Improving Randomized Metric Distortion to 2.1441
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 lotteries, proves their existence, and derives the new bound through a potential argument. All the proofs were obtained using GPT-5.6-Sol with significant guid...
| Authors | Nisarg Shah |
|---|---|
| Primary category | cs.GT |
| Published | 29 August 2026 |
| Last updated at source | 6 September 2026 |
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