Titel: Multivariate Lorenz Ma jorization and Heterogeneity Measures: An Axiomatic Approach
Autor: Wolfgang Eichhorn / Manfred Krtscha
Abstract: This work introduces two new curves that are multivariate generalizations of the ’classical’ Lorenz curve. All data of d-variate distributions can be visualized by drawing these curves in the plane, whereas Koshevoy’s and Mosler’s generalization by a lift zonoid in R^(d+1) can only be drawn for d = 2. The generalizations of the Lorenz curve induce partial orderings of d-variate distributions. Furthermore, two inequality or heterogeneity measures that are consistent with the induced rankings are proposed. They can be considered as new generalizations of the univariate Gini coefficient. For deciding which of the two measures is more appropriate for measuring a sort of convergence concerning different countries of an union or of regions of a country, we establish systems of axioms. Although these systems are reflecting natural properties, several of the axioms are new. Moreover, by means of these axioms well-known inequality measures are tested, too.
Perspectives on Social Choice
2007 (29) Heft 2
Guest-Editor: Marlies Ahlert
Introduction and Overview
This volume of Analyse & Kritik approaches social choice from different angles. Each of the papers thematically has some relation with the work of Wulf Gaertner. This provides some topical unity to the volume. However, other than in case of a typical Festschrift the refereed papers are in all other regards independent contributions to the field of social choice as very widely understood. Methods reach from axiomatic analyses over experiments to simulations and from t...