Evolutionary Dynamics of Social Inequality and Coincidence of Gini and Kolkata indices under Unrestricted Competition

Abstract

Social inequalities are ubiquitous and here we show that the values of the Gini (g) and Kolkata (k) indices, two generic inequality indices, approach each other (starting from g = 0 and k = 0.5 for equality) as the competitions grow in various social institutions like markets, universities, elections, etc. It is further showed that these two indices become equal and stabilize at a value (at g = k ≃ 0.87) under unrestricted competitions. We propose to view this coincidence of inequality indices as generalized version of the (more than a) century old 80-20 law of Pareto. Further, this proposition is validated by analyzing data from different social sectors and with analytical considerations of different Lorenz functions.

Near universal values of social inequality indices in self-organized critical models

“…9). A comparison with similar observations in socio-economic data (see e.g., [17]) suggests similar emergent inequality as a result of unconstrained competitions in the social dynamics.…”

“…1). It was seen before that g c = k c ≈ 0.87 in systems with unrestricted competitions (see e.g., [7,17]).…”