Composite indices are widely used in development economics and can often be highly influential. Yet most remain controversial owing to inter alia the arbitrary selection of component weights. Several studies have proposed testing the robustness of rankings generated by composite indices with respect to alternative weights but have not provided sufficient guidance on the choice of these alternatives. This paper proposes a holistic yet theoretically novel approach for selecting sets of alternative weights and assessing comparison robustness that is applicable to linear composite indices with any finite number of dimensions. Our approach is founded on the main normative assumption that a consensus has been reached on the minimum and the maximum allowable weights that should be assigned to the components. This approach is applied to robustness testing of inter-temporal country improvements generated by arguably the world’s most influential composite development index, the UNDP Human Development Index.