Sandpile Universality in Social Inequality: Gini and Kolkata Measures

Social inequalities are ubiquitous and also evolve towards some universal limit. Here we review extensively the values of inequality measures, namely the Gini ($g$) and Kolkata ($k$) indices, the two generic inequality indices, from data analysis of different social sectors. The kolkata index $k$ gives the fraction of `wealth' possessed by $(1 - k)$ fraction of `people'. We show that the values of both these indices approach each other (to $g = k \simeq 0.87$, starting from $g = 0, k = 0.5$ for equality) as the competitions grow in various social institutions like markets, movies, elections, universities, prize winning, battle fields, sports (Olympics) and etc. under unrestricted competitions (no social welfare or support mechanism). We propose to view this coincidence of inequality indices as a generalized version of the (more than a) century old 80-20 law of Pareto ($k$ = 0.80). Furthermore, this coincidence of the inequality indices noted here is very similar to the ones seen just prior to the arrival of the self-organized critical (SOC) state in well studied self-tuned physical systems like sand-piles. The observations here, therefore, stand as a quantitative support towards viewing interacting socio-economic systems in the framework of SOC, an idea conjectured for years.