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Kemeny Rank Aggregation for Three Voters

Is computing a Kemeny-optimal aggregate ranking NP-hard when the input consists of exactly three complete rankings? Hardness was known for every even $n \ge 4$; three voters was the minimal open case, and $n = 2$ is polynomial-time solvable.

Exact FrontierDelta

Prior state unknownproved

Scope and record

Occurred: Jul 28, 2026

Delta type: SOURCE CLAIM

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

Canonical aliases: Kemeny Rank Aggregation for Three Voters · Kemeny, 3 voters

Confidence: Not scored

Registry verification: lean verified · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

Dominik Peters
human · human collaborator

GPT-5.6 Sol Ultra
model · ai model contributor · OpenAI / Anthropic

Claude Fable 5
model · ai model contributor · OpenAI / Anthropic

Lineage and corrections

This event attributed to Dominik Peters

This event attributed to Claude Fable 5

This event attributed to GPT-5.6 Sol Ultra

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