IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v46y2023i3d10.1007_s10878-023-01075-w.html
   My bibliography  Save this article

Derivations of large classes of facet defining inequalities of the weak order polytope using ranking structures

Author

Listed:
  • Adolfo R. Escobedo

    (North Carolina State University)

  • Romena Yasmin

    (Arizona State University)

Abstract

Ordering polytopes have been instrumental to the study of combinatorial optimization problems arising in a variety of fields including comparative probability, computational social choice, and group decision-making. The weak order polytope is defined as the convex hull of the characteristic vectors of all binary orders on n alternatives that are reflexive, transitive, and total. By and large, facet defining inequalities (FDIs) of this polytope have been obtained through simple enumeration and through connections with other combinatorial polytopes. This paper derives five new large classes of FDIs by utilizing the equivalent representations of a weak order as a ranking of n alternatives that allows ties; this connection simplifies the construction of valid inequalities, and it enables groupings of characteristic vectors into useful structures. We demonstrate that a number of FDIs previously obtained through enumeration are actually special cases of the large classes. This work also introduces novel construction procedures for generating affinely independent members of the identified ranking structures. Additionally, it states two conjectures on how to derive many more large classes of FDIs using the featured techniques.

Suggested Citation

  • Adolfo R. Escobedo & Romena Yasmin, 2023. "Derivations of large classes of facet defining inequalities of the weak order polytope using ranking structures," Journal of Combinatorial Optimization, Springer, vol. 46(3), pages 1-45, October.
    • Handle: RePEc:spr:jcomop:v:46:y:2023:i:3:d:10.1007_s10878-023-01075-w
    DOI: 10.1007/s10878-023-01075-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-023-01075-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-023-01075-w?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Yeawon Yoo & Adolfo R. Escobedo, 2021. "A New Binary Programming Formulation and Social Choice Property for Kemeny Rank Aggregation," Decision Analysis, INFORMS, vol. 18(4), pages 296-320, December.
    2. Pierre Barthelemy, Jean & Monjardet, Bernard, 1981. "The median procedure in cluster analysis and social choice theory," Mathematical Social Sciences, Elsevier, vol. 1(3), pages 235-267, May.
    3. Pablo Coll & Javier Marenco & Isabel Méndez Díaz & Paula Zabala, 2002. "Facets of the Graph Coloring Polytope," Annals of Operations Research, Springer, vol. 116(1), pages 79-90, October.
    4. Fishburn, Peter C., 1992. "Induced binary probabilities and the linear ordering polytope: a status report," Mathematical Social Sciences, Elsevier, vol. 23(1), pages 67-80, February.
    5. Yoo, Yeawon & Escobedo, Adolfo R. & Skolfield, J. Kyle, 2020. "A new correlation coefficient for comparing and aggregating non-strict and incomplete rankings," European Journal of Operational Research, Elsevier, vol. 285(3), pages 1025-1041.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Akbari, Sina & Escobedo, Adolfo R., 2023. "Beyond kemeny rank aggregation: A parameterizable-penalty framework for robust ranking aggregation with ties," Omega, Elsevier, vol. 119(C).
    2. Irène Charon & Olivier Hudry, 2010. "An updated survey on the linear ordering problem for weighted or unweighted tournaments," Annals of Operations Research, Springer, vol. 175(1), pages 107-158, March.
    3. Fu, Yelin & Lu, Yihe & Yu, Chen & Lai, Kin Keung, 2022. "Inter-country comparisons of energy system performance with the energy trilemma index: An ensemble ranking methodology based on the half-quadratic theory," Energy, Elsevier, vol. 261(PA).
    4. Nathan Atkinson & Scott C. Ganz & Dorit S. Hochbaum & James B. Orlin, 2023. "The Strong Maximum Circulation Algorithm: A New Method for Aggregating Preference Rankings," Papers 2307.15702, arXiv.org, revised Oct 2024.
    5. De Donder, Philippe & Le Breton, Michel & Truchon, Michel, 2000. "Choosing from a weighted tournament1," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 85-109, July.
    6. Yuichi Kitamura & Jörg Stoye, 2018. "Nonparametric Analysis of Random Utility Models," Econometrica, Econometric Society, vol. 86(6), pages 1883-1909, November.
    7. Hudry, Olivier, 2009. "A survey on the complexity of tournament solutions," Mathematical Social Sciences, Elsevier, vol. 57(3), pages 292-303, May.
    8. Hannu Salonen, 2014. "Aggregating and Updating Information," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 8(2), pages 55-67, October.
    9. Faruk Gul & Wolfgang Pesendorfer, 2006. "Random Expected Utility," Econometrica, Econometric Society, vol. 74(1), pages 121-146, January.
    10. Nehring, Klaus & Pivato, Marcus & Puppe, Clemens, 2014. "The Condorcet set: Majority voting over interconnected propositions," Journal of Economic Theory, Elsevier, vol. 151(C), pages 268-303.
    11. Regenwetter, Michel & Marley, A. A. J. & Grofman, Bernard, 2002. "A general concept of majority rule," Mathematical Social Sciences, Elsevier, vol. 43(3), pages 405-428, July.
    12. Nehring, Klaus & Pivato, Marcus & Puppe, Clemens, 2011. "Condorcet admissibility: Indeterminacy and path-dependence under majority voting on interconnected decisions," MPRA Paper 32434, University Library of Munich, Germany.
    13. Charles F. Manski, 2014. "Identification of income–leisure preferences and evaluation of income tax policy," Quantitative Economics, Econometric Society, vol. 5, pages 145-174, March.
    14. Marley, A. A. J., 2002. "Random utility models and their applications: recent developments," Mathematical Social Sciences, Elsevier, vol. 43(3), pages 289-302, July.
    15. Marcus Pivato, 2013. "Voting rules as statistical estimators," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 581-630, February.
    16. Dewan F. Wahid & Elkafi Hassini, 2022. "A Literature Review on Correlation Clustering: Cross-disciplinary Taxonomy with Bibliometric Analysis," SN Operations Research Forum, Springer, vol. 3(3), pages 1-42, September.
    17. Pivato, Marcus, 2017. "Epistemic democracy with correlated voters," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 51-69.
    18. Bernard Monjardet, 2011. "G. Th. Guilbaud et la théorie du choix social," Documents de travail du Centre d'Economie de la Sorbonne 11047, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    19. Bernard Monjardet, 2006. "Condorcet domains and distributive lattices," Post-Print halshs-00119141, HAL.
    20. Katherine Baldiga & Jerry Green, 2013. "Assent-maximizing social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 439-460, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jcomop:v:46:y:2023:i:3:d:10.1007_s10878-023-01075-w. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.