IDEAS home Printed from https://ideas.repec.org/a/kap/pubcho/v173y2017i1d10.1007_s11127-017-0465-5.html
   My bibliography  Save this article

Closeness matters: monotonicity failure in IRV elections with three candidates

Author

Listed:
  • Nicholas R. Miller

    (University of Maryland Baltimore County)

Abstract

A striking attribute of instant runoff voting (IRV) is that it is subject to monotonicity failure—that is, getting more (first-preference) votes may result in defeat for a candidate who would otherwise have won and getting fewer votes may result in victory for a candidate who otherwise would have lost. Proponents of IRV have argued that monotonicity failure, while a mathematical possibility, is highly unlikely to occur in practice. This paper specifies the precise conditions under which this phenomenon arises in three-candidate elections and applies them to a number of large simulated data sets in order to get a sense of the likelihood of IRV’s monotonicity problem in varying circumstances. The basic finding is that the problem is significant in many circumstances and very substantial when IRV elections are closely contested by three candidates.

Suggested Citation

  • Nicholas R. Miller, 2017. "Closeness matters: monotonicity failure in IRV elections with three candidates," Public Choice, Springer, vol. 173(1), pages 91-108, October.
  • Handle: RePEc:kap:pubcho:v:173:y:2017:i:1:d:10.1007_s11127-017-0465-5
    DOI: 10.1007/s11127-017-0465-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11127-017-0465-5
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s11127-017-0465-5?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. Dan S. Felsenthal, 2012. "Review of Paradoxes Afflicting Procedures for Electing a Single Candidate," Studies in Choice and Welfare, in: Dan S. Felsenthal & Moshé Machover (ed.), Electoral Systems, chapter 0, pages 19-91, Springer.
    2. Joseph Ornstein & Robert Norman, 2014. "Frequency of monotonicity failure under Instant Runoff Voting: estimates based on a spatial model of elections," Public Choice, Springer, vol. 161(1), pages 1-9, October.
    3. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    4. Felsenthal, Dan S. & Tideman, Nicolaus, 2014. "Interacting double monotonicity failure with direction of impact under five voting methods," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 57-66.
    5. Lepelley, Dominique & Chantreuil, Frederic & Berg, Sven, 1996. "The likelihood of monotonicity paradoxes in run-off elections," Mathematical Social Sciences, Elsevier, vol. 31(3), pages 133-146, June.
    6. 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.
    7. 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.
    8. Dan Felsenthal & Nicolaus Tideman, 2013. "Varieties of failure of monotonicity and participation under five voting methods," Theory and Decision, Springer, vol. 75(1), pages 59-77, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Conal Duddy, 2017. "Geometry of run-off elections," Public Choice, Springer, vol. 173(3), pages 267-288, December.
    2. David McCune, 2023. "Ranked Choice Bedlam in a 2022 Oakland School Director Election," Papers 2303.05985, arXiv.org.
    3. 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.
    4. Stensholt, Eivind, 2020. "Anomalies of Instant Runoff Voting," Discussion Papers 2020/6, Norwegian School of Economics, Department of Business and Management Science.
    5. Eric Kamwa, 2023. "On two voting systems that combine approval and preferences: fallback voting and preference approval voting," Public Choice, Springer, vol. 196(1), pages 169-205, July.
    6. Umut Keskin & M. Remzi Sanver & H. Berkay Tosunlu, 2022. "Monotonicity violations under plurality with a runoff: the case of French presidential elections," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(2), pages 305-333, August.
    7. Adam Graham-Squire & Matthew I. Jones & David McCune, 2024. "New fairness criteria for truncated ballots in multi-winner ranked-choice elections," Papers 2408.03926, arXiv.org.
    8. Adam Graham-Squire & David McCune, 2022. "A Mathematical Analysis of the 2022 Alaska Special Election for US House," Papers 2209.04764, arXiv.org, revised Nov 2022.
    9. Adam Graham-Squire & David McCune, 2023. "Paradoxical Oddities in Two Multiwinner Elections from Scotland," Papers 2305.20078, arXiv.org.
    10. Stensholt, Eivind, 2019. "MMP-elections and the assembly size," Discussion Papers 2019/15, Norwegian School of Economics, Department of Business and Management Science.
    11. Eric Kamwa, 2023. "On Two Voting systems that combine approval and preferences: Fallback Voting and Preference Approval Voting," Working Papers hal-03614585, HAL.
    12. William V. Gehrlein & Dominique Lepelley & Florenz Plassmann, 2018. "An Evaluation of the Benefit of Using Two-Stage Election Procedures," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 35(1), pages 53-79, June.
    13. Adam Graham-Squire & David McCune, 2023. "An Examination of Ranked Choice Voting in the United States, 2004-2022," Papers 2301.12075, arXiv.org, revised Mar 2023.
    14. 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.
    15. 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.
    16. David McCune & Jennifer Wilson, 2023. "Ranked-choice voting and the spoiler effect," Public Choice, Springer, vol. 196(1), pages 19-50, July.
    17. David McCune & Adam Graham-Squire, 2023. "Monotonicity Anomalies in Scottish Local Government Elections," Papers 2305.17741, arXiv.org, revised Oct 2023.

    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. 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.
    2. Dominique Lepelley & Issofa Moyouwou & Hatem Smaoui, 2018. "Monotonicity paradoxes in three-candidate elections using scoring elimination rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(1), pages 1-33, January.
    3. 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.
    4. David McCune & Jennifer Wilson, 2023. "Ranked-choice voting and the spoiler effect," Public Choice, Springer, vol. 196(1), pages 19-50, July.
    5. Wesley H. Holliday & Eric Pacuit, 2021. "Measuring Violations of Positive Involvement in Voting," Papers 2106.11502, arXiv.org.
    6. Hatem Smaoui & Dominique Lepelley & Issofa Moyouwou, 2016. "Borda elimination rule and monotonicity paradoxes in three-candidate elections," Economics Bulletin, AccessEcon, vol. 36(3), pages 1722-1728.
    7. David McCune & Adam Graham-Squire, 2023. "Monotonicity Anomalies in Scottish Local Government Elections," Papers 2305.17741, arXiv.org, revised Oct 2023.
    8. Hannu Nurmi, 2020. "The Incidence of Some Voting Paradoxes Under Domain Restrictions," Group Decision and Negotiation, Springer, vol. 29(6), pages 1107-1120, December.
    9. Umut Keskin & M. Remzi Sanver & H. Berkay Tosunlu, 2022. "Monotonicity violations under plurality with a runoff: the case of French presidential elections," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(2), pages 305-333, August.
    10. 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.
    11. Dominique Lepelley & Hatem Smaoui, 2019. "Comparing Two Ways for Eliminating Candidates in Three-Alternative Elections Using Sequential Scoring Rules," Group Decision and Negotiation, Springer, vol. 28(4), pages 787-804, August.
    12. Moyouwou, Issofa & Tchantcho, Hugue, 2017. "Asymptotic vulnerability of positional voting rules to coalitional manipulation," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 70-82.
    13. Eric Kamwa & Vincent Merlin & Faty Mbaye Top, 2023. "Scoring Run-off Rules, Single-peaked Preferences and Paradoxes of Variable Electorate," Working Papers hal-03143741, HAL.
    14. 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.
    15. Conal Duddy, 2017. "Geometry of run-off elections," Public Choice, Springer, vol. 173(3), pages 267-288, December.
    16. Richard B. Darlington, 2023. "The case for minimax-TD," Constitutional Political Economy, Springer, vol. 34(3), pages 410-420, September.
    17. Conal Duddy, 2014. "Condorcet’s principle and the strong no-show paradoxes," Theory and Decision, Springer, vol. 77(2), pages 275-285, August.
    18. Tomas J. McIntee, 2017. "A geometric model of sensitivity of multistage elections to change," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(1), pages 89-115, June.
    19. Eric Kamwa & Issofa Moyouwou, 2019. "Susceptibility to Manipulation by Sincere Truncation : the Case of Scoring Rules and Scoring Runoff Systems," Working Papers hal-02185965, HAL.
    20. Adam Graham-Squire & David McCune, 2022. "A Mathematical Analysis of the 2022 Alaska Special Election for US House," Papers 2209.04764, arXiv.org, revised Nov 2022.

    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:kap:pubcho:v:173:y:2017:i:1:d:10.1007_s11127-017-0465-5. 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.