Logical Decisions - Classweb

Now think of adjusting P so that the decision maker prefers the
two alternatives equally. Then you can compute the scaling
constant for the member being assessed as follows.
The utility for the "one member for sure" alternative is 1.0 for the
member being assessed and 0.0 for the other active members from
the way we defined the alternative. Thus, its utility as computed
by the MUF is the weight for the member being assessed times
one plus the weights for the other active members times zero.
Thus, the "one member for sure" alternative's utility for the active
goal is equal to the weight for the member being assessed. Let's
call this w.
We can also compute the utility for the "all or nothing" alternative.
We know that the utility in a MUF is 1.0 if all active members are
at their most preferred level. We also know that, if all active
members are at their least preferred levels, the utility is 0.0.
Decision theory also tells us that the utility of an alternative with
uncertainties is the expected utility for the alternative. The
expected utility for the "all or nothing" alternative is P times 1.0
and (1 - P) times 0.0. This is equal to P itself.
Since the decision maker said she prefers the two simplified
alternatives equally they must have equal utilities. Thus w must
equal P.
Thus, you can assess weights for direct entry by assessing the w
for each active member by defining a "one member for sure"
alternative where only it has its most preferred level and
assessing the P for which the decision maker prefers it equally to
the "all or nothing" alternative. W for each member is equal to the
P that makes the two alternatives equal.
Note that if you use this method, the ws won't generally sum to
one. As described on page 9-55, ws that don't sum to one define a
multiplicative MUF that includes interactions between the active
members. This probabilistic method for assessing weights can
also be used to simultaneously assess interactions.
It is not clear how to compute weights using representatives when
there are also interactions. Thus, LDW does not let you use
representatives for sub-goals in the direct entry method.
Section 9 -- In Depth 9-49