An axiomatization of the Banzhaf index to measure influence in qualitative comparative analysis

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. This analysis of sufficiency is an integral part of Qualitative Comparative Analysis (QCA) widely used in the field of Business and International Management. Haake and Schneider (J Int Manag 30(2):101065, 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 an axiomatization of the Banzhaf index using 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.