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Ordinal attributes cannot be aggregated through linear combinations, averages or other functionals, designed for numerical variables. In fact, ordinal scores cannot be summed, multiplied by scalars or composed in other ways. For this reason, they are often transformed into numerical scores, through more or less sophisticated scaling tools, before aggregation. Unfortunately, there are evidences that such procedures may lead to controversial results (Madden 2010). Moreover, one could legitimately ask why concepts naturally conceived in ordinal terms should be forced into numerical settings. Is the idea of ordinal scores as rough manifestations of underlying continuous traits always well founded? Or is it actually motivated by the lack of consistent and effective procedures for the treatment of ordinal data? Such problems go beyond the setting of well-being measurement and arise in many other fields as well. For example, in marketing and customer segmentation, in ecological and environmental studies, in risk management and, more generally, in ordinal multi-criteria decision-making (Bruggemann et al. 1999; Annoni and Bruggemann 2009; Bruggemann and Patil 2010, 2011; Bruggemann and Voigt 2012; Bruggemann and Carlsen 2014; Carlsen and Bruggemann 2014). It is in fact a feature of modern information society that most of data we deal with are of a discrete and qualitative kind. The absence of statistical tools and procedures to manage such data types consistently may well turn into severe limitations in our capability to exploit the great amount of information they convey.

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