situation is met in military and possibly in business situationsit is
the object of the theory of games. In science and technology, the
opponent usually is "nature". Although this opponent may make
formidable difficulties, she (or he?) is essentially indifferent to
human success and failure and will not take deliberate counter
actions to prevent attainment of human goals. When nature is the
opponent, two cases can be distinguished.
a. All factors and aspects relevant to the decision problem are
known.
b. There is uncertainty about one or more aspects of the situation.
In case a. it may seem that there is no special decision problem.
By deterministic reasoning we can evaluate the consequences of
any decision and take the most favourable one. However, there
may be so many possible decisions that special techniques are
needed to find the optimum decision. The differential calculus is
a typical example of a mathematical technique for finding optimum
solutions in certain cases of such character. Linear programming
is another example of a tool for finding an optimum solution in
decision problems of great complexity (but without uncertainty).
An application of linear programming to a problem facing geodetic
organizations is given by K. V. Bazhanov in [i].
It may be noted that in real-life situations there cannot be abso
lute certainty about the "state of nature". By "certainty" is
meant that the mathematical model of the situation contains no
unknown parameters or random effects and is known from experi
ence to describe the situation sufficiently well for the purpose.
The cases classified under b. are considered in statistical decision
theory; in the formulation of A. Wald, statistics is the science of
decision making under uncertainty. In statistical decision theory,
two types of uncertainty are distinguished. The first is uncertainty
due to randomness, the second is uncertainty about the state of
nature, i.e. about the law of randomness which applies. When we
toss a coin that is known to be unbiased, we cannot predict whether
it will fall heads or tails, because the outcome is a random variable.
We do know, however, that the probability of heads is 0.5the state
of nature is known. If, on the other hand, we have a bent coin,
we do not know what the probability of heads is: the long-run
relative frequency of heads may be 0.45, or 0.70. In many cases we
can perform an experiment to obtain information about the state
of nature. Before engaging on a bet with the bent coin, we may
toss it e.g. 10 times and, depending on the outcome accept the bet
or not. Further elements in this decision problem are of course the
odds offered and our need of the money we can possibly win.
2. Utility
If in a decision making problem we choose a certain action, we
will be confronted with the consequences. A decision will be good
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