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A characterization of the maximin rule in the context of voting

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  • Ronan Congar
  • Vincent Merlin

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.
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Suggested Citation

  • Ronan Congar & Vincent Merlin, 2012. "A characterization of the maximin rule in the context of voting," Theory and Decision, Springer, vol. 72(1), pages 131-147, January.
    • Handle: RePEc:kap:theord:v:72:y:2012:i:1:p:131-147
    DOI: 10.1007/s11238-010-9229-0
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    References listed on IDEAS

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    1. Barbera, Salvador & Dutta, Bhaskar, 1986. "General, direct and self-implementation of social choice functions via protective equilibria," Mathematical Social Sciences, Elsevier, vol. 11(2), pages 109-127, April.
    2. Steven J. Brams & D. Marc Kilgour, 2001. "Fallback Bargaining," Group Decision and Negotiation, Springer, vol. 10(4), pages 287-316, July.
    3. 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.
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    7. Barbera, Salvador & Dutta, Bhaskar, 1982. "Implementability via protective equilibria," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 49-65, June.
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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. 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.
    3. 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.
    4. 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.
    5. García-Lapresta, José Luis & Martínez-Panero, Miguel, 2024. "Two characterizations of the dense rank," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    6. Matias Nunez & M. Remzi Sanver, 2021. "On the subgame perfect implementability of voting rules," Post-Print hal-03341697, HAL.
    7. 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.
    8. Vincent Merlin & İpek Özkal Sanver & M. Remzi Sanver, 2019. "Compromise Rules Revisited," Group Decision and Negotiation, Springer, vol. 28(1), pages 63-78, February.
    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.
    10. 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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    More about this item

    Keywords

    Maximin; Voting; Complete ignorance; Duplication; Separability; Scoring rules; D71;
    All these keywords.

    JEL classification:

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

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