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

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 \(g = k \simeq 0.87\)) under unrestricted competitions. 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. Furthermore, the coincidence of the inequality indices noted here is very similar to the ones seen before for self-organized critical (SOC) systems. 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.