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Multidimensional Generalized Gini Indices

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Author Info
Thibault Gajdos () (CNRS-CREST)
John A. Weymark () (Department of Economics, Vanderbilt University)

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Abstract

The axioms used to characterize the generalized Gini social evaluation orderings for one-dimensional distributions are extended to the multidimensional attributes case. A social evaluation ordering is shown to have a two-stage aggregation representation if these axioms and a separability assumption are satisfied. In the first stage, the distributions of each attribute are aggregated using generalized Gini social evaluation functions. The functional form of the second-stage aggregator depends on the number of attributes and on which version of a comonotonic additivity axiom is used. The implications of these results for the corresponding multidimensional indices of relative and absolute inequality are also considered.

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File URL: http://www.vanderbilt.edu/Econ/wparchive/workpaper/vu03-w11R.pdf
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File Function: Revised version, 2003
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Paper provided by Department of Economics, Vanderbilt University in its series Working Papers with number 0311.

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Date of creation: May 2003
Date of revision: Jul 2003
Handle: RePEc:van:wpaper:0311

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Related research
Keywords: Generalized Gini multidimensional inequality

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Find related papers by JEL classification:
D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    Other versions:
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    Other versions:
  6. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On rates of convergence for posterior distributions in infinite–dimensional models," ICER Working Papers - Applied Mathematics Series 24-2004, ICER - International Centre for Economic Research. [Downloadable!]
  2. Thibault Gajdos & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2002. "Decision Making with Imprecise Probabilistic Information," ICER Working Papers - Applied Mathematics Series 18-2003, ICER - International Centre for Economic Research, revised May 2003. [Downloadable!]
    Other versions:
  3. Thibault Gajdos & Eric Maurin, 2002. "Unequal uncertainties and uncertain inequalities: an axiomatic approach," ICER Working Papers - Applied Mathematics Series 15-2003, ICER - International Centre for Economic Research, revised Mar 2003. [Downloadable!]
    Other versions:
  4. John A. Weymark, 2003. "The Normative Approach to the Measurement of Multidimensional Inequality," Working Papers 0314, Department of Economics, Vanderbilt University, revised Jan 2004. [Downloadable!]
  5. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "Contributions to the understanding of Bayesian consistency," ICER Working Papers - Applied Mathematics Series 13-2004, ICER - International Centre for Economic Research. [Downloadable!]
  6. Alfred Müller & Marco Scarsini, 2003. "Archimedean Copulae and Positive Dependence," ICER Working Papers - Applied Mathematics Series 25-2003, ICER - International Centre for Economic Research. [Downloadable!]
  7. Marat Ibragimov & Rustam Ibragimov, 2007. "Market Demand Elasticity and Income Inequality," Economic Theory, Springer, vol. 32(3), pages 579-587, September. [Downloadable!] (restricted)
  8. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On consistency of nonparametric normal mixtures for Bayesian density estimation," ICER Working Papers - Applied Mathematics Series 23-2004, ICER - International Centre for Economic Research. [Downloadable!]
  9. Taizhong Hu & Alfred Müller & Marco Scarsini, 2002. "Some Counterexamples in Positive Dependence," ICER Working Papers - Applied Mathematics Series 28-2003, ICER - International Centre for Economic Research, revised Jul 2003. [Downloadable!]
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