Improving Randomized Metric Distortion to 2.3282

The paper proves that there exists a randomized voting rule using only ordinal rankings with metric distortion at most $11641/5000=2.3282$ . This improves the previous best upper bound of $2.5$ and closes about $44\%$ of the gap to the known asymptotic lower bound of approximately $2.1126$ . It does not determine the optimal randomized metric distortion: for $m\ge4$ , the exact optimum and its asymptotic limit remain open.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Aug 29, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-discovered. Imported under CC BY 4.0.

Canonical aliases: Improving Randomized Metric Distortion to 2.3282 · Randomized metric distortion 2.3282

Confidence: Not scored

Registry verification: unreviewed · preprint · partial

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Attribution

VibeMathed
registry · event recorded by

GPT-5.6 Sol
model · ai model contributor · OpenAI

Claude Opus 5.0
model · ai model contributor · Anthropic

Nisarg Shah
human · human collaborator

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Named evidence

VibeMathed record: Improving Randomized Metric Distortion to 2.3282

specialist registry · passed

Unreviewed. The author states that he verified all final mathematical details; by this site's ladder an author's own check does not move the tier, however expert, and Shah is among the leading researchers on metric distortion. The bound $11641/5000$ rests, per the abstract, on an exact rational verification via polynomial nonnegativity in the Bernstein basis, which is checkable in principle but has not been re-run here. No referee and no formalization.

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Improving Randomized Metric Distortion to 2.3282

preprint · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Lineage and corrections

VibeMathed record: Improving Randomized Metric Distortion to 2.3282 evidence for this event

This event attributed to Claude Opus 5.0

Improving Randomized Metric Distortion to 2.3282 evidence for this event

Improving Randomized Metric Distortion to 2.3282 parent of this event

This event attributed to GPT-5.6 Sol

In metric social choice, voters rank candidates by distance in an unknown metric space, while a randomized voting rule must use only these rankings. The paper introduces random-size stable lotteries and proves that, by mixing a suitably chosen random-size stable lottery with Integrated Veto, one obtains a randomized voting rule with metric distortion at most $11641/5000=2.3282$ . This improves the previous best upper bound of $2.5$ . The proof combines infinite-dimensional conic linear-programming duality, heuristic nonlinear optimization, and exact rational verification using polynomial nonnegativity in the Bernstein basis. parent of this event

This event attributed to Nisarg Shah

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