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The Axiom Of Equivalence To Individual Power And The Banzhaf Index

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  • Ori Haimanko

    (BGU)

Abstract

I introduce a new axiom for power indices on the domain of finite simple games that requires the total power of any given pair i,j of players in any given game v to be equivalent to some individual power, i.e., equal to the power of some single player k in some game w. I show that the Banzhaf power index is uniquely characterized by this new “equivalence to individual power” axiom in conjunction with the standard semivalue axioms: transfer (which is the version of additivity adapted for simple games), symmetry or equal treatment, positivity (which is strengthened to avoid zeroing-out of the index on some games), and dummy.
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Suggested Citation

  • Ori Haimanko, 2016. "The Axiom Of Equivalence To Individual Power And The Banzhaf Index," Working Papers 1604, Ben-Gurion University of the Negev, Department of Economics.
    • Handle: RePEc:bgu:wpaper:1604
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    References listed on IDEAS

    as
    1. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(2), pages 89-99.
    2. Marcin Malawski, 2002. "Equal treatment, symmetry and Banzhaf value axiomatizations," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(1), pages 47-67.
    3. Pradeep Dubey & Lloyd S. Shapley, 1979. "Mathematical Properties of the Banzhaf Power Index," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 99-131, May.
    4. Andrzej S. Nowak, 1997. "note: On an Axiomatization of the Banzhaf Value without the Additivity Axiom," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(1), pages 137-141.
    5. Ezra Einy, 1987. "Semivalues of Simple Games," Mathematics of Operations Research, INFORMS, vol. 12(2), pages 185-192, May.
    6. Pradeep Dubey & Abraham Neyman & Robert James Weber, 1981. "Value Theory Without Efficiency," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 122-128, February.
    7. André Casajus, 2012. "Amalgamating players, symmetry, and the Banzhaf value," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(3), pages 497-515, August.
    8. repec:cup:apsrev:v:48:y:1954:i:03:p:787-792_00 is not listed on IDEAS
    9. André Casajus, 2011. "Marginality, differential marginality, and the Banzhaf value," Theory and Decision, Springer, vol. 71(3), pages 365-372, September.
    10. 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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    2. André Casajus & Frank Huettner, 2019. "The Coleman–Shapley index: being decisive within the coalition of the interested," Public Choice, Springer, vol. 181(3), pages 275-289, December.
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    5. André Casajus & Rodrigue Tido Takeng, 2024. "Second-order productivity, second-order payoffs, and the Banzhaf value," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(3), pages 989-1004, September.

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    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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