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Closeness matters: monotonicity failure in IRV elections with three candidates


  • 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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    References listed on IDEAS

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    7. 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.
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    1. repec:kap:pubcho:v:173:y:2017:i:3:d:10.1007_s11127-017-0476-2 is not listed on IDEAS
    2. repec:spr:homoec:v:35:y:2018:i:1:d:10.1007_s41412-017-0055-2 is not listed on IDEAS
    3. repec:spr:grdene:v:27:y:2018:i:4:d:10.1007_s10726-018-9580-z is not listed on IDEAS


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