Limiting Value of the Kolkata Index for Social Inequality and a Possible Social Constant

TL;DR

This paper proposes a universal limiting value of approximately 0.865 for the Kolkata index, indicating a consistent level of social inequality across various contexts, and relates it to the Pareto principle.

Contribution

It introduces a conjecture about the limiting value of the Kolkata index based on structural properties of the Lorenz function, extending the understanding of social inequality.

Findings

The limiting value of the Kolkata index is approximately 0.865.

About 14% of entities account for 86% of wealth or citations.

This value modifies the traditional 80-20 Pareto law.

Abstract

Based on some analytic structural properties of the Gini and Kolkata indices for social inequality, as obtained from a generic form of the Lorenz function, we make a conjecture that the limiting (effective saturation) value of the above-mentioned indices is about 0.865. This, together with some more new observations on the citation statistics of individual authors (including Nobel laureates), suggests that about $14\%$ of people or papers or social conflicts tend to earn or attract or cause about $86\%$ of wealth or citations or deaths respectively in very competitive situations in markets, universities or wars. This is a modified form of the (more than a) century old $80-20$ law of Pareto in economy (not visible today because of various welfare and other strategies) and gives an universal value ($0.86$) of social (inequality) constant or number.