Set-theoretic methods and Qualitative Comparative Analysis (QCA) in particular are case-based methods. There are, however, only few guidelines on how to combine them with qualitative case studies. Contributing to the literature on multi-method research (MMR), we offer the first comprehensive elaboration of principles for the integration of QCA and case studies with a special focus on case selection. We show that QCA's reliance on setrelational causation in terms of necessity and sufficiency has important consequences for the choice of cases. Using real world data for both crispset and fuzzy-set QCA, we show what typical and deviant cases are in QCAbased MMR. In addition, we demonstrate how to select cases for comparative case studies aiming to discern causal mechanisms and address the puzzles behind deviant cases. Finally, we detail the implications of modifying the set-theoretic cross-case model in the light of case-study evidence. Following the principles developed in this article should increase the inferential leverage of set-theoretic MMR.

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In recent years, there has been increasing interest in the combination of two methods on the basis of set theory. In our introduction and this special issue, we focus on two variants of cross-case set-theoretic methods—qualitative comparative analysis (QCA) and typological theory (TT)—and their combination with process tracing (PT). Our goal is to broaden and deepen set-theoretic empirical research and equip scholars with guidance on how to implement it in multimethod research (MMR). At first glance, set-theoretic cross-case methods and PT seem to be highly compatible when causal relationships are conceptualized in terms of set theory. However, multiple issues have not so far been thoroughly addressed. Our article builds on the emerging MMR literature and seeks to enhance it in four ways. First, we offer a comprehensive and coherent elaboration of the two sequences in which case studies can be combined with a cross-case method. Second, we expand the perspective and discuss QCA and TT as two alternative methods for the cross-case analysis. Third, based on the idea of analytical priority, we introduce the distinction between a condition-centered and a mechanism-centered variant of set-theoretic MMR. Fourth, we point attention to the challenges of theorizing and analyzing arrangements of conditions and mechanisms associated with sufficient conjunctions.

The combination of Qualitative Comparative Analysis (QCA) with process tracing, which we call set-theoretic multimethod research (MMR), is steadily becoming more popular in empirical research. Despite the fact that both methods have an elected affinity based on set theory, it is not obvious how a within-case method operating in a single case and a cross-case method operating on a population of cases are compatible and can be combined in empirical research. There is a need to reflect on whether and how set-theoretic MMR is internally coherent and how QCA and process tracing can be integrated in causal analysis. We develop a unifying foundation for causal analysis in set-theoretic MMR that highlights the roles and interplay of QCA and process tracing. We argue that causal inference via counterfactuals on the level of single cases integrates QCA and process tracing and assigns proper and equally valuable roles to both methods.