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The Lorenz zonotope and multivariate majorizations

  • Gleb Koshevoy

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

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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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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