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.
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 , further improves the model’s ability to predict empirical wealth distribution data.
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 .
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.