Playing games with QCA: Measuring the explanatory power of single conditions with the Banzhaf index

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 tool box 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 as 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, 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 the QCA context, 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. The discussion section offers routes for exploring further how the relative Banzhaf and other power indexes can be applied in QCA.