This file is part of IDEAS, which uses RePEc data


[ Papers | Articles | Software | Books | Chapters | Authors | Institutions | JEL Classification | NEP reports | Search | New papers by email | Author registration | Rankings | Volunteers | FAQ | Blog | Help! ]

Multidimensional generalized Gini indices

Author info | Abstract | Publisher info | Download info | Related research | Statistics
Author Info
Thibault Gajdos ()
John A. Weymark ()

Additional information is available for the following registered author(s):

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.

Download Info
To download:

If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.icer.it/docs/wp2003/Gajdos16-03.pdf
File Format: application/pdf
File Function:
Download Restriction: no

Publisher Info
Paper provided by ICER - International Centre for Economic Research in its series ICER Working Papers - Applied Mathematics Series with number 16-2003.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Length: 30 pages
Date of creation: May 2003
Date of revision:
Handle: RePEc:icr:wpmath:16-2003

Contact details of provider:
Postal: Viale Settimio Severo, 63 - 10133 Torino - Italy
Phone: +39 011 6604828
Fax: +39 011 6600082
Email:
Web page: http://www.icer.it
More information through EDIRC

For technical questions regarding this item, or to correct its listing, contact: (Alessandra Calosso).

Related research
Keywords: Generalized Gini; multidimensional inequality;

Other versions of this item:

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

References listed on IDEAS
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. Erio Castagnoli & Fabio Maccheroni & Massimo Marinacci, 2002. "Choquet insurance pricing: a caveat," ICER Working Papers - Applied Mathematics Series 14-2003, ICER - International Centre for Economic Research, revised May 2003. [Downloadable!]
    Other versions:
  2. Kai-yuen Tsui, 1999. "Multidimensional inequality and multidimensional generalized entropy measures: An axiomatic derivation," Social Choice and Welfare, Springer, vol. 16(1), pages 145-157. [Downloadable!] (restricted)
  3. Domenico Menicucci, 2001. "Optimal two-object auctions with synergies," ICER Working Papers - Applied Mathematics Series 18-2001, ICER - International Centre for Economic Research. [Downloadable!]
    Other versions:
  4. Atkinson, Anthony B & Bourguignon, Francois, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," Review of Economic Studies, Blackwell Publishing, vol. 49(2), pages 183-201, April. [Downloadable!] (restricted)
  5. Gajdos, Thibault & Maurin, Eric, 2004. "Unequal uncertainties and uncertain inequalities: an axiomatic approach," Journal of Economic Theory, Elsevier, vol. 116(1), pages 93-118, May. [Downloadable!] (restricted)
    Other versions:
  6. François Bourguignon & Satya Chakravarty, 2003. "The Measurement of Multidimensional Poverty," Journal of Economic Inequality, Springer, vol. 1(1), pages 25-49, April. [Downloadable!] (restricted)
    Other versions:
  7. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August. [Downloadable!] (restricted)
  8. John A. Weymark & Kai-yuen Tsui, 1997. "Social welfare orderings for ratio-scale measurable utilities," Economic Theory, Springer, vol. 10(2), pages 241-256. [Downloadable!] (restricted)
    Other versions:
  9. Koshevoy, G.A. & Mosler, K., 1995. "Multivariate Gini Indices," Statistics and Econometrics 7/95, Universitaet zu Koeln. [Downloadable!]
    Other versions:
  10. Kolm, Serge-Christophe, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, MIT Press, vol. 91(1), pages 1-13, February. [Downloadable!] (restricted)
  11. List, C., 1999. "Multidimensional Inequality Measurement: a Proposal," Economics Papers 9927, Economics Group, Nuffield College, University of Oxford.
  12. 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!]
  13. Blackorby, C. & Bossert, W. & Donaldson, D., 1995. "Income Inequality Measurement: The Normative Approach," UBC Departmental Archives 95-23, UBC Department of Economics.
    Other versions:
  14. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May. [Downloadable!] (restricted)
  15. Tsui Kai-Yuen, 1995. "Multidimensional Generalizations of the Relative and Absolute Inequality Indices: The Atkinson-Kolm-Sen Approach," Journal of Economic Theory, Elsevier, vol. 67(1), pages 251-265, October. [Downloadable!] (restricted)
  16. Pollak, Robert A, 1971. "Additive Utility Functions and Linear Engel Curves," Review of Economic Studies, Blackwell Publishing, vol. 38(116), pages 401-14, October. [Downloadable!] (restricted)
  17. Blackorby, Charles & Donaldson, David, 1982. "Ratio-Scale and Translation-Scale Full Interpersonal Comparability without Domain Restrictions: Admissible Social-Evaluation Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(2), pages 249-68, June.
  18. Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Levine's Bibliography 7616, UCLA Department of Economics. [Downloadable!]
    Other versions:
  19. Charles Blackorby & David Donaldson & Maria Auersperg, 1981. "A New Procedure for the Measurement of Inequality within and among Population Subgroups," Canadian Journal of Economics, Canadian Economics Association, vol. 14(4), pages 665-85, November. [Downloadable!] (restricted)
  20. Boland, Philip J. & Proschan, Frank, 1988. "Multivariate arrangement increasing functions with applications in probability and statistics," Journal of Multivariate Analysis, Elsevier, vol. 25(2), pages 286-298, May. [Downloadable!] (restricted)
  21. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September. [Downloadable!] (restricted)
  22. Ben-Porath, Elchanan & Gilboa, Itzhak & Schmeidler, David, 1997. "On the Measurement of Inequality under Uncertainty," Journal of Economic Theory, Elsevier, vol. 75(1), pages 194-204, July. [Downloadable!] (restricted)
  23. Walter Bossert & John A. Weymark, . "Utility in Social Choice," Old UBC Departmental Papers 9623, UBC Department of Economics. [Downloadable!]
Full references

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. Rebeca Echávarri & Iñaki Permanyer, 2008. "Ranking profiles of capability sets," Social Choice and Welfare, Springer, vol. 31(3), pages 521-535, October. [Downloadable!] (restricted)
  2. 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!]
  3. 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:
  4. 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:
  5. 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!]
  6. 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!]
  7. Masato Okamoto, 2009. "Decomposition of gini and multivariate gini indices," Journal of Economic Inequality, Springer, vol. 7(2), pages 153-177, June. [Downloadable!] (restricted)
  8. 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!]
    Other versions:
  9. Marat Ibragimov & Rustam Ibragimov, 2007. "Market Demand Elasticity and Income Inequality," Economic Theory, Springer, vol. 32(3), pages 579-587, September. [Downloadable!] (restricted)
  10. 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!]
  11. Elisabetta Croci Angelini & Alessandra Michelangeli, 2008. "Measuring Well-Being differences across EU Countries. A Multidimensional Analysis of Income, Housing, Health, and Education," Working Papers 15-2008, Macerata University, Department of Studies on Economic Development (DiSSE), revised Nov 2008. [Downloadable!]
  12. 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!]
Statistics
Access and download statistics

Did you know? All top Economics journals are listed on RePEc.

This page was last updated on 2009-10-21.

This information is provided to you by IDEAS at the Department of Economics, College of Liberal Arts and Sciences, University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics.