### Satoshi Kanazawa

The Scientific Fundamentalist

# Why Your Friends Have More Friends Than You Do

## And why your girlfriend is a whore

Posted Nov 01, 2009

One of my all-time favorites among all the scientific papers that I have ever read in my life is “Why your friends have more friends than you do,” published in the American Journal of Sociology in 1991 by my old sociology friend Scott L. Feld, who is now Professor of Sociology at Purdue University.

The title of Feld’s paper says it all, and here’s a little demonstration you can do to confirm his conclusion.  List all of your friends.  Then ask each of your friends how many friends they have.  No matter who you are, whether you are a man or a woman, where you live, how many (or few) friends you have, and who your friends are, you will very likely discover that your friends on average have more friends than you do.

But how can this be?  Friendships are bilateral (unless you are a stalker):  If X is friends with Y, then Y is friends with X.  How can Y and other friends of X have more friends than X does?

Feld demonstrates (and explains) the seeming paradox with a simple example in his paper.  In this example, there are eight girls, and their mutual (bilateral) friendships are denoted by solid lines in the sociogram.  So, for example, Betty has only one friend (Sue), but Sue has four friends (Betty, Alice, Pam, and Dale).  The table summarizes the pattern of friendships among these friends.  It shows that, on average, these eight girls have 2.5 friends.  But the friends of these eight girls (who are the same eight girls themselves) on average have 3 friends.

If you think about it for a moment, you’ll figure out the source of this seeming paradox (although this simple insight did not occur to anyone before Feld published his paper in 1991).  You are more likely to be friends with someone who has more friends than with someone who has fewer friends.  There are 12 people who have a friend who has 12 friends, but there is only one person who has a friend who has only one friend.  And, of course, there is no one who has a friend who doesn’t have any friend.  Yet there is actually only one person who has 12 friends.  So “12” gets counted only once when you compute the average number of friends that people have, but it gets counted 12 times when you compute the average number of friends that their friends have.  Hence the seeming paradox that your friends have more friends than you do.