One of the recent big and, in my view, underappreciated innovations in the field of Qualitative Comparative Analysis (QCA) is Baumgartner’s formulation of the Coincidence Analysis algorithm (CNA). Baumgartner presents it as an alternative to QCA, which I do not find convincing because I do not see QCA married to a specific algorithm. I conceive of CNA as an alternative to the Quine-McCluskey (QMC) algorithm that Ragin chose as the default algorithm for QCA in his foundational book in 1987.
Baumgartner describes CNA in formal terms in various publications and I do not need to go into its details here (here the probably most accessible discussion). In (very) short, the argument is that a term – a single condition, a conjunction, or a disjunction – is causally related to the outcome when no proper part (superset) of the term is also related to the outcome. ABC is causal for Y when neither AB, AC, BC, A, B nor C are tied to the outcome. A, B and C are non-redundant conjuncts of ABC and the absence of any of these conjuncts is associated with the absence of the outcome.
In addition to the nature of the algorithm, CNA differs from QMC in two important ways. First, it dispenses with the counterfactuals that are essential for deriving the intermediate and parsimonious solution with QMC. As Baumgartner explains, this allows one to avoid untenable counterfactuals about issues such as female African American presidents of the United States or pregnant men. Second and relatedly, CNA produces only one solution that is identical with the parsimonious solution and that Baumgartner argues as being the only solution that is causally interpretable (an argument with which I disagree, but that is a topic for another blog post).
What is probably less well-understood among QCA researchers is that the algorithm is anchored in a regularity theory of causation. This can be inferred from Baumgartner’s discussions of CNA and because he anchors the algorithm in a regularity theory drawing on Mackie’s INUS theory of causation which is, in turn, a regularity theory of causation that further develops Hume’s widely known theory of causation as constant conjunction.
I belong to the group of probably not so many people in the social sciences who do not have fundamental problems with regularity theories that receive favorable treatment, neither in the quantitative literature nor in the qualitative literature (I would say much less in the qualitative literature that pits mechanisms and process tracing against regularity theories). Since it is always important to understand what the theory of causation is on which our methods are built, it is worth emphasizing that you buy in a regularity theory when you do CNA.
This is not bad per se, but one should know it and I doubt that everyone who referenced Mackie meant it to be a reference to his regularity theory as opposed to merely referring to the idea of INUS causes. In this sense, I disagree with Baumgartner who, for example, cites Mahoney and Goertz as subscribers to Mackie’s theory because they also favor an “asymmetric approach to causation” (chap. 5 in the A Tale of Two Cultures book) that does not fit with Mackie.
In addition, QCA researchers should note that regularity theories relate types to each other. As Baumgartner notes, they can hardly handle the causal analysis of singular cases (not the same as single cases) that are characterized by specific features related to place and time, for example. This challenges, in my reading, the idea of QCA as case-based method that also takes singular features of cases into account in the case-based part. As a regularity theorist of causation, this is not an issue for Baumgartner, but this is relevant for empirical QCA researchers who like the idea of QCA as a case-based method and do not want to conceive of singular cases as instantiations of regularities. This shows that the exciting invention of CNA as an alternative algorithm to QMC has implications that stretch beyond the truth table analysis for which algorithms are devised.