In the unidimensional poverty field, a number of axioms capture the distribution sensitivity among the poor. One of them is the monotonicity sensitivity axiom that demands that a poverty measure should be more sensitive to a reduction in the income of a poor person, the poorer that person is. On the other hand, the minimal transfer axiom requires poverty to decrease when a transfer of income is made from a poor person to a poorer one. These axioms turn out to be identical, but they provide different and interesting interpretations. Both of them rely deeply on the income-ranking of the poor.
Some generalizations of the minimal transfer axiom and its variations have been proposed in the multidimensional framework. In none of them the partial ordering of the poor is taken into account. No counterpart of the monotonicity sensitivity axiom exists.
This note introduces multidimensional generalizations of the two mentioned axioms, keeping the crucial assumption that only when the poor involved are unambiguously ranked are the axioms uncontroversial. We show that the two generalizations proposed are also identical in the multidimensional setting although offering different interpretations. Relationships between the new properties and those existing in the literature are analyzed.