Tuning the Probabilistic Distribution and the Gini Index

Abstract

The Gini index corresponding to the wealth or income is determined by the probability distribution of the corresponding quantity. It is an indicator of the inequality (of wealth or income): If only non-negative values of the quantity are allowed, the Gini index is between zero (complete equality) and one (extreme inequality). It has been argued that the probability distribution is essentially determined stochastically. Little can be done to control the Gini index, hence the inequality. The probability distribution is a Boltzmann distribution, and trying to change it is futile. This is like the situation in thermodynamics: an effort to change the second law of thermodynamics is a lost battle. Here, it is argued that while it is correct that the most probable weights for the states are the Boltzmann weights, there is still room for controlling the probability distribution. This can be done by controlling the density of states. In this paper, some general forms of such manipulations are discussed, and their effect on the Gini index is calculated. Some examples are discussed in more detail, and it is shown that by controlling the density of states, one can fix the Gini index to any desired value.