The Lorenz zonotope and multivariate majorizations
AbstractThe distribution of d commodities among n individuals is described by an nþd row stochastic matrix. We present a geometric approach to order such matrices. For a row stochastic matrix the Lorenz zonotope is investigated, which is a higher dimensional generalization of the Lorenz curve. The Lorenz zonotope is a convex polytope. The inclusion of Lorenz zonotopes defines an ordering between row stochastic matrices, which is a multivariate majorization. For a cone in nonnegative d-space, a cone extension of the Lorenz zonotope and the respective inclusion ordering are introduced. We study this class of orderings and establish equivalence with known majorizations. It is provided a finite set of inequalities to which the ordering is equivalent.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. 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.
Bibliographic InfoArticle provided by Springer in its journal Social Choice and Welfare.
Volume (Year): 15 (1997)
Issue (Month): 1 ()
Note: Received: 16 February 1994/Accepted: 22 May 1996
Contact details of provider:
Web page: http://link.springer.de/link/service/journals/00355/index.htm
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Karl Mosler, 2004.
"Restricted Lorenz dominance of economic inequality in one and many dimensions,"
Journal of Economic Inequality,
Springer, vol. 2(2), pages 89-103, August.
- Karl Mosler, 2005. "Restricted Lorenz dominance of economic inequality in one and many dimensions," Journal of Economic Inequality, Springer, vol. 2(2), pages 89-103, January.
- Nilsson, Therese, 2007. "Measuring Changes in Multidimensional Inequality - An Empirical Application," Working Papers 2007:14, Lund University, Department of Economics.
- Gleb A. Koshevoy & Karl Mosler, 2007. "Multivariate Lorenz dominance based on zonoids," AStA Advances in Statistical Analysis, Springer, vol. 91(1), pages 57-76, March.
- SPRUMONT, Yves, 2007.
"Resource Egalitarianism with a Dash of Efficiency,"
Cahiers de recherche
2007-03, Universite de Montreal, Departement de sciences economiques.
- Savaglio, Ernesto, 2011.
"On multidimensional inequality with variable distribution mean,"
Journal of Mathematical Economics,
Elsevier, vol. 47(4-5), pages 453-461.
- Ernesto Savaglio, 2007. "On multidimensional inequality with variable distribution mean," Department of Economics University of Siena 522, Department of Economics, University of Siena.
- Alain Trannoy & Christophe Muller, 2004.
"A Dominance Approach To Well-Being Inequality Across Countries,"
Working Papers. Serie AD
2004-27, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- Christophe Muller & Alain Trannoy, 2003. "A Dominance Approach to Well-Being Inequality across Countries," IDEP Working Papers 0313, Institut d'economie publique (IDEP), Marseille, France.
- Arie Beresteanu & Francesca Molinari, 2008.
"Asymptotic Properties for a Class of Partially Identified Models,"
Econometric Society, vol. 76(4), pages 763-814, 07.
- Arie Beresteanu & Francesca Molinari, 2006. "Asymptotic properties for a class of partially identified models," CeMMAP working papers CWP10/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Beresteanu, Arie & Molinari, Francesca, 2006. "Asymptotic Properties for a Class of Partially Identified Models," Working Papers 06-04, Duke University, Department of Economics.
- Beresteanu, Arie & Molinari, Francesca, 2006. "Asymptotic Properties for a Class of Partially Identified Models," Working Papers 06-07, Cornell University, Center for Analytic Economics.
- E. Abdul-Sathar & R. Suresh & K. Nair, 2007. "A vector valued bivariate gini index for truncated distributions," Statistical Papers, Springer, vol. 48(4), pages 543-557, October.
- Finn Tarp & Lars Peter Østerdal, 2007. "Multivariate Discrete First Order Stochastic Dominance," Discussion Papers 07-23, University of Copenhagen. Department of Economics.
- Stéphane Mussard, 2007.
"Between-Group Pigou Dalton Transfers,"
Cahiers de recherche
07-06, Departement d'Economique de la Faculte d'administration à l'Universite de Sherbrooke.
- Ernesto Savaglio, 2012. "Multidimensional Inequality with Variable Household Weight," Department of Economics University of Siena 667, Department of Economics, University of Siena.
- Masato Okamoto, 2009. "Decomposition of gini and multivariate gini indices," Journal of Economic Inequality, Springer, vol. 7(2), pages 153-177, June.
- Marco Dall’Aglio & Marco Scarsini, 2000. "Zonoids, Linear Dependence, and Size-Biased Distributions on the Simplex," ICER Working Papers - Applied Mathematics Series 27-2003, ICER - International Centre for Economic Research, revised Jul 2003.
- Ibragimov, Rustam & Ibragimov, Marat, 2007.
"Market Demand Elasticity and Income Inequality,"
2623728, Harvard University Department of Economics.
- Nicolas Gravel & Patrick Moyes, 2006. "Ethically Robust Comparisons of Distributions of Two Individual Attributes," IDEP Working Papers 0605, Institut d'economie publique (IDEP), Marseille, France, revised Aug 2006.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Guenther Eichhorn) or (Christopher F Baum).
If references are entirely missing, you can add them using this form.