The conservative QCA solution isn’t based on counterfactuals? Not so fast

When we use the Quine-McCluskey algorithm to derive a QCA solution, we can choose between the conservative, intermediate or parsimonious solution. While I do not have any figures about which solution has been produced how frequently in empirical research, it is safe to say that the conservative solution is quite popular.

The reason for the popularity lies in the name because the conventional view states that the solution is conservative due to the absence of any counterfactual assumptions. Although counterfactuals have a very solid basis in philosophy of science and are applied in history and the social sciences, they are viewed with suspicion because of the notorious problem of establishing the truth value of the counterfactual.

In this light, the conservative solution seems to be convenient if one is to avoid counterfactuals. The only problem is, it does not necessarily steer clear of counterfactuals. This is relatively easy to see once we recall that QCA runs an algorithm on the truth table for determining redundant conjuncts. For the Quine-McCluskey algorithm, a conjunct is a redundant element of a conjunction when two conjunctions share the outcome and all conjuncts except one, which is thus redundant. Conjunctions that have been stripped of all redundant conditions can be interpreted in causal terms (pending a proper identification strategy, evidence for mechanisms, etc.).

When we derive the conservative solution, we only use observed conjunctions for singling out redundant conditions. Relying on the observed conjunctions might suffice for this purpose, but perhaps it doesn’t. Suppose we have derived a conjunction ABC and C is in fact redundant. However, the conjunction ABc (c reading “not-C”) is not observed, meaning we are unable to designate C as redundant when we are generating the conservative solution.

What does this now mean for the interpretation of the conservative solution? The answer depends on how you interpret it. My reading of many studies operating with the conservative solution is that it is interpreted causally, which is wrong. It is only possible to assert that it is causal when one is prepared to claim that each conjunct is non-redundant. This, in turn, is only possible if one counterfactually assumes that each unobserved configuration that could be compared with an observed one is not associated with the outcome. A causal interpretation of the conservative solution cannot but instead requires counterfactuals.

The alternative is to treat the conservative solution in truly conservative terms; in this instance, one should stress that the conservative solution should not be interpreted in causal terms because some of the unobserved configurations could be associated with the outcome if there were cases described by these configurations. Since we do not know how many and what configurations these are, the conservative solution might be identical to the causally valid solution, but it might also be far from the true solution and contain many redundant conjuncts. In the latter instance, all what we can say is that the true, causal solution is likely to be a superset of the conservative solution because the simplification of a solution by means of the Quine-McCluskey algorithm always produces a superset of the non-simplified solution.

Because of the ambiguity of what the conservative solution stands for, QCA researchers working with this type of solution should therefore understand and make transparent whether they interpret it in conservative, non-causal terms or causal terms which necessarily involve counterfactuals.


About ingorohlfing

I am Professor for Methods of Comparative Political Research at the Cologne Center for Comparative Politics at the University of Cologne ( My research interests are social science methods with an emphasis on case studies, multi-method research, and philosophy of science concerned with causation and causal inference. Substantively, I am working on party competition and parties as organizations.
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