The Mathematics of Inequality

 

 

Mathematical analysis shows that without redistribution, wealth becomes increasingly more concentrated, and inequality grows until almost all assets are held by an extremely small percent of people.  History shows this analysis is accurate.   I first saw such an analysis years ago, I believe in Scientific American in the winter in 1990, 1991, or 1992. I haven't been able to find the article in the Scientific archives, because they don't have good enough descriptions for the column where it would have appeared. I bought several articles I hoped would be the right one, but didn't find it. Luckily, there were finally some more recent analyses I was able to reference in my blog.

 

https://now.tufts.edu/articles/mathematics-inequality

By Taylor McNeil
October 12, 2017

Seven years ago, the combined wealth of 388 billionaires equaled that of the poorest half of humanity, according to Oxfam International. This past January the equation was even more unbalanced: it took only eight billionaires, marking an unmistakable march toward increased concentration of wealth. Today that number has been reduced to five billionaires.

Trying to understand such growing inequality is usually the purview of economists, but Bruce Boghosian, a professor of mathematics, thinks he has found another explanation—and a warning.

Using a mathematical model devised to mimic a simplified version of the free market, he and colleagues are finding that, without redistribution, wealth becomes increasingly more concentrated, and inequality grows until almost all assets are held by an extremely small percent of people.

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It’s easy to imagine how wealth-attained advantage works in real life. “The people with that advantage receive better returns on their investments, lower interest rates on loans, and better financial advice,” said Boghosian. “Conversely, as Barbara Ehrenreich famously observed, it is expensive to be poor. If you are working two jobs, you don’t have time to shop for the best bargains. If you can’t afford the security deposit demanded by most landlords, you may end up staying in a motel at inflated prices.”

The model tracks the data with remarkable accuracy, he said.

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Putting aside ethical issues of growing inequality, it can also create an unhealthy economy, Boghosian said. “That’s because when wealth concentrates and the middle class is depleted too much, you may get very wealthy industrialists, very wealthy manufacturers, but to whom do they sell their products? It locks up the economy,” he said.

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https://www.austms.org.au/Jobs/Library4.html

THE MATHEMATICS OF INEQUALITY

By Mark Buchanan
reprinted from The Australian Financial Review
September 2002
(originally in New Statesman)

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Even if everyone starts out equally, and they remain equally adept at choosing investments, differences in investment luck will cause some people to accumulate more wealth than others. Those who are lucky will tend to invest more, and so have a chance to make greater gains still. Hence, a string of positive returns builds a person's wealth not merely by addition but by multiplication, as each subsequent gain grows ever bigger. This is enough, even in a world of equals where returns on investment are entirely random, to stir up huge disparities of wealth in the population.

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The Choice

The Choice
copyright 1993 Patricia M. Shannon
(can be sung to the tune of "Holy, Holy, Holy"

As I go out a-walking in the forest peaceful,
climbing up the mountain trail until I reach the top,
looking o'er the valley I feel a sense of wonder
rising within me, filling all my soul.

How wonderful is nature, tiny lifeless atoms
bring forth the multitude forms of all life.
We are one of many, sharing genes with one-celled beings,
dependent upon the interwoven web of life.

We have developed powers of terrible destruction,
wiping out whole species that used to roam the earth,
Threatening the whole world with utter devastation,
blithely ignoring what we don't want to know.

It is our own choice which path we choose to follow;
do we love our children enough to change our ways?
Will we change our pattern of long-term self-destruction?
History says "No", but we can prove it wrong.

..

The history and future of societal collapse

I suggest reading the whole article at the following link: 

https://www.theguardian.com/environment/2025/aug/02/self-termination-history-and-future-of-societal-collapse

 Damian Carrington Environment editor
Sat 2 Aug 2025 02.31 EDT

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 I’m pessimistic about the future,” he says. “But I’m optimistic about people.” Kemp’s new book covers the rise and collapse of more than 400 societies over 5,000 years and took seven years to write. The lessons he has drawn are often striking: people are fundamentally egalitarian but are led to collapses by enriched, status-obsessed elites, while past collapses often improved the lives of ordinary citizens.

Today’s global civilisation, however, is deeply interconnected and unequal and could lead to the worst societal collapse yet, he says. The threat is from leaders who are “walking versions of the dark triad” – narcissism, psychopathy and Machiavellianism – in a world menaced by the climate crisis, nuclear weapons, artificial intelligence and killer robots.

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 “History is best told as a story of organised crime,” Kemp says. “It is one group creating a monopoly on resources through the use of violence over a certain territory and population.”

All Goliaths, however, contain the seeds of their own demise, he says: “They are cursed and this is because of inequality.” 

  ---

History shows that increasing wealth inequality consistently precedes collapse, says Kemp, from the Classical Lowland Maya to the Han dynasty in China and the Western Roman empire. He also points out that for the citizens of early rapacious regimes, collapse often improved their lives because they were freed from domination and taxation and returned to farming. “After the fall of Rome, people actually got taller and healthier,” he says.

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He cites three reasons why the collapse of the global Goliath would be far worse than previous events. First is that collapses are accompanied by surges in violence as elites try to reassert their dominance. “In the past, those battles were waged with swords or muskets. Today we have nuclear weapons,” he says.

Second, people in the past were not heavily reliant on empires or states for services and, unlike today, could easily go back to farming or hunting and gathering. “Today, most of us are specialised, and we’re dependent upon global infrastructure. If that falls away, we too will fall,” he says.

“Last but not least is that, unfortunately, all the threats we face today are far worse than in the past,” he says. Past climatic changes that precipitated collapses, for example, usually involved a temperature change of 1C at a regional level. Today, we face 3C globally. There are also about 10,000 nuclear weapons, technologies such as artificial intelligence and killer robots and engineered pandemics, all sources of catastrophic global risk.

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 History shows that more democratic societies tend to be more resilient, he says.

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 Escaping collapse also requires taxing wealth, he says, otherwise the rich find ways to rig the democratic system. “I’d cap wealth at $10 million. That’s far more than anyone needs. A famous oil tycoon once said money is just a way for the rich to keep score. Why should we allow these people to keep score at the risk of destroying the entire planet?”

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“But even if you don’t have hope, it doesn’t really matter. This is about defiance. It’s about doing the right thing, fighting for democracy and for people to not be exploited. And even if we fail, at the very least, we didn’t contribute to the problem.”

 Goliath’s Curse by Luke Kemp was published in the UK on 31 July by Viking Penguin