This article evaluates the robustness of rankings obtained from composite indices that combine information from two or more components via a weighted sum. It examines the empirical prevalence of robust comparisons using the method proposed by Foster et al. (2010). Indices examined are the Human Development Index (HDI), the Index of Economic Freedom (IEF), and the Environmental Performance Index (EPI). Key theoretical results demonstrate links between the prevalence of robust comparisons, Kendall's tau rank correlation coefficient, and statistical association across components. Implications for redundancy among index components are also examined.