June 28 2022 at 10am. (online)
(please ask the link to the organizers)
Patrizia Perez Asurmendi (Universidad Complutense de Madrid)
Title: Can we built better Composite Indicators? An Alternative to the Geometric Mean.
Abstract: In economic framework, composite indicators are a powerful tool to summarize the information provided by simple indicators in a unique value. Many of them are designed aggregating simple indicators through arithmetic and geometric means (sometimes the weighted ones) given their simplicity and their properties. But using these aggregation functions is subject to criticisms in the literature. In the case of the arithmetic mean, the main one focuses on the compensability that it allows among the different simple indicators that aggregates. To solve this weakness, the use of the geometric mean is highly recommended given that the compensability among the different simple indicators is lower than in the former. Nevertheless, the geometric mean exhibits also a relevant drawback, namely, it is not invariant to changes in the scale. To be more concrete, it is not stable when linear transformations are performed on the scale used to represent the values of the indicators. Accordingly, the final ranking depends dramatically on the selected scale of the simple indicators. Moreover, in both cases, the possible and common interactions among simple indicators are not considered in the composite indicator. To overcome these issues, we propose a model based on the Choquet integral. On the one hand, our proposal allows to consider the usual interactions among the simple indicators in the composite indicator when necessary. On the other hand, it allows to control the degree of compensability among simple indicators.