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A characterization of the maximin rule in the context of voting

Author

Listed:
  • Ronan Congar

    (CARE - Centre d'Analyse et de Recherche en Économie - UNIROUEN - Université de Rouen Normandie - NU - Normandie Université)

  • Vincent Merlin

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

Abstract

In a voting context, when the preferences of voters are described by linear orderings over a finite set of alternatives, the Maximin rule orders the alternatives according to their minimal rank in the voters' preferences. It is equivalent to the Fallback bargaining process described by Brams and Kilgour (Group Decision and Negotiation 10:287-316, 2001). This article proposes a characterization of the Maximin rule as a social welfare function (SWF) based upon five conditions: Neutrality, Duplication, Unanimity, Top Invariance, and Weak Separability. In a similar way, we obtain a characterization for the Maximax SWF by using Bottom Invariance instead of Top Invariance. Then, these results are compared to the axiomatic characterizations of two famous scoring rules, the Plurality rule and the Antiplurality rule.

Suggested Citation

  • Ronan Congar & Vincent Merlin, 2012. "A characterization of the maximin rule in the context of voting," Post-Print halshs-00554833, HAL.
    • Handle: RePEc:hal:journl:halshs-00554833
    DOI: 10.1007/s11238-010-9229-0
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    Cited by:

    1. Matías Núñez & M. Remzi Sanver, 2021. "On the subgame perfect implementability of voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(2), pages 421-441, February.
    2. Hatzivelkos, Aleksandar, 2024. "Note on compromise axiom," Mathematical Social Sciences, Elsevier, vol. 130(C), pages 38-47.
    3. Brian Hill, 2012. "Confidence in preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 273-302, July.
    4. 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.
    5. García-Lapresta, José Luis & Martínez-Panero, Miguel, 2024. "Two characterizations of the dense rank," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    6. Olivier Cailloux & Matías Núñez & M. Remzi Sanver, 2025. "Two principles for two-person social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 65(1), pages 69-89, August.
    7. Matias Nunez & M. Remzi Sanver, 2021. "On the subgame perfect implementability of voting rules," Post-Print hal-03341697, HAL.
    8. Federico Fioravanti & Jordi Massó, 2024. "False-name-proof and strategy-proof voting rules under separable preferences," Theory and Decision, Springer, vol. 97(2), pages 391-408, September.
    9. Vincent Merlin & İpek Özkal Sanver & M. Remzi Sanver, 2019. "Compromise Rules Revisited," Group Decision and Negotiation, Springer, vol. 28(1), pages 63-78, February.
    10. Damien Bol & Jean-François Laslier & Matías Núñez, 2022. "Two Person Bargaining Mechanisms: A Laboratory Experiment," Group Decision and Negotiation, Springer, vol. 31(6), pages 1145-1177, December.
    11. Olivier Cailloux & Beatrice Napolitano & M. Remzi Sanver, 2023. "Compromising as an equal loss principle," Review of Economic Design, Springer;Society for Economic Design, vol. 27(3), pages 547-560, September.
    12. Jos'e Luis Garc'ia-Lapresta & Miguel Mart'inez-Panero, 2023. "Two characterizations of the dense rank," Papers 2306.17546, arXiv.org.

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    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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