Problem
1. Produce two substantially different but sensible scoring functions on the same set of items. How different are the resulting rankings? Does the fact that both have to be sensible constrain rankings to be grossly similar?
2. The scoring systems used by professional sports leagues to select the most valuable player award winner typically involves assigning positional weights to permutations specified by voters. What systems do they use in professional baseball, basketball, and football? Are they similar? Do you think they are sensible?