Composition by Joint Probabilities - Probabilistic Composition of Preferences, Theory and Applications - page 48

product of the differences to 1 of the four entries corresponding to T1, T2, P1 and
P2 in that same row.
If the goal of the evaluation is to determine the values of bonuses to be paid to
motivate drivers to increase output, a progressive point of view may be the most
appealing. Besides, a pessimistic point of view may be more appropriate to make
the drivers pay attention to both output and process attributes. This approach may
nevertheless be sometimes replaced by an optimistic approach that would make
easier to the drivers improve performance by focusing attention on a simple goal.
In the present study these distinctions may become irrelevant as high correlations
can be noticed between all the vectors of

final scores.
An even stronger concordance can yet be found between the scores in Tables 5.6
and 5.7 for the same composition point of view. This demonstrates the resistance of
the composition assumptions to the effects of dependence. In fact, changing the
assumption from maximal dependence to independence would result in signi

cant

change only in the ranks of D 13 for the optimistic approaches.
This last change is due to the greater importance given to the outputs if inde-
pendence is assumed. To avoid giving higher weight to a group with a larger
number of independent criteria, the probabilistic composition may be applied

rst
within the groups, replacing the products of the probabilities of preference by
criteria in the same group by geometric means.
In the present example, slightly different results are obtained if this procedure is
adopted. For the scores for the group of two process criteria, assumed as inde-
pendent, computed using square roots of the products while the scores for the group
of output criteria, assumed dependent, composed using the minimum, the nal

scores in Table 5.8 are obtained. Comparing the ranks derived from Table 5.8 to
those from the previous tables, again the few changes observed are small.

Table 5.8 Scores for equal group weights and dependence
PP OP PC OC

D 11 0.0023 0.2770 0.7509 0.9948

D 21 0.0003 0.0941 0.4828 0.9912

D 31 0.0019 0.1676 0.6288 0.9844

D 12 0.0209 0.3075 0.9165 0.9983

D 22 0.0162 0.2817 0.9127 0.9982

D 32 0.0132 0.2690 0.9075 0.9981

D 13 0.0034 0.3657 0.8895 0.9985

D 23 0.0025 0.1171 0.7720 0.9969

D 33 0.0009 0.0870 0.5970 0.9921

D 43 0.0065 0.2055 0.8856 0.9973