We address the following question in this paper: "What are the most robust
statistical methods for social choice?'' By leveraging the theory of uniformly
least favorable distributions in the Neyman-Pearson framework to finite models
and randomized tests, we characterize uniformly most powerful (UMP) tests,
which is a well-accepted statistical optimality w.r.t. robustness, for testing
whether a given alternative is the winner under Mallows' model and under
Condorcet's model, respectively