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An Axiomatic Foundation of the Multiplicative Human Development Index

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  • Yoko Kawada
  • Yuta Nakamura
  • Shuhei Otani

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).

Suggested Citation

  • Yoko Kawada & Yuta Nakamura & Shuhei Otani, 2019. "An Axiomatic Foundation of the Multiplicative Human Development Index," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 65(4), pages 771-784, December.
    • Handle: RePEc:bla:revinw:v:65:y:2019:i:4:p:771-784
    DOI: 10.1111/roiw.12370
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    References listed on IDEAS

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    2. Carmen Herrero & Ricardo Martínez & Antonio Villar, 2010. "Multidimensional Social Evaluation: An Application To The Measurement Of Human Development," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(3), pages 483-497, September.
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    4. Eduardo Zambrano, 2014. "An axiomatization of the human development index," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 853-872, April.
    5. Desai, Meghnad, 1991. "Human development : Concepts and measurement," European Economic Review, Elsevier, vol. 35(2-3), pages 350-357, April.
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    Cited by:

    1. Juan Gabriel Rodríguez, 2022. "Making the most of world talent for science? The Nobel Prize and Fields Medal experience," Scientometrics, Springer;Akadémiai Kiadó, vol. 127(2), pages 813-847, February.
    2. Herrero, Carmen & Pineda, José & Villar, Antonio & Zambrano, Eduardo, 2020. "Tracking progress towards accessible, green and efficient energy: The Inclusive Green Energy index," Applied Energy, Elsevier, vol. 279(C).
    3. Stephen Morse, 2020. "To Rank or Not to Rank with Indices? That Is the Question," Sustainability, MDPI, vol. 12(14), pages 1-20, July.
    4. Carmen Herrero & Jose' Pineda & Antonio Villar & Eduardo Zambrano, 2020. "The Inclusive Green Energy index of progress," Working Papers 2003, California Polytechnic State University, Department of Economics.

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