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Self-Duality and Transfer in Voting Games

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  • Takaaki Abe

Abstract

This study examines the role of self-duality in the axiomatization of the Shapley-Shubik power index. We show that, when self-duality is imposed, the transfer axiom can be weakened to a restricted version requiring transfer only among voting games with no veto player. This result shows that self-duality can partially substitute for the transfer axiom.

Suggested Citation

  • Takaaki Abe, 2026. "Self-Duality and Transfer in Voting Games," Papers 2606.01018, arXiv.org, revised Jun 2026.
    • Handle: RePEc:arx:papers:2606.01018
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    1. Oishi, Takayuki & Nakayama, Mikio & Hokari, Toru & Funaki, Yukihiko, 2016. "Duality and anti-duality in TU games applied to solutions, axioms, and axiomatizations," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 44-53.
    2. Ezra Einy, 1987. "Semivalues of Simple Games," Mathematics of Operations Research, INFORMS, vol. 12(2), pages 185-192, May.
    3. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
    4. Einy, Ezra & Haimanko, Ori, 2011. "Characterization of the Shapley–Shubik power index without the efficiency axiom," Games and Economic Behavior, Elsevier, vol. 73(2), pages 615-621.
    5. 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.
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