The Unbalance Penalisation Method for Metrics of Social Progress

This study contributes to the debate on the development of aggregate metrics of societal progress. Summarising societal progress into a single number poses various methodological challenges, including the choice of indicators, normalisation, weighting and aggregation. This paper addresses the issue of aggregation in the case of metrics of well-being and uses as a case study the European Union regional Social Progress Index—EU-SPI—published by the European Commission. The index is an aggregate measure of 55 social and environmental indicators observed for all the European regions grouped into 12 components. In metrics of this type, while complete substitutability among components is rarely acceptable, controlling their level of substitutability is highly desirable. To this aim, we adopt a modified version of the unbalance penalisation approach originally proposed by Casadio Tarabusi and Guarini (Soc Indic Res 112:9–45, 2013). A penalisation is applied to the regions whose performance across the index components is unbalanced, that is when they perform well on some components but worse on others. The penalisation applied by this approach depends on two parameters that, in its original formulation, are generally arbitrarily chosen. We design a data-driven approach allowing for an informed choice of the penalisation parameters. The comparison between the EU-SPI original and penalised scores shows that the penalisation effect is particularly evident for regions with a strongly unbalanced profile across the components. The proposed method allows for adjusting the level of substitutability between components when constructing an aggregate metric, an important functionality especially when measuring societal progress for policy-making.