The Friendship Paradox: Why People's Friends Have More Friends Than They Do

I wasn't aware this had a name, but I've proposed this in terms of families. Most people come from larger families than they have. That is, for most people, the number of brothers and sisters plus one (for the person we're talking about) is greater than the number of children that person will eventually have. Or at least it can be, even in a growing population.

Consider a family with four children. Alice, Bob, Charlie and Dave. Assume that Alice goes on to have four children of her own, and her brothers have none. So Alice has exactly as many children as brothers + sisters + 1. But 3/4 of the children in the original family have fewer children than siblings + 1.

It's a consequence of the counting being proportional to the size of the family. A family with 4 children gets counted four times, a family with 1 child gets counted only once. It's more complicated to show with friendships because the graph isn't directed, but it holds for the same reason. A social butterfly with lots of friends gets counted for each of his or her friends. Someone with few friends only gets counted for those few friends.

Do people just upvote on interesting titles because the Wikipedia article has no information on its own. Why not just link to this: http://www.psychologytoday.com/blog/the-scientific-fundament...

If you see a friend at a certain place by accident, you are bound to feel that your friend frequents the place more than you yourself do. I used to think that this is incorrect as there is no way to ascertain that. I may have to rethink now.

Is it oversimplifying to explain it as "you're statistically more likely to be friends with the guy who has a million friends than the guy who has one"?

It's not much of a paradox if you can come up with an easy to understand explanation immediately after reading the description. :/

Averages are easily skewed by a small number of large values...

I suspect if median were used instead this would vanish... you might even be able to prove this (assuming you could eliminate the social misconceptions).

When a power law applies, the majority is below average because of the long tail.

Of course, I would want to know what definition of "friend" people are using. It seems to me that some folks say "friend" where another person would say "acquaintance". If you are using a more shallow definition of "friend" than someone else, its easy to claim many "friends". But if push came to shove, a lot of those folks would abandon you.

Pity there's no real why, just an assertion that vaguely points to maths.