An Axiomatic Foundation of the Multiplicative Human Development Index

Yoko Kawada, Yuta Nakamura, Shuhei Otani

Research output: Contribution to journalArticle


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).

Original languageEnglish
JournalReview of Income and Wealth
Publication statusAccepted/In press - 2018 Jan 1


  • aggregation theory
  • geometric mean
  • Human Development Index
  • power mean
  • quasi-geometric mean

ASJC Scopus subject areas

  • Economics and Econometrics

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