Composition by DEA Distance to the Frontier - Probabilistic Composition of Preferences, Theory and Applications - page 61

first two scores are obtained by computing joint probabilities, assuming
maximal dependence between the components, what means using for the proba-
bility of the intersection the lowest probability. The

The

first of these scores follows
from application of the pessimistic approach, i.e., evaluates the country by the
probability of not being the worst by any criterion. The second results from the
optimistic joint probability composition: assesses the country by the probability of
not being the worst by at least one of the criteria.
The third form of composition is also optimistic, but uses the DEA algorithm for
constant input. The score is given by the proximity to the DEA excellence frontier
in the component more favorable to the country.
Finally, the fourth score is given by Choquet integral, modeling the preference
among the criteria by a capacity with equal preference of 1/3 for each indicator,
assuming additivity for different dimensions but assuming for the two indicators in
the educational dimension, instead of additivity, full substitutability.
One can easily see in Table 6.2 the strong concordance between the evaluations
by the different approaches, with each other and with the HDI presently computed
by UNDP, whose ranks are in the last column of Table 6.2 . If we consider the
vectors of evaluations of all the 187 countries, the lowest Spearman correlation
coef cient with the UN HDI ranking, obtained by optimistic joint probability, is

0.94. The others vectors of ranks present correlations with UN HDI ranks of 0.95
for DEA, 0.96 for the pessimistic composition and 0.99 for the composition by the
Choquet Integral with respect to the capacity above referred. For 165 of the 187
countries, the difference between the ranks by the current model and by the Choquet
integral is lower than 10. It is also 0.99 the rank correlation coef cient between the

HDI as currently computed and the result of applying the geometric mean algorithm
employed in it to the probabilities of reaching the extremes of worst performance
substituting for the partial components.
This close agreement demonstrates the robustness of the approach, the

nal

result not in uenced by changes in the calculation. Nevertheless, it is possible to

notice some systematic differences between the classi cations. Considering the goal

of taking into account all the dimensions considered, it is interesting to highlight the
differences caused by the use of the pessimistic approach, which maximizes this
feature.
Table 6.2 detaches, as examples of countries whose pessimistic score is
improved by performing well with respect to all the criteria, Switzerland, Israel,
France and Sweden, among those in the best positions. On the other hand, Sin-
gapore, Kuwait, Papua New Guinea and Djibouti are countries with worse ranks if
the pessimistic composition approach is taken. The

first two have good performance
in terms of income, what is enough to place them in good position by some forms of
composition, not accompanied by good performance in educational indicators. The
other two, on the contrary, have poor performances with respect to income, con-
tradicting a better performance for the other indicators, especially longevity.
A strategy that encourages countries to seek escape from underdevelopment in
some special aspect may also be preferred, as advances in some dimension may