Downloadable - About University

Exercises 293
Odds in favor
of events
Probability of
event
Evens 1:4 1:10 1:100 1:1000 1:10000
0.5
Figure 10.6 – A log-odds scale
0.2 0.1
0.01
0.001 0.0001
for probabilities below 0.5). An analyst using the scale would ask the
decision maker to mark the point that represents his or her assessment
of the likelihood of the event occurring. Note that the effect of using logodds
is to spread out the ends of the probability scale, making assessment
of very high and low probabilities clearer. The scale also ranges from
minus to plus infinity, which makes it very difficult for individuals to
assert that particular events are impossible or certain to occur. According
to Bunn and Thomas, 7 the log-odds scale appears to correspond to the
internal scale which individuals use when assessing odds.
Summary
In this chapter we have described the process by which a decision
analyst elicits subjective probability assessments from the decision
maker. Within the analyst’s toolbox of techniques are indirect and direct
methods for both discrete and continuous assessments. Consistency and
coherence checks are used extensively to police the assessment process,
since validity is a more problematic criterion. The chapter concluded
with a description of assessment methodologies that are used for very
rare events.
Exercises
(1) Use the probability wheel and direct estimate methods to elicit a colleague’s
subjective probabilities for the outcomes of a forthcoming
sports event (e.g. a snooker tournament). Check for consistency
between the assessment methods and use the addition rule to
evaluate the coherence of the probabilities that your colleague
has assessed.