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tree analysis and the former the “indirect value”. Some studies have illustrated that
the decision-makers’ estimates, judgements and choices are affected by the way
knowledge is elicited. This literature was reviewed in Chapter 2. Despite this, the
value of decision tree analysis is undisputed, not least because decision tree analysis is
not exclusively linked to the EMV with its inherent and questionable assumptions
about the decision-maker’s attitude to money. These are now reviewed.
The expected value decision rule makes several assumptions. Firstly, it assumes that
the decision-maker is impartial to money. This assumption, not surprisingly, has been
widely criticised. Such criticisms are well illustrated by the St Petersburg Paradox
first described by Daniel Bernoulli in 1738 and outlined here.
A decision-maker is offered the following gamble. A fair coin is to be tossed until a
head appears for the first time. If the head appears on the first throw then the
decision-maker will be paid £2, if it appears on the second throw, £4, if it appears on
the third throw £8, and so on. The question is then, how much should the decisionmaker be prepared to pay to have the chance of participating in this gamble?
The expected returns on this gamble are:
which is equivalent to 1+1+1+ … to infinity. So the expected returns will be infinitely large. On this basis, according to the EMV criterion, the decision-maker
should be prepared to pay a limitless sum of money to take part in the gamble.
However, given that there is a 50% chance that their return will only be £2, and an
87.5% chance that it will be £8 or less, it is unlikely that many decision-makers would
be prepared to pay the amount prescribed by the EMV criterion.
85 Secondly, the EMV criterion assumes that the decision-maker has a linear value
function for money. An increase in returns from £0 to £1 million may be regarded by
the decision-maker as much more preferable than an increase from £9 million to £10
million, yet the EMV criterion assumes that both increases are equally desirable.
Thirdly, the EMV criterion assumes that the decision-maker is only interested in
monetary gain (Goodwin and Wright, 1991 p64). However, when a company is
deciding how best to decommission an offshore production facility, for example, they
will want to consider other factors such as corporate image and environmental
concerns. All these attributes, like the monetary returns, would have some degree of
risk and uncertainty associated with them.
Users of expected value theory have long recognised these shortcomings. As early as
1720 academics were beginning to modify the concept to include the biases and
preferences that decision-makers associate with money into a quantitative decision
parameter. In essence these attempts were trying to capture the decision-maker’s
intangible feelings in a quantitative decision parameter which the decision-maker
could then use to guide judgements. This approach is typically referred to as preference theory and the following section discusses this further. It draws on...
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