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<titleInfo><title>An Axiomatization of the Banzhaf Index to Measure Influence in Qualitative Comparative Analysis</title></titleInfo>




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  <namePart type="given">Claus-Jochen</namePart>
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  <namePart type="given">Martin</namePart>
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<abstract lang="eng">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.</abstract>

<originInfo><publisher>Springer</publisher><dateIssued encoding="w3cdtf">2026</dateIssued>
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<language><languageTerm authority="iso639-2b" type="code">eng</languageTerm>
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<subject><topic>Banzhaf index</topic><topic>axiomatization</topic><topic>QCA</topic><topic>explanatory power</topic>
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<relatedItem type="host"><titleInfo><title>International Journal of Game Theory</title></titleInfo><identifier type="doi">10.1007/s00182-026-00978-2</identifier>
<part><detail type="volume"><number>55</number></detail>
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<apa>Haake, C.-J., &amp;#38; Schneider, M. (2026). An Axiomatization of the Banzhaf Index to Measure Influence in Qualitative Comparative Analysis. &lt;i&gt;International Journal of Game Theory&lt;/i&gt;, &lt;i&gt;55&lt;/i&gt;. &lt;a href=&quot;https://doi.org/10.1007/s00182-026-00978-2&quot;&gt;https://doi.org/10.1007/s00182-026-00978-2&lt;/a&gt;</apa>
<short>C.-J. Haake, M. Schneider, International Journal of Game Theory 55 (2026).</short>
<mla>Haake, Claus-Jochen, and Martin Schneider. “An Axiomatization of the Banzhaf Index to Measure Influence in Qualitative Comparative Analysis.” &lt;i&gt;International Journal of Game Theory&lt;/i&gt;, vol. 55, Springer, 2026, doi:&lt;a href=&quot;https://doi.org/10.1007/s00182-026-00978-2&quot;&gt;10.1007/s00182-026-00978-2&lt;/a&gt;.</mla>
<bibtex>@article{Haake_Schneider_2026, title={An Axiomatization of the Banzhaf Index to Measure Influence in Qualitative Comparative Analysis}, volume={55}, DOI={&lt;a href=&quot;https://doi.org/10.1007/s00182-026-00978-2&quot;&gt;10.1007/s00182-026-00978-2&lt;/a&gt;}, journal={International Journal of Game Theory}, publisher={Springer}, author={Haake, Claus-Jochen and Schneider, Martin}, year={2026} }</bibtex>
<ama>Haake C-J, Schneider M. An Axiomatization of the Banzhaf Index to Measure Influence in Qualitative Comparative Analysis. &lt;i&gt;International Journal of Game Theory&lt;/i&gt;. 2026;55. doi:&lt;a href=&quot;https://doi.org/10.1007/s00182-026-00978-2&quot;&gt;10.1007/s00182-026-00978-2&lt;/a&gt;</ama>
<chicago>Haake, Claus-Jochen, and Martin Schneider. “An Axiomatization of the Banzhaf Index to Measure Influence in Qualitative Comparative Analysis.” &lt;i&gt;International Journal of Game Theory&lt;/i&gt; 55 (2026). &lt;a href=&quot;https://doi.org/10.1007/s00182-026-00978-2&quot;&gt;https://doi.org/10.1007/s00182-026-00978-2&lt;/a&gt;.</chicago>
<ieee>C.-J. Haake and M. Schneider, “An Axiomatization of the Banzhaf Index to Measure Influence in Qualitative Comparative Analysis,” &lt;i&gt;International Journal of Game Theory&lt;/i&gt;, vol. 55, 2026, doi: &lt;a href=&quot;https://doi.org/10.1007/s00182-026-00978-2&quot;&gt;10.1007/s00182-026-00978-2&lt;/a&gt;.</ieee>
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