Sandpile Universality in Social Inequality: Gini and Kolkata Measures

Abstract

Social inequalities are ubiquitous and evolve towards a universal limit. Herein, we extensively review the values of inequality measures, namely the Gini ($g$) index and the Kolkata ($k$) index, two standard measures of inequality used in the analysis of various social sectors through data analysis. The Kolkata index, denoted as $k$, indicates the proportion of the `wealth' owned by $(1-k)$ fraction of the `people'. Our findings suggest that both the Gini index and the Kolkata index tend to converge to similar values (around $g=k\approx 0.87$, starting from the point of perfect equality, where $g=0$ and $k=0.5$) as competition increases in different social institutions, such as markets, movies, elections, universities, prize winning, battle fields, sports (Olympics), etc., under conditions of unrestricted competition (no social welfare or support mechanism). In this review, we present the concept of a generalized form of Pareto's 80/20 law ($k=0.80$), where the coincidence of inequality indices is observed. The observation of this coincidence is consistent with the precursor values of the $g$ and $k$ indices for the self-organized critical (SOC) state in self-tuned physical systems such as sand piles. These results provide quantitative support for the view that interacting socioeconomic systems can be understood within the framework of SOC, which has been hypothesized for many years. These findings suggest that the SOC model can be extended to capture the dynamics of complex socioeconomic systems and help us better understand their behavior.

30 pages, 15 figures and 13 tables, Invited Review

References in corpus (7)

• Physics-inspired analysis of the two-class income distribution in the USA in 1983-2018
• Evolutionary Dynamics of Social Inequality and Coincidence of Gini and Kolkata indices under Unrestricted Competition
• Homophily-based social group formation in a spin-glass self-assembly framework
• Limiting Value of the Kolkata Index for Social Inequality and a Possible Social Constant
• Variation of Gini and Kolkata Indices with Saving Propensity in the Kinetic Exchange Model of Wealth Distribution: An Analytical Study
• Success of Social Inequality Measures in Predicting Critical or Failure Points in Some Models of Physical Systems
• Gintropic Scaling of Scientometric Indexes

Cited by in corpus (4)

• Kinetic Models of Wealth Distribution Having Extreme Inequality: Numerical Study of Their Stability Against Random Exchanges
• Exploring Citation Diversity in Scholarly Literature: An Entropy-Based Approach
• Relations Among Different Inequality Measures in Complex Systems: From Kinetic Exchange to Earthquake Models
• Relations Between the Inequality Indices Gini, Pietra and Kolkata: Theory and Data Analysis