I was thinking it would be fun to have a competition in my class estimating various
quantities. It could be things like fractions of colors or M&Ms, or high and low
temperatures, or whatever. What I would like most is that they report not just the
estimate, but the uncertainty as well. Then I'd like to rank them in some way, and I
am not sure what is the best way to do this.
Intuitively, I want something that has the following properties:
1) for the same uncertainty, larger deviations of the estimate from the actual
yield lower rank
2) for the same estimate, larger uncertainty yields lower rank
Has anyone every tried this? I think it is important to communicate that the
uncertainty in an estimate is every bit as important as the estimate itself.