Probit and Wealth Inequality—How Random Events and the Laws of Probability Are Partially Responsible for Wealth Inequality

Abstract

Using two very simple coin-toss games, we demonstrate how the laws of probability affect wealth distribution. Even in a group of people who are identical in every way and are only subject to random costs (such as that incurred from severe weather, major illness, and bad accidents) or random benefits (such as those derived from lucky breaks), the distribution of wealth will be nudged towards taking the shape of the normal distribution’s cousin, the probit, with its very unequal allocation. The larger these random costs and benefits are and the more frequently they occur, the more severe inequality will become. Moreover, the inequality will tend to be most extreme at the very top and very bottom of the wealth distribution, reflecting the asymptotic curls at either end of the probit curve.