{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T07:27:21Z","timestamp":1778052441335,"version":"3.51.4"},"reference-count":48,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,4,28]],"date-time":"2023-04-28T00:00:00Z","timestamp":1682640000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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 \u2018wealth\u2019 owned by (1\u2212k) fraction of the \u2018people\u2019. Our findings suggest that both the Gini index and the Kolkata index tend to converge to similar values (around g=k\u22480.87, 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\u2019s 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.<\/jats:p>","DOI":"10.3390\/e25050735","type":"journal-article","created":{"date-parts":[[2023,5,1]],"date-time":"2023-05-01T12:14:08Z","timestamp":1682943248000},"page":"735","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Sandpile Universality in Social Inequality: Gini and Kolkata Measures"],"prefix":"10.3390","volume":"25","author":[{"given":"Suchismita","family":"Banerjee","sequence":"first","affiliation":[{"name":"Economic Research Unit, Indian Statistical Institute, Kolkata 700108, India"}]},{"given":"Soumyajyoti","family":"Biswas","sequence":"additional","affiliation":[{"name":"Department of Physics, SRM University-AP, Amaravati 522240, India"}]},{"given":"Bikas K.","family":"Chakrabarti","sequence":"additional","affiliation":[{"name":"Economic Research Unit, Indian Statistical Institute, Kolkata 700108, India"},{"name":"Condensed Matter Physics, Saha Institute of Nuclear Physics, Kolkata 700064, India"}]},{"given":"Asim","family":"Ghosh","sequence":"additional","affiliation":[{"name":"Department of Physics, Raghunathpur College, Purulia 723133, India"}]},{"given":"Manipushpak","family":"Mitra","sequence":"additional","affiliation":[{"name":"Economic Research Unit, Indian Statistical Institute, Kolkata 700108, India"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,28]]},"reference":[{"key":"ref_1","unstructured":"Pareto, V. (1965). Cours D\u2019\u00b4economie Politique. Reprinted as a Volume of Oeuvres Compl\u2018etes, Droz. Available online: https:\/\/www.britannica.com\/biography\/Vilfredo-Pareto."},{"key":"ref_2","first-page":"209","article-title":"Methods of measuring the concentration of wealth","volume":"9","author":"Lorenz","year":"1905","journal-title":"Publ. Am. Stat. Assoc."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1007\/s003550000046","article-title":"Characterizations of Lorenz curves and income distributions","volume":"17","author":"Aaberge","year":"2000","journal-title":"Soc. Choice Welf."},{"key":"ref_4","unstructured":"Gini, C.W. (1912). Variabilit\u00e1 e Mutabilit\u00e1: Contributo allo Studio delle Distribuzioni e delle Relazioni Statistiche, Cristiano Cuppini. Available online: https:\/\/en.wikipedia.org\/wiki\/Gini_coefficient#:~:text=The%20Gini%20coefficient%20measures%20the,reflects%20maximal%20inequality%20among%20values."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Bourguignon, F. (2015). Globalization of Inequality, Princeton University Press.","DOI":"10.1515\/9781400865659"},{"key":"ref_6","unstructured":"(2023, April 01). Available online: https:\/\/en.wikipedia.org\/wiki\/Occupy_Wall_Street."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.physa.2014.05.026","article-title":"Inequality in society, academic institutions and science journals: Gini and k-indices","volume":"410","author":"Ghosh","year":"2014","journal-title":"Physica A"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"123178","DOI":"10.1016\/j.physa.2019.123178","article-title":"On the Kolkata index as a measure of income inequality","volume":"545","author":"Banerjee","year":"2020","journal-title":"Physica A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"562182","DOI":"10.3389\/fphy.2020.562182","article-title":"Inequality measures: The kolkata index in comparison with other measures","volume":"8","author":"Banerjee","year":"2020","journal-title":"Front. Phys."},{"key":"ref_10","first-page":"1677","article-title":"Further tricks with the Lorenz curve","volume":"39","author":"Subramanian","year":"2019","journal-title":"Econ. Bull."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s11214-015-0155-x","article-title":"25 Years of Self-organized Criticality: Concepts and Controversies","volume":"198","author":"Watkins","year":"2016","journal-title":"Space Sci. Rev."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1103\/PhysRevLett.59.381","article-title":"Self-organized criticality: An explanation of 1\/f noise","volume":"59","author":"Bak","year":"1987","journal-title":"Phys. Rev. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Bak, P. (1996). How Nature Works: The Science of Self-Organized Criticality, Copernicus.","DOI":"10.1007\/978-1-4757-5426-1"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Piketty, T. (2017). Capital in Twenty First Century, Harvard University Press.","DOI":"10.4159\/9780674982918"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2350048","DOI":"10.1142\/S0129183123500481","article-title":"Evolutionary dynamics of social inequality and coincidence of Gini and Kolkata indices under unrestricted competition","volume":"34","author":"Banerjee","year":"2023","journal-title":"Int. J. Mod. Phys."},{"key":"ref_16","first-page":"12721","article-title":"Near universal values of social inequality indices in self-organized critical models","volume":"596","author":"Manna","year":"2022","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"127051","DOI":"10.1016\/j.physa.2022.127051","article-title":"Variation of Gini and Kolkata indices with saving propensity in the Kinetic Exchange model of wealth distribution: An analytical study","volume":"594","author":"Joseph","year":"2022","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_18","unstructured":"United Nations Development Program (1992). 1992 Human Development Report, Oxford University Press."},{"key":"ref_19","unstructured":"(2023, April 01). Available online: https:\/\/www.irs.gov\/statistics\/soi-tax-stats-individual-income-tax-returns-publication-1304-complete-report."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"20210162","DOI":"10.1098\/rsta.2021.0162","article-title":"Physics-inspired analysis of the two-class income distribution in the usa in 1983\u20132018","volume":"380","author":"Ludwig","year":"2021","journal-title":"Phil. Trans. R. Soc. A"},{"key":"ref_21","unstructured":"(2023, April 01). Available online: https:\/\/www.boxofficemojo.com\/year\/2011\/."},{"key":"ref_22","unstructured":"(2023, April 01). Available online: https:\/\/www.bollywoodhungama.com\/box-office-collections\/filterbycountry\/IND\/2011\/."},{"key":"ref_23","unstructured":"(2023, April 01). Available online: https:\/\/in.investing.com\/crypto\/bitcoin\/historical-data."},{"key":"ref_24","unstructured":"(2023, April 01). Available online: https:\/\/eci.gov.in\/files\/file\/2785-constituency-wise-detailed-result\/."},{"key":"ref_25","unstructured":"(2023, April 01). Available online: https:\/\/eci.gov.in\/files\/file\/10929-33constituency-wise-detailed-result\/."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Chatterjee, A., Ghosh, A., and Chakrabarti, B.K. (2016). Universality of Citation Distributions for Academic Institutions and Journals. PLoS ONE, 11.","DOI":"10.1371\/journal.pone.0146762"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1016\/j.physa.2016.09.027","article-title":"Socio-economic inequality: Relationship between Gini and Kolkata indices","volume":"466","author":"Chatterjee","year":"2017","journal-title":"Physica A"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"125944","DOI":"10.1016\/j.physa.2021.125944","article-title":"Limiting value of the Kolkata index for social inequality and a possible social constant","volume":"573","author":"Ghosh","year":"2021","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"121185","DOI":"10.1016\/j.physa.2019.121185","article-title":"Inequality in death from social conflicts: A Gini & Kolkata indices-based study","volume":"527","author":"Sinha","year":"2019","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_30","unstructured":"Pressman, R.S. (2010). Software Engineering: A Practitioner\u2019s Approach, McGraw-Hill. [7th ed.]."},{"key":"ref_31","unstructured":"Zimmerman, J. (2018, April 12). Applying the Pareto Principle (80-20 Rule) to Baseball. Available online: https:\/\/www.beyondtheboxscore.com\/2010\/6\/4\/1501048\/applying-the-parento-principle-80."},{"key":"ref_32","unstructured":"(2023, April 01). Available online: https:\/\/en.wikipedia.org\/wiki\/2008_Summer_Olympics_medal_table."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"105646","DOI":"10.1016\/j.cnsns.2020.105646","article-title":"Inequality, a scourge of the XXI century","volume":"95","author":"Iglesias","year":"2021","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1038\/scientificamerican1119-70","article-title":"Is inequality inevitable?","volume":"321","author":"Boghosian","year":"2019","journal-title":"Sci. Am."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1177\/20597991221100427","article-title":"How the theory of self-organized criticality explains punctuated equilibrium in social systems","volume":"15","author":"Zhukov","year":"2022","journal-title":"Methodol. Innov."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1016\/S0378-4371(02)01737-5","article-title":"Wealth redistribution with conservative exchanges","volume":"322","author":"Pianegonda","year":"2003","journal-title":"Physica A"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/S0378-4371(03)00430-8","article-title":"Wealth redistribution in our small world","volume":"327","author":"Iglesias","year":"2003","journal-title":"Physica A"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/j.physa.2004.04.078","article-title":"Inequalities of wealth distribution in a conservative economy","volume":"42","author":"Pianegonda","year":"2004","journal-title":"Physica A"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1007\/s11192-018-2734-6","article-title":"Discontinuities in citation relations among journals: Self-organized criticality as a model of scientific revolutions and change","volume":"116","author":"Leydesdorff","year":"2018","journal-title":"Scientometrics"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1016\/j.chaos.2016.03.001","article-title":"Order book, financial markets, and self-organized criticality","volume":"88","author":"Biondo","year":"2016","journal-title":"Chaos Solitons Fractals"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"128717","DOI":"10.1016\/j.physa.2023.128717","article-title":"Gintropic scaling of scientometric indexes","volume":"618","author":"Telcs","year":"2023","journal-title":"Physica A"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Minati, G. (2019). Big data: From forecasting to mesoscopic understanding. Meta-profiling as complex systems. Systems, 7.","DOI":"10.3390\/systems7010008"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1017\/S0007123401000163","article-title":"Self-organized criticality: A new theory of political behaviour and some of its implications","volume":"31","author":"Brunk","year":"2001","journal-title":"Br. J. Pol. Sci."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"803","DOI":"10.3389\/fphy.2022.990278","article-title":"Success of social inequality measures in predicting critical or failure points of some model physical systems","volume":"10","author":"Ghosh","year":"2022","journal-title":"Front. Phys."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"057401","DOI":"10.1103\/PhysRevLett.130.057401","article-title":"Homophily-Based Social Group Formation in a Spin Glass Self-Assembly Framework","volume":"130","author":"Korbel","year":"2023","journal-title":"Phys. Rev. Lett."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Bir\u00f3, T.S., and N\u00e9da, Z. (2020). Gintropy: Gini Index Based Generalization of Entropy. Entropy, 22.","DOI":"10.3390\/e22080879"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1098\/rsta.2009.0206","article-title":"Entropy production and self-organized (sub) criticality in earthquake dynamics","volume":"368","author":"Main","year":"2010","journal-title":"Phil. Trans. R. Soc. A"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"2821","DOI":"10.1073\/pnas.1812015116","article-title":"Harmonic dynamics of the abelian sandpile","volume":"116","author":"Lang","year":"2019","journal-title":"Proc. Natl. Acad. Sci. USA"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/5\/735\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:26:16Z","timestamp":1760124376000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/5\/735"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,28]]},"references-count":48,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2023,5]]}},"alternative-id":["e25050735"],"URL":"https:\/\/doi.org\/10.3390\/e25050735","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4,28]]}}}