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Inequality measures are quantitative measures that take values in the unit interval, with a zero value characterizing perfect equality. Although originally proposed to measure economic inequalities, they can be applied to several other…

Physics and Society · Physics 2024-01-26 Paolo Giudici , Emanuela Raffinetti , Giuseppe Toscani

Many existing fairness metrics measure group-wise demographic disparities in system behavior or model performance. Calculating these metrics requires access to demographic information, which, in industrial settings, is often unavailable. By…

Social and Information Networks · Computer Science 2024-09-13 Avijit Ghosh , Tomo Lazovich , Kristian Lum , Christo Wilson

The Gini's mean difference was defined as the expected absolute difference between a random variable and its independent copy. The corresponding normalized version, namely Gini's index, denotes two times the area between the egalitarian…

Probability · Mathematics 2024-01-08 Marco Capaldo , Jorge Navarro

We introduce the social welfare implications of the Zenga index, a recently proposed index of inequality. Our proposal is derived by following the seminal book by Son (2011) and the recent working paper by Kakwani and Son (2019). We compare…

General Economics · Economics 2020-06-24 Francesca Greselin , Simone Pellegrino , Achille Vernizzi

Income inequality is an important issue that has to be solved in order to make progress in our society. The study of income inequality is well received through the Gini coefficient, which is used to measure degrees of inequality in general.…

General Economics · Economics 2025-06-26 Wanetha Sudswong , Anon Plangprasopchok , Chainarong Amornbunchornvej

Concern about income inequality has become prominent in public discourse around the world. However, studies in behavioral economics and psychology have consistently shown that people prefer not equal but fair income distributions. Thus,…

General Economics · Economics 2022-09-13 Thitithep Sitthiyot , Kanyarat Holasut

The estimation of inequality and poverty measures is frequently constrained by a lack of individual data. Many countries, including China, continue to report income data in the form of aggregated income shares. In this context, the Beta…

Applications · Statistics 2026-04-02 José María Sarabia , Vanesa Jordá , Emilio Gómez-Déniz

We provide a survey of the Kolkata index of social inequality, focusing in particular on income inequality. Based on the observation that inequality functions (such as the Lorenz function), giving the measures of income or wealth against…

General Economics · Economics 2021-09-29 Suchismita Banerjee , Bikas K. Chakrabarti , Manipushpak Mitra , Suresh Mutuswami

Graph Neural Networks (GNNs) have demonstrated impressive performance across various tasks, leading to their increased adoption in high-stakes decision-making systems. However, concerns have arisen about GNNs potentially generating unfair…

Machine Learning · Computer Science 2026-01-09 Anuj Kumar Sirohi , Anjali Gupta , Sandeep Kumar , Amitabha Bagchi , Sayan Ranu

The underlying idea behind the construction of indices of economic inequality is based on measuring deviations of various portions of low incomes from certain references or benchmarks, that could be point measures like population mean or…

Methodology · Statistics 2015-08-04 Francesca Greselin , Ricardas Zitikis

"The rich are getting richer" implies that the population income distributions are getting more right skewed and heavily tailed. For such distributions, the mean is not the best measure of the center, but the classical indices of income…

Methodology · Statistics 2023-08-08 Vytaras Brazauskas , Francesca Greselin , Ricardas Zitikis

Combining global gridded population and fossil fuel based CO2 emission data at 1km scale, we investigate the spatial origin of CO2 emissions in relation to the population distribution within countries. We depict the correlations between…

Physics and Society · Physics 2018-10-03 Bin Zhou , Stephan Thies , Ramana Gudipudi , Matthias K. B. Lüdeke , Jürgen P. Kropp , Diego Rybski

Statistical physicists and social scientists both study extensively some characteristic features of the unequal distributions of energy, cluster or avalanche sizes and of income, wealth etc among the particles (or sites) and population…

Physics and Society · Physics 2022-10-26 Asim Ghosh , Soumyajyoti Biswas , Bikas K. Chakrabarti

A society or country with income equally distributed among its people is truly a fiction! The phenomena of socioeconomic inequalities have been plaguing mankind from times immemorial. We are interested in gaining an insight about the…

General Finance · Quantitative Finance 2018-08-07 Kiran Sharma , Subhradeep Das , Anirban Chakraborti

In the growing field of Shared Micromobility Systems, which holds great potential for shaping urban transportation, fairness-oriented approaches remain largely unexplored. This work addresses such a gap by investigating the balance between…

Systems and Control · Electrical Eng. & Systems 2025-07-08 Matteo Cederle , Marco Fabris , Gian Antonio Susto

This paper proposes the k-generalized distribution as a model for describing the distribution and dispersion of income within a population. Formulas for the shape, moments and standard tools for inequality measurement - such as the Lorenz…

General Finance · Quantitative Finance 2009-01-31 F. Clementi , T. Di Matteo , M. Gallegati , G. Kaniadakis

The centrality of a node within a network, however it is measured, is a vital proxy for the importance or influence of that node, and the differences in node centrality generate hierarchies and inequalities. If the network is evolving in…

Social and Information Networks · Computer Science 2023-01-09 Matthew Russell Barnes , Vincenzo Nicosia , Richard G. Clegg

The Gini index underestimates inequality for heavy-tailed distributions: for example, a Pareto distribution with exponent 1.5 (which has infinite variance) has the same Gini index as any exponential distribution (a mere 0.5). This is…

Methodology · Statistics 2021-10-06 Sabiou Inoua

We introduce a minimal agent-based model to qualitatively conceptualize the allocation of limited wealth among more abundant opportunities. We study the interplay of power, satisfaction and frustration in distribution, concentration, and…

Physics and Society · Physics 2015-10-05 Benoit Mahault , Avadh Saxena , Cristiano Nisoli

We present analytical results for the Gini coefficient of economic inequality under the dynamics of a modified Yard-Sale Model of kinetic asset exchange. A variant of the Yard-Sale Model is introduced by modifying the underlying binary…

Statistical Mechanics · Physics 2024-11-05 David W. Cohen , Bruce M. Boghosian