Optimal Statistical Hypothesis Testing for Social Choice
Lirong Xia
TL;DR
This paper develops robust statistical hypothesis tests for social choice scenarios, identifying optimal methods for determining winners under specific voting models using advanced statistical theory.
Contribution
It characterizes the uniformly most powerful tests for social choice problems under Mallows' and Condorcet's models, advancing the statistical robustness in voting analysis.
Findings
Identifies UMP tests for Mallows' model
Identifies UMP tests for Condorcet's model
Enhances robustness in social choice hypothesis testing
Abstract
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.
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Taxonomy
TopicsGame Theory and Voting Systems · Bayesian Modeling and Causal Inference · Complexity and Algorithms in Graphs