IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v123y2023icp128-136.html
   My bibliography  Save this article

When ties are possible: Weak Condorcet winners and Arrovian rationality

Author

Listed:
  • Diss, Mostapha
  • Dougherty, Keith
  • Heckelman, Jac C.

Abstract

We use Ehrhart polynomials to estimate the likelihood of each three-candidate social ranking produced by pairwise majority rule assuming an even number of voters and the Impartial Anonymous Culture condition. We then calculate the probability the ranking is transitive and the probability of a weak Condorcet winner. Finally, we determine the weak Condorcet efficiency of various voting rules. We prove that Baldwin, Nanson, Copeland, and ranked pairs are weak Condorcet efficient, as is Borda unless there are no ties. Simulations show that among the rest, Dowdall is typically the most efficient rule for small voter groups and anti-plurality the least.

Suggested Citation

  • Diss, Mostapha & Dougherty, Keith & Heckelman, Jac C., 2023. "When ties are possible: Weak Condorcet winners and Arrovian rationality," Mathematical Social Sciences, Elsevier, vol. 123(C), pages 128-136.
    • Handle: RePEc:eee:matsoc:v:123:y:2023:i:c:p:128-136
    DOI: 10.1016/j.mathsocsci.2023.03.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016548962300032X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.mathsocsci.2023.03.004?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Emerson Niou, 1987. "A note on Nanson's rule," Public Choice, Springer, vol. 54(2), pages 191-193, January.
    2. Healy, Paul J. & Peress, Michael, 2015. "Preference domains and the monotonicity of condorcet extensions," Economics Letters, Elsevier, vol. 130(C), pages 21-23.
    3. Abdelhalim El Ouafdi & Dominique Lepelley & Hatem Smaoui, 2020. "Probabilities of electoral outcomes: from three-candidate to four-candidate elections," Theory and Decision, Springer, vol. 88(2), pages 205-229, March.
    4. Dominique Lepelley & Ahmed Louichi & Hatem Smaoui, 2008. "On Ehrhart polynomials and probability calculations in voting theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(3), pages 363-383, April.
    5. Florenz Plassmann & T. Tideman, 2014. "How frequently do different voting rules encounter voting paradoxes in three-candidate elections?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(1), pages 31-75, January.
    6. Lepelley, Dominique & Gehrlein, William V., 2000. "Strong Condorcet efficiency of scoring rules," Economics Letters, Elsevier, vol. 68(2), pages 157-164, August.
    7. Nicholas R. Miller, 2017. "Closeness matters: monotonicity failure in IRV elections with three candidates," Public Choice, Springer, vol. 173(1), pages 91-108, October.
    8. William V. Gehrlein, 2006. "Condorcet’s Paradox," Theory and Decision Library C, Springer, number 978-3-540-33799-7, March.
    9. Hannu Nurmi & Maria Suojanen, 2004. "Assessing Contestability of Electoral Outcomes," Quality & Quantity: International Journal of Methodology, Springer, vol. 38(6), pages 719-733, December.
    10. William Gehrlein & Peter Fishburn, 1976. "Condorcet's paradox and anonymous preference profiles," Public Choice, Springer, vol. 26(1), pages 1-18, June.
    11. Dan Felsenthal & Nicolaus Tideman, 2014. "Weak Condorcet winner(s) revisited," Public Choice, Springer, vol. 160(3), pages 313-326, September.
    12. Dominique Lepelley & Ahmed Louichi & Fabrice Valognes, 2000. "Computer simulations of voting systems," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 3(01n04), pages 181-194.
    13. Amartya Sen, 2020. "Majority decision and Condorcet winners," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 211-217, March.
    14. Tovey, Craig A., 1997. "Probabilities of Preferences and Cycles with Super Majority Rules," Journal of Economic Theory, Elsevier, vol. 75(2), pages 271-279, August.
    15. Murat R. Sertel & M. Remzi Sanver, 2004. "Strong equilibrium outcomes of voting games ¶are the generalized Condorcet winners," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(2), pages 331-347, April.
    16. Kasper, Laura & Peters, Hans & Vermeulen, Dries, 2019. "Condorcet Consistency and the strong no show paradoxes," Mathematical Social Sciences, Elsevier, vol. 99(C), pages 36-42.
    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. Mostapha Diss & Michele Gori, 2022. "Majority properties of positional social preference correspondences," Theory and Decision, Springer, vol. 92(2), pages 319-347, March.
    2. Eric Kamwa, 2019. "On the Likelihood of the Borda Effect: The Overall Probabilities for General Weighted Scoring Rules and Scoring Runoff Rules," Group Decision and Negotiation, Springer, vol. 28(3), pages 519-541, June.
    3. Eric Kamwa, 2018. "On the Likelihood of the Borda Effect: The Overall Probabilities for General Weighted Scoring Rules and Scoring Runoff Rules," Working Papers hal-01786590, HAL.
    4. Mostapha Diss & Eric Kamwa, 2019. "Simulations in Models of Preference Aggregation," Working Papers hal-02424936, HAL.
    5. Mostapha Diss & Patrizia Pérez-Asurmendi, 2015. "Consistent collective decisions under majorities based on difference of votes," Working Papers 1533, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    6. Dan S. Felsenthal & Hannu Nurmi, 2018. "Monotonicity Violations by Borda’s Elimination and Nanson’s Rules: A Comparison," Group Decision and Negotiation, Springer, vol. 27(4), pages 637-664, August.
    7. Moyouwou, Issofa & Tchantcho, Hugue, 2017. "Asymptotic vulnerability of positional voting rules to coalitional manipulation," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 70-82.
    8. Eric Kamwa, 2022. "Scoring Rules, Ballot Truncation, and the Truncation Paradox," Working Papers hal-03632662, HAL.
    9. Eric Kamwa, 2022. "Scoring rules, ballot truncation, and the truncation paradox," Public Choice, Springer, vol. 192(1), pages 79-97, July.
    10. Dougherty, Keith L. & Heckelman, Jac C., 2020. "The probability of violating Arrow’s conditions," European Journal of Political Economy, Elsevier, vol. 65(C).
    11. Mostapha Diss & Patrizia Pérez-Asurmendi, 2016. "Consistent collective decisions under majorities based on difference of votes," Theory and Decision, Springer, vol. 80(3), pages 473-494, March.
    12. Mostapha Diss & Patrizia Pérez-Asurmendi, 2015. "Consistent collective decisions under majorities based on difference of votes," Working Papers halshs-01241996, HAL.
    13. Eric Kamwa, 2021. "To what extent does the model of processing sincereincomplete rankings affect the likelihood of the truncation paradox?," Working Papers hal-02879390, HAL.
    14. Mostapha Diss & Eric Kamwa & Issofa Moyouwou & Hatem Smaoui, 2021. "Condorcet Efficiency of General Weighted Scoring Rules Under IAC: Indifference and Abstention," Studies in Choice and Welfare, in: Mostapha Diss & Vincent Merlin (ed.), Evaluating Voting Systems with Probability Models, pages 55-73, Springer.
    15. David McCune & Erin Martin & Grant Latina & Kaitlyn Simms, 2023. "A Comparison of Sequential Ranked-Choice Voting and Single Transferable Vote," Papers 2306.17341, arXiv.org.
    16. Gehrlein, William V. & Moyouwou, Issofa & Lepelley, Dominique, 2013. "The impact of voters’ preference diversity on the probability of some electoral outcomes," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 352-365.
    17. Sylvain Béal & Marc Deschamps & Mostapha Diss & Issofa Moyouwou, 2022. "Inconsistent weighting in weighted voting games," Public Choice, Springer, vol. 191(1), pages 75-103, April.
    18. Benoît R. Kloeckner, 2022. "Cycles in synchronous iterative voting: general robustness and examples in Approval Voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(2), pages 423-466, August.
    19. Sébastien Courtin & Boniface Mbih & Issofa Moyouwou, 2014. "Are Condorcet procedures so bad according to the reinforcement axiom?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 927-940, April.
    20. D. Marc Kilgour & Jean-Charles Grégoire & Angèle M. Foley, 2020. "The prevalence and consequences of ballot truncation in ranked-choice elections," Public Choice, Springer, vol. 184(1), pages 197-218, July.

    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:eee:matsoc:v:123:y:2023:i:c:p:128-136. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505565 .

    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.