Composition by DEA Distance to the Frontier - Probabilistic Composition of Preferences, Theory and Applications - page 56

correlated with the qualities that matter. Therefore, there is a risk in the use of social
indicators. Used to set goals, they can divert initiatives from the true values to false
representatives.
This is what happens with the gross national product or the national income.
Even when computed on a per capita basis they deviate the focus of promoting
social development to isolated economic goals. The HDI was created to try to
reduce the importance attached to strictly economic indicators. In turn, to be a
simple indicator with the properties of direct and objective communication, it also
faces the same risk of moving away from the dimensions to be measured.
While, by one side, it is important to have a single indicator to substitute for per
capita GNP, on the other side it is important to validate and re ne this new indicator

by comparing to other complex indicators in the same way as other economic
indices are compared to per capita GNP.
In 2010 the form of computation of HDI was changed. From the viewpoint of
the calculation algorithm, the main change is that, instead of a weighted arithmetic
mean, a geometric mean is now employed. This approximates the algorithm to the
joint probabilities approach for probabilistic composition.
Other measures using the same components of HDI, but using probabilistic
composition to combine them into a single measure can be built with different
properties. A feature that all the measures discussed here share is taking as their
starting point the preliminary transformation of the partial indicators of preference
into probabilities of reaching the frontier of best or of worst performance in each of
them.
By 2009, the partial indicators combined in the HDI were:
Life expectancy at birth, as an indicator of development on the dimension of
health;
Literacy, weighing 2/3, combined with the gross school enrolment rate (ratio
between the total number of students attending school in the three levels of edu-
cation and the total number of persons of school age), weighing 1/3, as indicator of
development in the dimension of education;
Neperian logarithm of the per capita gross domestic product, as measured in
terms of PPP

purchase power parity (World Bank 2014 ), as an indicator of
economic welfare of the population of the country.
Each of these indicators was transformed to a scale from 0 to 1 by subtracting an
absolute minimum and dividing by an absolute amplitude. The maximum and
minimum for longevity in a country were then

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fixed in 25 - 85 years. For the per

capita GDP, the extremes were 100 and 40,000.
Finally, the HDI was calculated as the arithmetic mean of the measures of
development in the three directions.
Currently slightly different partial indicators and composition rule are employed.
The three dimensions remain.
The health indicator is still life expectancy at birth, measured as before, but with
limits of 20

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83.57 years. As an indicator of income the Neperian logarithm of per
capita GDP was replaced by that of per capita Gross National Income, with limits of
100 and 87478 PPP.