## TL;DR
Scott Feld wrote this paper when he was professor at Ston...
Scott L. Feld is a mathematical sociology professor at Purdue Unive...
It is actually possible for Facebook users to download their social...
The average number of friends of a person is given by the average o...
The friendship paradox was used in 2009 by Nicholas Christakis and ...
It's interesting to study other situations in which you can observe...
Why
Your
Friends Have More
Friends
than
You
Do1
Scott
L.
Feld
State
University
of
New York at
Stony
Brook
It is reasonable
to
suppose
that individuals use the
number of
friends that their
friends
have
as
one basis
for
determining
whether
they,
themselves,
have an
adequate
number of
friends.
This article
shows
that,
if
individuals
compare
themselves with their
friends,
it
is
likely
that most
of
them
will feel
relatively inadequate.
Data on
friendship
drawn
from
James
Coleman's (1961) classic
study The
Adolescent
Society are used to
illustrate the phenomenon
that most
people
have
fewer friends than
their
friends have. The
logic under-
lying the phenomenon
is mathematically explored, showing
that the
mean
number
of friends of friends is
always greater than
the mean
number of
friends
of
individuals.
Further analysis shows
that the
proportion
of individuals who
have fewer friends than
the mean
number of
friends their
own friends have is affected by
the exact
arrangement
of
friendships
in a
social network. This
disproportion-
ate
experiencing
of
friends with
many
friends
is
related to a
set
of
abstractly
similar "class size
paradoxes"
that includes such diverse
phenomena
as the
tendencies for
college
students to experience the
mean class
size as
larger
than
it
actually
is
and
for
people
to
experi-
ence beaches
and
parks
as more crowded than
they
usually
are.
Friendship
is
not
only
a source of satisfaction and
security;
it
is also
a
way
that individuals
evaluate
themselves
and others.
People expect
themselves
and others
to
have
friends
and wonder about the
normality
of those
individuals
who
appear
to
have
few or no friends. There has
been little
study
of how
people
determine what
is
an
adequate
number
of
friends,
but
it
is
reasonable
to
suppose
that individuals use the number
of
friends
that their friends
have as one
basis
of
comparison.
This article
shows
that,
if individuals make this
type
of
comparison,
it is
likely
that
1
A previous version of this paper
was presented at the 1986 Sunbelt
Social Network
Conference
in
Santa
Barbara,
Calif.
I
appreciate
the
helpful suggestions
of Bernard
Grofman,
Guillermo
Owen,
and
Jill
Suitor.
Requests
for
reprints
should be sent
to
Scott
Feld, Department
of
Sociology,
State
University
of New York, Stony
Brook,
New York 11794-4356.
?) 1991
by The
University of
Chicago.
All
rights
reserved.
0002-9602/91/9606-0005$01
.50
1464
AJS
Volume
96
Number
6
(May
1991):
1464-77
Friends
most of them
will feel
relatively inadequate.
I
use data on
friendship
drawn
from
James
Coleman's
(1961)
classic
study
The Adolescent
Society
to
illustrate
the
phenomenon
that most
people
have
fewer
friends than
their friends have.
I
will explore
mathematically the logic underlying the phenomenon,
showing
that
the mean number of friends of friends is
always greater
than
the
mean
number of friends
of
individuals. Further
analysis
shows
that
the
proportion
of
individuals
who have
fewer friends than the mean
number of friends
their own friends have
is
affected
by
the
exact arrange-
ment of
friendships
in
a social network. While it is not a mathematical
necessity
that
each
individual will have fewer friends than the
mean
of
her or his own friends,
it
is
likely
that most
people
will find
themselves
in
this situation.
The basic logic can be described
simply.
If
there are some
people with
many friendship
ties and others
with
few,
those
with
many
ties show
up
disproportionately
in
sets of friends. For
example,
those with 40
friends
show
up
in
each
of 40 individual
friendship
networks
and
thus
can make
40
people
feel
relatively
deprived,
while those with
only
one friend show
up
in
only
one
friendship
network and can
make
only
that one
person
feel
relatively advantaged. Thus,
it is
inevitable that individual
friendship
networks disproportionately
include those with the most
friends.
EMPIRICAL
EXAMPLES
Friendship
is
usually thought
to be a
symmetric relationship, as indicated
by
the common
phrase, "They
are friends."
One
way
to
operationalize
friendship
is to
consider
a
friendship
to
be
one
that
is so
regarded by
both of the individuals.
In The
Adolescent
Society,
Coleman
(1961)
col-
lected data
on
friendships
among
the
students
in
12
high
schools.
Individ-
uals were asked
to
name their
friends,
and
pairs
of
individuals who
named one another were given
particular attention. It is these "friend-
ships"
that
will
be used as
examples.
To illustrate
the
phenomenon
under
study here, consider the set
of
relationships depicted
in
figure
1,
found
among eight girls
in
"Mar-
ketville,"
one
of
the
high
schools included in
the
study. The names are
fictitious.
In
this example, Betty's only
friend, Sue, has more friends than Betty
has; Jane's two friends,
Dale and
Alice, average
more
friends than Jane
has; Dale's three friends, Sue,
Alice, and Jane, average more friends
than
Dale;
and so forth. Of the
eight girls,
five
(Betty, Jane, Pam, Dale,
and
Tina)
have fewer friends than the
average among
their
friends, while
only
two
(Sue
and
Alice)
have
more friends
than the average among their
friends;
one
(Carol)
has as
many
as the
average among
her
friends. Table
1465
American Journal of Sociology
1(4)
-
4(2.75)
-
4(3)
-
2(3.5)
Betty Sue
Alice
Jane
3(3.3)Pam
??(3.3)
Dale
2(2)
Carol
1
1(2)
Tima
The number beside each name
is
her
number of friends. The number
in
parentheses
beside each name
is
the
mean number of friends of her friends.
FIG. 1.-Friendships
among eight girls
at Marketville High
School
1 shows each girl's number
of friends in the first column and,
in the third
column,
the mean
number of friends
her
friends have.
Twice as
many
(5:2) have fewer
than
average
as have more
than the
average
among
their
friends.
The
complete
network of all of the
girls
in
Marketville shows
the same
pattern. Figure
2
reproduces
the entire
sociogram
of mutual choices. Of
the
146
girls
who
have
any
mutual
friends,
80 have
fewer friends than
the
mean
among
their friends while
41 have
more;
25 have
the same
as
the mean among
their
friends.
Thus, nearly
twice as
many
have fewer
as
have
more
than
the mean
among
their friends. The
same
pattern
TABLE
1
A
SUMMARY
OF THE NUMBERS OF FRIENDS AND
THE MEAN
NUMBERS
OF FRIENDS
OF
FRIENDS
FOR EACH
OF
THE
GIRLS
IN
FIGURE
1
Total Number of Mean Number
of
Number
of Friends of
Friends
of
Friends Her Friends Her Friends
(xt)
(Y-x,)
(-x,l/xt)
Betty
.1
4
4
Sue
.4 11
2.75
Alice
.4 12
3
Jane
.2 7
3.5
Pam
.3
10
3.3
Dale
.3
10 3.3
Carol
.2
4
2
Tina
.1 2
2
Total
.20 60
23.92
Mean
2.5*
3t
2.99*
*
For
eight girls.
t
For 20 friends.
1466