Geoscience Reference
In-Depth Information
consistent future scenarios. We now define variable clusters for these scenarios as
energy, pollution, and employment, necessary to distinguish between variables over
which priorities can be assigned. If we assemble a different composite scenario in
which the relative weights for combining the future scenarios are different for each
cluster of variables, then it is easy to show that the resulting composite scenario is
not necessarily consistent, and in general unlikely. To denote both different future
scenarios to be combined and different weights to be applied to clusters of
variables, instead of
β
3
we then define these weights for each cluster of
variables as
β
i
e
,
β
i
p
and
β
i
l
for scenarios
i
β
1
,
β
2
and
¼1, 2 and 3, where
e
,
p
and
l
denote, as
before, the energy, pollution and employment clusters of variables, respectively.
To account for the variable clusters, we can express each future scenario
i
as
e
i
p
éù
ê
êú
=
êú
ê
ê
ëû
x
x
éù
ê
êú
=
êú
ê
ê
ëû
x
x
e
i
p
i
i
x
or equivalently as
x
%
. Hence, we can define a composite scenario,
i
x
x
l
i
x
f
l
i
i
i
i
3
é
ù
å
b
ee
x
ê
ú
i
i
ê
i
=
1
ú
ê
ú
3
å
b
pp
x
ê
ú
i
i
ê
i
=
1
3
ú
reflecting the different weights for each cluster of variables, as:
x
=
ê
.
c
ú
å
b
ll
x
ê
ú
i
i
ê
i
=
1
3
ú
ê
ú
å
x
ê
ú
i
ê
ú
ë
û
i
=
1
This new composite scenario is not generally consistent, as defined earlier. The
problem of developing a
consistent composite scenario
can be addressed via GP, by
formulating the problem to find a consistent scenario that is “as close as possible” to
the composite scenario but that complies fully with the defined system process
functions. The literature is replete with attempts to extend the input-output frame-
work applied to environmental problems using various kinds of multiobjective
decision-making tools in addition to the simple approach illustrated here.
21
13.9
Strengths and Weaknesses of the Illustrative Model
Assumptions for Policy Applications
Note the contrast, conceptually, between the impact analysis and the planning
formulations just illustrated. The analytical assumptions in the impact analysis
formulation are already substantial from a policy making point of view, including
all the assumptions of the Leontief model, the assumptions of linear relationships
21
Also illustrated in Miller and Blair (
2009
) and Blair (
1979
). A similar example is given in
Hipel (
1992
).
