An Axiomatic Foundation of the Multiplicative Human Development Index. (21st October 2018) - Kawada, Yoko
Abstract: The aggregation formula in the Human Development Index (HDI) was changed to a geometric mean in 2010. In this paper, we search for a theoretical justification for employing this new HDI formula. First, we find a maximal class of index functions, what we call quasi‐geometric means, that satisfy symmetry for the characteristics, normalization, and separability . Second, we show that power means are the only quasi‐geometric means satisfying homogeneity . Finally, the new HDI is the only power mean satisfying minimal lower boundedness, which is a local complementability axiom proposed by Herrero et al . (2010).