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Positional Voting Systems Generated by Cumulative Standings Functions

Author

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  • Bonifacio Llamazares

    (Universidad de Valladolid)

  • Teresa Peña

    (Universidad de Valladolid)

Abstract

Positional voting systems are a class of voting systems where voters rank order the candidates from best to worst and a set of winners is selected using the positions of the candidates in the voters’ preference orders. Although scoring rules are the best known positional voting systems, this class includes other voting systems proposed in the literature as, for example, the Majoritarian Compromise or the $$q$$ q -Approval Fallback Bargaining. In this paper we show that some of these positional voting systems can be integrated in a model based on cumulative standings functions. The proposed model allows us to establish a general framework for the analysis of these voting systems, to extend to them some results in the literature for the particular case of the scoring rules, and also facilitates the study of the social choice properties considered in the paper: monotonicity, Pareto-optimality, immunity to the absolute winner paradox, Condorcet consistency, immunity to the absolute loser paradox and immunity to the Condorcet loser paradox.

Suggested Citation

  • Bonifacio Llamazares & Teresa Peña, 2015. "Positional Voting Systems Generated by Cumulative Standings Functions," Group Decision and Negotiation, Springer, vol. 24(5), pages 777-801, September.
    • Handle: RePEc:spr:grdene:v:24:y:2015:i:5:d:10.1007_s10726-014-9412-8
    DOI: 10.1007/s10726-014-9412-8
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    References listed on IDEAS

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    Cited by:

    1. Raúl Pérez-Fernández & Bernard De Baets, 2017. "Recursive Monotonicity of the Scorix: Borda Meets Condorcet," Group Decision and Negotiation, Springer, vol. 26(4), pages 793-813, July.
    2. Mostapha Diss & Clinton Gubong Gassi & Issofa Moyouwou, 2023. "Social acceptability and the majoritarian compromise rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(3), pages 489-510, October.
    3. Bonifacio Llamazares, 2016. "Ranking Candidates Through Convex Sequences of Variable Weights," Group Decision and Negotiation, Springer, vol. 25(3), pages 567-584, May.
    4. Paolo Viappiani, 2024. "Volumetric Aggregation Methods for Scoring Rules with Unknown Weights," Post-Print hal-04440153, HAL.
    5. Raúl Pérez-Fernández & Bernard De Baets, 2019. "The superdominance relation, the positional winner, and more missing links between Borda and Condorcet," Journal of Theoretical Politics, , vol. 31(1), pages 46-65, January.
    6. Llamazares, Bonifacio, 2024. "Ranking voting systems and surrogate weights: Explicit formulas for centroid weights," European Journal of Operational Research, Elsevier, vol. 317(3), pages 967-976.
    7. Paolo Viappiani, 2020. "Robust winner determination in positional scoring rules with uncertain weights," Theory and Decision, Springer, vol. 88(3), pages 323-367, April.
    8. Marcella Maia Urtiga & Danielle Costa Morais & Keith W. Hipel & D. Marc Kilgour, 2017. "Group Decision Methodology to Support Watershed Committees in Choosing Among Combinations of Alternatives," Group Decision and Negotiation, Springer, vol. 26(4), pages 729-752, July.

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