{"payload":{"schema_version":"research-record-v0","publication":{"version":1,"sha256":"cdba2a051bf5b97d59275f429bb1e371df6ff1238fadbd9f5219cec1f5d8a5d0","published_at":"2026-10-14T14:52:33.213820+00:00","reason":"Source-linked pilot import; independent mathematical review remains pending.","withdrawn":false,"draft":{"reader_guide":{"reading":[{"entry_id":"kemeny-three-voters:entry:question:v1","role":"original_question","note":"Read the definition, score translation and original three-list question."},{"entry_id":"kemeny-three-voters:entry:decision:v1","role":"proof","note":"Follow both directions of the reduction and the three-ballot realization."}],"definitions":[{"id":"kemeny-three-voters-distance","term":"Kendall-tau distance","explanation":"Count each pair of alternatives once when the two orders disagree on which comes first. 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The forward and reverse directions relate cut size to disagreement cost; a proposed ranking’s score is polynomial-time checkable.","limitation":"A tiny ballot example explains the objective but does not establish the hardness reduction. The paper’s scores differ by an explicitly computable constant.","dependencies":[],"source_entry_ids":["kemeny-three-voters:entry:decision:v1","kemeny-three-voters:entry:question:v1"],"report_ids":["kemeny-three-voters:report:decision:v1"]}],"bounds":[],"witnesses":[{"id":"kemeny-three-voters-ballot-example","claim":{"id":"claim-kemeny-three-decision","version":1},"kind":"ranking","title":"Three ballots with a cyclic majority","fields":[{"label":"Ballots","value":"A > B > C; B > C > A; C > A > B"},{"label":"Pairwise majorities","value":"A beats B, B beats C, C beats A, each by 2 votes to 1"},{"label":"Best total disagreement","value":"4; three of the six consensus orders achieve it"},{"label":"Score conventions","value":"For this profile the constant is 3, so total Kendall-tau score = 3 + majority-disagreement score."}],"limitation":"OpenMath’s small illustrative profile is not the paper’s MAX CUT instance or a certificate of NP-hardness.","source_entry_ids":["kemeny-three-voters:entry:question:v1","kemeny-three-voters:entry:decision:v1"],"ranking":{"alternatives":["A","B","C"],"ballots":[["A","B","C"],["B","C","A"],["C","A","B"]]}}],"contributors":{"summary":"Dominik Peters authored the paper, checked and simplified the reduction, supplied mathematical improvements and wrote the manuscript. 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