Optimal Statistical Hypothesis Testing for Social Choice
This work addresses statistical robustness in social choice, which is incremental as it applies established Neyman-Pearson theory to specific voting models.
The paper tackles the problem of identifying the most robust statistical methods for social choice by characterizing uniformly most powerful tests for determining a winner under Mallows' and Condorcet's models, achieving optimality in statistical hypothesis testing.
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.