1006 PONTIFTCIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
may be symmetrical or asymmetrical. The flow of participation 
or the exercise of influence may be upward throughout, down- 
ward throughout, or both ways throughout; or it may be cha- 
racterized by any one of the many possible combinations of 
npward and downward movements. 
Take the symmetrical tree-like hierarchy of Figure 1. Each 
node, starting from the peak, leads to four subordinate nodes. 
The tree consists of four orders. the number of nodes of the 
Erc 
A regular Hievarchy of Nodes 
CE à 
20 
£ 
2! 
\ AN 85 
first, second, third and fourth-orders being 1, 4, 16 and 64, 
respectively. Their numbers run from 2 to 5 in the second- 
order, 6 to 21 in the third, and 22 to 85 in the fourth. At the 
start, let there be one person at each node, each person having 
the same weight of unity. We also set d;=¢= = and let 
G;, 8, b=1. When dz, represents the distance between two 
nodes of orders f and g along any given branch from the peak 
(the bar being placed over the subscript to indicate that we are 
speaking about the order of node), d7=1 when f>g; and 
d;; 0 when f<g. The sense of the last assumption is that 
only upward flow of participation is permitted. A person can- 
‘12] Isard - pag.