Capacities Determination - Probabilistic Composition of Preferences, Theory and Applications - page 97

The capacity derived from the probabilities of presenting the best scores on the
components of HDI assuming triangular distributions is given in Table 9.1 , for L
denoting longevity, MS denoting mean schooling, ES denoting expected schooling
and I denoting income.
If the decision maker desires to pay more attention to the small values of the
attributes, the probabilities of minimizing may be used instead of the probabilities
of maximizing. The capacity derived from the probabilities of minimizing, shown
in Table 9.2 , gives a much lower importance to income.
Table 9.3 presents the scores for the same 30 countries analyzed in preceding
chapters, obtained combining the probabilities of maximizing and minimizing
preference by the Choquet integral with respect to the respective capacities.
As the clearest extremes for the probability of maximizing are given by the
income component, the countries with best performance on this feature will reach
the best global score by the

first approach. Thus, employing to combine the
probabilities of maximization the capacity in Table 9.1 , the 17 first countries of the

list of 30 are those occupying the 17 first positions among the 187. Specially

noticeable are the positions of Qatar and Lichtenstein as the first and the third. The

evaluation based on the probabilities of minimization is much closer to those
obtained in the previous chapter and to the ranking by HDI.

Table 9.1 Capacity for IDH components derived from the probabilities of maximizing
Criterion Importance Criteria Importance Criteria Importance

L 0.3084 L or MS L or MS or ES 0.8204

0.5141

MS 0.3887 L or ES L or MS or I 0.9334

0.6098

ES 0.4304 L or I L or ES or I 0.9395

0.8727

I 0.7533 MS or ES MS or ES or I 0.8816

0.6555

MS or I

0.8145

ES or I

0.8206

Table 9.2 Capacity for IDH components derived from the probabilities of minimizing
Criterion Importance Criteria Importance Criteria Importance

L 0.4459 L or MS L or MS or ES 0.8624

0.674

MS 0.4251 L or ES L or MS or I 0.8103

0.6013

ES 0.4603 L or I L or ES or I 0.7393

0.5857

I 0.1534 MS or ES MS or ES or I 0.8504

0.7205

MS or I

0.5636

ES or I

0.5860