Multidimensional Generalized Gini Indices
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.
(This abstract was borrowed from another version of this item.)
|Date of creation:||2003|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: 01 41 17 60 81
Web page: http://www.crest.fr
More information through EDIRC
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.:
- Domenico Menicucci, 2003.
"Optimal two-object auctions with synergies,"
Review of Economic Design,
Springer, vol. 8(2), pages 143-164, October.
- 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.
- Koshevoy, G. A. & Mosler, K., 1997.
"Multivariate Gini Indices,"
Journal of Multivariate Analysis,
Elsevier, vol. 60(2), pages 252-276, February.
- Ghirardato, Paolo & Marinacci, Massimo, 2000.
"Risk, Ambigity and the Separation of Utility and Beliefs,"
1085, California Institute of Technology, Division of the Humanities and Social Sciences.
- Massimo Marinacci & Paolo Ghirardato, 2001. "Risk, ambiguity, and the separation of utility and beliefs," ICER Working Papers - Applied Mathematics Series 21-2001, ICER - International Centre for Economic Research.
- Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity and the Separation of Utility and Beliefs," Econometric Society World Congress 2000 Contributed Papers 1143, Econometric Society.
- Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Levine's Working Paper Archive 7616, David K. Levine.
- Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
- David Schmeidler, 1989.
"Subjective Probability and Expected Utility without Additivity,"
Levine's Working Paper Archive
7662, David K. Levine.
- Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
- Christian List, 1999.
"Multidimensional Inequality Measurement: A Proposal,"
Economics Series Working Papers
1999-W27, University of Oxford, Department of Economics.
- List, C., 1999. "Multidimensional Inequality Measurement: a Proposal," Economics Papers 9927, Economics Group, Nuffield College, University of Oxford.
- 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.
- 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.
- 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.
- WEYMARK, John A., .
"Generalized Gini inequality indices,"
CORE Discussion Papers RP
-453, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Thibault Gajdos & Eric Maurin, 2004.
"Unequal Uncertainties and Uncertain Inequalities: An Axiomatic Approach,"
Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers)
- 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.
- 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.
- Thibault Gadjos & Eric Maurin, 2002. "Unequal Uncertainties and Uncertain Inequalities : An Axiomatic Approach," Working Papers 2002-32, Centre de Recherche en Economie et Statistique.
- 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.
- Gerard Debreu, 1959. "Topological Methods in Cardinal Utility Theory," Cowles Foundation Discussion Papers 76, Cowles Foundation for Research in Economics, Yale University.
- Bourguignon, F. & Chakravarty, S.R., 1998.
"The Measurement of Multidimensional Poverty,"
DELTA Working Papers
98-12, DELTA (Ecole normale supérieure).
- Pollak, Robert A, 1971. "Additive Utility Functions and Linear Engel Curves," Review of Economic Studies, Wiley Blackwell, vol. 38(116), pages 401-14, October.
- 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.
- Atkinson, Anthony B & Bourguignon, Francois, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," Review of Economic Studies, Wiley Blackwell, vol. 49(2), pages 183-201, April.
- 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.
- John A. Weymark & Kai-yuen Tsui, 1997. "Social welfare orderings for ratio-scale measurable utilities," Economic Theory, Springer, vol. 10(2), pages 241-256.
- Kolm, Serge-Christophe, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, MIT Press, vol. 91(1), pages 1-13, February.
- Maasoumi, Esfandiar, 1986. "The Measurement and Decomposition of Multi-dimensional Inequality," Econometrica, Econometric Society, vol. 54(4), pages 991-97, July.
- John A. Weymark, 2003. "The Normative Approach to the Measurement of Multidimensional Inequality," Vanderbilt University Department of Economics Working Papers 0314, Vanderbilt University Department of Economics, revised Jan 2004.
When requesting a correction, please mention this item's handle: RePEc:crs:wpaper:2003-16. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Florian Sallaberry)
If references are entirely missing, you can add them using this form.