Power laws and the laws of power

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The confirmation hearings for the elevation of Ketanji Brown Jackson to the Supreme Court highlighted for me the fight-to-the-death of two types of political power currently jousting both in Washington and Ukraine. In math terms, I describe democracy as a linear function, but autocracy is an exponential “power law.” In democracy, you need to add up millions of equal “integer” votes in order to win a national race; in autocracy, a handful of “big money” votes win the prize. Democracy is winning some battles lately, but autocracy is unfortunately winning the larger war.

Power laws are everywhere in nature as described by physics and biology. While humans learned to count in a linear fashion with integer math (i.e., 1, 2, 3…but without a zero for centuries), nature more often “counts” proportionally, or in algebraic terms, displays exponential growth functions. It is no coincidence that so many of those who don’t understand the power laws of nature also don’t understand the exponential math of money and political power that is screwing us over.

The “big gun” power law of personal wealth

Before we look at a few examples from nature, let’s throw the moose on the table and look at the distribution of net worth (including house equity) by percentile across American families:

If you are in the bottom 80% of American families in terms of your net worth, including your home, the distribution of wealth appears to be almost linear. At the bottom second percentile, families were “under water” by about $55,000 in 2019. At the halfway point of the population, families owned about $121,000 of net worth, rising to about $560,000 at the 80th percentile. You can find your own place in the pecking order here. But past the 90th percentile, “something happens,” and family net worth starts to soar.

I had to stop the graph at the 99.5 percentile and $18 million of net worth because your screen is not big enough, indeed, your ceiling is not high enough, to track where the final 0.5% of the country’s family net worth grows to. According to the U.S. Census Bureau, that last one-half percent encompasses about 650,000 very wealthy households, out of 130 million total households in the U.S. by their count (84 million of these households being “family units” with the rest single-person households).

By several reports, Jeff Bezos is closing in on $200 billion of net worth, so you can try to plot Mr. Bezos that on the graph above. If that graph is three inches high on your screen, then Jeff Bezos is some 2500 feet above your house!

A power law is the math behind what is happening in this case above the 90th percentile. Each percentile (or about 1.3 million households) shows a modest 0.25% (one-quarter of one percent) compounded, or exponential growth in net worth from the percentile below well past the 98th percentile. That makes the first eighty percentile points appear quite flat. Compounded rates can grow subtly, as we learned in the early days of the Covid pandemic, before they then “take off” until something else in nature (or the economy) applies a brake on that growth. If there is no brake, then there is no limit, as Mr. Bezos demonstrates.

Democracy in the flat part of the curve

In a democracy, the vote of a person in the 20th percentile in the chart above counts the same as a person in the 95th percentile. That is basic linear math. If each of those families in the graph above had an equal share of votes, it is easy to see how that “flat middle 50%” would seem to have a lot in common as a voting bloc on economic issues. All of them are above water financially, but none has more than $400,000, probably in house equity for most. That is theoretically enough of a voting bloc to sway a fair election in a democracy if the main criterion is financial self-interest.

However, instead of the theoretical “one person, one vote” in America, there is a lot of evidence that we are really living in a “one dollar, one vote” society, with the votes of the middle swayed by purchased messages financed by the phenomenal wealth at the high end of that graph. You have likely been convinced by the media you consume daily that the people in the 95%+ range have your own best interests at heart when it comes to brand consumption, taxes, military spending and healthcare, and so you vote them low taxes and great political power.

What about the influence of religion? Let me suggest that “big money” is a force here as well. During the 1950s, the Catholic church and the “old mainstream” Protestant denominations were awash in a demographic wave of baby boom families and their financial support. Scandals, an aging population, and a “southernization” of religion in America all contributed to the decline of Catholic and “old mainstream” power and a replacement “big money” rise in fundamentalist and “Dominionist” denominations, mostly of an Evangelical stripe. The current composition of the U.S. courts demonstrate their financial power.

Citizens United and the purchase of democracy

When I bought my first Subaru automobile a couple of decades ago, the car dealer commented, while writing up the deal, “I’ll bet you are a teacher.” Busted!

Most Americans insist that they are not swayed by the multitude of media messages that flood their televisions and computers daily trying to influence their buying behavior. That is demonstrably wrong. If it were not true, then the financial model for most of America’s media throughout our history, beginning with advertiser-supported broadsheets during the American Revolution through to web page click-through Google advertisements, has been a multi-trillion-dollar waste of money. It has not.

It works the same way for media-based political messaging. We are all influenced by the media company that we keep. Rich Americans have pretty much had their way politically ever since our founding as a country, but when the U.S. Supreme Court blew the legislative lid off political spending by corporations and rich individuals in the Citizens United v. FEC case of 2010, the business of political influence moved well into the soaring right side of that graph above.

Political fund-raising from the masses is a linear function. It is possible to raise a lot of money at $25 a head for a broad-consensus candidate representing the bottom 80% in our graph above. However, the super-wealthy Koch brothers reportedly spent over $14 million in campaign contributions in the 2020 election cycle, cancelling out over 500,000 small-dollar contributors. That is the difference between “linear math” fundraising versus “power law” fundraising. And it works.

Here is where Ukraine comes in. Russian oligarchs have reportedly funneled millions of dollars into the campaigns of prominent Republican politicians in recent years. Some of these same politicians have been very reluctant (cough, cough, Ron DeSantis) to criticize and take action against the Russian invasion into Ukraine. To say they are not related would be foolish on its face. And yet so far, all that gets prosecuted is small potatoes stuff like a Nebraska congressman convicted of lying to the FBI about a relatively-small bribe from a Nigerian businessman

The power law of war

Democracies generally do not go to war with other democracies. Sometimes the autocrat to blame is obvious, such as with the Ukraine invasion by Vladimir Putin. Sometimes, as with America’s war against Iraq’s Saddam Hussein, the calculus is fuzzier. My personal take is that the autocratic wanna-be rich American industrialists “owned” the Bush administration and sold the American public on a multi-trillion dollar, million-death expansion of the Afghanistan incursion into Iraq on dubious evidence.

Those trillions of dollars did not “disappear,” by the way. They were largely spent in American “defense industries” who have perfected the business model of building things, blowing them up, and building them again, all at the expense of the “linear mass” of American taxpayers. Very rich men (and almost always men) use their power to force the masses of American young people to die for them in war, while sucking up taxpayer money to fund it.

Nature’s power laws

Mathematics is a human-created language that allows us to translate some of nature’s reality in terms we can understand and communicate. As I have written in the past, we perceive a musical scale, for instance, as linear steps in frequency (“do–re–mi”) but the distance between the frequencies of those notes is actually logarithmic, like a guitar’s changing fret distances, with every octave doubling the frequency of every note in the octave below it (or halving the string length). That is the power law of music.

DAngelico EXL fretboard

Likewise, we perceive the loudness of a sound as best represented by a linear scale, say, a volume knob’s one-to-ten (or eleven if you are a Spinal Tap fan). Physically, however, the intensity of the sound wave is increasing at an exponential rate. Your brain is “doing the logarithmic math” to compress the signal for “good enough” processing.


Our perception of light frequencies and intensity work the same way, as does our perception of the intensity of touch. The best explanation for this biologically is that your brain can store and measure in your neurons the approximate logarithm of a sensation much more efficiently, while also representing a much broader range of that sensation, than if they were trying to encode a linear value. This logarithmic encoding happens everywhere in nature, far more than you will find some linear biological representation of “1…2…3”. Everything from seashells to coronavirus populations grow at exponential, not linear, rates until some natural brake shows up.

Back to politics and Supreme Court nominations

Why was I reminded of power laws during the hearings for confirming Ketanji Brown Jackson to the Supreme Court? As I have written in the past, the confirmation hearing remark of current Chief Justice John Roberts that he “only calls balls and strikes” belies the dominante reality of his legal career.

Justice Roberts, along with current Justices Brett Kavanaugh and Amy Coney Barrett in their pre-judicial careers, were “coincidentally” all part of the Republican Party legal team that swung the disputed 2000 Florida vote, and thus the presidential election, from Al Gore to George W Bush. That is legal “power law” at work.

As Judge Ketanji Brown Jackson has been attacked for her role as a public defender and her challenging of sentencing guidelines, I was reminded that much of our “justice” system is a facade for the exercise of this “power law” math. So many court cases look to be the “calling of balls and strikes” in a game between the Boston Red Sox and a Little League team. As Donald Trump has demonstrated through his strategy in facing some 3500 lawsuits during his business and political career, when you have enough money, you can hold Justice at least at bay most of the time, fighting to a tie game in thousands of “extra innings,” and win by (sometimes literal) default.

As I noted earlier, if there is no brake on exponential growth, then there is no limit. We all could use a brake here.

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  1. Pingback: The “Great Replacement” math revisited – When God Plays Dice

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