Tournaments Determined by Three and Five Voters
Around the Kemeny median problem, which stays open for and voters, the paper refutes three conjectures on tournament inducibility: both conjectures of Milosz, Hamel and Pierrot (the 3-cycle extension for odd , and at ), and the Shepardson-Tovey threshold conjecture.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI-assisted
- Method
- Construction
- Field
- Social Choice, Tournaments
- Posed by
- Milosz, Hamel and Pierrot; Shepardson, Tovey
- Year posed
- 2018
- Years open
- 8y
- Solved
- 2026-07-29
- Model
- Claude
- Vendor
- Anthropic
- Collaborators
- Leonid Chindelevitch, Ararat Harutyunyan
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The authors report using Claude for exploratory reasoning, implementation assistance, drafting and editing. Exploration and implementation are mathematical work; drafting and editing are not, and the disclosure does not separate them, so the lowest tier applies.
Verification
No independent check, and the disclosure bundles mathematical exploration together with drafting, leaving the model's actual share unclear. Preprint, not refereed. All theorems in the paper LP or ILP-verified.
Sources
- PaperarXiv
- CodeGithub repo of the computations used
- Problem recordMilosz, Hamel, Pierot 2019 - Problem statement