{
  "abstract": "The Kemeny rule aggregates multiple strict rankings into a single strict ranking that minimizes the sum of its distances from the input rankings. The resulting optimization problem, called the Kemeny problem (\\texttt{KP}), is a special case of the linear ordering problem (\\texttt{LOP}). The Kemeny rule satisfies several desirable properties in social choice theory, including the extended Condorcet criterion (\\texttt{XCC}). Ando et al. strengthened this result by introducing the strong Condorcet criterion (\\texttt{SCC}) and showing that it holds for every optimal solution to an arbitrary \\texttt{LOP} instance. Yoo and Escobedo extended the Kemeny rule to rankings with ties and showed that the resulting rule satisfies the non-strict extended Condorcet criterion (\\texttt{NXCC}). This criterion gives a condition under which one candidate must be ranked strictly above another in every optimal solution. In this paper, we introduce the non-strict strong Condorcet criterion (\\texttt{NSCC}), a counterpart of the \\texttt{SCC} for rankings with ties, and show that it holds for every optimal solution to an arbitrary instance of the linear ordering problem with ties (\\texttt{LOPT}). We also establish a complementary structural property that gives conditions under which two candidates must be tied in every optimal solution to an arbitrary \\texttt{LOPT} instance.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19593",
  "author_total": 2,
  "authors": [
    {
      "name": "Daichi Kawashima"
    },
    {
      "name": "Noriyoshi Sukegawa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/25gp9w205n10q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19593",
  "fulltext_url": null,
  "id": "25gp9w205n10q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19593",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.GT"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2002|Game Theory and Voting Systems"
    ]
  ],
  "openalex": "W7213576886",
  "pdf_url": "https://arxiv.org/pdf/2609.19593",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/25gp9w205n10q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.19593",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19593"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Condorcet-type properties of the linear ordering problem with ties",
  "title_text": "Condorcet-type properties of the linear ordering problem with ties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/25gp9w205n10q",
  "venue": "arXiv",
  "versions": []
}