When comparing poverty across distributions, an analyst must select a poverty line to identify the poor, an equivalence scale to compare individuals from households of di erent compositions and sizes, and a poverty index to aggregate individual deprivation into an index of total poverty. A di erent c hoice of poverty line, poverty index or equivalence scale can of course reverse an initial poverty ordering. This paper develops sequential stochastic dominance conditions that throw light on the robustness of poverty comparisons to these important measurement issues. These general conditions extend well-known results to any order of dominance, to the choice of individual versus family based aggregation, and to the estimation of critical sets of measurement assumptions. Our theoretical results are brie y illustrated using data for four countries drawn from the Luxembourg Income Study data bases.