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of each approach have improved and codified their techniques, reducing some of the problems identified by their critics but also gaining renewed appreciation for the remaining limits of their methods. The mix of methods has become fairly stable, at least in our own field, with each method secure in its ability to contribute to theoretical progress. In contrast to the sharp changes in methods used in journal articles in the 1960s and 1970s, the mix of methods used in articles in the top political science journals has been fairly stable since the mid-1980s, and in recent years roughly half of these articles used statistics, about the same proportion used case studies, slightly fewer than a quarter used formal models, and about one in five used more than one method.11

Moreover, a new generation of scholars has emerged with training in or at least exposure to more than one methodology, allowing easier translation among the different forms through which fundamental epistemological limits are embodied in different methods. Developments in the philosophy of science have also clarified the philosophical foundations of alternative approaches. Finally, the various fields in the social sciences have, at different speeds and to different degrees, addressed the historical, sociological, and postmodernist “turns” by focusing on norms, institutions, and actors’ identities and preferences, but doing so through largely neopositivist means. As a result, scholars are increasingly working collaboratively across methodological divides to advance shared substantive research programs. Most of this cross-method collaboration has taken place sequentially, as different researchers have used the methods in which they are most adept but have also drawn on the findings of those using other methods. Because cross-method collaboration in the social sciences has until recently rarely involved one or more individuals working on the same publication with different methods, it has been underappreciated.

A prerequisite for this revitalized methodological dialogue is a clear understanding of the comparative strengths and limits of various methods, and how they complement each other. This book contributes to this dialogue by focusing on the comparative advantages of case study methods and on these methods’ ability to contribute to the development of theories that can accommodate various forms of complex causality.

The case study approach—the detailed examination of an aspect of a historical episode to develop or test historical explanations that may be generalizable to other events—has come in and out of favor over the past five decades as researchers have explored the possibilities of statistical methods (which excel at estimating the generalized causal weight or causal effects of variables) and formal models (in which rigorous deductive logic is used to develop both intuitive and counterintuitive hypotheses about the dynamics of causal mechanisms). Perhaps because case study methods are somewhat intuitive—they have in some sense been around as long as recorded history—the systematic development of case study methods for the cumulative building of social science theories is a comparatively recent phenomenon (notwithstanding notable contributions to these methods by John Stuart Mill). Only in the past three de-cades have scholars formalized case study methods more completely and linked them to underlying arguments in the philosophy of science.

Indeed, statistical methods have been so prominent in recent decades that scholars’ understanding of case studies is often distorted by critiques based on the assumptions of statistical methods. We argue that while case studies share a similar epistemological logic with statistical methods and with formal modeling that is coupled with empirical research, these methods have different methodological logics. Epistemologically, all three approaches attempt to develop logically consistent models or theories, they derive observable implications from these theories, they test these implications against empirical observations