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of advance to the next higher level, we get the special version
of Champernowne's model described at the beginning of this
paper: There are again two geometric distributions, from which
the result is obtained by elimination of L, which stands here
in place of time.
This, in fact, leads to criticism of Simon's explanation. It is,
on the face of it, timeless, it does not show how the pattern
arises from a stochastic process in time.
One does not have to go very far however, in order to see the
dynamic implications of the matter. A certain span of control
implies that the managers of a given level have a limited chance
of advancing to the next level. To the span of control corres
ponds a certain transition probability. It might be argued that
the transition probabilities only reflect the given structure
of the organisation. This, however, has itself arisen as a result
of an evolution (including trial and error) and it is changing
continously albeit slowly. Thus the chances of advancement in the
^ -th
individual's life carreer determine the structure: If —
n
of the occupants of a certain level expect to move m levels in
a life-time then there must be n times as many occupants on the
lower level than on the higher (compare for these topics Bartholo
new /4/.
To be precise we have also to take account of movements into and
out of management, ftoin other oooupatlsm (£o* example, polities) •