Uncertainty in Weights for Composite Indicators Generated by Weighted Sums
51
Fig. 2 The Hasse diagram
resulting from Table 1. The
total number of
incomparabilities,U0 = 3
8
92
95
48
24
6
42
33
22
9
45
2
1
8 6
Table 1 Fictitious data
matrix
SEQ q(1)
q(2)
q(3)
1
4,356,708,827 4,110,873,864 3,891,820,298
2
0,693,147,181 0
0
6
4,189,654,742 3,850,147,602 363,758,616
8
5,017,279,837 4,976,733,742 4,905,274,778
9
2,890,371,758 2,772,588,722 1,386,294,361
22
3,044,522,438 2,833,213,344 2,564,949,357
24
4,204,692,619 3,850,147,602 3,663,561,646
33
3,218,875,825 3,044,522,438 2,833,213,344
42
336,729,583
336,729,583
3,218,875,825
45
0
0
0
48
5,003,946,306 5,164,785,974 5,030,437,921
86
4,234,106,505 4,248,495,242 3,828,641,396
92
49,698,133
5,081,404,365 4,955,827,058
95
4,418,840,608 4,465,908,119 4,043,051,268
The Hasse diagram is shown in Fig. 2:
Checking Fig. 1 the deviations from Eq. 9 seem to be not too large Thus, Eq. 9 can
still be used as a general guide for the evolution of posets due to increasing values
of s (given a certain weight tuple g). Nevertheless, it is of interest, to understand the
deviation, which we are considering as a “fine-structure” of the evolution. It is clear
that the low number of incomparabilities (U0 = 3) implies at maximum 3 jumps in