Wealth Inequality is the Result of Pure Randomness

In the wake of a study of Silicon Valley wealth, income and other economic measures that showed vast disparities in the region – with the top 10% of households holding 66% of the investable assets last year – a team of Tufts University researchers has found that wealth inequality is the result of chance.

While people are often taught to believe that anyone can get rich if they make the right choices, the researchers are turning this long-held notion on its head by suggesting that pure randomness causes the rich to always get richer and the poor to always get poorer — with a concentration of extreme wealth at the top.

The findings – recently featured in SIAM News, a publication of Society for Industrial and Applied Mathematics (SIAM) – demonstrate that even if everybody were equally talented and industrious and followed the same rules, a string of chance events determines the ultimate distribution of societal wealth, no differently than a coin toss or a game of Monopoly. In fact, government intervention is the only known way to amend this outcome.

“Neoclassical economic theory would have us think that prices are set by supply and demand, that everybody enters into transactions of their own free will, and that people who are a bit more astute will therefore end up with more than others,” said Bruce Boghosian, a professor of mathematics at Tufts University and lead researcher of the study.

Boghosian has been modeling wealth distribution for more than a decade. “What this novel mathematical model tells us is that the shape of the wealth distribution, including the concentration of wealth at the very top, is mostly due to luck,” he explained. “We show that wealth inequality – in particular, the runaway wealth that leads to oligarchy – is actually a naturally occurring phenomenon in society that can only be corrected through interventions like a wealth tax.”

Their message comes at a time when Oxfam International reports that over the past two years, the world’s richest one percent amassed nearly twice as much wealth as the rest of the world put together, with 26 people now holding as much wealth as the poorest half of the global population combined. More recently, the EU Tax Observatory reported a growing level of wealth inequality worldwide and noted that calls for the richest citizens to bear more of the tax burden are growing — including in the U.S., where the pros and cons of a wealth tax are hotly debated.

The researchers’ first-of-its-kind model pushes the boundaries of distribution theory and modifies earlier work to account for the oligarchy phenomenon: the idea that an ever-smaller number of people carry an ever-larger amount of wealth. With the right parameters, the model can reproduce U.S. wealth distribution data to within one-fifth of a percent accuracy. The most surprising outcome of the model is that wealth redistribution must outweigh wealth-acquired advantages in order to stop oligarchy.

“According to the mathematical model, in the absence of government intervention, eventually one person will own everything and the others will be left with nothing,” said Christoph Börgers, a professor of mathematics at Tufts and contributor to the study. “At that point, the rich will always be rich and the poor will always be poor.”

Börgers described the essential mathematical mechanism behind wealth inequality as a natural occurrence that is tied to random economic fluctuations. The principal assumption underlying the model is that in many economics trades, small mistakes in judgment occur, resulting in the effective transfer of wealth – a small fraction of the transaction amount – from one trading partner to the other.  For the poor (but not the wealthy), the typical transaction amounts will be proportional to their net worth. For example, if this year they have a little more money than last year, they’ll spend a little more this year than last.

However, a sequence of gains and losses equal to a small percentage of a person’s wealth will eventually impoverish them, even if gains and losses are equally frequent. For instance, if you have $1,000, then gain 10% (bringing the total to $1,100), and then lose 10%, you end up with $990. This is the mechanism by which the poor get poorer. As long as no wealth is destroyed, somebody else must then get richer.

The group’s novel model is important because it lays the foundation for a better understanding of wealth distribution and how to influence it. For example, one result of the study is the suggestion that a sufficiently heavy or progressive wealth tax could eliminate oligarchy altogether. The researchers argue that if the U.S. is willing to introduce a tax that corrects wealth inequality, their model could be used to explore the outcome of different taxation options.

“In short, this model demonstrates that a wealth tax has to be strong enough – that is, above a certain threshold – to prevent the emergence of oligarchs,” said Börgers.

Boghosian believes that mathematical models could play a key role as U.S. policymakers discuss the proposed wealth tax, as well as any changes to income, capital gains, and inheritance tax in the future.

“Does anybody really know the effect of progressive taxation versus a flat tax, or of a wealth tax versus an income tax?” Boghosian asked. “I don’t think they do and that’s where models like this will be helpful. If we’re serious about closing the gap between the rich and the poor in this country and around the world, insights from mathematical models like this one can help.”

About Society for Industrial and Applied Mathematics (www.siam.org)

Society for Industrial and Applied Mathematics (SIAM), headquartered in Philadelphia, Pennsylvania, is an international society of 14,000 individual, academic, and corporate members from 85 countries. SIAM helps build cooperation between mathematics and the worlds of science and technology to solve real-world problems through publications, conferences, and communities like chapters, sections, and activity groups. Learn more at siam.org.

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