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An Axiomatization of the Banzhaf Index to Measure Influence in Qualitative Comparative Analysis

Author

Listed:
  • Claus-Jochen Haake

    (Paderborn University)

  • Martin R. Schneider

    (Paderborn University)

Abstract

The Banzhaf power index can be used to quantify the explanatory power of single conditions in a configurational analysis that aims at identifying whether combinations of conditions are sufficient for an outcome. The latter method is an integral part of the Qualitative Comparative Analysis (QCA) approach. It is widely used in the literature, e.g., in the field of International Management. Haake and Schneider (2023) give a rigorous description of the connection between the empirical and game theoretic modeling. To justify that the Banzhaf index is an appropriate tool to measure the influence of a condition, this paper discusses a novel axiomatization of the Banzhaf index that uses axioms that are directly linked to the QCA methodology. As a side result, we demonstrate that in our model the Banzhaf index can be reinterpreted as an average of Shapley-Shubik indices.

Suggested Citation

  • Claus-Jochen Haake & Martin R. Schneider, 2025. "An Axiomatization of the Banzhaf Index to Measure Influence in Qualitative Comparative Analysis," Working Papers CIE 162, Paderborn University, CIE Center for International Economics.
    • Handle: RePEc:pdn:ciepap:162
    as

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    File URL: http://groups.uni-paderborn.de/wp-wiwi/RePEc/pdf/ciepap/WP162.pdf
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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. 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.
    3. Ragin, Charles C., 2000. "Fuzzy-Set Social Science," University of Chicago Press Economics Books, University of Chicago Press, edition 1, number 9780226702773, January.
    4. 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.
    5. Feltkamp, Vincent, 1995. "Alternative Axiomatic Characterizations of the Shapley and Banzhaf Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(2), pages 179-186.
    6. repec:ucp:bkecon:9780226702766 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Banzhaf index; axiomatization; QCA; explanatory power;
    All these keywords.

    JEL classification:

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

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