Unidimensional Underpinnings of Multidimensional Counting Measures

Traditional unidimensional measures aggregate information at the individual level then gauge poverty in the distribution of a single variable using a poverty line and measurement methodology. This paper provides an intuitive parallel procedure for creating a multidimensional poverty measure from a distribution of aggregate attainments of persons in across dimensions. The paper elaborates the multidimensional properties that follow from properties satisfied by the unidimensional methodology that is applied to that distribution, with the exception of dimensional breakdown which has no unidimensional precursor. Indeed, dimensional breakdown combined with subgroup decomposability seems to be nearly unique to the adjusted headcount ratio and to the unidimensional measure that generates it - the augmented poverty gap – which is a convex combination of the first two FGT measures.

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