Multi-criteria analysis and sustainable accounting. Defining indices of sustainability under Choquet’s integral

The assessment of sustainability—in its three meanings: economic, social, and environmental ones—needs to be supported by specific econometric and statistical methodologies in order to be properly considered in policymaking processes. In the current literature the use of specific indices, capable of summarizing the three fields of sustainability, is a proven operational practice to express judgments on the convenience and the feasibility of investment in cities. It is necessary to specify that most sustainability indices are ordinarily calculated as arithmetic and geometric means of sub-dimensions. However, these two approaches do not allow investigation of the potential interactions between the various dimensions considered and, specifically, the geometric mean fails to smooth out unbalanced links. The research carried out here is aimed at implementing the use of the Choquet integral, as a non-additive and flexible aggregation model, to calculate evaluation indices able to consider the relationships between the different sustainable dimensions to be used in urban transformation projects. The methodology was tested on a case study, concerning an analysis—under economic, social, and environmental points of view—of different European countries. The evaluation frame based on the Choquet integral is referred to a ranking case aimed to establish the most sustainable country under the economic, environmental, and social point of view. The results obtained from the index processing show that the geometric mean scores and arithmetic ones are rather homogeneous, while the variations obtained among the three dimensions are moderately large. In the synoptic picture obtained with Choquet’s integral, countries with balanced results across dimensions are in higher positions. Therefore, the Choquet integral allows positive interactions to be taken into account across sustainable dimensions, and it is able to detect unbalanced achievements.