The problem with the existing protocol is that it forces the choice of a single winner. If multiple players are all basically right, the protocol you describe forces them into a deathmatch because only one player can be “the winner”.
(Another problem with the existing protocol is that it has some players making their predictions “before” others, in a way that is visible to the others.)
Here’s a better protocol: everyone makes their prediction at the same time without seeing anyone else’s prediction. If someone is off by X units then their score for that round is 1/(X+1). For best results, play several rounds and compute the average score.
You might also be interested in Wits And Wagers, which is the “everyone predicts a number” activity made into a six-player board game. I’ve played it. It’s pretty fun.
Everyone settling on an answer before anyone speaks is a good norm in general to avoid anchoring, in many settings.
However, when playing with non-rationalists, I feel like one would need paper in order to implement it in a trustworthy way, which makes me think it’s not going to be popular for that use-case.
The problem with the existing protocol is that it forces the choice of a single winner. If multiple players are all basically right, the protocol you describe forces them into a deathmatch because only one player can be “the winner”.
(Another problem with the existing protocol is that it has some players making their predictions “before” others, in a way that is visible to the others.)
Here’s a better protocol: everyone makes their prediction at the same time without seeing anyone else’s prediction. If someone is off by X units then their score for that round is 1/(X+1). For best results, play several rounds and compute the average score.
You might also be interested in Wits And Wagers, which is the “everyone predicts a number” activity made into a six-player board game. I’ve played it. It’s pretty fun.
What they said. Adjust the protocol to allow everyone equally close to be the “winner”
As a simple protocol, take the true number, and check at each order of magnitude:
0. Anyone who got it exact wins
Anyone within 90% − 110% of the true value wins. If that’s nobody
Anyone within 50% − 200% of the true value wins. If that’s still nobody
Anyone within 10% − 1000% of the true value wins.
If that’s nobody, then everyone loses.
Everyone settling on an answer before anyone speaks is a good norm in general to avoid anchoring, in many settings.
However, when playing with non-rationalists, I feel like one would need paper in order to implement it in a trustworthy way, which makes me think it’s not going to be popular for that use-case.