SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIQUE ETc. 1009 
tion. For every branch, the fraction of all decisions made at 
the single first-order node is 0.9. Each 2nd-order node makes 
0.1 of all decisions on any branch on which it is located. Each 
3rd-order and 4th-order node makes zero fraction of all deci- 
sions. In the situation represented by Q, 0.4 of all decision- 
making authority resides at the top; 0.2 of all decision-making 
authority along any branch resides in the 2nd order node of 
that branch; o.1 of all decision-making authority along any 
branch resides in the 3rd-order node of that branch; and 0.3 
of all decision-making authority along any branch resides in 
the 4th-order node of that branch. At the bottom of table 1, 
row Z represents the case where all decisions for any branch 
are made at the 4th-order node of that branch, none being 
made at any node of any other order. Note that, because the 
flow of participation and exercise of influence can only proceed 
upward, no node can influence decisions at any other node of 
the same or higher order. 
Given our assumptions and this framework we compute 
total participation potential, P, of all individuals over all de- 
cisions for each of the situations of table 1. By definition, in 
n 
our normalized cases. P=27;-.V, where 7, is the fraction of all 
i=1 
decisions to be made at node ¢, this fraction being the same for 
all nodes of the same order as 7 (9). The values for P are re- 
(*) If there are s spatial patterns of decision-making authority to be 
considered, each corresponding to a degree of spatial decentralization, then 
for our set of assumptions the participation potential corresponding to each 
degree is given by the single row vector [P.] 
I 1 —I s 
[P,] = 6-41 | EL fs ] 7=1) 
! re, [Fou fe=1,.. À 
where: Æ is the constant defining the number of nodes in the next higher 
order directly linked to any given node; [k:-"), g=1, …, h is a single row 
vector Ixh, h being the number of orders in the hierarchy; da is the 
distance between a node nf order f and the node of order g to which it is 
most directly connected; iz | is an A xh matrix (f, & , h); and 
L fg 
h< < matrix. each column of which describes a spatial pattern 
av” 
F121 Isard - pag. 
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