Why You Aren’t Popular

You aren’t popular. Don’t take it personally, but mathematically speaking, on average, your friends have more friends than you do. Cue the Friends theme song, “So no one told you life was gonna be this waaaay!”

You might be thinking, “What friends?” It’s okay, I’m your friend, and one is better than none! <3

But seriously, the phenomenon of the number of friends of your friends being, on average, greater than your friends is known as the friendship paradox. This paradox was first introduced by sociologist Scott Field in 1991. (I heard that, by 1992, his friend count went down to 0. Wonder why…)

How in the world is this true? It seems like we would run out of people at some point, right? If my friends have more friends than me, but their friends have more friends than them, and their friends have more friends than them, won’t we need an infinite number of friends? No! We have forgotten one key fact: people can count more than once because friendship is mutual (hopefully). Also, the friendship paradox is based on an average, which can be a very misleading measure. For example, if I took the average of 1, 2, and 3, I would get (1+2+3)/3 = 2. But, if I took the average of 1, 2, 3, and 94, I would get (1+2+3+94)/4 = 25. With just one extra value (an outlier, if you will), the average COMPLETELY changes. Now, this is a very simple example, but you get the idea: your popular friends are to blame for your comparative unpopularity.

Think of your most extroverted, sociable friend, who seems to have people around them all the time. For me, that’s my very good friend Andrew Garfield.

my favorite spider-man

Alright FINE, we’re not “real” friends in the technical sense of the word, but in my head we’re besties so it still counts. Anyways, Andrew knows all the cool celebrities and is literally Spider-man, so he has like hundreds of friends. Now, think of someone you know who prefers their own company, maybe only has a couple friends (it’s okay, you can say yourself). Our social circles (or webs, if you will) tend to have more of the Andrew Garfield type, just because there’s a higher chance of being caught in their bigger web to be one of their many many friends. We’re less likely to be caught in the smaller web of someone who is a little more introverted, though it’s still possible! However, the average often overshadows these friendships with introverts.

This is why the friendship paradox happens: the distribution of your friends is not linear. Most people have a couple close friends, but the small number of people that have TONS of friends is why this average becomes suddenly skewed, making your number of friends pale in comparison. It’s a form of sampling bias, because your friends are not an accurate representation of the general population’s friend counts!

This paradox translates to very similar situations: your Facebook friends have more friends than you have on average, your Twitter followers have more followers than you do on average, and your friends also have more money than you do, say it with me, on average. This is an expected result because all these networks are connected very similarly!

Let’s just say this isn’t very helpful for our general happiness levels. That’s why it always seems like the people around us are happier, richer, and just doing better than you are, especially on social media where networks are even broader. But remember, that’s just the horrible sampling bias at work.

It’s like going to the gym for the first time. You might be distraught by how much bigger muscles the people there have. However! You forgot that the sample of people at the gym doesn’t account for the many others who don’t go to the gym, so you’re comparing yourself to a very small part of the population that isn’t an accurate representation of the general muscle size. Don’t worry, you’ll get those big muscles eventually!

So, is the friendship paradox’s only purpose to torture me with the knowledge that my friends are popular-er, richer, and better than me? Thankfully, no! Otherwise, I would be squaring up with Scott Field right now.

This paradox can be applied to help prevent the spread of infectious disease! Sound familiar? This makes sense, because “popular” people who meet more of their friends are more likely to catch it and spread it, making them “super-spreaders.” The lesson? Don’t have friends and you won’t catch diseases! (The actual lesson is to be responsible during a pandemic, but that’s besides the point.) The friendship paradox can actually detect these outbreaks faster than traditional methods. In the past, it has caught flu outbreaks two weeks earlier than the old methods.

So, the paradox isn’t really a paradox, and you aren’t really unpopular. But, even if you are, I’ll be there for youuuuuu!

Until next time! If you found this interesting, make sure to follow to be updated when the next article comes out!

In the meantime, check out other articles in my column here! If you have any questions or comments, please email me at apoorvapwrites@gmail.com.

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As a reminder: this column, Gems in STEM, is a place to learn about various STEM topics that I find exciting, and that I hope will excite you too! It will always be written to be fairly accessible, so you don’t have to worry about not having background knowledge. However, it does occasionally get more advanced towards the end. Thanks for reading!

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17 y/o math student, artist, and advocate for youth & gender minorities in STEAM. Winner of Strogatz Prize for Math Communication & Davidson Fellows Laureate.

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Apoorva Panidapu

Apoorva Panidapu

17 y/o math student, artist, and advocate for youth & gender minorities in STEAM. Winner of Strogatz Prize for Math Communication & Davidson Fellows Laureate.

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