a man preparing to flip a coin
A research paper, from Tufts University and in an online publication of the Society for Industrial and Applied Mathematics (SIAM), makes an interesting claim.
Bruce Boghosian and Christoph Börgers, two mathematics professors at Tufts University, and motivated by the vast state of wealth inequality in the world, wondered what might happen if everyone started from the same place. Equal talent, equal learning, equal industry, and all make the right choices.
Both used mathematics from the kinetic theory of gases and applied it to simplified economic models “in order to explore both the possible mechanisms through which wealth inequality arises and the effects of government interventions that attempt to reduce it.”
The result, which may sound crazy at first, but isn’t when you think about how they built their model, is that under perfectly uniform conditions, inequality would grow through a chain of coin flips.
Let’s break this down. First, a series of coin flips can create a complex distribution like a bell curve. You may have seen a game or experimented at school sometime with a board full of pegs. A set of balls drop, one by one, through a gap at the top. They bounce this way and that until they settle to the bottom. By the time it’s done, you have a baseline probability curve.
Don’t get stuck in this example. It’s just to show how the luck of the draw repeated many times can result in an extremely uneven distribution.
Boghosian and Börgers pointed out models of wealth distribution that use a yard sale structure. People meet in pairs, have a transaction, and one does better and one does worse. The math is complicated, though click on the link and you can see it.
As Boghosian pointed out in prepared remarks, the theory that many follow is that everything happens through understandable dynamics. Supply and demand control the trading world. People enter trades of their choice and those who are more insightful do better in the game.
But the modeling in that paper suggests otherwise, “that the shape of the distribution of wealth, including the concentration of wealth at the top, is largely due to chance.” One who begins to lose a series of gains and losses of a small percentage of his wealth eventually loses everything, even if the gains and losses are equal. For example, if you have $1,000 and earn 10%, you have $1,100. Now you lose 10% of that and you’re left with $990. It becomes a cruelly efficient math that constantly drains what you have. Because money doesn’t really disappear, someone else gets richer.
Invisible wealth, as we see in the world of billionaires, naturally occurs in a way “that can only be remedied through interventions such as wealth tax.”
This model can and should include the ability to add biases in favor of the wealthiest, as this happens regularly to provide accurate results.
“With the right parameters, the model can reproduce US wealth distribution data to within one-fifth of a percent,” said a press release from SIAM. “The most surprising result of the model is that the redistribution of wealth must offset the advantages gained by wealth in order to stop oligarchy.”
In other words, according to the researchers, if without some kind of control of the situation, such as government interaction or other unpredictable external actions, the rich only get richer.
