Capacities Determination - Probabilistic Composition of Preferences, Theory and Applications - page 96

P s ð 1 Þ P s ð 2 Þ P s ð 3 Þ P s ð 4 Þ :

The fist summand will be P a τ (1) .

The second, the product of

P s ð 2 Þ P s ð 1 Þ

by

. 1 P a s ð 3 Þ 1 P a s ð 4 Þ

max
a

1 1 P a s ð 2 Þ max

a

ð 1 ð 1 P a1 Þ ð 1 P a2 Þ ð 1 P a3 Þ ð 1 P a4 Þ Þ:

The third, the product of

P s ð 3 Þ P s ð 2 Þ

by

.

1

max
a

1 1 P a s ðÞ P a s ðÞ max

a

ð 1 ð 1 P a1 Þ ð 1 P a2 Þ ð 1 P a3 Þ ð 1 P a4 Þ Þ:

Finally, the fourth will be the product of

P s ð 4 Þ P s ð 3 Þ

by

.

max
a

P a s ð 4 Þ max

a

ð 1 ð 1 P a1 Þ ð 1 P a2 Þ ð 1 P a3 Þ ð 1 P a4 Þ Þ:

9.3 Example of Capacity Estimation

Here will be studied again the problem of determining capacities for the con-
struction of an aggregate index of sustainable management of resources or of
sustainable development of regions or countries.
An index of sustainable development must compose evaluations of environ-
mental, social and economic risks (Stiglitz et al. 2009 ). As seen in the preceding
chapters, to cover all the necessary dimensions, the indicators composed may
intercept and some of them may be substitutable by others in the set considered.
The criteria will be the same considered in the preceding chapters. The alter-
natives will be the 187 countries and the initial probabilities of maximizing pref-
erence for each alternative according to isolated criteria will be those there
considered.