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Varieties of failure of monotonicity and participation under five voting methods

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  • Dan Felsenthal
  • Nicolaus Tideman

Abstract

In voting theory, monotonicity is the axiom that an improvement in the ranking of a candidate by voters cannot cause a candidate who would otherwise win to lose. The participation axiom states that the sincere report of a voter’s preferences cannot cause an outcome that the voter regards as less attractive than the one that would result from the voter’s non-participation. This article identifies three binary distinctions in the types of circumstances in which failures of monotonicity or participation can occur. Two of the three distinctions apply to monotonicity, while one of those and the third apply to participation. The distinction that is unique to monotonicity is whether the voters whose changed rankings demonstrate non-monotonicity are better off or worse off. The distinction that is unique to participation is whether the marginally participating voter causes his first choice to lose or his last choice to win. The overlapping distinction is whether the profile of voters’ rankings has a Condorcet winner or a cycle at the top. This article traces the occurrence of all of the resulting combination of characteristics in the voting methods that can exhibit failures of monotonicity. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • 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.
    • Handle: RePEc:kap:theord:v:75:y:2013:i:1:p:59-77
    DOI: 10.1007/s11238-012-9306-7
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    References listed on IDEAS

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    1. Richard Potthoff, 2011. "Condorcet Polling," Public Choice, Springer, vol. 148(1), pages 67-86, July.
    2. Moulin, Herve, 1988. "Condorcet's principle implies the no show paradox," Journal of Economic Theory, Elsevier, vol. 45(1), pages 53-64, June.
    3. Jerry S. Kelly & Donald E. Campbell, 2002. "Non-monotonicity does not imply the no-show paradox," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(3), pages 513-515.
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    Citations

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    Cited by:

    1. 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.
    2. Uuganbaatar Ninjbat, 2015. "Impossibility theorems are modified and unified," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 849-866, December.
    3. 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.
    4. David McCune, 2024. "Single Transferable Vote and Paradoxes of Negative and Positive Involvement," Papers 2406.20045, arXiv.org, revised Nov 2024.
    5. Hannu Nurmi, 2020. "The Incidence of Some Voting Paradoxes Under Domain Restrictions," Group Decision and Negotiation, Springer, vol. 29(6), pages 1107-1120, December.
    6. Wesley H. Holliday & Eric Pacuit, 2021. "Measuring Violations of Positive Involvement in Voting," Papers 2106.11502, arXiv.org.
    7. Conal Duddy, 2014. "Condorcet’s principle and the strong no-show paradoxes," Theory and Decision, Springer, vol. 77(2), pages 275-285, August.
    8. 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.
    9. 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.
    10. Nicholas R. Miller, 2017. "Closeness matters: monotonicity failure in IRV elections with three candidates," Public Choice, Springer, vol. 173(1), pages 91-108, October.
    11. 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.
    12. David McCune & Jennifer Wilson, 2023. "Ranked-choice voting and the spoiler effect," Public Choice, Springer, vol. 196(1), pages 19-50, July.
    13. 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.
    14. 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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    More about this item

    Keywords

    Elections; Non-monotonicity; Participation; Strategic voting; Voting paradoxes; Voting methods; Voting procedures; D71; D72;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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