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methods or making perfectly controlled comparisons bedevils rigorous application of the comparative method and have discussed several ways to minimize the difficulties.298 In this chapter, we survey some of the most important alternatives to controlled comparison methodologists have proposed. We start by discussing John Stuart Mill’s methods, the foundational work on comparative methods. We then discuss equifinality—the fact that different causal explanations often exist for similar outcomes—and the difficult challenges it poses to comparative methods. Next we discuss a number of alternatives to Mill’s methods, including Qualitative Comparative Analysis (QCA), before-after case study designs, counterfactual analysis, and others. Unfortunately, practically all efforts to make use of the controlled comparison method fail to achieve its strict requirements. This limitation is often recognized by investigators employing the method, but they proceed nonetheless to do the best they can with an admittedly imperfect controlled comparison. They do so because they believe that there is no acceptable alternative and no way of compensating for the limitations of controlled comparison.299

One alternative, proposed by Gary King, Robert Keohane, and Sidney Verba, focuses on the observable implications of a theory for independent and dependent variables, and not for intervening variables. In effect, it puts any processes that occur between independent and dependent variables in a “black box.” We discuss this alternative—and our substantial reservations about it—in this chapter.

We end by briefly discussing how the within-case methods of congruence and process-tracing can serve as an alternative and supplement to comparative methods. These tools do not seek to replicate the logic of scientific experimentation. Instead, they seek to increase our confidence in a theory: the congruence method seeks to show that a theory is congruent (or not congruent) with the outcome in a case. Process-tracing seeks to uncover a causal chain coupling independent variables with dependent variables and evidence of the causal mechanisms posited by a theory. These methods are discussed in detail in Chapters 9 and 10.

Mill’s Methods: Their Uses and Limitations

As numerous writers have noted, the essential logic of the comparative method is derived from John Stuart Mill’s A System of Logic (1843).300 In this work, Mill discussed the “method of agreement” and the “method of difference,” which are sometimes referred to as the “positive” and “negative” comparative methods.301 The (positive) method of agreement attempts to identify a similarity in the independent variable associated with a common outcome in two or more cases. The (negative) method of difference attempts to identify independent variables associated with different outcomes. A third method identified by Mill was the method of concomitant variations, a more sophisticated version of the method of difference. Instead of observing merely the presence or absence of key variables, concomitant variation measures the quantitative variations of the variables and relates them to each other, a method that is in some sense a precursor to statistical methods.

Mill himself emphasized the serious obstacles to making effective use of these methods in social science inquiry. He noted that the multiplicity and complexity of causes of social phenomena make it difficult to apply the logic of elimination relied upon by the methods of agreement and difference, thereby making it difficult to isolate the possible cause of a phenomenon. Mill judged the method of difference to be somewhat stronger than the method of agreement, and he also proposed the method of concomitant variation to deal with some of the limitations of the other two methods.

Mill, then, was pessimistic regarding the possibility of satisfactory empirical applications of these logics in social science inquiry. Other logicians and methodologists have subsequently expressed strong reservations. 302

Since the logics associated with Mill’s methods are