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A general model for dealing with ranking voting systems

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  • Llamazares, Bonifacio

Abstract

A key problem in decision-making is selecting a winning candidate or establishing a global ranking for a set of candidates when individuals’ preferences are expressed through linear orders. Scoring rules are a specific case of positional voting systems (PVSs) that are widely used in sports competitions. Likewise, some scoring rules, such as the Borda rule and plurality, have also been extensively analyzed in the field of social choice. However, the choice of the scoring vector may significantly influence the results, leading to the development of models that avoid subjective vector selection. In this paper, we introduce a general model that encompasses some previous proposals present in the literature. Our model does not have an important deficiency that some other models do, such as the fact that the relative order between two candidates may change even if there is no variation in the positions obtained by those candidates. We give an explicit formula for calculating candidate scores, enabling direct determination of winners or rankings without solving the model for each candidate, and we also analyze the fulfillment of some well-known properties. Likewise, through theoretical analysis and examples, we identify and rule out specific PVSs that may yield questionable outcomes.

Suggested Citation

  • Llamazares, Bonifacio, 2026. "A general model for dealing with ranking voting systems," European Journal of Operational Research, Elsevier, vol. 329(3), pages 1004-1014.
    • Handle: RePEc:eee:ejores:v:329:y:2026:i:3:p:1004-1014
    DOI: 10.1016/j.ejor.2025.07.061
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    References listed on IDEAS

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    1. Elliot Anshelevich & Aris Filos-Ratsikas & Nisarg Shah & Alexandros A. Voudouris, 2021. "Distortion in Social Choice Problems: The First 15 Years and Beyond," Papers 2103.00911, arXiv.org.
    2. Paolo Viappiani, 2024. "Volumetric Aggregation Methods for Scoring Rules with Unknown Weights," Group Decision and Negotiation, Springer, vol. 33(3), pages 515-563, June.
    3. Dan S. Felsenthal, 2012. "Review of Paradoxes Afflicting Procedures for Electing a Single Candidate," Studies in Choice and Welfare, in: Dan S. Felsenthal & Moshé Machover (ed.), Electoral Systems, chapter 0, pages 19-91, Springer.
    4. 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.
    5. Paolo Viappiani, 2020. "Robust winner determination in positional scoring rules with uncertain weights," Theory and Decision, Springer, vol. 88(3), pages 323-367, April.
    6. Stein, William E. & Mizzi, Philip J. & Pfaffenberger, Roger C., 1994. "A stochastic dominance analysis of ranked voting systems with scoring," European Journal of Operational Research, Elsevier, vol. 74(1), pages 78-85, April.
    7. Foroughi, A.A. & Tamiz, M., 2005. "An effective total ranking model for a ranked voting system," Omega, Elsevier, vol. 33(6), pages 491-496, December.
    8. Llamazares, Bonifacio & Peña, Teresa, 2013. "Aggregating preferences rankings with variable weights," European Journal of Operational Research, Elsevier, vol. 230(2), pages 348-355.
    9. Green, Rodney H. & Doyle, John R. & Cook, Wade D., 1996. "Preference voting and project ranking using DEA and cross-evaluation," European Journal of Operational Research, Elsevier, vol. 90(3), pages 461-472, May.
    10. Wade D. Cook & Moshe Kress, 1990. "A Data Envelopment Model for Aggregating Preference Rankings," Management Science, INFORMS, vol. 36(11), pages 1302-1310, November.
    11. Paolo Viappiani, 2024. "Volumetric Aggregation Methods for Scoring Rules with Unknown Weights," Post-Print hal-04440153, HAL.
    12. Walter Bossert & Kotaro Suzumura, 2020. "Positionalist voting rules: a general definition and axiomatic characterizations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(1), pages 85-116, June.
    13. Bonifacio Llamazares, 2016. "Ranking Candidates Through Convex Sequences of Variable Weights," Group Decision and Negotiation, Springer, vol. 25(3), pages 567-584, May.
    14. Llamazares, Bonifacio & Pea, Teresa, 2009. "Preference aggregation and DEA: An analysis of the methods proposed to discriminate efficient candidates," European Journal of Operational Research, Elsevier, vol. 197(2), pages 714-721, September.
    15. Dan Felsenthal & Nicolaus Tideman, 2014. "Weak Condorcet winner(s) revisited," Public Choice, Springer, vol. 160(3), pages 313-326, September.
    16. Mats Danielson & Love Ekenberg, 2017. "A Robustness Study of State-of-the-Art Surrogate Weights for MCDM," Group Decision and Negotiation, Springer, vol. 26(4), pages 677-691, July.
    17. Carrizosa, E. & Conde, E. & Fernandez, F. R. & Puerto, J., 1995. "Multi-criteria analysis with partial information about the weighting coefficients," European Journal of Operational Research, Elsevier, vol. 81(2), pages 291-301, March.
    18. Fishburn, Peter C., 1974. "Paradoxes of Voting," American Political Science Review, Cambridge University Press, vol. 68(2), pages 537-546, June.
    19. Ahn, Byeong Seok, 2017. "Approximate weighting method for multiattribute decision problems with imprecise parameters," Omega, Elsevier, vol. 72(C), pages 87-95.
    20. Obata, Tsuneshi & Ishii, Hiroaki, 2003. "A method for discriminating efficient candidates with ranked voting data," European Journal of Operational Research, Elsevier, vol. 151(1), pages 233-237, November.
    21. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    22. 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.
    23. Hashimoto, Akihiro, 1997. "A ranked voting system using a DEA/AR exclusion model: A note," European Journal of Operational Research, Elsevier, vol. 97(3), pages 600-604, March.
    24. Paolo Viappiani, 2020. "Robust Winner Determination in Positional Scoring Rules with Uncertain Weights," Post-Print hal-02373399, HAL.
    25. Y M Wang & K S Chin & J B Yang, 2007. "Three new models for preference voting and aggregation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(10), pages 1389-1393, October.
    26. Aleksei Y. Kondratev & Egor Ianovski & Alexander S. Nesterov, 2024. "How Should We Score Athletes and Candidates: Geometric Scoring Rules," Operations Research, INFORMS, vol. 72(6), pages 2507-2525, November.
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