The Friendship Paradox

The latest, 10 September, Lost Cousins newsletter available here has an intriguing item on the Friendship Paradox.

According to the paradox, "if you pick someone at random, the chances are that most of their friends have more friends than they do - or to put it another way, most people have fewer friends than their friends do."

To explain by example, suppose there are three people, one is friends with the other two, but they aren't friends with each other. So two people have one friend and one has two friends.The total number of friendships is four making an average number of 4 friendships/3 people, or an average 1.333 friendships. Two have fewer than that, one has more.

Peter of the Lost Cousins newsletter extrapolates the paradox claiming that "When you discover a 'lost cousin', the chances are that person not only knows more cousins than you do, but it is likely to have more relatives on their family tree."

I have doubts about the extrapolation, just as someone who had worked at making friends, rather than a random person, would be less likely to find s/he had less than the average number of friends, so a genealogist who had worked assiduously on his/her family history would not be as likely to make a contact with a lost cousin who had more information than they did.

There's an interesting extension of the friendship paradox more relevant to genealogy in one of the references to the friendship paradox item on Wikipedia.

“Why (did) our mothers had more children than women in her generation did.”  There are 12 children whose mother had 12 children, but there is only one child whose mother had one child.  And, of course, there are no children whose mother had no children.  Yet there is only one woman who had 12 children.  So if we ask around how many children everyone’s mother had (or how many siblings we have), we get the erroneous impression that our mothers were much more fertile than they actually were."