Suppose several people are guessing a number, and then find an estimate to see who is right.
The super-common protocol is: whoever is closest, wins.
This protocol is really bad. If there are three people, and I guess 50, then the other two people can guess 51 and 49. This means I'll almost certainly lose. Unless it's within 1/2 of 50, one of the other guesses will be closer.
There are lots of ways to fix this protocol. However, most of them suffer from too much added complexity. For example, squared error incentivises everyone to guess their expected value (mean). However, people don't generally want to calculate squares, and if they did, they'd still feel like the lowest squared error was the winner (which amounts to the usual protocol).
Or, we could give confidence intervals. But how should they be scored?
My question is this: what are some ways to play this game that combine simplicity with good incentives?