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This paper presents axiomatic arguments to make the case for distribution-sensitive multidimensional poverty measures. The commonly-used counting measures violate the strong transfer axiom which requires regressive transfers to be unambiguously poverty-increasing and they are also invariant to changes in the distribution of a given set of deprivations amongst the poor. The paper appeals to strong transfer as well as an additional cross-dimensional convexity property to offer axiomatic justification for distribution-sensitive multidimensional poverty measures. Given the nonlinear structure of these measures, it is al also shown how the problem of an exact dimensional decomposition can be solved using Shapley decomposition methods to assess dimensional contributions to poverty. An empirical illustration for India highlights distinctive features of the distribution-sensitive measures.

Crossdimensional Convexity --- Multidimensional Poverty --- Poverty Assessment --- Poverty Measurement --- Poverty Reduction --- Shapley Decomposition --- Transfer Axiom