This chapter examines different approaches to the measurement of multidimensional
inequality and poverty. It first outlines three aspects preliminary to any multidimensional …

In a one-good world, there is a nice correspondence between the Pigou-Dalton principle of
transfer and social welfare dominance. In this paper we study the case of multiple goods …

The classical Lorenz curve visualizes and measures the disparity of items which are
characterized by a single variable: The more the curve bends, the more scatter the data …

We consider the convex ordering for random vectors and some weaker versions of it, like the
convex ordering for linear combinations of random variables. First we establish conditions of …

This paper proposes a dominance approach to study inequality of well-being across
countries. We consider a class of well-being indices based on the three attributes used in …

A fundamental result in the theory of stochastic dominance tells that first order dominance
between two finite multivariate distributions is equivalent to the property that the one can be …

This paper deals with the important notion of majorization. We study majorization for
matrices, and focus on (0, 1)-matrices. We prove several results concerning such matrix …

We obtain a complete characterization of linear operators that preserve strong majorization
on (0, 1)-matrices. To do this we introduce a new matrix invariant of combinatorial nature …

This paper generalizes the poverty ordering criteria available for single dimensional income
poverty to the case of multidimensional welfare attributes. A set of properties to be satisfied …

We provide a unified treatment of the two approaches pioneered by Atkinson and
Bourguignon (1982, 1987)[3, 4] by resorting to compensation principles in the bivariate …