The idea of most-likely and least-likely cases dates back to Eckstein and was one of the few remaining things in qualitative research there seemed to be no disagreement about because they are considered an asset in causal analysis. In a paper that is advance access, Beach and Pedersen (BP) now argue that process tracing and the analysis of mechanisms does not make sense with most-likely and least-likely cases. This made me stunned, but a closer look at their reasoning shows that they are wrong. If you like, you can safely choose most-likely and least-likely cases for process tracing.
BP misrepresent the position and reasoning of researchers arguing in favor of most-likely/least-likely cases. BP claim these people conflate “theoretical (ontological) and empirical (epistemological) likelihood” (probability and likelihood are not the same, but let’s leave this aside here). This means most-likely/least-likely researchers are said to define causation in terms of probability-raising which is what BP mean with “theoretical (ontological)” probabilism. (BP actually forgot to add Beach/Pedersen in 2013 to their list of supposedly mistaken people because they argue in favor of most-likely/least-likely cases in their book). In this view on causation, advanced by philosophers such as Suppes, X is a cause of Y if p(Y|X) > p(Y|~X). In plain words, X is a cause when its presence makes the presence of Y more probable than X’s absence (it also works with continuous measures).
There is no evidence in BP’s article that researchers advancing the idea of most-likely cases subscribe to the idea of causation as probability-raising. They cite Gerring’s 2005 article on causation in which he defines causation as probability-raising. However, Gerring is now firmly anchored in a counterfactual theory of causation, which BP know because they reviewed his 2011 book in which he makes this more than clear. Beyond this quote, there is no reference suggesting that people like Bennett, Levy, and me either explicitly or implicitly define causation as probability-raising (a look at their research record should make you believe they don’t). The claim that many researchers conflate two understandings of probabilism therefore is, in my eyes, not substantiated.
More importantly, the formalization of most-likely/least-likely cases is p(E|H), i.e., we are interested in the probability of finding evidence E confirming hypothesis H (see chapter 3 and 8 of my case study book). There is no inequality relation whatsoever involved because most-likely/least-likely cases are about the level of probability. A probability-raising account of causation is about the change in probability. This demonstrates that causation as probability-raising and most-likely/least-likely reasoning are two different things.
This can be further demonstrated by getting the terms clear: ‘probability-raising’ pertains to a causal relation between events; ‘most-likely’ and ‘least-likely’ refer to our epistemic uncertainty about what is going on in cases. This means our knowledge about the cases at hand is uncertain because we haven’t studied them yet or not in sufficient detail. We express this uncertainty by stating that it is more or less probable to gather certain observations, given the theory at hand and our empirical knowledge about the cases. For some cases, we have more ex ante confidence in collecting supporting evidence (most-likely cases), for others we have less confidence (least-likely cases). You would have different expectations about the probability of finding evidence for a mechanism underlying the democratic peace phenomenon when you study two established democracies with no beef between them and that haven’t fought each other for decades, compared to two countries that just finished their transition to democracy, have recently fought each other and confront unresolved issues straining their relations.
In any case, we would not say we expect to find evidence with certainty (p = 1) or not find it with certainty (p = 0). Our theory might be wrong or incomplete, or unforeseen case-specific factors interfere that explain why our expectations prove wrong. We would also hold such uncertainty when we believe in deterministic causal relationships, as BP do, because we all know there is noise in empirical research and there are reasons why find or fail to find expected evidence other than for the hypothesis being correct or false (Eckstein is still the classic read for this).
All in all, this shows that probabilistic causation and epistemic uncertainty are two completely different things. Most-likely and least-likely cases are available and useful for process tracing and you can choose them without subscribing to a probabilistic view on causation.