Logical Decisions - Classweb

The first member to be improved is given an importance ordering
of one. Then you repeat the question with the caveat that the
decision maker must choose a member other than the first one.
You can continue in this way until the decision maker has ordered
all of the active members.
LDW computes weights from the ordering using an average of
the extremes of the possible weights. The following example with
two members illustrates the approach:
Suppose the "Performance" goal has two members --
"Power" and "Fuel Economy," and suppose that the
decision maker orders "Power" first and "Fuel Economy"
second.
If we put as much weight as possible on "Power," it will
have a weight of 1.0 and "Fuel Economy" will have a
weight of 0.0. If we put as much weight as possible on
"Fuel Economy," it will have a weight of 0.5. "Power" will
also have a weight of 0.5, since its weight must be greater
than or equal to Fuel Economy's if Power is more
important.
These two possibilities define the extremes of the possible
weights. If we average the weights assigned to the two
members under the two scenarios we get the following:
Scenario Power Weight Fuel Econ. Weight
1 1.0 0.0
2 0.5 0.5
Average 0.75 0.25
These weights -- 0.75 for "Power" and 0.25 for "Fuel
Economy" are the weights assigned by LDW using the
smarter method. Note that any case where two members
are involved will result in the same weights. The
extension to more members is easy. Each new member
adds another extreme case. If a third member was added
to the example a new extreme case of 1/3, 1/3, 1/3 would be
added to the average.
The weight for the member with the highest order number drops
sharply as more members are added. Therefore, LDW lets you
specify a minimum weight to assign to each member. LDW
9-38 Section 9 -- In Depth