58
R. Bruggemann and L. Carlsen
Fig. 8 The Hasse diagram of
21 nations, with the indicator
set {fa, ed.}. The
incomparabilities due to the
m-2-system reproduce 40%
of the original ones
NE
SU
IRE
CA
PL
PT
HU
BE
IT
SW
DK
FI
ES
CZ
DE
NO
GR
FR
UK
AU
US
Fig. 9 gc-distribution of the poset of 21 nations and the indicators ed. and fa. The units at the
ordinate are arbitrary. The abscissa: gc-values
3.2.2 Adaptation to an m = 2-System
Once again the number of incomparabilities is used as a leading quantity. The
idea behind this is that any reduction in the number of indicators will reduce the
incomparabilities. However, the incomparabilities themselves are the reason, why
weights are introduced, because otherwise a complete order is already obtained
within the reduced set of indicators. Thus, the procedure is to select those two
indicators, which preserve the highest number of the incomparabilities of the
original indicator set. It turns out by use of the program weight2evolution_vs6_2
of PyHasse that with ed. and fa the number of incomparabilities, Fig. 8.
In Fig. 9 the distribution of the gc-values for the m = 2-system is shown. The
distribution is evidently similar to the second type, shown in Sect. 3.1 (item b).
Hence U based on Eq. 12 should follow a sigmoid function.