Robust human development rankings

The United Nations' Human Development Index (HDI) takes several dimensions ---income, school enrolment and literacy rate, longevity--- and combines them into a single figure that measures the degree of development of a given country. However, there is disagreement about (i) how to normalize the scores for the different criteria to make them comparable and (ii) how to aggregate the (normalized) scores over the different criteria. At the risk of stressing the obvious, changes in normalization and/or aggregation will affect the country rankings. First, we focus on robust rankings, i.e., rankings which hold for a wide set of normalization and/or aggregation procedures. Second, we show that all proposed ranking procedures can be implemented via linear programming techniques. Third, we illustrate how our methodology can prove useful in assessing the robustness of the human development country ranking/classification (produced annually by the United Nations) in a descriptive and statistical way.