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290 Methods for eliciting probabilities
Assessing probabilities for very rare events
Assessment techniques that differ from those we have so far discussed
are generally required when probabilities for very rare events have to
be assessed. Such events are often of interest because of the disastrous
consequences which may be associated with their occurrence. The catastrophic
failure of a nuclear power plant, the collapse of a dam or the
release of toxic fumes from a chemical factory are obvious examples of
this event.
Because of the rarity of such events, there is usually little or no
reliable past data which can support a relative frequency approach to
the probability assessment, and subjective estimates may be subject
to biases which result from the use of the availability heuristic. For
example, it may be easy to imagine circumstances which would lead
to the event occurring even though these circumstances are extremely
improbable. Moreover, as von Winterfeldt and Edwards 18 point out, rare
events are newsworthy almost by definition, and widespread reports
of their occurrence may have the effect of intensifying the availability
bias. Decision makers are also likely to have problems in conceiving
the magnitudes involved in the probability assessment. It is difficult to
distinguish between probabilities such as 0.0001 and 0.000001, yet the
first probability is a hundred times greater than the second.
Obviously, a probability wheel would be of little use in assessing
probabilities like these. There are, however, a number of ways in which
the problems of assessing very low probabilities can be tackled. Event
trees and fault trees allow the problem to be decomposed so that the
combinations of factors which may cause the rare event to occur can be
identified. Each of the individual factors may have a relatively high (and
therefore more easily assessed) probability of occurrence. A log-odds
scale allows the individual to discriminate more clearly between very
low probabilities. We will examine each of these approaches below.
Event trees
Event trees are the same as the probability trees which we met in
Chapter 4. Figure 10.4 shows a simplified tree for a catastrophic failure
at an industrial plant. Each stage of the tree represents a factor which
might, in combination with others, lead to the catastrophe. Rather than
being asked to perform the difficult task of directly estimating the
probability of catastrophic failure, the decision maker is asked instead