Abstract:
The Sennian capability approach has facilitated to capture poverty
in its multi-dimensional incidence and thus to raise a new aggregate
poverty index – the UNDP's Human Poverty Index (HPI). The UNDP has
found power mean of order α > 1 as possessing some of the most
desirable properties in describing the distribution of deprivation
dimensions and hence as the most appropriate aggregate index of multidimensional deprivation. The UNDP elevates power mean of order
α > 1 (PM) in comparison with arithmetic mean (AM) commonly used
for averaging, leaving out others. It would hence be worthwhile to look
into the links among the means, both the known and the potential ones,
and their strengths and weaknesses in terms of their properties in
comparison with each other. The present paper is a preliminary attempt
at this. We find that the means we commonly use, the AM, the geometric
mean (GM) and the harmonic mean (HM), along with the PM, are special
cases of the CES function. We acknowledge the possibility of an inverse
CES function, and hence, that of an inverse power mean (IPM) also.
Among these means, the AM is an average, typical of all the components,
but its infinite elasticity of substitution renders it less desirable. To the
extent that we need an average, typical of the components, we seek for
one that is closer to the AM, so that this second best choice will have the
minimum deviations next to the AM. And we find this basic criterion is
satisfied by the IPM only. Hence, while the PM captures the multidimensional deprivation, its inverse, the IPM, seems to offer a multidimensional development index
