Problem
1. Use Elo ratings to rank all the teams in a sport such as baseball, football, or basketball, which adjusts the rating in response to each new game outcome. How accurately do these Elo ratings predict the results of future contests?
2. Evaluate the robustness of Borda's method by applying k random swaps to each of m distinct copies of the permutation p = {1, 2, . . . , n}. What is the threshold where Borda's method fails to reconstruct p, as a function of n, k, and m?