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.
|Date of creation:||May 2003|
|Date of revision:||Jul 2003|
|Contact details of provider:|| Web page: http://www.vanderbilt.edu/econ/wparchive/index.html|
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.:
- 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.
- Paolo Ghirardato & Massimo Marinacci, 2000.
"Risk, Ambiguity, and the Separation of Utility and Beliefs,"
Levine's Working Paper Archive
7616, David K. Levine.
- Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity and the Separation of Utility and Beliefs," Econometric Society World Congress 2000 Contributed Papers 1143, Econometric Society.
- Ghirardato, Paolo & Marinacci, Massimo, 2000. "Risk, Ambigity and the Separation of Utility and Beliefs," Working Papers 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.
- Weymark, John A., 1981.
"Generalized gini inequality indices,"
Mathematical Social Sciences,
Elsevier, vol. 1(4), pages 409-430, August.
- 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.
- 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, 2004. "Unequal Uncertainties and Uncertain Inequalities: An Axiomatic Approach," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00085940, HAL.
- Thibault Gadjos & Eric Maurin, 2002. "Unequal Uncertainties and Uncertain Inequalities : An Axiomatic Approach," Working Papers 2002-32, Centre de Recherche en Economie et Statistique.
- Itzhak Gilboa & Elchanan Ben-Porath & David Schmeidler, 1997.
"On the Measurement of Inequality under Uncertainty,"
- 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.
- Domenico Menicucci, 2003.
"Optimal two-object auctions with synergies,"
Review of Economic Design,
Springer;Society for Economic Design, vol. 8(2), pages 143-164, October.
- Erio Castagnoli & Fabio Maccheroni & Massimo Marinacci, 2004.
"Choquet Insurance Pricing: A Caveat,"
Wiley Blackwell, vol. 14(3), pages 481-485.
- John A. Weymark & Kai-yuen Tsui, 1997. "Social welfare orderings for ratio-scale measurable utilities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(2), pages 241-256.
- Itzhak Gilboa & David Schmeidler, 1989.
"Maxmin Expected Utility with Non-Unique Prior,"
- Gerard Debreu, 1959. "Topological Methods in Cardinal Utility Theory," Cowles Foundation Discussion Papers 76, Cowles Foundation for Research in Economics, Yale University.
- Koshevoy, Gleb & Mosler, Karl, 1995.
"Multivariate Gini indices,"
Discussion Papers in Econometrics and Statistics
7/95, University of Cologne, Institute of Econometrics and Statistics.
- Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931, December.
- 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.
- Serge-Christophe Kolm, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, Oxford University Press, vol. 91(1), pages 1-13.
- Schmeidler, David, 1989.
"Subjective Probability and Expected Utility without Additivity,"
Econometric Society, vol. 57(3), pages 571-87, May.
- David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
- Robert A. Pollak, 1971. "Additive Utility Functions and Linear Engel Curves," Review of Economic Studies, Oxford University Press, vol. 38(4), pages 401-414.
- 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.
- François Bourguignon & Satya Chakravarty, 2003.
"The Measurement of Multidimensional Poverty,"
The Journal of Economic Inequality,
Springer;Society for the Study of Economic Inequality, vol. 1(1), pages 25-49, April.
- A. B. Atkinson & F. Bourguignon, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," Review of Economic Studies, Oxford University Press, vol. 49(2), pages 183-201.
- Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
- 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.
- W. M. Gorman, 1968. "The Structure of Utility Functions," Review of Economic Studies, Oxford University Press, vol. 35(4), pages 367-390.
- List, C., 1999. "Multidimensional Inequality Measurement: a Proposal," Economics Papers 9927, Economics Group, Nuffield College, University of Oxford.
- Maasoumi, Esfandiar, 1986. "The Measurement and Decomposition of Multi-dimensional Inequality," Econometrica, Econometric Society, vol. 54(4), pages 991-97, July.
When requesting a correction, please mention this item's handle: RePEc:van:wpaper:0311. 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: (John P. Conley)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.