Robust Human Development Rankings

Preliminary version. Do not quote without permission. A Human Development Index (HDI) tries to capture the degree to which a coun-try is developed along several dimensions e.g. income, literacy rate, longevity into one single number. However, there is disagreement about (i) how to transform the di¤erent dimensions to make them comparable and (ii) how to aggregate the resulting equivalized dimensions. At the risk of stressing the obvious, changes in transformation and/or aggregation will a¤ect the country rankings. We focus on robust rankings, i.e., rankings which hold for a wide set of (i) transformation and/or (ii) aggregation procedures. First, we propose a ranking procedure that is robust with respect a wide class of initial variable transformations (reected in alterna-tive benchmark performance selections). Second, we suggest a robust (generalized Lorenz) dominance criterion by focusing on the class of aggregation indices which are (i) increasing and (ii) S-concave. We show that the robust ranking procedure can be implemented via linear programming. An assessment of the well-known HDI ranking (yearly produced by the United Nations) illustrates our methodology. This application shows the practical usefulness of the suggested framework as an operational tool for robustness analysis. It is better to be vaguely right, than precisely wrong (A.K. Sen, 1989) 1