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144 Decision trees and influence diagrams
Decision trees can also help a decision maker to judge the nature of the
information which needs to be gathered in order to tackle a problem and,
because they are generally easy to understand, they can be an excellent
medium for communicating one person’s perception of a problem to
other individuals.
The process of constructing a decision tree is usually iterative, with
many changes being made to the original structure as the decision
maker’s understanding of the problem develops. Because the intention
is to help the decision maker to think about the problem, very large
and complex trees, which are designed to represent every possible scenario
which can occur, can be counterproductive in many circumstances.
Decision trees are models, and as such are simplifications of the real
problem. The simplification is the very strength of the modeling process
because it fosters the understanding and insight which would be
obscured by detail and complexity. Nevertheless, in rare circumstances
highly complex trees may be appropriate and software developments
mean that their structuring and analysis can now be facilitated with
relative ease. For example, Dunning et al. 1 used software to apply a
decision tree with over 200 million paths to a ten-year scheduling problem
faced by the New York Power Authority. Similarly, Beccue 2 used
a tree with around half-a-million scenarios to help a pharmaceutical
company to make decisions relating to the development and marketing
of a new drug.
Influence diagrams offer an alternative way of structuring a complex
decision problem and some analysts find that people relate to them much
more easily. Indeed Howard 3 has called them: ‘The greatest advance I
have seen in the communication, elicitation and detailed representation
of human knowledge ... the best tool I know of for crossing the bridge
from the original opaque situation in the person’s mind to a clear and
crisp decision basis.’ As we shall show later, influence diagrams can
be converted to decision trees and we will therefore regard them in
this chapter as a method for eliciting decision trees. However, some
computer programs now exist which use complex algorithms to enable
the influence diagram to be used not just as an initial elicitation tool but
as a means for identifying the best sequence of decisions.
Constructing a decision tree
You may recall from earlier chapters that two symbols are used in
decision trees. A square is used to represent a decision node and,