Measuring complex and rather intuitive qualities such as sustainability requires combining many different measures together. These measures often quantify contrasting effects. The resulting composite index then also depends not only on the component indices but also on the way that these have been combined together. An example of such a measure is the Happy Planet Index (HPI) that aggregates information on positive qualities like life-expectancy and human well-being with negative ones like ecological footprint to rank countries according to their sustainability. However, since component indices are often mutually correlated and feature quite different distributions of entities ranked, elaborate rules are used in the process of combination. As a result, the resulting composite index may look somewhat contrived and its rankings may depend heavily on subjective parameters in the combination process. We propose a geometrically motivated parameter-free method for combining indices with contrasting effects together. The method is independent of the number of contrasting indices to be combined and eliminates mutual correlation between component indices by using Singular Value Decomposition (SVD) analysis. As an example of its use, we revisit the Happy Planet Index and demonstrate the impact of adding new component indices to HPI on ranking nations by their sustainability.
