SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIQUE ETc. 1011 
table 2 are reproduced the figures of the last column of table 1. 
In column 2 are recorded the figures for the case as character- 
ized at the top of column 2 (which case is the same as that of 
column 1 except that dy; is taken to be equal to 2 instead ot 
unity). In columns 3 to 7 are recorded the figures for several 
other cases, each case being characterized at the top of the 
respective column. 
The computations for many other cases might be made, for 
example cases involving different values for ¢, 3, b, G;;, and 
different assumptions on the number of individuals at each 
node (all the cases of table 2 assume only one individual at 
each node). These the reader may do for himself (°). 
We now wish to proceed to the next step, namely, the trans- 
formation of values for participation potential into values for 
average productivity, i.e. the mapping of a participation po- 
tential space onto an average productivity space. 
Since we are unaware of any comprehensive empirical work 
on this problem, we can only pose the question of the validity 
of certain hypotheses which seem reasonable in the light of 
social science knowledge. Can we state a certain functional 
relationship between average productivity (dependent variable) 
and P (independent variable) which can be represented by a 
curve such as one of the curves on Figure 2 (6)? Starting with 
the extreme at which P is at a minimum (which tends to cor- 
respond to the pattern of 100%, spatial centralization), can 
(®) He may also perform calculations for irregular tree structures as well 
as for regular tree structures where the number of nodes at any given order 
(except the first) is other than a k multiple of the number of nodes at the 
next lower order. 
() As previously noted, we do not treat explicitly the effect of P upon 
the total amount of decision-making authority (which may be viewed as 
control), and vice-versa. In a more general framework, this effect would 
be recognized; and the influence of the variable, total amount of decision: 
making authority, upon productivity would be recognized. In this con- 
nection, see ARNOLD S. TANNENBAUM, Control and Effectiveness in a Vo- 
luntary Organization, « American Journal of Sociology », Vol. 67, July 
1961, pp. 33-46, and Control in Organizations: Individual Adjustment and 
Organizational Performance, « Administrative Science Quarterly ». Vol. 7 
September 19062. pp, 236-257 
.1 Isard - pag. a