An amazing article called The Inescapable Casino, written by mathematician Bruce Boghosian of Tufts University in the November edition of Scientific American, merits great attention. Boghosian and others have developed a mathematical model that accurately reproduces real-life wealth inequalities in a wide range of free-market countries.
This model also shows that in a pure free-market economy, ie in the absence of wealth redistribution mechanisms, all the wealth inevitably falls into the hands of one or a few people (an oligarchy).
Mathematical analysis such as this is critically important today because wealth inequality is escalating across the world (eg Russia, India, Brazil), particularly in the United States. Boghosian quotes the report from investment bank Credit Suisse that the fraction of global household wealth owned by the richest 1 per cent of the world's population increased from 42.5 per cent to 47.2 per cent between the financial crisis of 2008 and 2018. Today, Oxfam estimates that 26 individuals own as much household wealth as the entire bottom half of the world's population – about 3.5 billion people.
The most striking thing to me about Boghosian’s paper is the mathematical description of wealth distribution in a pure free-market system. In this economy innumerable pairs of people sell and buy goods to and from each other over and over again, agree on a price and shake hands. Assuming the system is initially symmetrical, ie everyone starts out with equal wealth, everyone acts fairly and everyone is equally industrious and bright, how will it evolve?
Initial symmetry broken
Well, amazingly, to me anyway, mathematics shows that, once the initial symmetry is broken, which inevitably happens (despite their best intentions, some people will either overpay or accept less than an item is worth, thereby transferring some wealth between them), further transactions inexorably transfer all the wealth into the hands of a few individuals, an oligarchy, and everybody else ends up with little or nothing. Living in a pure free-market is, for the great majority of people, like gambling in a casino rigged to favour the house.
Of course oligarchies don't usually arise in real-world economies because pure free-markets are subjected to modification through government-enforced redistribution of wealth from the richer to the poorer. When the mathematical model described by Boghosian is modified to accommodate typical mechanisms for redistribution of wealth, wealth distribution stabilises and oligarchies don't appear. Applying this mathematical model to real world economies predicts the empirical data on wealth distribution in America and Europe between 1989 and 2016 with better than 2 per cent accuracy.
Wealth redistribution is absolutely required on scientific grounds in order to set limits on inequality and to give everyone a chance to thrive
Wealthy people enjoy various wealth-attained advantages relative to poorer people, for example lower interest rates on loans and availability of money to buy when prices are low. Factoring wealth-attained advantage into the mathematical model, and a factor to accommodate negative wealth (some people are in debt), further improves the model’s ability to predict empirical wealth distribution data.
Boghosian’s model
In Boghosian’s mathematical model, no wealthy oligarchy is possible when wealth-attained advantage is less than wealth redistribution, but when it is greater than wealth redistribution oligarchy suddenly appears. Boghosian explains that this is probably what happened when the USSR finally broke up in 1991.
The former USSR republics suddenly experienced dramatically reduced government wealth redistribution, coinciding with a sharp increase in wealth-attained advantage from privatisation and deregulation. This threw these countries into a wealth-condensing state and many quickly became partial oligarchies.
Boghosian’s mathematical model offers a powerful means of analysing wealth distribution in market economies, allowing governments to adjust wealth redistribution and wealth-attained advantage to ensure equitable distribution of wealth and to avoid conditions that would precipitate the emergence of oligarchies or economic stagnation (overdoing wealth redistribution would create economic stagnation, penalising everybody).
Startlingly counterintuitive
The mathematical demonstration that a pure free-market economy concentrates almost all wealth in the hands of a few, regardless of the industry or cleverness of the rest, is startlingly counterintuitive. Wealth redistribution is therefore absolutely required on scientific grounds, not exclusively on ethical-philosophical grounds, in order to set limits on inequality and to give everyone a chance to thrive.
So much for the traditional notion, popular in some quarters, that redistribution of wealth is soft-hearted generosity that panders to the lazy and the shiftless and penalises the clever and the industrious. In the absence of redistribution almost everybody suffers grievously, the lazy and the industrious alike.
William Reville is an emeritus professor of biochemistry at UCC