

The Friendship Paradox: Why People's Friends Have More Friends Than They Do - asimjalis
http://en.wikipedia.org/wiki/Friendship_paradox

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kevinpet
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.

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

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mvp
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.

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sz
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"?

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

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roundsquare
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).

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

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Mz
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.

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

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

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orangecat
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.

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cynicalkane
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.

