The Ordinal Input for Cardinal Output Approach of Non-compensatory Composite Indicators: The PROMETHEE Scoring Method

Despite serious threats as to their soundness, the adoption of composite indicators is constantly growing alongside their popularity, especially when it comes to their adoption in policy-making exercises. This study presents a robust non-compensatory approach to construct composite indicators mainly based, at least with respect to the basic ideas, on the classic Borda scoring procedure. The non- compensatory indicators we are proposing can be seen as aggregation of ordinal non-compensatory preferences between considered units supplying a numerical cardinal comprehensive evaluation. For this reason we define our methodology, the ordinal input for cardinal output non-compensatory approach for composite indicators. To take into account hesitation, imprecision and ill-determination in defining preference relations with respect to the elementary indices, we adopt the PROMETHEE methods, whose net flow score can be seen as an extension to the fuzzy preferences of the Borda score. Moreover, we systematically deal with robustness of the results with respect to weighting and parameters such as indifference and preference thresholds, permitting to define preference relations of elementary indices. In this regard, we couple PROMETHEE methods with the recently proposed σ−μ approach, which permits to explore the whole domain of feasible preference parameters mentioned above, giving a synthetic representation of the distribution of the values assumed by the composite indicators in terms of mean, μ, and standard deviation, σ. μ and σ are also used to define a comprehensive overall composite indicator. Finally, we enrich the results of this analysis with a set of graphical visualizations based on principal component analysis applied to the PROMETHEE methods with the GAIA technique, providing better understanding of the outcomes of our approach. To illustrate its assets, we provide a case study of inclusive development evaluation, based on the data of the homonymous report produced by the World Economic Forum.