474 
PONTIFICIAE ACADEMIAE S3CIENTIARVM SCRIPTA VARIA - 28 
under conditions of uncertainty. (The v’s are the only un- 
certain factors which enter into the problem as it is posed 
here, which is of course highly restrictive, but it is easy enough 
to extend the list of such factors). We shall attack this 
problem by assuming that the uncertainty is of the proba- 
bilistic type and that the decision maker is interested in 
maximizing expected utility. That is, he is supposed to 
maximize the expectation of the preference function (3.4) 
subject to the constraint (3.4), the latter being interpreted 
stochastically (with random v’s). 
It is worthwhile to consider the implications of this pro- 
cedure in somewhat more detail. Take the first year, at the 
beginning of which the decision x, has to be made. The rates 
of increase of the population, Vi, Vo, ..., Vr, are then unknown 
and are supposed to be subject to a T-dimensional joint distri- 
bution. One year later the decision x, has to be made and 
the decision maker will then know more, particularly about v, 
but perhaps also about later v’s, because the development of 
the population during the first year may have shed some 
light on the probable development during later years. Clearly, 
the decision maker should be able to use this information 
gained during the first year when he formulates his decision x, 
at the beginning of the second year. In the same way, at the 
beginning of the third year he knows still more (particularly 
about v,) and he can use this additional information for his 
decision x;. And so on. 
It follows that it is the decision maker's task to formulate, 
for each year ¢=1, ..., T, the decision x,.as a function of the 
information that will be available at that time. Such a series 
of decisions x, ..., Xp written as functions of relevant in- 
formation is a strategy or decision rule. More specifically, 
the decision maker’s task is to find the maximizing strategy, 
i.e., the strategy which maximizes the expectation of the pre- 
ference function subject to the contraints. In general it is 
71 Theil - pag. To