The Friendship Paradox Explained

Steven Strogatz explains why “Our friends are typically more popular than we are.”

Short version: If they are friends with the likes of us, they’re friends with lots of people. (Presumably, the people who are really unpopular have no friends at all, so we’re not friends with them?)

This also explains what we would have to call the Gym Paradox,

… imagine going to the gym. When you look around, does it seem that just about everybody there is in better shape than you are? Well, you’re probably right. But that’s inevitable and nothing to feel ashamed of. If you’re an average gym member, that’s exactly what you should expect to see, because the people sweating and grunting around you are not average. They’re the types who spend time at the gym, which is why you’re seeing them there in the first place. The couch potatoes are snoozing at home where you can’t count them. In other words, your sample of the gym’s membership is not representative. It’s biased toward gym rats.

(Actually, the gym I go to is biased towards undergraduates, and if they’re not in better shape than I am then something is Not Right With The World.)

And the there’s what I call the Falling Tree in the Forest paradox:

This is also why people experience airplanes, restaurants, parks and beaches to be more crowded than the averages would suggest. When they’re empty, nobody’s there to notice.

Strogatz’s essay has lots more goodies, and also some math for those who fancy such delicacies.

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