An Axiomatic Foundation of the Multiplicative Human Development Index
An Axiomatic Foundation of the Multiplicative Human Development Index
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DOI：
10.1111/roiw.12370
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发表时间：
2018-08
期刊：
影响因子：
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通讯作者：
Yoko Kawada;Yuta Nakamura;Shuhei Otani
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文献类型：
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作者：
Yoko Kawada;Yuta Nakamura;Shuhei Otani
2010年，人类发展指数(HDI)中的聚集公式改为几何平均。在这篇文章中，我们寻求采用这个新的HDI公式的理论依据。首先，我们找到了一类指标函数的极大类，我们称之为拟几何平均，它满足特征的对称性、正规化和可分性。其次，我们证明了幂平均是唯一满足齐性的拟几何平均。最后，新的HDI是唯一满足极小下界的幂平均，这是由Herrero，Martinez和Villar(2010)提出的局部可互补性公理。
The aggregation formula in the Human Development Index (HDI) was changed to 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, Martinez, and Villar (2010).