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A new axiomatization of the Banzhaf semivalue

Author

Listed:
  • M. Josune Albizuri

    (Departamento de Economía Aplicada I, Facultad de Ciencias Económicas, Universidad del Pais Vasco, Avenida Lehendakari Agirre, 83, 48015 Bilbao, Spain)

  • Luis M. Ruiz

    (Departamento de Economía Aplicada I, Facultad de Ciencias Económicas, Universidad del Pais Vasco, Avenida Lehendakari Agirre, 83, 48015 Bilbao, Spain)

Abstract

A new characterization of the Banzhaf semivalue on the domain of monotonic simple games is given. We use the well-known valuation and dummy axioms plus two additional properties. The first one simply requires that the power-index be bigger for those players belonging to more winning coalitions. The second one is the proportionality axiom introduced by Owen in (1982) which is suitable for those simple games that represent an indirect voting process.

Suggested Citation

  • M. Josune Albizuri & Luis M. Ruiz, 2001. "A new axiomatization of the Banzhaf semivalue," Spanish Economic Review, Springer;Spanish Economic Association, vol. 3(2), pages 97-109.
    • Handle: RePEc:spr:specre:v:3:y:2001:i:2:p:97-109
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    Citations

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    Cited by:

    1. Ori Haimanko, 2019. "Composition independence in compound games: a characterization of the Banzhaf power index and the Banzhaf value," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(3), pages 755-768, September.
    2. Dubey, Pradeep & Einy, Ezra & Haimanko, Ori, 2005. "Compound voting and the Banzhaf index," Games and Economic Behavior, Elsevier, vol. 51(1), pages 20-30, April.
    3. Pradeep Dubey & Ezra Einy & Ori Haimanko, 2003. "Compound Voting and the Banzhaf Power Index," Discussion Paper Series dp333, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    4. Josep Freixas & Montserrat Pons, 2021. "An Appropriate Way to Extend the Banzhaf Index for Multiple Levels of Approval," Group Decision and Negotiation, Springer, vol. 30(2), pages 447-462, April.
    5. Josep Freixas & Roberto Lucchetti, 2016. "Power in voting rules with abstention: an axiomatization of a two components power index," Annals of Operations Research, Springer, vol. 244(2), pages 455-474, September.

    More about this item

    Keywords

    Banzhaf; power-index;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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