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relationship. While the less ambitious uses of typologies may facilitate the development of theory, they do not in themselves constitute theory. As Paul Diesing has noted, types and typologies are at best only implicit theories or starting points for theory construction; hence “typologies must eventually be controlled by [explicit] theory of some sort to be reliable.”474 Even if it exhibits a perfect correlation among a set of factors, a typology alone cannot separate causal from spurious factors, or possible from unlikely or impossible combinations of variables.

However, the finding of a typological regularity can spur the search for underlying theoretical explanations or typological theories, which can then be tested through within-case analysis. For example, in research on the democratic peace, the findings of correlations among types of states and wars preceded the development of satisfying theoretical explanations for these correlations. The types of states and wars have become more refined at each stage of this process, including a shift from a general democratic peace to an interdemocratic peace, from democracies in general to transitional, parliamentary, and presidential democracies, and from wars to various levels and kinds of militarized interstate disputes. Our focus is on this more ambitious use of case studies to move from typologies to the development of typological theories, and on the use of typological theories for the design of case study research and the selection of cases to study.

Inductive and Deductive Means of Developing Typological Theories

Typological theories may be constructed through either inductive or deductive modes of inquiry. In many research projects and research programs, a combination of induction and deduction is useful or even necessary, depending upon the research objective, state of development of the research program in question, and availability of relevant cases to study. Case studies can contribute to the inductive development of typological theories in the early stages of a research program by identifying an initial list of possible theoretical variables. In the later stages of a research program’s development, when theories have already been established and tested to some extent, the inductive study of deviant cases that do not fit the existing theory may refine the typological theory and perhaps add new variables or a new causal path to it.475 Theoretical arguments derived through these inductive processes must of course be subjected to further testing to prevent “overfitting” and forestall the introduction of spurious variables.476

The construction of deductive typological theories can suggest an initial list of variables and point out the cases whose study is most likely to provide theoretical insights. Often, a single researcher or a succession of researchers will move back and forth between induction and deduction, depending on the needs of a research program as it develops.

THE INDUCTIVE DEVELOPMENT OF TYPOLOGICAL THEORIES

In the early stages of reflection and research on a complex problem, an investigator may hesitate to build a research design and select cases based on a full, logically complete typology, or a typology that includes all of the logically possible types of a phenomenon. While the investigator may aim to develop a typological theory eventually, he or she may hope to develop such a theory through a series of individual case studies. Research at this stage may be of an exploratory nature, relying on feedback from the initial case studies to assess, refine, or alter the theoretical framework in which explanation of individual cases will be couched and to identify components of a useful typology. That is, the investigator seeks to gradually build a typology and a typological theory via empirical analysis of cases within a theoretical framework. This reduces the risk that a well-defined, comprehensive typology may prove inadequate after much research on a set of cases selected for that typology. While this strategy relies on induction, it is