My mental model of the NPR experimenters suggests that, after running a simulated Keynesian bubble, they are modeling an "anti-bubble", where the participants are expected to pick a very low number, probably 0, which is the number that would let everyone win, were it a cooperative game.
However, my mental model of an average NPR contest participant without any feedback from others is that of a one- or two-leveler (people rarely spend a lot of time thinking about poll answers). The former would expect the average to be 50 and then pick 25, the latter would pick something like 12. Any higher, and you are likely to converge to the fixed point.
The best guess would depend on your exact priors, but, given that there likely to be a fraction of participants who would not recurse all the way, the answer is likely to be non-zero. As any closed-loop model, this one is also subject to positive feedback, so there should be a correction for that, etc.
Of course, if the current average was publicly known, it would quickly drop to zero.
However, my mental model of an average NPR contest participant without any feedback from others is that of a one- or two-leveler (people rarely spend a lot of time thinking about poll answers).
I would be interested in knowing the values of the individual votes, perhaps after the poll is ended. In particular, I'm curious whether anyone picked a number higher than twenty-five - what would you call that, a zero-leveler? I guess someone who picked a number higher than fifty would be a negative-one-leveler.
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.