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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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    References listed on IDEAS

    as
    1. Steven J. Brams & D. Marc Kilgour, 2001. "Fallback Bargaining," Group Decision and Negotiation, Springer, vol. 10(4), pages 287-316, July.
    2. Muller, Eitan & Satterthwaite, Mark A., 1977. "The equivalence of strong positive association and strategy-proofness," Journal of Economic Theory, Elsevier, vol. 14(2), pages 412-418, April.
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    5. Bilge Yilmaz & Murat R. Sertel, 1999. "The majoritarian compromise is majoritarian-optimal and subgame-perfect implementable," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 615-627.
    6. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    7. Fuad Aleskerov & Vyacheslav Chistyakov & Valery Kalyagin, 2010. "Social threshold aggregations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(4), pages 627-646, October.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    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. Vincent Merlin & İpek Özkal Sanver & M. Remzi Sanver, 2019. "Compromise Rules Revisited," Group Decision and Negotiation, Springer, vol. 28(1), pages 63-78, February.
    6. García-Lapresta, José Luis & Martínez-Panero, Miguel, 2024. "Two characterizations of the dense rank," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    7. Matias Nunez & M. Remzi Sanver, 2021. "On the subgame perfect implementability of voting rules," Post-Print hal-03341697, HAL.
    8. Jos'e Luis Garc'ia-Lapresta & Miguel Mart'inez-Panero, 2023. "Two characterizations of the dense rank," Papers 2306.17546, arXiv.org.
    9. 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.

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    More about this item

    Keywords

    maximin; voting; ignorance; duplication; separability; scoring rules;
    All these keywords.

    JEL classification:

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

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