Comparing Non-Compensatory Composite Indicators: A Case Study Based on SDG for Mediterranean Countries

Composite indicators provide a summary picture of multidimensional phenomena and the corresponding rankings facilitate evaluations and comparisons over time and space. Standard composite indicators often assume compensability among the indicators. We argue that the compensability hypothesis needs to be restricted, especially when analysing economic, social, and environmental aspects. In this paper, we start with the simplest non-compensatory index, namely the geometric mean, and we introduce a new aggregation method. The method, called the weighted penalized geometric mean, is a generalization of the penalized geometric mean used to consider weights. The method introduces a penalty in the weighted geometric mean in terms of the (horizontal) variability of the normalized indicators transformed via the zero-order Box-Cox function. To illustrate the appeal of our proposal, we compare the above-mentioned non-compensatory approaches by proposing an application to selected targets of the Sustainable Development Goals (SDGs) for Mediterranean countries.