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Closeness matters: monotonicity failure in IRV elections with three candidates

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  • 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
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    Cited by:

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    2. Eric Kamwa, 2023. "On Two Voting systems that combine approval and preferences: Fallback Voting and Preference Approval Voting," Working Papers hal-03614585, HAL.
    3. 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.
    4. David McCune, 2023. "Ranked Choice Bedlam in a 2022 Oakland School Director Election," Papers 2303.05985, arXiv.org.
    5. 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.
    6. Maciel, Marcelo Veloso, 2024. "Was Bolsonaro’s 2018 electoral victory an institutional accident?," European Journal of Political Economy, Elsevier, vol. 83(C).
    7. 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.
    8. David McCune & Adam Graham-Squire, 2024. "Monotonicity anomalies in Scottish local government elections," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 63(1), pages 69-101, August.
    9. Stensholt, Eivind, 2020. "Anomalies of Instant Runoff Voting," Discussion Papers 2020/6, Norwegian School of Economics, Department of Business and Management Science.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. David McCune & Jennifer Wilson, 2023. "Ranked-choice voting and the spoiler effect," Public Choice, Springer, vol. 196(1), pages 19-50, July.
    15. 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.
    16. 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.
    17. Adam Graham-Squire & David McCune, 2023. "Paradoxical Oddities in Two Multiwinner Elections from Scotland," Papers 2305.20078, arXiv.org.
    18. David McCune & Adam Graham-Squire, 2023. "Monotonicity Anomalies in Scottish Local Government Elections," Papers 2305.17741, arXiv.org, revised Oct 2023.
    19. Stensholt, Eivind, 2019. "MMP-elections and the assembly size," Discussion Papers 2019/15, Norwegian School of Economics, Department of Business and Management Science.

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