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From unidimensional to multidimensional inequality: a review

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  • Francesco Andreoli

    (University of Verona)

  • Claudio Zoli

    (University of Verona)

Abstract

We review results concerning the representation of partial orders of univariate distributions via stochastic orders and investigate their applications to some classes of stochastic dominance conditions applied in inequality and welfare measurement. The results obtained in an unidimensional framework are extended to multidimensional analysis. We discuss difficulties arising from aggregation of multidimensional distributions into synthetic indicators that value both inequality in the distribution of each attribute and the association between the attributes. We explore the potential for multidimensional evaluations that are based on the partial orders induced by different criteria of majorization and organize related and equivalent inequality and welfare representations.

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  • Francesco Andreoli & Claudio Zoli, 2020. "From unidimensional to multidimensional inequality: a review," METRON, Springer;Sapienza Università di Roma, vol. 78(1), pages 5-42, April.
    • Handle: RePEc:spr:metron:v:78:y:2020:i:1:d:10.1007_s40300-020-00168-4
    DOI: 10.1007/s40300-020-00168-4
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    3. Karl Mosler, 2020. "Commentary on “From unidimensional to multidimensional inequality: a review”," METRON, Springer;Sapienza Università di Roma, vol. 78(1), pages 51-54, April.
    4. Koen Decancq, 2020. "Measuring cumulative deprivation and affluence based on the diagonal dependence diagram," METRON, Springer;Sapienza Università di Roma, vol. 78(2), pages 103-117, August.
    5. Michele Costa, 2020. "Fuzzy poverty measurement: multidimensional and unidimensional indicators," Working Papers wp1156, Dipartimento Scienze Economiche, Universita' di Bologna.
    6. Mohamad Khaled & Paul Makdissi & Prasada Rao & Myra Yazbeck, 2023. "A Unidimensional Representation of Multidimensional Inequality: An Econometric Analysis of Inequalities in the Arab Region," Working Papers 2304E Classification- D63, University of Ottawa, Department of Economics.
    7. Mohamad A. Khaled & Paul Makdissi & D.S. Prasada Rao & Myra Yazbeck, 2023. "A unidimensional representation of multidimensional inequality, with an application to the Arab region," Discussion Papers Series 659, School of Economics, University of Queensland, Australia.
    8. Xu, Aiting & Qiu, Keyang & Zhu, Yuhan, 2023. "The measurements and decomposition of innovation inequality: Based on Industry − University − Research perspective," Journal of Business Research, Elsevier, vol. 157(C).
    9. John A. Weymark, 2020. "Commentary on “From unidimensional to multidimensional inequality: a review”," METRON, Springer;Sapienza Università di Roma, vol. 78(1), pages 55-59, April.
    10. Yanqin Fan & Marc Henry & Brendan Pass & Jorge A. Rivero, 2022. "Lorenz map, inequality ordering and curves based on multidimensional rearrangements," Papers 2203.09000, arXiv.org, revised Apr 2024.
    11. José María Sarabia & Vanesa Jorda, 2020. "Lorenz Surfaces Based on the Sarmanov–Lee Distribution with Applications to Multidimensional Inequality in Well-Being," Mathematics, MDPI, vol. 8(11), pages 1-17, November.
    12. Francesco Andreoli & Mauro Mussini & Vincenzo Prete & Claudio Zoli, 2021. "Urban poverty: Measurement theory and evidence from American cities," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 19(4), pages 599-642, December.
    13. Francesco Andreoli & Claudio Zoli, 2023. "Robust dissimilarity comparisons with categorical outcomes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(3), pages 397-437, April.

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