SEMAINE D'ETUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIOUE ETC. 1005 
2. PARTICIPATION POTENTIAL AND DEGREE OF SPATIAL DECEN- 
TRALIZATION 
Elsewhere I have proposed to measure participation poten- 
tial for a system of #» nodes (points. central places, regions) as 
follows : 
where d 
Boo 
Er 
ow oP 
3Gy 5 
ab 
d 
JV; = 
= distance between nodes à and 7, however defined, 
on 
M; = mass at j, however defined; 
b and 3 = adjustment factors, whether constant or vari 
able, applying to d;; and M,, respectively; 
w. = a weight, however constructed, to be applied to M; 
G;; = an appropriate constant applicable to potential inter 
action between nodes 7 and 7; 
;V; = participation potential of individuals (mass) at ÿ per 
unit decision to be reached at 7: and 
+ 
total participation potential of all nodes in the system 
per unit decision to be reached at 1. 
Now consider a hierarchy which may be defined by several 
levels or orders of nodes. (Assume 4 orders of nodes, an order 
being indicated by f or g; f, g=1, ..., A). In a simple hierar- 
chy, the single first-order node may be represented by the peak 
of the pyramid or the top of the tree. An h'” order node is one 
of the many at the base of the pyramid or tree. Intermediate 
nodes may exist at one or more intermediate levels or orders. 
The hierarchy may be regularly or irregularly structured, and 
‘127 Isard - pag. 3