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← The Arithmetic of a Feed

The Arithmetic of a Feed

Three short lessons for parents on why a feed is not typical: the long tail, the friendship paradox, and why "trending" is the opposite of normal.

Spark & Whetstone · sparkwhetstone.org/learn/the-arithmetic-of-a-feed · CC BY-NC-SA 4.0. Answers are at the end, so you can try each question first.

Lesson 1. The long tail

Attention is spread very unevenly: a few posts get most of the views, and most get very few. When numbers are skewed like this, the average sits far above the typical value.

Picture ten posts, nine with 10 views and one with 910. The mean is 100 views; the median, the middle post, is 10. Neither number is wrong; they answer different questions.

Question. Five posts get 2, 3, 3, 4 and 88 likes. Which number describes a typical post best?

  1. The median, 3
  2. The largest, 88
  3. The mean, 20

Say it back. In your own words: why can an average be higher than almost everyone in the group?

Lesson 2. The friendship paradox

On average, your friends have more friends than you do. The sociologist Scott Feld explained why in 1991: well-connected people appear in many friend lists, so they are counted again and again when you look at "friends".

It is not a flaw in you. It is a sampling effect: anything you meet through other people over-represents the most connected people.

Question. In a small club one person is friends with all nine others, and the nine are friends only with that person. What is the average number of friends a member’s friends have?

  1. About 1
  2. About 8
  3. About 18

Say it back. In your own words: why do your friends seem to have more friends than you?

Lesson 3. Trending is not normal

"Trending" means unusual: a post rises because it is far above the usual level. A feed built from the most-shared things shows the extremes, not the middle.

That is why a feed of other people’s best moments is a poor picture of anyone’s ordinary day. The arithmetic chose the extremes before anyone looked.

Question. A feed shows only the top 1% most-shared posts. What kind of picture does it give of everyone’s posts?

  1. A picture of the middle
  2. A fair sample of all posts
  3. A picture of the extremes

Say it back. In your own words: why is a feed of top posts not a picture of normal life?

At the table: Map the family’s friendships

Players: Two or more, ages 9 and up. You'll need: A big sheet of paper, pencils.

  1. Write the first names of six to ten people you all know as dots on the paper.
  2. Draw a line between any two who are friends. Count each person’s lines.
  3. For each person, work out the average number of lines their friends have.
  4. Compare: how many people have fewer friends than their friends do on average?

Answers

  1. The median, 3 — The median is 3. The mean, (2 + 3 + 3 + 4 + 88) ÷ 5 = 20, is pulled up by the one big post and describes none of them.
  2. About 8 — Each of the nine sees a friend with 9 friends; the hub sees nine friends with 1 each. (9 × 9 + 1) ÷ 10 = 8.2, while the plain average of friend counts is only 1.8.
  3. A picture of the extremes — Choosing by being shared most selects the extremes. Any conclusion about ordinary posts drawn from it is biased by the choosing.