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The sociogeometry of inequality: Part I

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  • Eliazar, Iddo

Abstract

The study of socioeconomic inequality is of prime economic and social importance, and the key quantitative gauges of socioeconomic inequality are Lorenz curves and inequality indices—the most notable of the latter being the popular Gini index. In this series of papers we present a sociogeometric framework to the study of socioeconomic inequality. In this part we shift from the notion of Lorenz curves to the notion of Lorenz sets, define inequality indices in terms of Lorenz sets, and introduce and explore a collection of distance-based and width-based inequality indices stemming from the geometry of Lorenz sets. In particular, three principle diameters of Lorenz sets are established as meaningful quantitative gauges of socioeconomic inequality—thus indeed providing a geometric quantification of socioeconomic inequality.

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  • Eliazar, Iddo, 2015. "The sociogeometry of inequality: Part I," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 426(C), pages 93-115.
    • Handle: RePEc:eee:phsmap:v:426:y:2015:i:c:p:93-115
    DOI: 10.1016/j.physa.2015.01.016
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    1. Frédéric Abergel & Hideaki Aoyama & Bikas K. Chakrabarti & Anirban Chakraborti & Asim Gosh, 2015. "Econophysics and data-driven modelling of market dynamics," Post-Print hal-01226816, HAL.
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    3. Cowell, Frank, 2011. "Measuring Inequality," OUP Catalogue, Oxford University Press, edition 3, number 9780199594047, Decembrie.
    4. Chakrabarti,Bikas K. & Chakraborti,Anirban & Chakravarty,Satya R. & Chatterjee,Arnab, 2013. "Econophysics of Income and Wealth Distributions," Cambridge Books, Cambridge University Press, number 9781107013445.
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    1. Iddo Eliazar & Giovanni M. Giorgi, 2020. "From Gini to Bonferroni to Tsallis: an inequality-indices trek," METRON, Springer;Sapienza Università di Roma, vol. 78(2), pages 119-153, August.
    2. Palestini, Arsen & Pignataro, Giuseppe, 2016. "A graph-based approach to inequality assessment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 455(C), pages 65-78.
    3. Tommaso Lando & Lucio Bertoli-Barsotti, 2016. "Weak orderings for intersecting Lorenz curves," METRON, Springer;Sapienza Università di Roma, vol. 74(2), pages 177-192, August.
    4. Ghosh, Asim & Chakrabarti, Bikas K., 2021. "Limiting value of the Kolkata index for social inequality and a possible social constant," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    5. Banerjee, Suchismita & Chakrabarti, Bikas K. & Mitra, Manipushpak & Mutuswami, Suresh, 2020. "On the Kolkata index as a measure of income inequality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    6. Eliazar, Iddo, 2015. "The sociogeometry of inequality: Part II," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 426(C), pages 116-137.
    7. Suchismita Banerjee & Bikas K. Chakrabarti & Manipushpak Mitra & Suresh Mutuswami, 2020. "Inequality Measures: The Kolkata index in comparison with other measures," Papers 2005.08762, arXiv.org, revised Oct 2020.
    8. Chatterjee, Arnab & Ghosh, Asim & Chakrabarti, Bikas K., 2017. "Socio-economic inequality: Relationship between Gini and Kolkata indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 583-595.

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