@article{63731,
  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.}},
  author       = {{Haake, Claus-Jochen and Schneider, Martin}},
  journal      = {{International Journal of Game Theory}},
  keywords     = {{Banzhaf index, axiomatization, QCA, explanatory power}},
  publisher    = {{Springer}},
  title        = {{{An Axiomatization of the Banzhaf Index to Measure Influence in Qualitative Comparative Analysis}}},
  doi          = {{10.1007/s00182-026-00978-2}},
  volume       = {{55}},
  year         = {{2026}},
}

@article{34114,
  abstract     = {{Qualitative comparative analysis (QCA) enables researchers in international management to better understand how the impact of a single explanatory factor depends on the context of other factors. But the analytical toolbox of QCA does not include a parameter for the explanatory power of a single explanatory factor or “condition”. In this paper, we therefore reinterpret the Banzhaf power index, originally developed in cooperative game theory, to establish a goodness-of-fit parameter in QCA. The relative Banzhaf index we suggest measures the explanatory power of one condition averaged across all sufficient combinations of conditions. The paper argues that the index is especially informative in three situations that are all salient in international management and call for a context-sensitive analysis of single conditions, namely substantial limited diversity in the data, the emergence of strong INUS conditions in the analysis, and theorizing with contingency factors. The paper derives the properties of the relative Banzhaf index in QCA, demonstrates how the index can be computed easily from a rudimentary truth table, and explores its insights by revisiting selected papers in international management that apply fuzzy-set QCA. It finally suggests a three-step procedure for utilizing the relative Banzhaf index when the causal structure involves both contingency effects and configurational causation.
}},
  author       = {{Haake, Claus-Jochen and Schneider, Martin}},
  journal      = {{Journal of International Management}},
  keywords     = {{Qualitative comparative analysis, Banzhaf power index, causality, explanatory power}},
  number       = {{2}},
  publisher    = {{Elsevier}},
  title        = {{{Playing games with QCA: Measuring the explanatory power of single conditions with the Banzhaf index}}},
  volume       = {{30}},
  year         = {{2024}},
}