# 1
Introduction
It is a paradigm of economy that an
organization has to grow (increase output) in order to prosper. Growth can be
achieved with increased productivity. In most cases it also means adding staff.
This paper looks at the effect that
adding staff has on the internal communication within an organization, on a
purely mathematical basis.
** 2
Paths of Communications**
## 2.1 Definition
A path of communication exists
between any two people in a group. In a group of two, you have one path of
communication. If you add a third person, the number of paths increases to
three, add a fourth person, and the number of paths is already at 6, etc.
Fig. 1: the 6 Paths of
Communications between 4 people
** ****2.2**
**Bigger Groups**
Looking at bigger groups, the
number of possible Paths of Communications (PoC) grows roughly with the formula
PoC = n² / 2 (With n being the number of people in
the group)
(the bigger n the more accurate the formula, for
smaller n it is slightly less)
Organizations follow the same basic
laws. Even if one might rightfully object, that not everyone has to communicate
with everyone in an organization, it is probably a safe assumption that the
number of ‘active’ Paths of Communications grows accordingly (if the headcount
doubles, there are roughly 4 times the number of active Paths of Communications
to cover).
Fig. 2 shows the relationship
between the number of possible Paths of Communication and number of
Participants.
Fig. 2: Paths of Communications = f
(Number of Participants)
** ****2.3**
**Additional Factors**
In very small organizations all
people involved are often concentrated in one single office. A lot of
information is ‘distributed’ by involuntarily overhearing what is going on.
As an organization grows, functions
become more specialized. With increasing workload the duties of one single
individual are ‘reorganized’ into the tasks of one or even several departments.
It is also no longer possible to have all the people work in the same office,
and even if they do, they are not able to ‘overhear’ what is going on. In other
words, passing on or gathering the information needed is not only complicated by
the increased number of Paths of Communications, but also by the geographical
separation between the individuals.
** 3
Conclusion**
The increasing size of an
organization increases the complexity of disseminating information and data
over-proportionally. E.g. if you increase your headcount by 10% per year for two
years, your organization has to handle roughly 50% more ‘Paths of
Communications’.
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