The power law and the law of power

Continuing with the theme that "the market" under laissez-faire capitalism does not distribute wealth equitably or fairly. Instead, wealth distribution tends to follow the classic power law:

The economist Edward N Wolff, of New York University, has pointed out that, as of 2007, the top 1% of households in America owned 34.6% of all privately held wealth, and the next 19% had 50.5% of the wealth. This means that just 20% of the people owned 85% of the wealth, leaving only 15% for the bottom 80% of the people...the 80/20 rule – variously called Pareto's principle, Zipf's law, the long tail or Benford's law, depending on what you are studying – a staple in scientific, economic and business textbooks, the go-to idea to show how the frequency of a set of natural events is not always what you might recognise as, well, natural.

The maths underlying the 80/20 rule, known as the power law distribution, is found in many natural systems over which no single human has much influence. Its concentration of the extremes seems built into the fabric of complex systems that depend on numerous factors that continually change over time....A distribution based on a power law says extreme events (or richest people, or biggest websites) account for most of the impact in that particular world, and everything falls off quickly afterwards. The combined wealth of the top 10 richest people in the world is orders of magnitude greater than the next 10, which is orders of magnitude greater than the next 10, and so on. The rest of the field sits in a long, almost-irrelevant tail.

This distribution might sound odd. At school, we're introduced to a different distribution, the more familiar "normal" (or Gaussian), which is best displayed in the bell-curve spread of values around an average. Measure the heights of a random selection of men, say, and most will be around the average value, with progressively fewer as you go in either direction away from the middle. Plot this on a graph and you get the bell curve.

Power law distributions, however, do not cluster around a single value. The impact of one big earthquake, for example, is bigger than the sum of millions of smaller, more common ones. Very few huge solar flares erupt from the surface of the sun, but those few are more significant than the endless thousands of smaller ones. The same applies to the numbers of big cities, the size of the Moon's craters and the occurrence and citations of scientific papers.

Once you know power law distributions exist, they become very useful. The concept of the "average" is useless, for example, when talking about things that follow power laws. The average height of the people in a room (following the normal distribution) might tell you a lot about the spread heights of people in that room, but the average wealth of a country's citizens (which follows a power law distribution) tells you little or nothing about how rich or poor most people are.

The mathematical law that shows why wealth flows to the 1% (The Guardian)

But it has nothing to do with skill. If you start off with equal fortunes, some will get fabulously wealthy by sheer luck alone:

The wealth project took shape as Fargione read Kevin Phillips' "Wealth and Democracy: A Political History of the American Rich." As Phillips notes, Alexis de Tocqueville in 1837 warned the young American republic that its industrial class, "one of the harshest that ever existed," could create "permanent inequality of conditions and aristocracy." And so it did. Despite the interruptions of the Populist and Progressive eras and the New Deal, writes Phillips, by 2000 "the United States was not only the world's wealthiest nation and leading economic power, but also the Western industrial nation with the greatest percentage of the world's rich and greatest gap between rich and poor."

Fargione discovered that other mathematical models of wealth have failed to account fully for its concentration. Some economists blamed wealth concentration on political factors such as cronyism, or on differences in the sharpness of investors. "What would you expect would happen on its own without a lot of intervention for redistribution of wealth?" Fargione wondered.

He began his research with a simple question: Can chance alone account for wealth concentration?Fargione focused on entrepreneurs (who make up one in nine Americans) because, contrary to all advice to diversify portfolios, they typically plow their earnings back into their businesses. "Twenty years ago, Bill Gates didn't say, 'Well, I made some money -- I think I'm going to diversify my investment.'" The all-in strategy is risky, but when it works it leads to rapid accumulation of wealth.

He assumed that all entrepreneurs began with equal wealth. Returns varied, solely by chance. (Past performance is not an indicator of future success -- you've heard that before.) Earnings were reinvested. And for the purposes of the study, the investors seamlessly passed their wealth on to heirs. Says Fargione, "I started out with an Excel spreadsheet and just did some simulations that ran out over time."

I'll spare you the calculus, but according to Fargione's model, by the "inexorable effect of chance," and chance alone, "a small proportion of entrepreneurs come to possess essentially all of the wealth. ... The concentration of wealth occurs merely because some individuals are lucky by randomly receiving a series of high growth rates, and once they are ahead with exponentially growing capital, they tend to stay ahead."

According to Fargione, greater variation in rates of return hastened the concentration of wealth. Inequality grows with time. Wealth concentration continues despite periods of recession and depression. And splitting estates among heirs does not appreciably slow concentration.

In the real world, of course, some people are more skilled at making money than others. And business owners who are making a high rate of return, by operating highly successful companies, tend to continue earning high rates of return. And the rich have connections and other means to increase their wealth that most folks lack. "Those other factors would exacerbate the underlying pattern," says Fargione.

That underlying pattern is the inexorable concentration of wealth and the inevitable result -- winner takes all. Says Fargione, "If you play long enough, someone will end up with all the money." Indeed, that is what has been happening in the United States, where the top 1 percent owns about 40 percent of total wealth.

The 1 percent: How lucky they are (Minneapolis Star-Tribune)

This may help to visualize this in action: The Height of Inequality (The Atlantic). A summary:

Jan Pen, a Dutch economist who died last year, came up with a striking way to picture inequality. Imagine people's height being proportional to their income, so that someone with an average income is of average height. Now imagine that the entire adult population of America is walking past you in a single hour, in ascending order of income.

The first passers-by, the owners of loss-making businesses, are invisible: their heads are below ground. Then come the jobless and the working poor, who are midgets. After half an hour the strollers are still only waist-high, since America's median income is only half the mean. It takes nearly 45 minutes before normal-sized people appear. But then, in the final minutes, giants thunder by. With six minutes to go they are 12 feet tall. When the 400 highest earners walk by, right at the end, each is more than two miles tall.

The above study was taken from ecology. Indeed, this has been the pattern for most of human history. During the twentieth century, it was disrupted by rapid growth, technological innovation, the emergence of major new industries, political reform and legislation, populist movements, two world wars, competition with Communism and so on. But are we now doomed to return to the pyramid-shaped structure of the past due to the power law?