Downloadable - About University

Summary 57
we hope to obtain. Analysts sometimes find that these insights only
emerge when the decision maker is forced to grapple with more demanding
judgmental tasks which require deeper thinking about the issues.
Finally, the ROC weights themselves raise a number of concerns. The
method through which they are derived involves some sophisticated
mathematics, which means that they will lack transparency to most
decision makers. To be told that your implied weight for an attribute is
15.8, without understanding why this is the case, is likely to reduce your
sense of ownership of the model that is purporting to represent your
decision problem and it may therefore also reduce the model’s credibility.
Furthermore, Belton and Stewart 17 point out that the ratio of the ROC
weights between the most and least important attributes is generally very
high. For example, in a seven-attribute problem this ratio is 37/2 = 18.5.
This makes the relative importance of the lowest ranked attribute so low
that, in practice, it would probably be discarded from the analysis.
Both of these problems can be mitigated to some extent by using
an alternative weight approximation method. Several methods exist,
but Roberts and Goodwin 18 recently recommended the much simpler
rank-sum method for problems that involve more than 2 or 3 attributes.
Rank-sum weights are easily calculated and hence are more transparent.
Suppose that 3 attributes have been ranked. The sum of their ranks will
be 1 + 2 + 3 = 6. The least important attribute is therefore assigned a
rank of 1/6, the second-ranked attribute 2/6 and the highest-ranked
attribute 3/6 (i.e. the weights are 0.167, 0.333 and 0.5). For 4 attributes
the weights will be 0.1, 0.2, 0.3 and 0.4, and so on.
Summary
In this chapter we have looked at a method for analyzing decision
problems where each alternative had several attributes associated with it.
This meant that the performance of each alternative had to be measured
on each attribute and then the attributes themselves had to be ‘weighed
against’ each other before a decision could be made. The central idea
was that, by splitting the problem into small parts and focusing on
each part separately, the decision maker was likely to acquire a better
understanding of his or her problem than would have been achieved by
taking a holistic view. We saw that the method required the decision
maker to quantify his or her strengths of preferences. While this may not
have been an easy process, we found that the figures put forward did not
need to be exact, though we did try to ensure that they were consistent.