My thought process when I saw this:
Okay, if most people on there are NPR listeners, they'll think: "The average will be around 50, so I'll pick 25." The smarter NPR commenters and all the LW commenters will iterate it one more time, and pick 11. If about 2/3 will do the first, and the other 1/3 the second, the average will be [grabs calculator] about 20, so I'll pick 10. Or better yet 7 or 8, because I'm hardly going to be the first to think this. Oh darn, comments are closed.
ETA (rot13'd because it contains the answer): V infgyl haqrerfgvzngrq gur cbchynevgl bs Cynarg Zbarl naq gurersber bs gur cebcbegvba bs ACE yvfgraref, jvgu gur erfhyg gung V thrffrq n yvggyr ybjre guna gur jvaavat inyhr bs ryrira naq bar unys.
This is a cool game.
NPR's Planet Money is running an experiment which could be an interesting way to test your other-people-modeling skills.
This is a guessing game. To play, pick a number between 0 and 100. The goal is to pick the number that's closest to half the average of all guesses.
http://www.npr.org/blogs/money/2011/10/03/133654225/please-help-us-pick-a-number?sc=fb&cc=fp
The other people guessing are self-selected, I would assume primarily NPR listeners.