Improving Randomized Metric Distortion to 2.1441

Quick summary

arXiv:2608.29308v2 Announce Type: replace-cross Abstract: In metric social choice, voters rank candidates by their distances in an unknown metric space. A voting rule uses these rankings to select a candidate or a lottery over candidates, aiming to minimize the average distance to voters. Distortion measures the worst-case approximation ratio. While the best distortion of deterministic rules is $3$, prior work pins down the best distortion of randomized rules to $[2.1126,2.5]$. We improve the upper bound to $2.1441$, closing over $90\%$ of this gap. The proof introduces random-size stable lott