Case studies nested in fuzzy-set QCA on sufficiency: formalizing case selection and causal inference

Qualitative Comparative Analysis (QCA) is a method for cross-case analyses that works best when complemented with follow-up case studies focusing on the causal quality of the solution and its constitutive terms, the underlying causal mechanisms, and potentially omitted conditions. The anchorage of QCA in set theory demands criteria for follow-up case studies that are distinctively different from those known from regression-based multi-method research (MMR). Based on the evolving research on set-theoretic MMR, we introduce principles for formalized case selection and causal inference after a fuzzy-set QCA on sufficiency. Using an empirical example for illustration, we elaborate on the principles of counterfactuals for intelligible causal inference in the analysis of three different types of cases. Furthermore, we explain how case-based counterfactual inferences on the basis of QCA solutions are related to counterfactuals in the course of processing a truth table in order to produce a solution. We then elaborate on two important functions that ideal types play for QCA-based case studies: first, they inform the development of formulas for the choice of the best available cases for with-case analysis and, second, establish the boundaries of generalization of the causal inferences.