Geoscience Reference
In-Depth Information
Table 14.2
Matrix
C
Agents/Options
O
1
O
2
O
3
A
1
1
0
0
A
2
0
1
0
A
3
0
0
1
Fig. 14.4
Topographical
representation
A
B
D
C
Figure
14.4
hereafter gives an example of representation of this situation for
¼
k
,4, the radius of the circle being equal to 1.
If the circle is centered on (0,0), the four end points
A, B, C, D
will have
coordinates (0,1), (1,0), (0,
1,
...
1,0).
The idea is to follow and measure the process of conflict resolution, in particular
as a function of the
1), (
˄
k
*; two more figures follow to picture this (Figs.
14.5
and
14.6
)
.
A first indicator of the “displacement' of the conflict would be the coordinates of
the new centres of gravity,
g
l
, where
l
is the index of the conflict situation (here
l
¼
1, 2, 3
); in the example they moved from (0,0) to (
0.1875,
0.0625) and then
to (
0.0625, 0); one notices in situation 2 the role of the weights of
C
and
D
, and in
situation 3 that of the weight of
. If conflict resolution were to be completed, the
coordinates would again be (0,0), but this could also be the case in intermediate
situations, so
g
l
is not a sufficient statistic.
So an additional indicator, borrowed from Paelinck (
2001
), computes the qua-
dratic envelopment of the relevant points and measure its area,
s
l
; for the initial
situation, this area is obviously equal to
D
ˀ
. The mathematics of the envelopment
process are exposed in Appendix.
14.3.3 Computational Results
Table
14.3
hereafter presents the results of the envelopments computations for the
three situations presented above; the method used is the following.
