On the Coherence of Composite Indexes: Multiversal Model and Specification Analysis for an Index of Well-Being

Composite indexes are the alternative to GDP for the measurement of socio-economic dimensions, but they are sensitive to the specification of the model of measurement. This study adopts multiversal modelling to comparatively check the uncertainty of 68 models of aggregation of the Italian system of social-economic indicators of sustainable and equitable well-being (BES), across three paradigms for weighting schemes: vectorial distances, Principal Component Analysis (PCA), and Benefit-of-Doubt. As a result, high-performing Italian provinces are associated with higher uncertainty in performance. Results plus theory discourage the adoption of the method of PCA with implicit weights for formative measurement models. Furthermore, switching from arithmetic mean to non-linear functions has no significant effect on the uncertainty of outcomes.