IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v15y1997i1p1-14.html
   My bibliography  Save this article

The Lorenz zonotope and multivariate majorizations

Author

Listed:
  • 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.

Suggested Citation

  • Gleb Koshevoy, 1997. "The Lorenz zonotope and multivariate majorizations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(1), pages 1-14.
    • Handle: RePEc:spr:sochwe:v:15:y:1997:i:1:p:1-14
    Note: Received: 16 February 1994/Accepted: 22 May 1996
    as

    Download full text from publisher

    File URL: http://link.springer.de/link/service/journals/00355/papers/7015001/70150001.pdf
    Download Restriction: Access to the full text of the articles in this series is restricted
    File URL: http://link.springer.de/link/service/journals/00355/papers/7015001/70150001.ps.gz
    Download Restriction: Access to the full text of the articles in this series is restricted
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, July.
    2. Muller, Christophe & Trannoy, Alain, 2011. "A dominance approach to the appraisal of the distribution of well-being across countries," Journal of Public Economics, Elsevier, vol. 95(3), pages 239-246.
    3. 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.
    4. Sprumont, Yves, 2012. "Resource egalitarianism with a dash of efficiency," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1602-1613.
    5. Karl Mosler, 2005. "Restricted Lorenz dominance of economic inequality in one and many dimensions," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 2(2), pages 89-103, January.
    6. Østerdal, Lars Peter, 2010. "The mass transfer approach to multivariate discrete first order stochastic dominance: Direct proof and implications," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1222-1228, November.
    7. 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.
    8. Nilsson, Therese, 2007. "Measuring Changes in Multidimensional Inequality - An Empirical Application," Working Papers 2007:14, Lund University, Department of Economics.
    9. 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.
    10. Francesco Andreoli & Claudio Zoli, 2012. "On the Measurement of Dissimilarity and Related Orders," Working Papers 274, ECINEQ, Society for the Study of Economic Inequality.
    11. Savaglio, Ernesto, 2011. "On multidimensional inequality with variable distribution mean," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 453-461.
    12. Masato Okamoto, 2009. "Decomposition of gini and multivariate gini indices," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 7(2), pages 153-177, June.
    13. Finn Tarp & Lars Peter Østerdal, 2007. "Multivariate Discrete First Order Stochastic Dominance," Discussion Papers 07-23, University of Copenhagen. Department of Economics.
    14. Marat Ibragimov & Rustam Ibragimov, 2007. "Market Demand Elasticity and Income Inequality," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(3), pages 579-587, September.
    15. Gleb A. Koshevoy & Karl Mosler, 2007. "Multivariate Lorenz dominance based on zonoids," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 91(1), pages 57-76, March.
    16. Olena Nizalova, 2014. "Inequality in Total Returns to Work in Ukraine: Taking A Closer Look at Workplace (Dis)amenities," Discussion Papers 52, Kyiv School of Economics.
    17. Stéphane Mussard, 2007. "Between-Group Pigou Dalton Transfers," Cahiers de recherche 07-06, Departement d'économique de l'École de gestion à l'Université de Sherbrooke.
    18. Francesco Andreoli & Claudio Zoli, 2014. "Measuring Dissimilarity," Working Papers 23/2014, University of Verona, Department of Economics.
    19. 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.
    20. Ernesto Savaglio, 2012. "Multidimensional Inequality with Variable Household Weight," Department of Economics University of Siena 667, Department of Economics, University of Siena.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sochwe:v:15:y:1997:i:1:p:1-14. See general information about how to correct material in RePEc.

    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.

    We have no bibliographic references for this item. You can help adding them by using 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.