The Lorenz zonotope and multivariate majorizations

Gleb Koshevoy
Additional contact information
Gleb Koshevoy: Russian Academy of Sciences, CEMI, Krasikova 32, Moscow 117418, Russia

Social Choice and Welfare, 1997, vol. 15, issue 1, 14 pages

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.

Date: 1997-11-13
Note: Received: 16 February 1994/Accepted: 22 May 1996
References: Add references at CitEc
Citations: View citations in EconPapers (26)

Downloads: (external link)
http://link.springer.de/link/service/journals/00355/papers/7015001/70150001.pdf (application/pdf)
http://link.springer.de/link/service/journals/0035 ... 15001/70150001.ps.gz (application/postscript)
Access to the full text of the articles in this series is restricted

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sochwe:v:15:y:1997:i:1:p:1-14

Ordering information: This journal article can be ordered from
http://www.springer. ... c+theory/journal/355

Access Statistics for this article

Social Choice and Welfare is currently edited by Bhaskar Dutta, Marc Fleurbaey, Elizabeth Maggie Penn and Clemens Puppe

More articles in Social Choice and Welfare from Springer, The Society for Social Choice and Welfare Contact information at EDIRC.
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().