Vilfredo Pareto

The “Pareto principle” is sometimes referred to as the “80-20 rule,” but that is giving Vilfredo Pareto short shrift. The precise distribution figures of wealth in any given society do not always match the 80/20 distribution Pareto first observed in Italy; for any given nation at any given time the precise numbers might be “20% of the population controls 90% of the wealth,” or “15% of the population controls 95%” of the wealth,” etc., etc. As of 2007, for example, 20% of the American population controlled about 93% of the wealth in the United States. That concentration has almost certainly gone up since then.

No, what is really interesting about Pareto’s study is that regardless of the actual distribution of wealth for any given population at any given time, the manner in which that distribution manifests itself is always the same: not by a symmetrical “bell-shaped” distribution pattern (the only distribution pattern most of us were taught in school), but – as one gets closer and closer to the wealthy end of the spectrum -- by a power-law distribution. As Mark Buchanan describes it in Nexus: Small Worlds and the Groundbreaking Science of Networks:

[T]oward the wealthy end of the distribution, each time the value for wealth is doubled, the number of people who have that much [wealth] falls off by a constant factor. Up-to-date numbers show the same pattern for countries all over the earth. In Japan, for example, the constant factor turns out to be close to four. (emphasis added).



(Buchanan, p. 189).

Again, what is interesting is not the specific numbers. The power factor by which wealth is concentrated is different for any given society, just as the actual wealth concentration percentages are different for any given society. What is interesting is that the manner of distribution is always the same: a heavy concentration of wealth in the hands of the few, that concentration being easily plotted using some power-law distribution.

It is the universality of the distribution pattern that presents the puzzle. Pareto’s Law isn’t concerned with differences in creativity or productivity between individuals, and it isn’t concerned with differences in economic systems, it just describes very accurately wealth distribution in a population as a whole. It can’t tell you why a particular person or family got rich, only that a certain number of people or families will inevitably become rich and by a very definite amount of wealth relative to the society in which they live.

But since the general pattern of distribution is always the same in every society, one is led to believe that no matter how a society’s economy is engineered there is something fundamental to our economic network that leads inexorably to the same type of wealth distribution. But what?

Jean Phillippe Bouchard and Marc Mezard

One potential answer was suggested by University of Paris physicists Jean Phillippe Bouchard and Marc Mezard in their 2000 paper Wealth Condensation in a Simple Model of Economy. The term “wealth condensation” means exactly what it sounds like. It describes “a process by which, in certain conditions, newly created wealth tends to become concentrated in the hands of the already wealthy individuals or entities, a form of preferential attachment.” In other words, it describes the already rich getting even richer over time.

(I’ve read Bouchard and Mezard’s paper – or, at least, I’ve allowed my eyeballs to stare at it – and I have to admit that their math is well beyond me. Accordingly, there is a link to the actual paper provided above, but I am going to describe their findings by paraphrasing the explanation/translation Mark Buchanan sets forth in Nexus. The relevant passage in Buchanan’s book can be found in pages 188 – 96.)

Essentially, Bouchard and Mezard created an extremely simplistic model of a “wealth distribution network,” i.e., an economy, that took into account only three basic distribution factors.

The first might be thought of as the “dispersal factor,” and it is the primary means by which wealth spreads itself throughout society. Essentially, this factor consists of nothing more than trade. Every time someone purchases a product or a service they transfer money from their own pocket into those of others, and those others then use some of that money to purchase goods and services from others in turn, who then do the same (and so on, and so on, etc.)

This basic -- almost osmotic -- process is what tends to keep wealth flowing from areas of high concentration (the wealthy) to areas of low concentration (the less wealthy). This is the factor – whether they know it or not – that Conservatives are referencing when they keep telling us to “hold on – trickle down prosperity will happen any minute now.” And, indeed, if this were the only factor affecting wealth distribution one might expect to eventually reach equilibrium where wealth was distributed uniformly across society and nobody was especially poor or especially rich. But that obviously is not what happens in the real world.

No, in the real world there is a second factor at play that kind of screws that idea up. This second factor might be thought of as the “concentration factor,” and it is the primary means by which wealth accumulates in one place. Essentially, this factor consists of nothing more than investment of money over time. Every time someone purchases a capital good that may accumulate value, or that same person invests money in a profit making venture, that person is sinking wealth into an operation that might draw even more wealth toward it. This process isn’t so much osmotic as gravitational, like a black hole where any additional wealth that crosses the event horizon gets sucked in and becomes one with the hole. [See what I did there? While not a Buddhist myself, I am a big fan.]

These two factors – the dispersal factor and the concentration factor – obviously operate at cross-purposes. So one naturally wonders whether they eventually balance each other out or whether one proves to be more powerful than the other. And this is where the insight of Bouchard and Mezard comes into play.

Prior to 2000, everybody else who had attempted this type of simplistic distributive modeling had also restricted themselves to deriving equations based on the dispersal and concentration factors already identified. But Bouchard and Mezard did something new: they posited a third factor.

It seems kind of commonsensical once someone says it out loud, but Bouchard and Mezard pointed out that not every investment scheme succeeds. Sometimes new money gets plowed into a scheme and the scheme just goes bankrupt; when that happens, all that seed money is lost. Investment is not risk-free. And that, of course, means that any given economic actor is not equally as free to engage in investment activity as is any other given economic actor – if you’ve only got $1,000 in the bank you will naturally be leery of sinking $500 into a new, potentially risky venture. On the other hand, if you’ve got $100 million in the bank, you probably are willing to risk $100,000 on something equally as risky.

It is kind of like what Chris Rock talks about when he argues that prenuptial agreements are more important for poor people than for rich people:

People think you gotta be rich to get a pre-nup. Oh no. You got twenty million and your wife wants ten, big deal, you ain’t starving. But if you make thirty thousand, and your wife wants fifteen, you might have to kill her!

With this simple observation, Bouchard and Mezard found that they could turn the network picture into a set of explicit and fundamental equations to follow wealth as it shifts from person to person, and as each person receives random gains or losses from their investments. With equations in hand for a network of 1,000 people, the two physicists set to work with the computer to see what they might imply. Not knowing precisely how to link people together into a network of transactions, they tried various patterns. And unsure of how precisely to set the balance between the importance of interpersonal transactions [read: trade] versus investment returns, they tried shifting the balance first one way and then the other. What they discovered is that none of these details alters the basic shape of wealth distribution. Giving people random amounts of wealth to start out, and letting the economy run for a long time, Bouchard and Mezard found that a small fraction of the people always ended up possessing a large fraction of the entire wealth. What’s more, the precise mathematical distribution followed Pareto’s law exactly – in excellent correspondence with data from the real world. This result occurred despite the fact that every person in the model was endowed with identical “money-making” skills, suggesting that difference in talent may have little to do with the basic inequality in the distribution of wealth seen in most societies. Rather, what appears is akin to a fundamental law of economic life, a law that emerges naturally as an organizational feature of the network. (emphasis in the original)



I’ll let Mark Buchanan explain the difference this basic insight made:(Buchanan, pp 191 – 92).

What Do You Mean “It’s Inevitable”?

Pareto, Bouchard and Mezard’s studies all strongly indicate that the economic networks we create will by their very nature lead to inequalities in wealth distribution. And not because the wealthy are inherently smarter, or more virtuous, or more qualified – on average – than any other random person, but only because someone has to end up on the receiving end of the network’s distribution pattern and – hey! – you just got lucky, big guy! Without interference by human agency, income inequality seems to be an inevitable result of any free market economy.

Here’s one way to look at it: suppose you have 100,000 test subjects whose job it is to flip a coin and call the results. The only object is to stay in the game. After the first flip, 50,000 people will have washed out . . . but 50,000 people will have called the coin flip correctly.

After the second flip, 25,000 people will wash out, but 25,000 other people will now have correctly called the coin flip twice in a row. After a third flip, 12,500 people will wash out, but 12,500 people will have correctly called the coin flip three times in a row! And on and on and on.

After 15 iterations, you will be down to about 4 people who have correctly called the coin result 15 times in a row! But does this mean these four are precognitive, or especially lucky, or just really, really good at calling coin flips? No, it just means that these were the 4 people that Fate’s random waiting fist of chance settled on – after all, somebody needed to call all those flips correctly, these four just happened to be the ones to have done so. It was inevitable that four people would do it, but it was random chance that it would be these four.

Now imagine the same scenario, but with a minimum $1,000 bet being placed on the outcome of each coin flip. 100 participants start the game with $1 million each, and the other 999,900 participants start with only $1,000 each. Whenever someone runs out of money, they have to leave the game. The last 5 people left standing get to keep all the money.

Who can afford to play the game longer, do you think? Who has a greater appetite for risk? Who can absorb a long period of bad luck and yet still come out on top? What do you want to bet that at least one of the participants who started with $1 million will end up taking it all?

‘Cause my money’s on the rich guys.

* * *

So let’s be real clear about what the “inevitability” of wealth inequality entails.

It does not reflect any kind of moral determination. Plagues, earthquakes, hurricanes and a certain percentage of fatal accidents are all inevitable as well – but since we climbed out of the Dark Ages most of us have ceased to believe that it is “God’s Will” we suffer such things. That is why we enact sanitation codes, take care not to dig the village well too close to the communal privy, and wash our hands. It is why we invented antibiotics and chemotherapy. It is why we spend money monitoring earthquakes, invest in a national weather system, and fund the Center for Disease Control. It is why we put on our seatbelts, wear condoms and – oh, yeah – vaccinate our children against HPV. Yes, some bad things are inevitable -- that doesn’t mean we don’t do what we can to avoid or lessen their effects.

Nor does the inevitability of wealth inequality necessarily reflect the working of some efficient Social Darwinism (i.e., what Conservatives call “the good Darwinism”). While it is true that some individuals do acquire great wealth because of their innate ability, talent, intelligence, and hard work, the inevitableness of wealth inequality in society springs from none of that. The inevitableness of societal inequality as a whole springs out of nothing more than (i) the difference in the amount of money different people bring to the table when they start The Game of Life and, (ii) the brutal laws of probability and risk that apply to us all.

These all may seem like very basic points, but then again so does the case for evolution or getting the HPV vaccine. Given the state of our political discourse, I am not so sanguine as to just ignore the possibility that if low information voters decide that income inequality is “inevitable” they won’t just treat this news as further evidence of “God’s Will.”

This is especially true in light of a recent Baylor University study that found:

[a]bout one in five Americans combine a view of God as actively engaged in daily workings of the world with an economic conservative view that opposes government regulation and champions the free market as a matter of faith. “They say the invisible hand of the free market is really God at work,” says sociologist Paul Froese, co-author of the Baylor Religion Survey, released today by Baylor University in Waco, Texas. “They think the economy works because God wants it to work. It’s a new religious economic idealism,” with politicians “invoking God while chanting ‘less government,’” he says. “When Rick Perry or Michele Bachmann say ‘God blesses us, God watches us, God helps us,’ religious conservatives get the shorthand. They see ‘government’ as a profane object – a word that is used to signal working against God’s plan for the United States. To argue against this is to argue with their religion.” Most (81%) political conservatives say there is one “ultimate truth in the world, and new economic information of cost-benefit analysis is not going to change their mind about how the economy should work,” Froese says.

I despair to think that pointing out to these people that the wealthy didn’t get to be rich because they are better, or smarter, or “more productive” just means that these people will then be forced to conclude that the rich must be wealthy because they are “holy.”

Ye Gods.

What’s to be Done?

It's simple.

Unlike the 20% referenced in the Baylor University study, the rest of us can actually learn from and make use of Pareto, Bouchard and Mezard’s work – all we have to do is recognize that the economy is not “God’s Will” or something “divinely ordained” but is instead just a network that we create ourselves, sustain ourselves, and that has value only so long as it works for us . . . and that we can tweak and correct that system as needs be.

(Brief aside . . . I am a religious agnostic, but one of my favorite stories is the story of Jesus and his disciples picking grains of wheat on the Sabbath and eating them because they were hungry. (Matthew 12:1-45) The Pharisees berated Jesus for this, because it was against the Law. And Jesus, essentially, told them to shut the hell up because it was more important that people not starve than that the law be fulfilled. The Law – like the economy – exists for Us, and not the other way ‘round.)

One of Bouchard and Mezard’s chief conclusions, unsurprisingly (as they themselves put it), was that taxation by the body politic went a long way toward minimizing the inequitableness of an unfettered market. In an ideal world, perhaps, a way could be found to force the already wealthy to trade more than they invest, but in the real world this is impracticable. However, taxation essentially functions as the equivalent of forced trade, and thus fosters the dispersal effect of wealth – which, due to existing inequalities, will otherwise always be seriously outgunned by the concentration effect.

You know . . . there has been a lot of ink spilled over the past few years about why America has seen such a rise in its income inequality. Paul Krugman laid the facts out back when Ben Bernanke first testified to Congress as Fed Chairman:

So who are the winners from rising inequality? It’s not the top 20 percent, or even the top 10 percent. The big gains have gone to a much smaller, much richer group than that. . . . . Between 1972 and 2001 the wage and salary income of Americans at the 90th percentile of the income distribution rose only 34 percent, or about 1 percent per year. So being in the top 10 percent of the income distribution, like being a college graduate, wasn’t a ticket to big income gains. But income at the 99th percentile rose 87 percent; income at the 99.9th percentile rose 181 percent; and income at the 99.99th percentile rose 497 percent. No that’s not a misprint. (emphasis added).

And about a year ago, in an effort to understand why the already extremely wealthy have been sucking up ever and ever greater slices of the American pie over the past 40 years, Timothy Noah wrote a series of articles at Slate.com titled The United States of Inequality: the Great Divergence , in which he looked at the income effect of productivity gains, education, globalization, race, gender, immigration, a less powerful labor force, etc., . . .

But maybe that is all just missing the forest for the trees.

Rather than getting into the nitty gritty of economic reform, why not address the problem first using broad strokes, and then refine our solutions as the problem becomes more manageable?

Want to reduce income inequality? The data suggest that it’s very simple, even if the perfect optimization is a bit foggy: Raise taxes. Raise ‘em on upper-level income, raise ‘em on capital gains, raise ‘em on the estates of rich dead people. Then pump that money back into the economic system. Forced trade through taxation, dispersal effect strengthened, problem solved. Just as it has been before by every modern capitalist society.

And, yeah . . . I am advocating wealth redistribution by the government. That is what taxation is. And I am doing so not because I like taxes or hate rich people or out of some misguided ideological bent, but simply because the data seem to make it clear that if the government doesn’t start this kind of forced dispersal effect soon – but instead relies on an unfettered free market to allocate wealth – then it is inevitable that America will slide into a third-world, Banana Republic state.

I want to raise taxes and redistribute wealth because I am just too goddamned patriotic to let that happen to the country I love. I’m not a socialist or a terrorist or a communist or a hippie – I’m an American who wants to do the right thing for my country. The uber-rich (other than Warren Buffett) might want to start thinking about doing the same.

Cross-posted at Casa Cognito.