5
2 5
io
20
125
for other values he will decide the opposite: he chooses a strategy,
a decision rule which will tell him what action to take. The object
of decision theory is to find good strategies, i.e. strategies which
have some optimum property regarding the expected losses of
utility.
It will be clear that the surveyor's situation has already been
simplified very much in the above description. We have restricted
the possibility of a gross error to one of 10 cm in one of the measure
ments, whereas in reality he might have made a gross error of any
size in both measurements. Furthermore he has more available
actions than just remeasure or not remeasure: for example he may
go home and ask his wife what to do. In other respects too, we have
idealized the situation, in other words, we have adopted a model
to describe the situation. As remarked before, the simplification is
very drastic for expository reasons, but any more detailed descrip
tion would still be only a model, leaving less important aspects out
of consideration. We will now specify the model more systematically.
(The computation of the losses of utility is of course based on fancy
the losses have been expressed in some monetary unit denoted by
which should not give rise to the impression that utility is the
same as amount of money). The model is as follows:
a. The possible states of nature 0.
0ithere is a gross error of io cm in one of the measure
ments.
02there is no gross error.
b. The available actions a.
ai\ remeasure.
«2: not remeasure.
c. The losses of utility l(%,a).
c.i 0i, «i (there is a gross error, the distance is
remeasured)
a.
a. Half an hour's work
b. Another small job in the same area which might
have been done on the same day has to be post
poned to to-morrow. The surveyor will have to
return for it. Travelling time etc.
b.
fio
20
l(Qi,ai)
c.2 02, «i (no gross error, the distance is remeasured)
a. The same costs as under c.i
b. Annoyance because the remeasurement was
actually unnecessary
^(02,«l)
