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100 Decision making under uncertainty
Table 5.3 – Returns and probabilities for the new component problem
Outcome
Total failure Partial success Total success
Returns Returns Returns
Course of action ($m) Probability ($m) Probability ($m) Probability
Choose design 1 −1 0.1 0 0.1 03 0.8
Choose design 2 −6 0.3 1 0.1 10 0.6
would have been of relevance to him. Let us now consider a different
decision problem.
Imagine that you own a high-technology company which has been
given the task of developing a new component for a large engineering
corporation. Two alternative, but untried, designs are being considered
(for simplicity, we will refer to these as designs 1 and 2), and
because of time and resource constraints only one design can be developed.
Table 5.3 shows the estimated net returns which will accrue to your
company if each design is developed. Note that these returns depend on
how successful the design is. The estimated probabilities of failure, partial
success and total success for each design are also shown in the table.
The expected returns for design 1 are:
0.1 × (−$1 m) + 0.1 × $0 + 0.8 × ($3 m) = $2.3 m
while for design 2 the expected returns are:
0.3 × (−$6 m) + 0.1 × ($1 m) + 0.6 × ($10 m) = $4.3 m
Thus according to the EMV criterion you should develop design 2,
but would this really be your preferred course of action? There is a
30% chance that design 2 will fail and lead to a loss of $6 million. If
your company is a small one or facing financial problems then these
sort of losses might put you out of business. Design 1 has a smaller
chance of failure, and if failure does occur then the losses are also
smaller. Remember that this is a one-off decision, and there is therefore
no chance of recouping losses on subsequent repetitions of the decision.
Clearly, the risks of design 2 would deter many people. The EMV
criterion therefore fails to take into account the attitude to risk of the
decision maker.
This can also be seen in the famous St Petersburg paradox described
by Bernoulli. Imagine that you are offered the following gamble. A fair