Composition by Joint Probabilities - Probabilistic Composition of Preferences, Theory and Applications - page 43

Another possible way to address the case of dependence is by conditional rea-
soning. After somehow ordering the criteria, measures of preference for each
alternative can be calculated successively according to each criterion conditionally
on the preference according to the previously applied criteria. This calculation may
follow the same pattern of calculation of probabilities of being the best according to
the isolated criterion by randomizing ranks. The conditional probabilities of pref-
erence thus obtained can be combined with the previous vector of preferences to
derive a new joint probability of preference and so on until a joint preference by all
the criteria is obtained.

5.3 Examples

Table 5.1 presents the results of the composition of the preferences for car models
treated in the preceding chapters considering now the criteria divided into two

Table 5.1 Preferences assuming independence, priority to reliability and safety
Models Scores Standardized Scores Ranks Weighted average ranks

Car1 15 13

0.00003238 0.0032

Car2 16 9

0.00003055 0.0030

Car3 5 3

0.00086102 0.0859

Car4 7 7

0.00081111 0.0810

Car5 19 20

0.00002351 0.0023

Car6 20 19

0.00002218 0.0022

Car7 6 6

0.00083387 0.0832

Car8 18 18

0.00002417 0.0024

Car9 13 12

0.00054902 0.0548

Car10 3 4

0.00089604 0.0894

Car11 17 17

0.00002511 0.0025

Car12 4 8

0.00086922 0.0868

Car13 12 16

0.00058797 0.0587

Car14 10 15

0.00061253 0.0611

Car15 14 11

0.00003367 0.0034

Car16 2 2

0.00091023 0.0908

Car17 1 1

0.00093219 0.0930

Car18 11 10

0.00060376 0.0603

Car19 8 5

0.00069493 0.0694

Car20 9 14

0.00066615 0.0665