It is often argued that multi-dimensional measures of well-being and poverty—such as those based on the capability approach and related views—are ad hoc. Rankings based on them are not, for this reason, robust to changes in the selection of weights used. In this paper, it is argued that the extent of potential arbitrariness and the range of issues relating to robustness have been underestimated in this context. Several issues relating to both the identification of the poor and the use of dimension-specific data are distinguished. These issues are then discussed in the context of the inter-provincial ranking of poverty in South Africa in 1995-6. It turns out that this ranking is fairly robust, and that some important policy-relevant results about the distinction between ‘income’/‘expenditure’ and ‘human’ poverty for the South African context are reinforced rather than undermined by checking for robustness. In particular, while KwaZulu Natal is in the best three in terms of the standard expenditure measures for various choices of poverty line, it is third worst in terms of all the multi-dimensional rankings presented here.