Agriculture Reference
In-Depth Information
was pulse stable under all simple pulse processes (Roberts and Brown, 1975). A
digraph was value stable under all simple pulse processes if it was pulse stable and
1 was not an eigenvalue of
D
(Roberts and Brown, 1975). A digraph was semistable
under all pulse processes if and only if each eigenvalue had a nonpositive real part
(Klee, 1989).
4.2.4 A
p p l i C At i of in
of f
s
y s t e m
t
h e o r y
t
of of l s
i in
v
i l l A g e s
Sources in a digraph were seen as representing those factors requiring external inter-
vention. Perceived impacts and expected outputs of community goals were assessed
in two ways. The first was through geometric analysis of the cognitive maps, which
involved examination of the total impacts of vertices corresponding to each of the
goals. The total number of positive impacts was used to rank community goals, and
this was compared to the ranking done by communities during the participatory
workshops. Presence of indeterminate effects was considered a result of path imbal-
ance. Path imbalances were seen as those relationships in which the outcome could
be either negative or positive depending on the weight and time lags placed on the
arcs of the various paths linking the vertices. These were considered important as
they represented aspects for which trade-offs and balances were critical to the over-
all outcome of community goals. Presence of ambivalent impacts was seen as an
indication of the system's increased amplitude instability.
The second method of assessing the impact of community goals was simple
autonomous pulse processes initiated at each of the vertices corresponding to a
community goal. The impact was assessed based on (
n
− 1) iterations, equivalent
to the longest path in the digraph. The usefulness of this approach was in assessing
the importance of path imbalance in the outcome of community goals. Digraphs in
which community goals had only positive impacts were said to be in regenerative
spirals. Those in which there was a preponderance of negative impacts were said to
be in degenerative spirals.
Two kinds of value-stabilizing strategies were assessed. First was where the
signs of arcs in the digraph were changed either individually or as a group. Stabiliz-
ing strategies involving the fewest changes were considered the simplest. The other
type of stabilizing strategies was where the weights associated with the arcs were
altered—with the simplest strategies—those that involved the fewest changes. The
importance of assessing value stability was to evaluate the key relationships on which
the impacts of community goals were predicated. Existence of many simple stabiliz-
ing strategies was considered an indication of increased system inertia. Absence of
stabilizing strategies was considered an indication not only of cognitive imbalance
but also as possible trajectory stability.
4.3 Results
Three groups of concepts were common to cognitive maps of the six communi-
ties. These were problems, outputs, and institutions. For ease of analysis, the com-
mon categories were retained, while the rest of the concepts were placed into one
general category: system-state (Figure 4.2). The number of concepts depicted in the
Search WWH ::
Custom Search