In grade school, I read a series of books titled Sideways Stories from Wayside School by Louis Sachar, who you may know as the author of the novel Holes which was made into a movie in 2003. The series included two books of math problems, Sideways Arithmetic from Wayside School and More Sideways Arithmetic from Wayside School, the latter of which included the following problem (paraphrased):

The students have Mrs. Jewl's class have been given the privilege of voting on the height of the school's new flagpole. She has each of them write down what they think would be the best hight for the flagpole. The votes are distributed as follows:

• 1 student votes for 6 feet.
• 1 student votes for 10 feet.
• 7 students vote for 25 feet.
• 1 student votes for 30 feet.
• 2 students vote for 50 feet.
• 2 students vote for 60 feet.
• 1 student votes for 65 feet.
• 3 students vote for 75 feet.
• 1 student votes for 80 feet, 6 inches.
• 4 students vote for 85 feet.
• 1 student votes for 91 feet.
• 5 students vote for 100 feet.

At first, Mrs. Jewls declares 25 feet the winning answer, but one of the students who voted for 100 feet convinces her there should be a runoff between 25 feet and 100 feet. In the runoff, each student votes for the height closest to their original answer. But after that round of voting, one of the students who voted for 85 feet wants their turn, so 85 feet goes up against the winner of the previous round of voting, and the students vote the same way, with each student voting for the height closest to their original answer. Then the same thing happens again with the 50 foot option. And so on, with each number, again and again, "very much like a game of tether ball."

Question: if this process continues until it settles on an answer that can't be beaten by any other answer, how tall will the new flagpole be?

Answer (rot13'd): fvkgl-svir srrg, orpnhfr gung'f gur zrqvna inyhr bs gur bevtvany frg bs ibgrf. Naq abj lbh xabj gur fgbel bs zl svefg rapbhagre jvgu gur zrqvna ibgre gurberz.

Why am I telling you this? There's a minor reason and a major reason. The minor reason is that this shows it is possible to explain little-known academic concepts, at least certain ones, in a way that grade schoolers will understand. It's a data point that fits nicely with what Eliezer has written about how to explain things. The major reason, though, is that a month ago I finished my systematic read-through of the sequences and while I generally agree that they're awesome (perhaps moreso than most people; I didn't see the problem with the metaethics sequence), I thought the mini-discussion of political parties and voting was on reflection weak and indicative of a broader nerd failure mode.

TLDR (courtesy of lavalamp):

1. Politicians probably conform to the median voter's views.
2. Most voters are not the median, so most people usually dislike the winning politicians.
3. But people dislike the politicians for different reasons.
4. Nerds should avoid giving advice that boils down to "behave optimally". Instead, analyze the reasons for the current failure to behave optimally and give more targeted advice.