Here’s a brain-boggling challenge from Psychology Today blogger Satoshi Kanazawa:
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.
It seems impossible—given that friendships are reciprocal—but it’s true. The apparent friendship paradox is explained in what the evolutionary psychologist calls one of his “all-time” favorite papers: “Why Your Friends Have More Friends Than You Do,” by sociologist Scott L. Feld, published in the American Journal of Sociology in 1991.
In his blog post, Kanazawa reproduces some charts, which show that in a hypothetical group of eight friends, each individual has an average of two-and-a-half friends. Those friends, however, each have an average of three friends. What causes the disparity? Kanazawa explains:
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.