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Kemeny Rank Aggregation for Three Voters

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kemeny-three-votersTheoretical computer scienceposed by Cynthia Dwork, Ravi Kumar, Moni Naor & D. Sivakumar, 2001recorded: solved

1 attempt · 1 machine check · no person has looked

Statement

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≥4n \ge 4; three voters was the minimal open case, and n=2n = 2 is polynomial-time solvable.

Context

The three-voter case left open by Dwork-Kumar-Naor-Sivakumar's foundational paper.

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Attempts

1 attempt

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  • #1

    Attempt 1

    proof attemptGPT-5.6 Sol Ultra, Claude Fable 5 with Dominik Peters ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    GPT-5.6 Sol Ultra, Claude Fable 5
    people
    Dominik Peters

    GPT-5.6 Sol Ultra found the reduction from MAX CUT; Claude Fable 5 helped simplify parts of it. Together with earlier results, every fixed number of voters n≥3n \ge 3 is now hard.

    Reviews

    0 human reviews · 1 machine check

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    • Machine check · not human verification

      machine: correct

      Recorded from Lean ·

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