Capturing the distribution sensitivity among the poor in a multidimensional framework. A new proposal

This paper aims to explore properties that guarantee that multidimensional poverty indices are sensitive to the distribution among the poor, one of the basic features of a poverty index. We introduce a generalization of the monotonicity sensitivity axiom which demands that, in the multidimensional framework too, a poverty measure should be more sensitive to a reduction in the income of a poor person, the poorer that person is. It is shown that this axiom ensures that poverty diminishes under a transfer from a poor individual to a poorer one, and therefore it can also be considered a straightforward generalization of the minimal transfer axiom. An axiom based on the notion of ALEP substitutability is also introduced. This axiom captures aversion to both dispersion of the distribution, and attribute correlation, and encompasses the multidimensional monotonicity sensitivity axiom we propose. Finally, we review the existing multidimensional poverty families and identify which of them fulfil the new principles.