6 ms·

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

41 points by asimjalis 17y ago

foulmouthboy 17y ago
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-fundamentalist/200911/why-your-friends-have-more-friends-you-do http://www.psychologytoday.com/blog/the-scientific-fundament...
mattmanser 17y ago
Pity there's no real why, just an assertion that vaguely points to maths.
- _delirium 17y ago
  The paper cited as ref [1] has a good explanation. Unfortunately that paper doesn't seem to be available freely online, but here's a press writeup of it: http://www.psychologytoday.com/blog/the-scientific-fundamentalist/200911/why-your-friends-have-more-friends-you-do http://www.psychologytoday.com/blog/the-scientific-fundament...
- orangecat 17y ago
  Say Alice has 100 friends and Bob has 5, and the average is 20. That means Alice has 100 people whose "number of friends of friends" statistic she's increasing, while Bob is only lowering it for 5.
  - cynicalkane 17y ago
    This is pretty much it. I'd make an intuitive guess that the average number of friends of friends is Sum((F_n)^2) / Sum(F_n), where F_n is the number of friends that person n has.
- Anon84 17y ago
  It's pretty easy to explain actually. There's a few "hubs" that have a large number of friends (since it's a power-law, the number of hubs will be relatively large) and that, in aggregate, are connected to everyone. On the other hand, "normal joes" despite only having a few friends are also likely to be connected to these hubs thus biasing their own averages. As a simple example, consider websites. The websites you link to likely have more links pointing to them than your site does, since everybody links to the likes of CNN, google, etc and "nobody" (comparatively) links to you. You can get a better (and more rigorous) explanation here: http://arxiv.org/abs/cond-mat/0209450 http://arxiv.org/abs/cond-mat/0209450
- kmak 17y ago
  Basically, if there's a group of people out there with one friend, chances are you're not that friend.
kevinpet 17y ago
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.
mvp 17y ago
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.
namin 17y ago
When a power law applies, the majority is below average because of the long tail.
Mz 17y ago
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.
- dunstad 17y ago
  As long as your definition is consistent, I rather doubt it matters, for this purpose, whether acquaintances are included.
roundsquare 17y ago
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).
devinj 17y ago
It's not much of a paradox if you can come up with an easy to understand explanation immediately after reading the description. :/
sz 17y ago
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"?

41 points by asimjalis 17y ago

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-fundamentalist/200911/why-your-friends-have-more-friends-you-do http://www.psychologytoday.com/blog/the-scientific-fundament...

mattmanser 17y ago

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

_delirium 17y ago
The paper cited as ref [1] has a good explanation. Unfortunately that paper doesn't seem to be available freely online, but here's a press writeup of it: http://www.psychologytoday.com/blog/the-scientific-fundamentalist/200911/why-your-friends-have-more-friends-you-do http://www.psychologytoday.com/blog/the-scientific-fundament...
orangecat 17y ago
Say Alice has 100 friends and Bob has 5, and the average is 20. That means Alice has 100 people whose "number of friends of friends" statistic she's increasing, while Bob is only lowering it for 5.
- cynicalkane 17y ago
  This is pretty much it. I'd make an intuitive guess that the average number of friends of friends is Sum((F_n)^2) / Sum(F_n), where F_n is the number of friends that person n has.
Anon84 17y ago
It's pretty easy to explain actually. There's a few "hubs" that have a large number of friends (since it's a power-law, the number of hubs will be relatively large) and that, in aggregate, are connected to everyone. On the other hand, "normal joes" despite only having a few friends are also likely to be connected to these hubs thus biasing their own averages. As a simple example, consider websites. The websites you link to likely have more links pointing to them than your site does, since everybody links to the likes of CNN, google, etc and "nobody" (comparatively) links to you. You can get a better (and more rigorous) explanation here: http://arxiv.org/abs/cond-mat/0209450 http://arxiv.org/abs/cond-mat/0209450
kmak 17y ago
Basically, if there's a group of people out there with one friend, chances are you're not that friend.

kevinpet 17y ago

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.

mvp 17y ago

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.

namin 17y ago

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

Mz 17y ago

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.

dunstad 17y ago
As long as your definition is consistent, I rather doubt it matters, for this purpose, whether acquaintances are included.

roundsquare 17y ago

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).

devinj 17y ago

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

sz 17y ago

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"?