1026 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA 
a 
age) of this pattern relative to the pattern of 100 percent spatial 
centralization. Where curve DD lies below the horizontal axis, 
there is a net disadvantage for the corresponding pattern. 
Where DD lies above the horizontal, there is a net advantage. 
Obviously, where the entire set of hypotheses underlying he 
curves of Figure 10 is accepted, the optimal degree of spatial 
centralization would correspond to that point at which curve DD 
reaches a maximum. 
The curves of Figure 10, and the discussion thus far, relate 
to decision making on a representative concrete issue (or set 
of concrete issues) when it is hypothesized that only one, well- 
defined state of the environment can occur. It is now appro- 
priate to relax this restriction and permit the occurrence of 
several states of the environment. 
Elsewhere, ISARD and Tune have extended the simple 
example cited above so that the occurrence of each of three 
states of the environment is possible (**). These states have 
reference to the international situation and were designated: 
I) good will, 2) usual, and 3) extremely tense, as indicated at 
the head of the columns of table 3. In this example, only 
overview advantage was permitted to vary with the state of 
environment for the specific set of assumptions which was 
adopted. The resulting figures for the case examined are re- 
corded in table 3. In net form, these figures constitute the 
elements of the payoff matrix of table 4. It is immediately seen 
that there is no one pattern of spatial decentralization which 
can be designated optimal. In the light of modern decision- 
making theory it becomes necessary to introduce still another 
assumption which pertains to the attitude of the decision- 
making individual or group (%). 
(2) Isarp and Tung, op. cit., Part. IT. 
(5) SEE W. IsSARD and M. Dacky, On the Projection of Individual Be 
havior in Regional Analysis, Parts I and II, « Journal of Regional Science » 
Vol. a. Nos. T and » respectively and articles cited therein 
121 Isard - pag. 24