Variations in Group Composition

The number of relationships possible in a group, according to James H. S.
Bosard, is a direct consequence of the size of the group: the larger the
group, the larger the number of possible relationships the individual might
find within the group. It is possible to express the precise mathematical
function relating the number of possible relationships between individuals
in a group and group size (N): This function is represented by the formula (N2−N)/ 2. For example, if the group is made of Tom and Dick, there is only
one possible relationship between members of the group (Tom-Dick). If the
group is made up of the three people Tom, Dick, and Harry, there are three
possible relationships (Tom-Dick, Tom-Harry, and Dick-Harry). If the group
is made up of seven people, there are twenty-one possible relationships between
individuals; if there are ten people in the group, there are forty-five
possible relationships between individuals.
Thus, groups have the potential to become increasingly complex as the
number of people in the group increases. There are many possible consequences
of this increasing complexity. For one thing, it becomes increasingly
harder to pay an equal amount of attention to everyone in the group as
it increases in size. Brian Mullen and colleagues state that the person in the
group who talks the most is paid the most attention, and in turn is most
likely to emerge as the leader of the group; this effect (sometimes referred
to as the “blabbermouth” theory of leadership) increases as the size of the
group increases. It also becomes increasingly difficult to get to know everyone
in the group and to spend equal amounts of time with everyone in the
group as the group increases in size.