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Approval voting, Condorcet's principle, and runoff elections

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  • Peter Fishburn
  • Steven Brams

Abstract

Approval voting allows each voter to vote for as many candidates as he wishes in an election but not cast more than one vote for each candidate of whom he approves. If there is a strict Condorcet candidate — a candidate who defeats all others in pairwise contests — approval voting is shown to be the only nonranked voting system that is always able to elect the strict Condorcet candidate when voters use sincere admissible strategies. Moreover, if a strict Condorcet candidate must be elected under ordinary plurality voting when voters use admissible strategies, then he must also be elected under approval voting when voters use admissible strategies, but the converse does not hold. The widely used plurality runoff method can also elect a strict Condorcet candidate when voters use admissible strategies on the first ballot, but some of these may have to be insincere to get the strict Condorcet candidate onto the runoff ballot. Furthermore, there is no case in which the strict Condorcet candidate is invariably elected under the plurality runoff method when voters use admissible first-ballot strategies. Thus, approval voting is superior to the plurality runoff method with respect to the Condorcet principle in its ability to elect the strict Condorcet candidate by sincere voting and in its ability to guarantee the election of the strict Condorcet candidate when voters use admissible strategies. In addition, approval voting is more efficient since it requires only one election and is probably less subject to strategic manipulation. Copyright Martinus Nijhoff Publishers bv 1981

Suggested Citation

  • Peter Fishburn & Steven Brams, 1981. "Approval voting, Condorcet's principle, and runoff elections," Public Choice, Springer, vol. 36(1), pages 89-114, January.
    • Handle: RePEc:kap:pubcho:v:36:y:1981:i:1:p:89-114
    DOI: 10.1007/BF00163773
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    Citations

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    Cited by:

    1. Mostapha Diss & Ahmed Doghmi, 2016. "Multi-winner scoring election methods: Condorcet consistency and paradoxes," Public Choice, Springer, vol. 169(1), pages 97-116, October.
    2. Begoña Subiza & Josep E. Peris, 2017. "A Representative Committee by Approval Balloting," Group Decision and Negotiation, Springer, vol. 26(5), pages 1029-1040, September.
    3. Francesco Sinopoli & Giovanna Iannantuoni & Carlos Pimienta, 2014. "Counterexamples on the Superiority of Approval versus Plurality," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 16(5), pages 824-834, October.
    4. Subiza, Begoña & Peris, Josep E., 2014. "A Consensual Committee Using Approval Balloting," QM&ET Working Papers 14-5, University of Alicante, D. Quantitative Methods and Economic Theory.
    5. Athanasios Spyridakos & Denis Yannacopoulos, 2015. "Incorporating collective functions to multicriteria disaggregation–aggregation approaches for small group decision making," Annals of Operations Research, Springer, vol. 227(1), pages 119-136, April.
    6. Jeffrey O’Neill, 2007. "Choosing a runoff election threshold," Public Choice, Springer, vol. 131(3), pages 351-364, June.
    7. Postl, Peter, 2017. "Évaluation et comparaison des règles de vote derrière le voile de l’ignorance : Tour d'horizon sélectif et analyse des règles de scores à deux paramètres," L'Actualité Economique, Société Canadienne de Science Economique, vol. 93(1-2), pages 249-290, Mars-Juin.
    8. DE SINOPOLI, Francesco, 1999. "Two examples of strategic equilibria in approval voting games," LIDAM Discussion Papers CORE 1999031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Francesco Sinopoli & Giovanna Iannantuoni & Carlos Pimienta, 2015. "On stable outcomes of approval, plurality, and negative plurality games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(4), pages 889-909, April.
    10. Matias Nuñez, 2010. "Condorcet Consistency of Approval Voting: a Counter Example in Large Poisson Games," Journal of Theoretical Politics, , vol. 22(1), pages 64-84, January.
    11. Joshua Holzer, 2020. "The effect of two-round presidential elections on human rights," PLOS ONE, Public Library of Science, vol. 15(12), pages 1-15, December.
    12. Dellis, Arnaud & Oak, Mandar P., 2006. "Approval voting with endogenous candidates," Games and Economic Behavior, Elsevier, vol. 54(1), pages 47-76, January.

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