Computation of Probabilities of Preference - Probabilistic Composition of Preferences, Theory and Applications - page 36

taken as a standard for comparison that, for a completely homogeneous population,
the probabilities of preference will be equal to 0.1, this number becoming a pattern
for comparison of easy memorization.
To explain the possibility of loss in information due to the reduction of the size
of the sample, the example of 20 cars of Chap. 2 may be enlightening. With 20
alternatives there is no need to simplify the analysis, as the sample of 20 is perfectly
manageable. But it is interesting to verify that if the reduction to nine deciles is
applied no substantial difference occurs. On the other side, comparing only to the
quartiles, the result is considerably changed.
The samples of three and nine reference units for each criterion are, respectively,
the quartiles given in Table 4.1 and the deciles given in Table 4.2 . The probabilities of
maximization of the preference when the comparison is to the quartiles are presented
in Table 4.3 and the probabilities of preference with respect to the deciles in Table 4.4 .
The correlation between the vector of ranks resulting from the comparison to the
reduced sample, shown in Table 4.5 , and that resulting from the comparison to the
full sample in Chap. 3 reaches a value of 0.98 if the reduction is for the sample of

Table 4.4 Probabilities of maximization in a sample of 9
Beauty Comfort Consumption Power Price Reliability Safety

Car1

0.1383 0.1394 0.1866 0.0134 0.1843 0.1105 0.0079

Car2

0.1383 0.1394 0.1866 0.0134 0.1843 0.0064 0.1226

Car3

0.1383 0.1394 0.1866 0.0134 0.0174 0.1105 0.1226

Car4

0.1383 0.1394 0.0181 0.1599 0.0174 0.1105 0.1226

Car5

0.1383 0.1394 0.0181 0.1599 0.0174 0.1105 0.0079

Car6

0.1383 0.1394 0.0181 0.1599 0.0174 0.0064 0.1226

Car7

0.1383 0.1394 0.0181 0.0134 0.1843 0.1105 0.1226

Car8

0.1383 0.1394 0.0181 0.0134 0.1843 0.1105 0.0079

Car9

0.1383 0.1394 0.0181 0.0134 0.0174 0.1105 0.1226

Car10

0.1383 0.0102 0.1866 0.1599 0.0174 0.1105 0.1226

Car11

0.1383 0.0102 0.1866 0.0134 0.1843 0.0064 0.1226

Car12

0.1383 0.0102 0.0181 0.1599 0.1843 0.1105 0.1226

Car13

0.1383 0.0102 0.0181 0.1599 0.0174 0.1105 0.1226

Car14

0.1383 0.0102 0.0181 0.0134 0.1843 0.1105 0.1226

Car15

0.01 0.1394 0.1866 0.1599 0.1843 0.1105 0.0079

Car16

0.01 0.1394 0.1866 0.1599 0.0174 0.1105 0.1226

Car17

0.01 0.1394 0.1866 0.0134 0.1843 0.1105 0.1226

Car18

0.01 0.1394 0.0181 0.1599 0.0174 0.1105 0.1226

Car19

0.01 0.0102 0.1866 0.1599 0.0174 0.1105 0.1226

Car20

0.01 0.0102 0.0181 0.1599 0.1843 0.1105 0.1226