IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v64y2025i3d10.1007_s00355-024-01539-w.html
   My bibliography  Save this article

An axiomatic characterization of Split Cycle

Author

Listed:
  • Yifeng Ding

    (Peking University)

  • Wesley H. Holliday

    (University of California, Berkeley)

  • Eric Pacuit

    (University of Maryland)

Abstract

A number of rules for resolving majority cycles in elections have been proposed in the literature. Recently, Holliday and Pacuit (J Theor Polit 33:475–524, 2021) axiomatically characterized the class of rules refined by one such cycle-resolving rule, dubbed Split Cycle: in each majority cycle, discard the majority preferences with the smallest majority margin. They showed that any rule satisfying five standard axioms plus a weakening of Arrow’s Independence of Irrelevant Alternatives (IIA), called Coherent IIA, is refined by Split Cycle. In this paper, we go further and show that Split Cycle is the only rule satisfying the axioms of Holliday and Pacuit together with two additional axioms, which characterize the class of rules that refine Split Cycle: Coherent Defeat and Positive Involvement in Defeat. Coherent Defeat states that any majority preference not occurring in a cycle is retained, while Positive Involvement in Defeat is closely related to the well-known axiom of Positive Involvement (as in J Pérez Soc Choice Welf 18:601–616, 2001). We characterize Split Cycle not only as a collective choice rule but also as a social choice correspondence, over both profiles of linear ballots and profiles of ballots allowing ties.

Suggested Citation

  • Yifeng Ding & Wesley H. Holliday & Eric Pacuit, 2025. "An axiomatic characterization of Split Cycle," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 64(3), pages 557-601, May.
    • Handle: RePEc:spr:sochwe:v:64:y:2025:i:3:d:10.1007_s00355-024-01539-w
    DOI: 10.1007/s00355-024-01539-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00355-024-01539-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/s00355-024-01539-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

    for a different version of it.

    References listed on IDEAS

    as
    1. Markus Schulze, 2011. "A new monotonic, clone-independent, reversal symmetric, and condorcet-consistent single-winner election method," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 36(2), pages 267-303, February.
    2. Joaqui´n Pérez, 2001. "The Strong No Show Paradoxes are a common flaw in Condorcet voting correspondences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 601-616.
    3. Mihara, H. Reiju, 2017. "Characterizing the Borda ranking rule for a fixed population," MPRA Paper 78093, University Library of Munich, Germany.
    4. Holliday, Wesley H., 2024. "An impossibility theorem concerning positive involvement in voting," Economics Letters, Elsevier, vol. 236(C).
    5. Raúl Pérez-Fernández & Bernard De Baets, 2018. "The supercovering relation, the pairwise winner, and more missing links between Borda and Condorcet," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(2), pages 329-352, February.
    6. Bhaskar Dutta & Jean-Francois Laslier, 1999. "Comparison functions and choice correspondences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 513-532.
    7. Paul B. Simpson, 1969. "On Defining Areas of Voter Choice: Professor Tullock on Stable Voting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 83(3), pages 478-490.
    8. Blair, Douglas H & Pollak, Robert A, 1982. "Acyclic Collective Choice Rules," Econometrica, Econometric Society, vol. 50(4), pages 931-943, July.
    9. Kramer, Gerald H., 1977. "A dynamical model of political equilibrium," Journal of Economic Theory, Elsevier, vol. 16(2), pages 310-334, December.
    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. Holliday, Wesley H., 2024. "An impossibility theorem concerning positive involvement in voting," Economics Letters, Elsevier, vol. 236(C).
    2. Wesley H. Holliday & Eric Pacuit, 2023. "Split Cycle: a new Condorcet-consistent voting method independent of clones and immune to spoilers," Public Choice, Springer, vol. 197(1), pages 1-62, October.
    3. Wesley H. Holliday & Mikayla Kelley, 2025. "Escaping Arrow’s theorem: the Advantage-Standard model," Theory and Decision, Springer, vol. 98(2), pages 165-204, March.
    4. Wesley H. Holliday, 2024. "An impossibility theorem concerning positive involvement in voting," Papers 2401.05657, arXiv.org, revised Mar 2025.
    5. Wesley H. Holliday & Eric Pacuit, 2020. "Axioms for Defeat in Democratic Elections," Papers 2008.08451, arXiv.org, revised Oct 2023.
    6. Yifeng Ding & Wesley H. Holliday & Eric Pacuit, 2025. "Characterizations of voting rules based on majority margins," Papers 2501.08595, arXiv.org, revised Apr 2025.
    7. Wesley H. Holliday & Eric Pacuit, 2021. "Axioms for defeat in democratic elections," Journal of Theoretical Politics, , vol. 33(4), pages 475-524, October.
    8. Harrison-Trainor, Matthew, 2022. "An analysis of random elections with large numbers of voters," Mathematical Social Sciences, Elsevier, vol. 116(C), pages 68-84.
    9. Matthew Harrison-Trainor, 2020. "An Analysis of Random Elections with Large Numbers of Voters," Papers 2009.02979, arXiv.org.
    10. Yifeng Ding & Wesley H. Holliday & Eric Pacuit, 2022. "An Axiomatic Characterization of Split Cycle," Papers 2210.12503, arXiv.org, revised Jun 2024.
    11. 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.
    12. Daniela Bubboloni & Mostapha Diss & Michele Gori, 2020. "Extensions of the Simpson voting rule to the committee selection setting," Public Choice, Springer, vol. 183(1), pages 151-185, April.
    13. Wesley H. Holliday & Chase Norman & Eric Pacuit & Saam Zahedian, 2022. "Impossibility theorems involving weakenings of expansion consistency and resoluteness in voting," Papers 2208.06907, arXiv.org, revised Mar 2023.
    14. Hans Gersbach & Rodrigo Casado Noguerales & Samuel Schenk, 2024. "A Better Cycle-Breaker for Swiss Democracy?," CESifo Working Paper Series 11265, CESifo.
    15. Aleksei Y. Kondratev & Alexander S. Nesterov, 2020. "Measuring majority power and veto power of voting rules," Public Choice, Springer, vol. 183(1), pages 187-210, April.
    16. Wesley H. Holliday & Eric Pacuit, 2021. "Measuring Violations of Positive Involvement in Voting," Papers 2106.11502, arXiv.org.
    17. Dan S. Felsenthal & Hannu Nurmi, 2016. "Two types of participation failure under nine voting methods in variable electorates," Public Choice, Springer, vol. 168(1), pages 115-135, July.
    18. Martin, Mathieu & Merlin, Vincent, 2002. "The stability set as a social choice correspondence," Mathematical Social Sciences, Elsevier, vol. 44(1), pages 91-113, September.
    19. Wesley H. Holliday & Eric Pacuit, 2020. "Split Cycle: A New Condorcet Consistent Voting Method Independent of Clones and Immune to Spoilers," Papers 2004.02350, arXiv.org, revised Nov 2023.
    20. Aleksei Yu. Kondratev & Alexander S. Nesterov, 2018. "Measuring Majority Tyranny: Axiomatic Approach," HSE Working papers WP BRP 194/EC/2018, National Research University Higher School of Economics.

    More about this item

    Statistics

    Access and download statistics

    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:sochwe:v:64:y:2025:i:3:d:10.1007_s00355-024-01539-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.