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Classical inequality indices, welfare functions, and the dual decomposition

  • Oihana Aristondo

    (BRIDGE Research Group, Universidad del País Vasco)

  • José Luis García-Lapres

    ()

    (PRESAD Research Group, IMUVA, Universidad Valladolid)

  • Casilda Lasso de la Vega

    ()

    (BRIDGE Research Group, Universidad del País Vasco)

  • Ricardo Alberto Marques Pereira

    ()

    (Dipartimento di Informatica e Studi Aziendali, Universitμa degli Studi di Trento)

We consider the classical inequality measures due to Gini, Bonferroni, and De Vergottini and we present a brief review of the three inequality indices and the associated welfare functions, in the correspondence scheme introduced by Blackorby and Donaldson, and Weymark. The three classical inequality indices incorporate different value judgments in the measurement of inequality, leading to different behavior under income transfers between individuals in the population. The welfare functions associated with the Gini, Bonferroni, and (normalized) De Vergottini indices are Schur-concave OWA functions, with larger weights for lower incomes. We examine the dual decomposition and the orness degree of the three welfare functions in the standard framework of aggregation functions on the [0; 1]n domain, and show that it offers interesting insight on the distinct and complementary nature of the classical inequality indices.

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File URL: http://www.ecineq.org/milano/WP/ECINEQ2012-253.pdf
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Paper provided by ECINEQ, Society for the Study of Economic Inequality in its series Working Papers with number 253.

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Length: 29 pages
Date of creation: Apr 2012
Date of revision:
Handle: RePEc:inq:inqwps:ecineq2012-253
Contact details of provider: Web page: http://www.ecineq.org
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  1. Garcia-Lapresta, Jose Luis & Llamazares, Bonifacio, 2001. "Majority decisions based on difference of votes," Journal of Mathematical Economics, Elsevier, vol. 35(3), pages 463-481, June.
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  4. Satya R. Chakravarty & Pietro Muliere, 2003. "Welfare indicators: A review and new perspectives. 1. Measurement of inequality," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 457-497.
  5. Porath Elchanan Ben & Gilboa Itzhak, 1994. "Linear Measures, the Gini Index, and The Income-Equality Trade-off," Journal of Economic Theory, Elsevier, vol. 64(2), pages 443-467, December.
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  8. Satya Chakravarty, 2007. "A deprivation-based axiomatic characterization of the absolute Bonferroni index of inequality," Journal of Economic Inequality, Springer, vol. 5(3), pages 339-351, December.
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  10. Donaldson, David & Weymark, John A., 1983. "Ethically flexible gini indices for income distributions in the continuum," Journal of Economic Theory, Elsevier, vol. 29(2), pages 353-358, April.
  11. Claudio Zoli, 1999. "Intersecting generalized Lorenz curves and the Gini index," Social Choice and Welfare, Springer, vol. 16(2), pages 183-196.
  12. Oihana Aristondo & José Luis García-Lapresta & Casilda Lasso de la Vega & Ricardo Alberto Marques Pereira, 2011. "The Gini index,the dual decomposition of aggregation functions, and the consistent measurement of inequality," Working Papers 203, ECINEQ, Society for the Study of Economic Inequality.
  13. Donaldson, David & Weymark, John A., 1980. "A single-parameter generalization of the Gini indices of inequality," Journal of Economic Theory, Elsevier, vol. 22(1), pages 67-86, February.
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  18. Giovanni Maria Giorgi & Riccardo Mondani, 2005. "Sampling distribution of the Bonferroni inequality index from exponential population," Econometrics 0507008, EconWPA.
  19. Giovanni Maria Giorgi, 2005. "A methodological survey of recent studies for the measurement of inequality of economic welfare carried out by some Italian statisticians," Econometrics 0509007, EconWPA.
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