Axiomatic measurement of multidimensional well-being inequality: Some distributional questions

Multidimensional Poverty and Inequality

“…After restricting the class of social evaluation functions to be continuous, strictly increasing, anonymous, strictly quasi-concave, separable and scale invariant, Tsui (1995) derives the two following multidimensional (relative) inequality indices: 47 46 For instance, in their applications of Maasoumi's approach, Nilsson (2010), Justino (2012) and Rohde and Guest (2013) use the Theil indices. 47 Abul Naga and Geoffard (2006), Brambilla andCroci Angelini andMichelangeli (2012) provide decompositions of this class of indices into the univariate inequality indices of the attributes and a residual term capturing their joint distributions. See also Kobus (2012) for a stronger definition of decomposition by attributes.…”

The Impact of the Great Recession on Well-Being across Europe Ten Years On: A Cluster Analysis

“…The PCA is a reliable method meant to overcome the trade-off between comprehensiveness (which compresses the variety of dimensions of life into a synthetic index) and meaning (whereby the focus on the impact of the crisis on well-being prompts preserving the distinct short-term evolutionary path of well-being in each dimension) and so helps in weighting performances and devising policies (Nardo et al 2008). To evaluate unobservable variables such as well-being or quality of life, an alternative method is the fuzzy set approach (Betti 2016) where the methodological focus is on the appropriate weights, while another method is by axiomatic measurement, which keeps a desirable decomposition characteristic and was proposed in a previous paper (Croci Angelini and Michelangeli 2012).…”

Multidimensional polarization for ordinal data

“…This can also be treated as a form of obtaining a multidimensional measure which is alternative to, for example, first computing individual welfare levels and then computing the overall index. Zhong (2009) applies the Abul Naga-Geoffard decomposition in a health-income context and Crocci Angelini and Michelangeli (2012) to study the evolution of well-being inequality in some EU countries. Kobus and Miłoś (2012) characterizes attribute decomposability in the strongest form, namely when association is not taken into account, and provides a simple proof to check the decomposability of specific indices.…”