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282 Methods for eliciting probabilities
it should be, and the result will be a distribution which is too ‘tight’.
Because of this, the following procedure, 4 which we will refer to as the
probability method, is recommended:
Step 1: Establish the range of values within which the decision maker
thinks that the uncertain quantity will lie.
Step 2: Ask the decision maker to imagine scenarios that could lead to
the true value lying outside the range.
Step 3: Revise the range in the light of the responses in Step 2.
Step 4: Divide the range into six or seven roughly equal intervals.
Step 5: Ask the decision maker for the cumulative probability at each
interval. This can either be a cumulative ‘less than’ distribution
(e.g. what is the probability that the uncertain quantity will fall
below each of these values?) or a cumulative ‘greater than’ (e.g.
what is the probability that the uncertain quantity will exceed
each of these values?), depending on which approach is easiest
for the decision maker.
Step 6: Fit a curve, by hand, through the assessed points.
Step 7: Carry out checks as follows.
(i) Split the possible range into three equally likely intervals
and find out if the decision maker would be equally happy
to place a bet on the uncertain quantity falling in each
interval. If he is not, then make appropriate revisions to the
distribution.
(ii) Check the modality of the elicited distribution (a mode is
a value where the probability distribution has a peak). For
example, if the elicited probability distribution has a single
mode (this can usually be recognized by examining the
cumulative curve and seeing if it has a single inflection), ask
the decision maker if he does have a single best guess as to
the value the uncertain quantity will assume. Again revise
the distribution, if necessary.
Graph drawing
Graphs can be used in a number of ways to elicit probability distributions.
In one approach the analyst produces a set of graphs, each representing
a different probability density function (pdf), and then asks the decision
maker to select the graph which most closely represents his or her
judgment. In other approaches the decision maker might be asked to
draw a graph to represent either a probability density function or a
cumulative distribution function (cdf).