Breaking Ranks

# You're Less Popular Than Your Friends

756 Views Jan 20, 2011

Some of us may fancy ourselves immensely popular, magnanimously bestowing our friendship on worthy peers. But in truth, mathematics professor John Allen Paulos says, our friends are likely more popular than us.

Over at Scientific American, Paulos tells us why. It's a matter of probability, he argues:

We are all more likely to become friends with someone who has a lot of friends than we are to befriend someone with few friends. It's not that we avoid those with few friends; rather it's more probable that we will be among a popular person's friends simply because he or she has a larger number of them.

This seeming paradox holds true for social media too, Paulos explains: "most people have fewer followers than their followers do." How is that possible? Paulos talks about the difference in numbers--and, specifically, averages--when you account for perspective, using class size as an example:

Let's imagine a small department offering three courses for the semester. One is a survey course with 80 students, one an upper-level course with 15 students, and one a seminar with five students. Now what is the average class size? Clearly, it is (80 + 15 + 5)/3, or 33.3 students. This is the number the department is likely to publicize.

But once again, let's adopt the perspective of the average person and reexamine these numbers. Eighty of the 100 students find themselves in a class with 80 students, 15 find themselves in a class of 15 students, and five in a class of five students. Thus, the average student’s class size is (80 × 80 + 15 × 15 + 5 × 5)/­100, or 66.5 students. This number is less likely to be publicized by the department.

So here's how that applies back to the issue of most people being less popular than their friends: just as the average student perceives him or herself to be in a class of above-average size, the average friend has fewer friends than his friends do. Or, as Paulos puts it, "most of us are less popular than average."
Do you follow?

(h/t: Paul Kedrosky at Infection Greed)

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