much every complex human interaction, from wealth and income to book sales and blog visits.  The power law chart shows a sharp peak and a long tail.  Because, necessarily, most of us live in the long tail, conditions there will determine the character and worth of the community in which we live.

But how are we to characterize those at the top of the power law’s crazy spike — the very few who surpass us long-tail dwellers by so very much?  Are they simply a fact of life, members of a natural aristocracy, or moral monstrosities worthy of a French Revolution?

The question makes sense only when the skewed distribution of the power law reflects differences in wealth, income, or power.  Nobody worries that the same disproportion applies to, for example, volunteer hours or blockbuster movies — much less the recurrence of words in the English language.

The power law depicts a vast inequality.  That’s the moral dilemma.  Further, such inequality isn’t an American or a capitalist attribute.  It’s universal, as Vilfredo Pareto discovered a century ago.  Every human community at a certain level of complexity produces highly skewed distributions of wealth and income.  The obvious question is:  why?  What causes the statistical gulf between the head of the chart and the long tail — between Warren Buffett and the rest of us?

Although the power law until recently has been relegated to our intellectual attic, and seldom discussed, I suspect the answers would tend to follow predicable — and conflicting — ideological paths.  Those who favor government controls over the economy will see conspiracies of selfish interests; those who favor free markets will see great fortunes amassed by people who serve great needs.

Nassim Nicholas Taleb, in Fooled by Randomness, proposes a third way.

Taleb’s style is self-consciously eccentric — some of it charming, much of it annoying.  He’s an options trader, but he’s desperate to be thought of as an esthete and a philosopher — he quotes Thucydides, Karl Popper, Rimbaud.  He’s liable to write, on any given page, something like:  “People have often had the bad taste of asking if my day in trading was profitable.”  We are told, many times, that he comes from an illustrious Greek Orthodox Lebanese family.  He mentions every famous person he knows, and shows us, with a certain aggressiveness, how much smarter than them he is.

His family’s wealth was wiped out in the 1970’s civil war in Lebanon.  Taleb is an exile, victim of a random catastrophe, and he is obviously driven by insecurity.  Unlike most in his condition, however, he has turned insecurity into a philosophy of life.

Warren Buffett, Taleb suggests, may just be lucky.  The massively wealthy who inhabit the top of the power law’s spike are the survivors of a much larger number.  They gambled and won; the majority gambled and lost.  Mathematically, someone had to win.  Hindsight bias persuades the winners that they are masters of the universe, and knew what they were doing when they won.  Survivorship bias persuades the world that these people become bigtime winners because they are very good at what they do.  Taleb suspects this actually turns “causality on its head”:  “we consider them good because they make money.”  He adds, “One can make money in the financial markets totally out of randomness.”

Taleb deals in mathematical probabilities:  his favorite toy is a virtual “Monte Carlo machine” which generates alternative histories.  He explains, persuasively, how some fraction of all financial traders must randomly win their bets.  He observes that the human mind didn’t evolve for probabilistic thinking.  The winners have no idea they were simply favored by chance.  They credit their own superior qualities and brilliant systems, and thus imagine they will continue to win their bets indefinitely.  They are “fools of randomness.”

This is hubris — a kind of madness brought on by arrogance.  In the classical world, it led inevitably to a tragic outcome.  In the financial world in which Taleb labors, it almost always leads to a “blow up.”  The winners pile their winnings on a sure bet, and lose.  Fooled by Randomness at one level consists of a series of morality plays involving luck, arrogance, and downfall.  Carlos, the emerging markets trader, for example, was successful for years, earning his bank $80 million.  “He could do no wrong.  He believed that the economic intuition he was endowed with allowed him to make good trading decisions.”  Then he blew up over a single summer to the tune of $300 million.

At a deeper level, however, Taleb’s story isn’t about lucky bets, but about the radical uncertainty of human knowledge.  In a complex event, an indefinite number of forces push and pull at all the actors.  Cause and effect become diffused and impossible to replicate.  Every generalization, every regularity, must be provisional, subject to future refutation.  This is what Taleb, harking back to David Hume, calls “the problem of induction.”  Truth is the hostage of time.  What appears general will turn out, given time, to be partial.  Those who bet on the whiteness of swans will be blown up by the appearance of a single black swan.

Taleb coined the term “black swan event“:  that is, a low-probability, high-impact outcome, which by definition is unpredictable yet unavoidable.  It is the theoretical backbone of an exile’s insecurity.  Luck rules like a mad king.  Given enough time, every plan will be derailed by the unexpected.  Every Carlos can be considered, in a sense, a black swan event, lifted out of his competence by randomness.  Every catastrophe that befalls a Carlos is also a black swan event, the negation of a system, the explosion of a generality:  the problem of induction felt as humiliation, devastation, loss.  9/11 was a black swan event.  So was the civil war in Lebanon.

If Taleb has got it right, the top of the power law chart is the natural habitat of the black swan event.  It is a place of blind selection and random churning.  This is true across all domains — sales, productivity, scientific citations, rates of experimental success, number of hits and links on blogs.  When considering the power law’s inequality in wealth and income, the “cause” is likely to be a noncause:  probability, the chance determination of a cosmic Monte Carlo machine.

If one wins that bet, it’s best not to take oneself too seriously.  If one fails to climb to the top of the chart, it’s also best not to take the winners too seriously.  Arrogance will breed hubris, and most random fools will topple down faster than they rose — to be left wondering, in loss and misery, how their brilliance could have failed so suddenly.

Prudence and resignation, ancient virtues, are recommended if this state of affairs holds true.  Of course, the long tail of the power law distribution — our humble home — is less prone to randomness than the financial markets.  Few plumbers or dentists will ever be wiped out overnight.  But in the world according to Taleb, randomness is pervasive.  A black swan event, bred in the instability of the spike, will come crashing down on the long tail, and we will find ourselves, sooner or later, coping with a terrorist-induced horror or a financial meltdown.


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