TY - JOUR
T1 - An Axiomatic Foundation of the Multiplicative Human Development Index
AU - Kawada, Yoko
AU - Nakamura, Yuta
AU - Otani, Shuhei
PY - 2019/12/1
Y1 - 2019/12/1
N2 - 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).
AB - 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).
KW - Human Development Index
KW - aggregation theory
KW - geometric mean
KW - power mean
KW - quasi-geometric mean
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U2 - 10.1111/roiw.12370
DO - 10.1111/roiw.12370
M3 - Article
AN - SCOPUS:85055256921
SN - 0034-6586
VL - 65
SP - 771
EP - 784
JO - Review of Income and Wealth
JF - Review of Income and Wealth
IS - 4
ER -