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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 - UR1 - Université de Rennes 1 - UNIV-RENNES - 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
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00554833
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    References listed on IDEAS

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    1. repec:spr:grdene:v:10:y:2001:i:4:d:10.1023_a:1011252808608 is not listed on IDEAS
    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.
    3. 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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    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.
    8. Steven J. Brams & D. Marc Kilgour, 2001. "Fallback Bargaining," Group Decision and Negotiation, Springer, vol. 10(4), pages 287-316, July.
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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. repec:spr:grdene:v:24:y:2015:i:5:d:10.1007_s10726-014-9412-8 is not listed on IDEAS

    More about this item

    Keywords

    maximin; voting; ignorance; duplication; separability; scoring rules;

    JEL classification:

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

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