Deterministic tournament rules have metric distortion between 3.1128 and 3.9312, and deterministic k-tournament rules approach distortion 3 while randomized 3-tournament rules can beat 3.
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Metric Distortion for Tournament Voting and Beyond
Deterministic tournament rules have metric distortion between 3.1128 and 3.9312, and deterministic k-tournament rules approach distortion 3 while randomized 3-tournament rules can beat 3.