A comment on Computational Complexity blog blog inspired me to look at the following problem
Suppose you give true/false test to students and want them to put down their subjective probabilities that answer is true/false. To make them honest, you would want to award points in such a way, that in order to maximize their expected points, the student would need to report their correct probabilities. Which utility function to use? It turns out, f(x)=A log x + B is one such family. Here's the derivation
1) Does any other such utility function exist?
2) What are other fun ways to torture students?
Here are graphs of three possible functions that can be used for eliciting probabilities from students. They are all concave, maybe one can prove any suitable function must be concave?