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Dilemma with approval and disapproval votes

Author

Listed:
  • Stéphane Gonzalez

    (Université de Saint-Etienne, UMR 5824 GATE Lyon Saint-Etienne)

  • Annick Laruelle

    (University of the Basque Country (UPV/EHU)
    Basque Foundation of Science)

  • Philippe Solal

    (Université de Saint-Etienne, UMR 5824 GATE Lyon Saint-Etienne)

Abstract

This paper looks at the issue of selecting candidates when the votes cast in ballots enable voters to approve or disapprove each candidate. More precisely, three options are offered: voters can approve, disapprove or remain neutral in regard to each candidate. We define a large family of rules that satisfy desirable properties and prove that solving a dilemma is sufficient to characterize any rule which belongs to this family. In this context a dilemma appears when candidates with only neutral votes face candidates with both supporters and opponents. On the basis of this result, we provide comparable axiomatizations of four rules including some proposed in the literature.

Suggested Citation

  • Stéphane Gonzalez & Annick Laruelle & Philippe Solal, 2019. "Dilemma with approval and disapproval votes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(3), pages 497-517, October.
    • Handle: RePEc:spr:sochwe:v:53:y:2019:i:3:d:10.1007_s00355-019-01194-6
    DOI: 10.1007/s00355-019-01194-6
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    References listed on IDEAS

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    7. Aleskerov, Fuad & Yakuba, Vyacheslav & Yuzbashev, Dmitriy, 2007. "A `threshold aggregation' of three-graded rankings," Mathematical Social Sciences, Elsevier, vol. 53(1), pages 106-110, January.
    8. José Alcantud & Annick Laruelle, 2014. "Dis&approval voting: a characterization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(1), pages 1-10, June.
    9. Gaertner, Wulf & Xu, Yongsheng, 2012. "A general scoring rule," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 193-196.
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    Citations

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    Cited by:

    1. Federica Ceron & Stéphane Gonzalez, 2019. "A characterization of Approval Voting without the approval balloting assumption," Working Papers halshs-02440615, HAL.
    2. Susumu Cato & Stéphane Gonzalez & Eric Rémila & Philippe Solal, 2022. "Approval voting versus proportional threshold methods: so far and yet so near," Working Papers halshs-03858356, HAL.
    3. Antoinette Baujard & Herrade Igersheim & Isabelle Lebon, 2021. "Some regrettable grading scale effects under different versions of evaluative voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(4), pages 803-834, May.
    4. Annick Laruelle, 2021. "“Not This One”: Experimental Use of the Approval and Disapproval Ballot," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 38(1), pages 15-28, December.
    5. Barberà, Salvador & Bossert, Walter, 2023. "Opinion aggregation: Borda and Condorcet revisited," Journal of Economic Theory, Elsevier, vol. 210(C).
    6. Antoinette Baujard & Herrade Igersheim & Isabelle Lebon, 2020. "Some regrettable grading scale effects under different versions of evaluative voting," Working Papers halshs-02926780, HAL.

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