Do your friends really have more friends than you? A five-person check
Do your friends have more friends than you? On average, yes. Scott Feld's 1991 arithmetic shows why, and a five-person example lets you verify it by hand.
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Take a party of five where one person, Ana, knows everyone and the other four know only Ana. Ask each of them to compare their friend count with the average of their friends’ counts, and four out of five will come out behind. Nobody in that room is unpopular. The arithmetic is simply tilted toward whoever has the most connections.
So, do your friends have more friends than you? On average, yes. The sociologist Scott Feld showed in a 1991 paper in the American Journal of Sociology that the average number of friends your friends have is never lower than the average number anybody has, and is higher in almost every real network.
Why does the average friend have more friends than the average person?
A person with 50 friends appears on 50 friend lists. A person with 2 friends appears on 2. When you pick a friend at random, you are far more likely to land on the 50 than on the 2, so your sample of friends over-represents the well-connected. Feld described this as a cousin of the class-size paradox: students report their classes as bigger than the registrar does, because big classes contain more students to do the reporting. Feld’s illustration used data from James Coleman’s 1961 study of teenagers, The Adolescent Society, which I could confirm only through secondary summaries.
You can check the whole thing in a two-minute exercise. Here is the five-person party:
| Person | Own friends | Friend counts of their friends | Average of those | Fewer friends than that average? |
|---|---|---|---|---|
| Ana | 4 | 1, 1, 1, 1 | 1 | No |
| Ben | 1 | 4 | 4 | Yes |
| Cy | 1 | 4 | 4 | Yes |
| Dee | 1 | 4 | 4 | Yes |
| Eli | 1 | 4 | 4 | Yes |
Everyone’s own count averages 8 ÷ 5 = 1.6 friends. Now count friendships from the other end. There are 8 friend slots (each of the 4 friendships is listed twice), and the person in each slot has 4 friends when the slot is Ana’s, or 1 when it is a leaf’s. The average is (4 × 1 + 4 × 4) ÷ 8 = 2.5. That is above 1.6, and Feld proved it must be, because the average of the squared friend counts divided by the plain average can never be smaller than the plain average.
Notice who is the exception. Ana, the hub, is the only one whose friends have fewer friends than she does.
Does this mean you are unpopular?
No, and the table is the reason. Ben has one friend, and the arithmetic still says his friend has four. Nothing about Ben is deficient; he happens to be next to the person everyone is next to. The same comparison feels like a verdict on your own life only because you can see your friends’ crowds and not their emptier weeks. For the related trap of assuming everyone else privately has it figured out, see pluralistic ignorance in group chats.
What did the flu study do with this?
In a 2010 PLOS ONE paper, Nicholas Christakis and James Fowler turned the bias into a tool. They enrolled 744 Harvard undergraduates: a random group of 319, and a friend group of 425 made up of people the random students had named. During the 2009 flu season, the friend group’s epidemic curve ran about 13.9 days ahead of the random group’s for medical diagnoses (95% CI 9.9 to 16.6), and a significant lead was visible 46 days before the population’s peak. Friends were better connected on the network measures the authors computed, which is why the virus found them first.
The authors’ point was practical: you can find the central people without mapping the whole network, just by asking random people to name someone. Whether the lead would hold in a bigger, older or less tightly packed population, one Harvard season cannot say.
What should you do with this?
The useful half of the paradox is that your friends’ friends are the well-connected ones, and you are the link to them. A friend of yours might know a dozen people you have never met. Those people have a dozen friends each. Most of them will never meet one another unless somebody puts them in a room.
That somebody is cheap to be. Sending the invite, picking the restaurant, adding your climbing friend to the dinner with your coworker: these are small tasks that put you in the middle of several circles at once, which is the position Ana holds in the table. The extra step is to ask each friend who they would bring if they could bring anyone. Dunbar’s rings suggest how many people you can keep warm, and the bridge position works inside those limits. If a small group of friends already coordinates by chat, splitting the organiser role keeps one person from carrying it alone.
Feld’s result describes averages in networks, so it cannot tell you how many friends you have, or how well your friends know you.