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A Class of Two-Group Polarization Measures

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  • Bossert, Walter
  • Schworm, William

Abstract

The phenomenon of income polarization is generally associated with a disappearing middle class but there does not seem to be a generally accepted definition of this notion. We characterize classes of polarization quasi‐orderings and polarization measures in a framework where there are two income groups separated by the median. The axioms we employ are variants of within‐group clustering and between‐group spread properties, and an independence property. Furthermore, we illustrate that attempts to extend the axioms to more general settings severely restrict their appeal and conclude that alternative approaches may be required to capture concepts involving polarization.
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Suggested Citation

  • Bossert, Walter & Schworm, William, 2007. "A Class of Two-Group Polarization Measures," Cahiers de recherche 2007-09, Universite de Montreal, Departement de sciences economiques.
    • Handle: RePEc:mtl:montde:2007-09
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    File URL: http://hdl.handle.net/1866/2142
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    Cited by:

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    3. Gaston Yalonetzky, 2013. "Relative bipolarization quasi-ordering based on Between-Group Gini (BGG) curves," Working Papers 318, ECINEQ, Society for the Study of Economic Inequality.
    4. Silber, Jacques & Yalonetzky, Gaston, 2021. "Measuring welfare, inequality and poverty with ordinal variables," GLO Discussion Paper Series 962, Global Labor Organization (GLO).
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    6. Gaston Yalonetzky, 2014. "Relative bipolarization Lorenz curve," Economics Bulletin, AccessEcon, vol. 34(2), pages 1103-1113.
    7. Oriol Carbonell-Nicolau & Humberto Llavador, 2021. "Inequality, Bipolarization, and Tax Progressivity," American Economic Journal: Microeconomics, American Economic Association, vol. 13(4), pages 492-513, November.
    8. Iñaki Permanyer & Conchita D'Ambrosio, 2015. "Measuring Social Polarization with Ordinal and Categorical Data," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 17(3), pages 311-327, June.
    9. Tomasz Panek & Jan Zwierzchowski, 2020. "Median Relative Partial Income Polarization Indices: Investigating Economic Polarization in Poland During the Years 2005–2015," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 149(3), pages 1025-1044, June.
    10. Gaston Yalonetzky, 2017. "The Necessary Requirement of Median Independence for Relative Bipolarisation Measurement," Research on Economic Inequality, in: Research on Economic Inequality, volume 25, pages 51-62, Emerald Group Publishing Limited.
    11. Chakravarty, Satya R. & Sarkar, Palash, 2022. "A synthesis of local and effective tax progressivity measurement," MPRA Paper 115180, University Library of Munich, Germany.
    12. Juan Gabriel Rodríguez, 2015. "A Class of Social Welfare Functions That Depend on Mean Income and Income Polarization," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 61(3), pages 422-439, September.
    13. Jones, Andrew M. & Rice, Nigel & Robone, Silvana & Dias, Pedro Rosa, 2011. "Inequality and polarisation in health systems' responsiveness: A cross-country analysis," Journal of Health Economics, Elsevier, vol. 30(4), pages 616-625, July.
    14. Muhammad Touseef-Ur-Rehman & Usman Mustafa & Humayun Rashid, 2015. "Trends of Income Inequality and Polarisation in Pakistan for the Period 1990-2008," The Pakistan Development Review, Pakistan Institute of Development Economics, vol. 54(4), pages 447-467.
    15. Marek Kosny & Gaston Yalonetzky, 2016. "Relative p-bipolarisation measurement with generalised means and hybrid Lorenz curves," Working Papers 404, ECINEQ, Society for the Study of Economic Inequality.
    16. Florent Bresson & Marek Kosny & Gaston Yalonetzky, 2023. "Bipolarisation measurement: A two-income approach with an application to nine Sub-Saharan African countries," Working Papers 653, ECINEQ, Society for the Study of Economic Inequality.
    17. Satya R. Chakravarty & Rama Pal & Rupayan Pal & Palash Sarkar, 2022. "Minimum inequality taxation, average and minimally progressive taxations and depolarization," Indira Gandhi Institute of Development Research, Mumbai Working Papers 2022-010, Indira Gandhi Institute of Development Research, Mumbai, India.
    18. Mauro Mussini, 2018. "On Measuring Polarization For Ordinal Data: An Approach Based On The Decomposition Of The Leti Index," Statistics in Transition New Series, Polish Statistical Association, vol. 19(2), pages 277-296, June.
    19. Maria Livia ŞTEFĂNESCU, 2015. "Analyzing the health status of the population using ordinal data," Computational Methods in Social Sciences (CMSS), "Nicolae Titulescu" University of Bucharest, Faculty of Economic Sciences, vol. 3(1), pages 18-24, June.
    20. Mauro Mussini & Biancamaria Zavanella, 2015. "Measuring bipolarization in labour productivity in Italy: a new index and its decomposition by sectors and regional factors," RIVISTA DI ECONOMIA E STATISTICA DEL TERRITORIO, FrancoAngeli Editore, vol. 2015(3), pages 29-55.
    21. Peter Lambert, 2010. "James Foster and Michael Wolfson’s 1992 paper “Polarization and the decline of the middle class”," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 8(2), pages 241-245, June.
    22. Rolf Aaberge & A B Atkinson, 2013. "The median as watershed," Discussion Papers 749, Statistics Norway, Research Department.
    23. Chiara Assunta Ricci & Sergio Scicchitano, 2021. "Decomposing changes in income polarization by population group: what happened during the crisis?," Economia Politica: Journal of Analytical and Institutional Economics, Springer;Fondazione Edison, vol. 38(1), pages 235-259, April.

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