Composite Indices, Alternative Weights, and Comparison Robustness

Abstract

Composite indices are widely used and can 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 alternatives weights and assessing comparison robustness that is applicable to linear composite indices with any finite number of dimensions. 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 (HDI). More than two-thirds of HDI country improvements between 1980 and 2013 were found to be not robust to the selected set of alternative weights.