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The Lorenz zonotope and multivariate majorizations

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  • Gleb Koshevoy

    (Russian Academy of Sciences, CEMI, Krasikova 32, Moscow 117418, Russia)

Abstract

The 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.

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Bibliographic Info

Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 15 (1997)
Issue (Month): 1 ()
Pages: 1-14

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Handle: RePEc:spr:sochwe:v:15:y:1997:i:1:p:1-14

Note: Received: 16 February 1994/Accepted: 22 May 1996
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Web page: http://link.springer.de/link/service/journals/00355/index.htm

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Cited by:
  1. 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.
  2. 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.
  3. Ibragimov, Rustam & Ibragimov, Marat, 2007. "Market Demand Elasticity and Income Inequality," Scholarly Articles 2623728, Harvard University Department of Economics.
  4. 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.
  5. 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.
  6. Masato Okamoto, 2009. "Decomposition of gini and multivariate gini indices," Journal of Economic Inequality, Springer, vol. 7(2), pages 153-177, June.
  7. 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.
  8. Finn Tarp & Lars Peter Østerdal, 2007. "Multivariate Discrete First Order Stochastic Dominance," Discussion Papers 07-23, University of Copenhagen. Department of Economics.
  9. Nilsson, Therese, 2007. "Measuring Changes in Multidimensional Inequality - An Empirical Application," Working Papers 2007:14, Lund University, Department of Economics.
  10. Sprumont, Yves, 2012. "Resource egalitarianism with a dash of efficiency," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1602-1613.
  11. Marat Ibragimov & Rustam Ibragimov, 2007. "Market Demand Elasticity and Income Inequality," Economic Theory, Springer, vol. 32(3), pages 579-587, September.
  12. 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.
  13. 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.
  14. Ernesto Savaglio, 2007. "On multidimensional inequality with variable distribution mean," Department of Economics University of Siena 522, Department of Economics, University of Siena.
  15. 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.

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