Selecting Appropriate Cases When Tracing Causal Mechanisms

Mechanisms as Systems

At the most fundamental level, the understanding of mechanisms as systems builds on a different ontological understanding of causation from a counterfactual/manipulation understanding of the relationship between causes and outcomes. ¹⁰ Causation is seen as more than just X:Y patterns of constant conjunction or manipulation of X to produce a difference in the value of Y. Given the need to ensure methodological alignment between the nature of the causal relations we want to study and the methods we use to investigate them (Hall 2003), adopting a mechanism understanding of causation has significant methodological implications. Understanding causation in terms of mechanisms means that the focus of analysis is on unpacking the causal arrow(s) linking cause and outcome into a series of interlocking and interacting parts that transmit causal forces from X to Y. Only by unpacking the causal arrow and studying it empirically by tracing how the mechanism works in a particular case can we make strong inferences that a causal relationship is present in a case by using what can be termed “mechanistic evidence.” ¹¹

How then should we define a mechanism? Glennan defines a mechanism as a “complex system, which produces an outcome by the interaction of a number of parts” (1996:52). Andrew Bennett has defined causal mechanisms as “… processes through which agents with causal capacities operate in specific contexts to transfer energy, information or matter to other entities” (2008b:207). A causal mechanism is a theorized link ¹² between a cause (or set of causes) and an outcome, where each part of the mechanism is clearly described in an ordered sequence, and, in particular, in terms of entities engaging in activities that transfer causal forces (Beach and Pedersen 2016; Hernes 1998; Hedström and Swedburg 1998; Machamer et al. 2000; Machamer 2004).

Each part of the theorized mechanism can helpfully be disaggregated into entities engaging in activities, with entities being the factors engaging in activities, whereas the activities are what actually transmit causal forces from X to Y (Machamer et al. 2000). In the system understanding, each of the parts of a causal mechanism has no independent existence in relation to producing Y; instead, they are integral parts of a system that transmits causal forces to Y. They are therefore not intervening variables; instead, theorizing a mechanism can be thought of as developing the causal story linking X with Y in more or less abstract terms. A good theory of a mechanism does not have logical holes, thereby ensuring what Machamer, Darden, and Craven term the “productive continuity” of the mechanism in-between causes and outcomes (2000:3).

The main contending understanding of mechanisms is to see them as intervening variables (e.g., Gerring 2007; King et al. 1994). However, strictly speaking, the use of the term variable implies a research design where we have variation that provides evidence of the difference making of independent and/or intervening variables, with multiple observations of the values of X, the intervening variable (mechanism, M) and Y that enable us to assess the mean causal effects of X and/or M on values of Y (Gerring 2007). King, Keohane, and Verba suggest that to do this we can disaggregate our case, for example, by transforming a single case (national level) into multiple cases by observing values of variables at a lower-level (e.g., the state level) or by comparing the same case at different times (before/after). Yet, this in effect transforms the within-case study of causal mechanisms into a cross-case analysis of patterns of variation where we lose focus on the process between the causes and outcome (Hedström and Swedberg 1998; Hedström and Ylikoski 2010:51-52; Mahoney 2001:578; Mayntz 2004:244-45). Yet, studying the process between X and Y was the very reason we would want to trace causal mechanisms in the first place. The analytical result is that the actual mechanism is “black boxed.” Another way of getting “variation” is, as Nielsen suggests, to use counterfactual thought experiments to assess the difference a mechanism makes when it is present and absent. However, this suggestion uses hypothetical “thought experiments” as evidence, whereas in case-based tracing of mechanisms we want to investigate the actual empirical fingerprints that they leave in actual cases, assessing using mechanistic evidence the degree of match between predicted evidence and the facts of the case in hand in order to make inferences (Beach and Pedersen 2016; Bennett and Checkel 2014; Waldner 2012). In other words, tracing mechanisms using case-based methods like process tracing makes inferences not by assessing difference making by varying values of causes, outcomes and mechanisms, but instead by assessing whether there is empirical evidence in the actual case that enables us to infer the mechanism was present (Russo and Williamson 2007).

The analytical value-added of tracing mechanisms as systems is that we both gain greater confidence in a causal relationship actually existing between X and Y because we have found empirical evidence of it in a case study, and we gain a greater understanding of how X is causally related to Y. Reaping these gains requires that the mechanism between X and Y is theorized explicitly, typically a mid-range theory that can be present within a bounded population of cases. However, when we look at the literature, many scholars claim they are theorizing mechanisms but never unpack the causal process in-between X and Y.

For example, Ziblatt claims that he theorizes a “capture” mechanism that details how landholding inequality (X) is linked to electoral fraud (Y; 2009:12-18). However, the actual causal mechanism linking X and Y is not explicitly theorized in the article. The closest we get to the theoretical development of a causal mechanism is where he writes, “… they [landed elites] exert influence indirectly via the capture of rural public officials such as mayors, county commissioners, police officials, and election officials, who in turn are the actors that interfere with free and fair elections. In its most acute form, capture occurs as socioeconomic interests infiltrate the state by using their own personnel to staff the state …” (2009:14). While telling us something about the process between X and Y— that is, it goes through local officials—he does not detail a causal mechanism in enough detail to trace it empirically. In particular, he tells us precious little about the actual causal process whereby landed elites are able to capture local officials. For example, what types of power resources do landed elites deploy to capture officials?

By not theorizing the mechanism more explicitly, we cannot evaluate the underlying causal logic, nor are we able to assess systematically whether there is empirical evidence that the hypothesized capture mechanism actually worked in a given case. The evidence provided by Ziblatt for the mechanism existing is therefore anecdotal, at best. For instance, he writes, “As one Landrat from Posen reported in his memoirs in 1894, “I had to join the local branch of the Agrarian League, because everyone I interact with socially—and everyone I hunt with—is a member!” (2009:16). It is obvious that this piece of empirical material relates in some fashion to an underlying part of mechanism whereby landed elites can pressure local officials. But by not detailing the underlying causal mechanism, we are left unsure about basic questions such as whether social pressure is the only means whereby local officials are captured.

If we were going to trace Ziblatt’s proposed capture mechanism, we would first want to flesh out the mechanism in more detail. This can be done by theorizing about it in terms of a series of interlocking parts linking landed elites with electoral fraud, drawing on existing theorization and empirical research to better understand each of the causal links. In Figure 1, we depict a slightly revised mechanism that more explicitly describes the activities that provide the causal links in the mechanism, telling us more about how and why capture is theorized to happen. The first part of the mechanism details the how and why process whereby local officials are captured, followed by theorizations on the process whereby captured officials influence elections, resulting in electoral fraud.

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Figure 1.

A “capture” causal mechanism linking landed elites with electoral fraud.

Before we turn to the other assumptions underlying case-based research in mechanisms, it is important to note that mechanisms linking causes and outcomes do not logically have to be sufficient or necessary to produce Y. While the assumption that a mechanism is sufficient to produce an outcome is found in the literature (Anderson 2012:416; Mahoney 2001:580; Mayntz 2004:241, 253; Waskan 2011:403), there are no logical reasons that the mechanism itself has to be necessary or sufficient in relation to the outcome. A mechanism logically cannot be causally more or less important than the cause that triggers its operation. If we theorize that a cause like economic development is “merely” a contributing cause of democratization, the causal mechanism linking the two cannot be theorized to be sufficient to produce democratization. The mechanism is merely the link and therefore cannot be causally more important than the cause or set of causes that triggers the mechanism. This point has implications for case selection that have been overlooked in the existing literature; we return to this in the next section.

Case-based Methods and Determinism

The argument that case-based research builds on deterministic ontological foundations is well-established in social-science methodology (e.g., Beach and Pedersen 2016; Goertz and Mahoney 2012; Mahoney 2008; Schneider and Wagemann 2012) but also widely misunderstood. The case selection guidelines developed in this article build on the assumption that mechanisms are deterministic at the ontological level.

Case-based research takes as its point of departure causal relationships within individual cases, whereas variance-based research builds on population-level mean causal effects in which probabilistic assumptions make most sense. ¹³ But without deterministic claims being made, the study of individual cases makes little sense because if we do not find evidence of a relationship in a single case, we will not know whether that was an exception to an otherwise strong cross-case probabilistic relationship or not. This is why case studies play a secondary role in probabilistic, variance-based methods, acting as a means to double-check the findings of cross-case analyses of mean causal effects. ¹⁴

When operating with deterministic assumptions, if we find strong disconfirming mechanistic evidence in a particular case, we would not just discount this as an exception to an otherwise strong cross-case trend. Instead, we are forced to reappraise our theory of the mechanism, attempting to figure out why what we expected did not occur in the studied case, for example, because an unknown scope condition that had to be present was not there (Dion 2003:106-7; Adcock 2007). These “failures” are intensely interesting for case-based research, enabling us to build better theories of mechanisms.

Ontological determinism does not imply that we have perfect knowledge about why things happen in the empirical world. While the social world at the ontological level can be claimed to be deterministic (i.e., things do not happen randomly), our empirics-based knowledge about why things occur will always be imperfect. ¹⁵ Epistemological probabilism means that if we find disconfirming evidence of a mechanism in a case, we would only make disconfirming inferences after we have assessed transparently the level of trust we can have in the measurements being accurate (for more, see Beach and Pedersen 2016). The more we can trust our empirical measures, the stronger the inferences we can make. If we cannot justify transparently that our measures are relatively accurate, we would not begin revising the theorized mechanism based on one failure.

The ontological assumption of determinism fits well with the understanding of mechanisms as systems, viewing mechanisms as invariant, deterministic processes that will be triggered if the cause and relevant scope conditions that allow it to function are present (Anderson 2012; Mayntz 2004; Waldner 2012). Some argue that mechanisms as systems can also be probabilistically related to outcomes (e.g., Hedström and Ylikowski 2010:51), but here we contend that what might empirically appear to be a probabilistic relationship is typically the product of an inadequate understanding of the scope conditions under which a given mechanism functions.

Causal Homogeneity and the Importance of Context for Mechanisms

Ontological determinism has the downstream consequence that case-based research has to operate with small, bounded populations of cases that are as causally homogeneous as possible (Collier and Mahoney 1996:68-69; Goertz 2006:29; Mahoney 2007; Skocpol and Somers 1980). Naturally, if we want to make inferences to a broader, more heterogeneous population, we have to hedge our bets by only making probabilistic claims, whereas we can make deterministic causal claims about small populations—as in case-based research (Skocpol and Somers 1980; Mahoney 2008). A causally homogeneous population is a set of cases where the same cause (or set of causes) is linked to the same outcome through the same causal mechanism(s). If we are able to empirically demonstrate that the population of cases is causally homogeneous by using comparative methods (see below), we can then make cross-case inferences from studied cases to other causally similar cases. But comparative methods by themselves do not enable causal inferences (unless they are experiments that provide difference-making evidence); here, the causal inferences are enabled by the use of within-case, mechanistic evidence.

Causal homogeneity is particularly important when studying causal mechanisms between X and Y. For mechanisms to operate correctly in a case, the requisite scope conditions need to be present (Falleti and Lynch 2009; Goertz and Mahoney 2004:655, 660-61). Contextual (or scope) conditions are defined as the “… relevant aspects of a setting (analytical, temporal, spatial, or institutional) in which a set of initial conditions leads … to an outcome of a defined scope and meaning via a specified causal mechanism or set of causal mechanisms” (Falleti and Lynch 2009:1152). The same cause in a different context can in principle be linked to the same outcome through different mechanisms, meaning there can exist equifinality at the level of mechanisms unless we can demonstrate that the population of cases is causally homogenous also with regard to contextual conditions present (Falleti and Lynch 2009; George and Bennett 2005:chapter 10; Gerring 2010). For example, hypothetically, economic development (X) and democratization (Y) can be linked through a number of different mechanisms, depending on the contextual conditions.

Given that we almost never have complete knowledge of the contextual conditions that enable or prevent mechanisms from being triggered or that result in different mechanisms linking the same cause and outcome, there is a very real risk of making flawed cross-case inferences about mechanisms being present unless we both (1) only operate with small, bounded population of cases to which we intend to infer to, and (2) always trace mechanisms in multiple cases to ensure that the mechanisms we found in one case also are present in other cases.

Case-based Methods and Asymmetric Causation

The final assumption that has implications for case selection guidelines is that case-based tracing of mechanisms involves making asymmetric causal claims. While it is well known that case-based research makes asymmetric claims (Ragin 1987, 2000, 2008; Goertz and Mahoney 2012), what is less recognized is that asymmetry becomes even more important when we are studying what causally links X and Y together. An asymmetric causal claim could be that economic development (X) is necessary for democratization to occur (Y). Here, no claims are made about whether less-developed countries (∼X) are not democratic (∼Y; Ragin 2008:15).

When we then are interested in tracing what mechanism(s) link X and Y together, we are making strongly asymmetric claims. For example, making claims about the causal mechanism that links mutual democracy (X) with avoidance of war in crisis situations (Y) does not make any claims about what mechanisms link autocracies (∼X) and war (∼Y). In cases where ∼Y is the outcome, we would expect very different mechanisms to produce this outcome. Therefore, it makes little sense to compare the mechanisms that produce an outcome with those that produce its negation, given that they would be very different at both the theoretical level and in their empirical manifestations.

The strong asymmetry of mechanism-based claims implies that we only operate with difference-of-kind distinctions when conceptualizing causal concepts, which means that cases are either in the set of cases where a causal relationship is possible or not (we return to this below in more detail). Differences-of-degrees that are captured using ordinal or higher scales are either causally irrelevant in relation to the core categorical distinction included in a given concept (the kind difference) or at worst conflate degree- and kind differences, resulting in a causally heterogeneous population where different values have different causal properties instead of mere degree differences in the magnitude of the causal relationship (Michell 2011). In the rest of this article, we only operate with categorical in/out distinctions that capture the causally relevant differences-of-kind in concepts.

Do We Need to Control for Other Causes When Selecting Typical Cases?

Variance-based scholars question whether we can make within-case inferences about mechanisms when we do not control for other causes by selecting cases in which only one potential cause is present. Gerring and Seawright write that, “… researchers are well advised to focus on a case where the causal effect of one factor can be isolated from other potentially confounding factors” (2007:122). They term this type of case a pathway case. Schneider and Rohlfing draw on this guidance in their discussion of case selection for process tracing when they state that we should choose “unique set” cases, where we “… focus on one term … to unravel the mechanism through which it contributes to the outcome in the case under study” (2013:8). Goertz writes that one should avoid cases that exemplify multiple causal mechanisms (2012:18).

Our argument is that while the logic of controlling for other potential causal conditions is relevant for variance-based designs aimed at assessing probabilistic claims about the mean causal effects of individual causes at the population level (i.e., evidence of difference making), it is not relevant for the study of mechanisms in case-based research because process tracing offers us analytical tools that can enable us to control for other causes working at the empirical level. When evaluating empirical evidence of the workings of parts of mechanisms using process tracing, we assess whether the particular piece of evidence is theoretically unique, or whether finding it is just as plausible with other explanations (be they competing theories or case-specific factors). ²⁰ If finding the particular piece of evidence is just as plausible with alternative explanations, then no confirming causal inferences based on it are possible. Control for other causes occurs therefore at the level of evidence within a case, which matches with the level of our causal inferences being made (within case).

The difference between case-based and variance-based principles of case selection is most pronounced when dealing with potential overdetermination, defined as multiple sufficient causes being present in a case. If there is overdetermination in a given case, variance-based designs are unable to disentangle which cause actually produced the outcome because there are more than one possible cause of difference, making control for other causes through case selection even more important. However, overdetermination is not a serious problem when studying mechanisms as systems because we can isolate the workings of individual mechanisms empirically from each other through our evaluation of the theoretical uniqueness of each piece of mechanistic evidence, asking whether finding the evidence can be accounted for with any other plausible explanation. Basically, we should expect to find when we operate at the level of within-case mechanistic evidence that different causes will be linked to outcomes through different mechanisms that would leave empirical fingerprints that can be distinguished from each other. Therefore, choosing a case where both X1 and another potentially sufficient cause X2 are both present should not matter because we can distinguish empirically the workings of the two causes and their mechanisms from each other.

For example, using the classic example from the philosophy of science, a person is found dead after wandering in the desert. It is found that there was poison in the person’s canteen, but there was also a hole in the canteen. In this instance, both poison (X1) and thirst (X2) are potentially sufficient causes, but only one can actually have had a causal relationship with the outcome, that is, he either died of poisoning or dehydration. However, overdetermination at the theoretical level does not mean that we cannot figure out why the man in the desert died in practice. This is because we can distinguish at the empirical evidence level between the fingerprints that causes X1 and X2 would leave. For example, we would expect to find poor skin turgor, tinting of skin, sunken eyes, and/or dry galea and dry organ surfaces if the man died of dehydration (Madea and Lachenmeier 2005), whereas poisoning by cyanide could be detected as increased levels of cyanide in the blood if the autopsy is conducted relatively quickly after death (Musshoff et al. 2002).

A natural counterargument would be to claim that parts of mechanisms in the social sciences often do not leave theoretically unique empirical evidence. However, we claim that we should not throw in the towel, but instead we should expend more effort on creatively developing as many potential observables as possible in order to uncover some that have a degree of uniqueness. Additionally, while one piece of evidence might not be very unique, when independent pieces are combined, they can together become quite unique (Bennett 2014). Together they can form a “signature” that is quite unique to one particular part of a mechanism at the empirical level.

Systematically selecting pathway cases where only X1 is present also has the downside that it reduces even further the population of potential cases that can be inferred to afterward. Given the sensitivity of mechanisms to context, there is a risk that X1 is linked to Y through M1 in cases where only X1 is present, whereas in cases where X1 and X2 are present, X1 is linked to Y through M2. This situation is depicted in Figure 3. If we follow Gerring and Seawright’s advice, after studying a pathway case (X1, Y, and ∼X2) we would only be able to infer to other cases where only X1 and Y are present instead of the full population of cases where X1 and Y are present. We suggest if there are significant concerns about the potential impact of X2 on which mechanism is working that we engage in a two-step process where we first select two cases for tracing mechanisms where X1 and Y are present but not X2, followed by two cases where X1 and X2 are present in order to assess whether the presence of other causes impacts on which mechanism works in order to be able to make inferences to the full population of cases where X1 and Y are present.

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Figure 3.

Pathway cases actually reduce the bounds of the population being studied.

Should We Select Typical Cases That Are Most Likely or Least Likely?

Within the set of typical cases, one could argue that depending on prior confidence in a mechanism being present, one should select most- or least-likely cases. Unfortunately, the logic of most/least-likely cases is not compatible with deterministic claims in case-based research. Selecting most/least-likely cases is a long-standing qualitative practice that goes back at least to Eckstein in the mid-1970s (Eckstein 1975). The basic logic is Bayesian-inspired, where the argument is that finding a relationship where one least expects it enables one to infer across cases that it should therefore be everywhere (least likely) and vice versa. However, while intuitively pleasing, the logic both conflates theoretical and empirical likelihood, and also within-case and cross-case likelihoods in ways that are not compatible with the underlying ontological assumptions about the nature of causality in case-based research. These problems lead us to suggest dropping the distinction between “most” and “least” likely when selecting cases in case-based research because it is a vestige of variance-based designs. Instead, we should use a logic that is in alignment with the assumptions about deterministic and asymmetric causation underlying case-based research, focusing only on typical cases without any causally irrelevant distinctions.

Before we proceed, it is important to note that there are a variety of different ways in which most- and least-likely cases have been defined in the literature (see Table 1). Common to most definitions is the idea that a most-likely case is one where other conditions except the X in focus suggests that Y should occur but it does not, implying that we can disconfirm X being a cause across the population. A least-likely case is where other conditions except X point in the direction of Y not occurring but it does, enabling us to infer that given that it occurred where we least expected it, it should also occur in more probable places. It is vital to note that the likelihood of a causal relationship occurring in a case is based on theoretical reasons, for example, contextual conditions that are more/less conducive determine the likelihood of the causal relationship occurring. As can also be seen in the table, there is also a variety of ways in which cases are scored, either by scores on causal conditions and outcomes (variables; or changes therein, e.g., Eckstein) or based on the assumptions of theories. We have also included Schneider and Rohlfing’s definition of “most-typical” case given that is similar to a most-likely case but is understood in more set-theoretic terms.

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Table 1.

Different Definitions of Most- and Least-likely Cases.

(Eckstein 1975: 118-20)	Cases categorized based on scores of cases on variables, but if marked change in X has occurred and other causes remain constant, the case can also be crucial Most likely = X1 strongly predicts Y but X2 found to matter (disconfirmatory for X1) Least likely = X2 strongly predicts Y but X1 found to matter (confirmatory for X1)
King, Keohane, and Verba (1994:209)	Cases categorized based on case scores on pertinent variables Most likely = “if predictions of what appear to be an implausible theory confirm with observations of a “most-likely” observation, the theory will not have passed a rigorous test but will have survived a “plausibility probe” and may be worthy of further scrutiny” Least likely = case that “seems on a priori grounds unlikely to accord with theoretical predictions—a “least-likely” observation—but the theory turns out to be correct regardless”
George and Bennett (2005)	Cases categorized based on scores on variables Most likely = single variable X at such an extreme value that its underlying causal mechanism, even when considered alone, should strongly determine Y. If the predicted Y does not occur, then hypothesized causal mechanism strongly impugned Least likely = case least likely for causal mechanism and alternative hypotheses offer different predictions, but causal mechanism correctly predicts Y
Gerring (2007:115)	Cases categorized based on scores on variables, in particular the outcome Most likely = “on all dimensions except the dimension of theoretical interest, is predicted to achieve a certain outcome, and yet does not” Least likely = “on all dimensions except the dimension of theoretical interest, is predicted not to achieve a certain outcome, and yet does”
Levy (2008:12)	Cases categorized based on values of key variables, or theory’s assumptions and scope conditions satisfied/not satisfied Most likely = case is likely to fit a theory but data from case does not fit, strongest if case is least likely for alternative theory Least likely = case is not likely to fit a theory but data supports theory, strongest if case is most likely for alternative theory
Schneider and Rohlfing (2013:23)	Cases categorized based on case membership scores above qualitative threshold Most-typical case = displays maximum set membership scores in the subset and the superset

The most serious problem with most/least-likely logic is that it conflates theoretical (ontological) and empirical (epistemological) likelihood. The use of the term likelihood in relation to causation requires a probabilistic ontological understanding of causation, where “a cause raises the probability of an event occurring” (Gerring 2005:167). Causal relationships are more likely in more conducive circumstances (more contextual conditions present) and less likely in less conducive (contextual conditions mostly absent). However, this type of ontological probabilism is not compatible with case-based designs. In case-based research, we want to produce explanations that can account for what happened in particular cases instead of just producing theoretical odds for whether something might occur. In a deterministic understanding of causation, if a sufficient cause is present along with the requisite contextual conditions, the outcome will occur. Any case that fulfills these conditions should demonstrate the relationship, meaning that logically the relationship is not more or less likely in any particular case (Mahoney 2008).

Understood in deterministic and asymmetric causal terms, the relevant distinction is therefore not most/least likely but simply possible and not possible. If an outcome occurs when we did not theoretically expect it (a least-likely case), this should result in revision of the theory about what contextual factors matter instead of leading us to make a strong cross-case inference that the relationship is present across the population!

Second, and related, case studies produce within-case mechanistic evidence, updating our confidence in a causal relationship being present within a single case. Inferring beyond the studied case to the rest of the population requires that the chosen case is causally similar to the rest of the typical cases. However, given the large differences in the contextual conditions present in least-likely, most-likely cases, and more “normal” typical cases and given the sensitivity of causal processes to contextual and/or causal conditions that are typically assumed in case-based research, we should expect the different types of cases to exhibit high degrees of causal heterogeneity. This means that we cannot just infer that because we found a relationship in a least-likely case that it should also be present in other, causally dissimilar cases throughout the population (for example most-likely).

Schneider and Rohfling (2013) have developed a definition of most-likely cases that is more compatible with asymmetric causation. They suggest that causal relationships are easier to study when both X and Y are strongly present (high set membership scores). Yet, this assumes a “more is better” logic in the theory we are studying in relation to whether it is empirically observable and assumes that degree differences make the causal effect of causes stronger. First, on an empirical level, using an analogy, if the outcome is fire, the outcome would have higher values the more fuel is present, and given that more fire is more observable, other things equal, it would also be easier to study empirically up to the point where the fire gets so big that you would be scorched. And at the theoretical level, if X is theorized to be necessary, it is necessary in a case when the cause and requisite contextual conditions are present in the case; a cause cannot logically be more or less necessary.

Concluding, most/least-likely logic conflates ontological and epistemological probabilism, and within-case and cross-case evidence in ways that are impossible to untangle. We therefore recommend the use of the term typical case without any qualifications about likelihood, referring to cases where the theorized causal relationship is possible because both X, Y, and the requisite contextual conditions for it to occur are present.

At the same time, we do recommend thinking about whether: one has access to empirical material or not when selecting typical cases, and the chosen case is one where the mechanism might actually have left empirical fingerprints that can be observed. In some cases, the mechanism might leave very distinct and unique traces that enable strong within-case inferences to be made, whereas in others the data-generating processes might leave few traces. For example, bureaucratic politic mechanisms might leave few traces in a highly oral context, whereas in a context where extensive written records are kept, it might be easier to study. Second, accessibility concerns are also important. If we do not speak Spanish, it might be difficult to interview civil servants in Costa Rica, meaning we probably would not select it as a case unless we have no alternative. Similarly, studying elite decision making is easier when archives are declassified, other things equal. Given that tracing mechanisms is very data-demanding, selecting typical cases that are expected to be data-rich is a wise strategy.

Inferring from the Studied Typical Case to Other Typical Cases

What types of inferences are possible if we find confirming mechanistic evidence of a causal mechanism operating in one typical case? Existing case selection guidelines suggest that one case can be enough to make a cross-case inference to other cases. Lieberman writes that in testing a theory using a case study, “… if one or more intensive case studies can demonstrate the validity of the theoretical model—which had already passed muster in the LNA—by plausibly linking cause to effect in the expected manner, then the nested analysis provides ringing support for the model (End analysis I …)” (2005:448—italics added). In the flowchart illustrating his case selection strategy, if one finds support in the single case study, he suggests we can end our analysis. Similarly, Schneider and Rohlfing in their flowchart state that if a theory is confirmed using a single case study we can end our analysis, enabling us to infer that the found mechanism is also present in other cases that are members of X and Y. ²¹

In case-based tracing of mechanisms, given the sensitivity of mechanisms to context, we would be averse to making any cross-case claims about similar mechanisms being present in similar cases to the studied unless we can demonstrate transparently that the population of other typical cases is actually causally homogenous, meaning the same cause should be linked to the same mechanism and outcome because similar sets of contextual and causal conditions are present in the other cases. Unless we can provide strong evidence of causal homogeneity, which is very difficult given that we often have imperfect knowledge of contextual conditions, the best solution is to trace mechanisms in multiple typical cases. Finding mechanistic evidence of a causal mechanism between X and Y in case 5 in Figure 2 (above) does not necessarily mean that the same causal mechanism links X and Y in case 7. If we find that economic development contributed to produce democracy in the South Korean case through a middle-class mechanism, this does not necessarily mean that economic development contributed to producing democracy in Taiwan through the same causal mechanism.

This implies that we should never be content with a one-shot case study of mechanisms, but in contrast to existing case selection guidelines, we should always select two or more typical cases within quadrant I. If we can muster strong evidence that the population of typical cases is (relatively) causally homogeneous, we can make cross-case inferences more confidently based on fewer cases, other things equal. If on the other hand, we are not able to provide strong evidence of homogeneity—usually because the population is larger (i.e., more than a handful of cases)—we then need to trace mechanisms in more typical cases to be confident about the same mechanism linking X and Y within quadrant I. Note that we will never be 100 percent certain when we try to transfer our findings from the single case to similar cases in the population; our confidence in the external validity of our within-case findings is a function of the strength of the evidence we can provide in the degree of causal homogeneity of the bounded population, in particular whether there are similar contextual conditions. Unfortunately, there is always a trade-off between internal and external validity. Selecting more cases enables us to be more confident about the external validity of our findings because we have studied a higher ratio of cases in the population but it would result in the mechanistic evidence to be used being more superficial (lower internal validity). However, tracing mechanisms using in-depth case studies requires considerable analytical effort to make strong within-case inferences (i.e., high internal validity), and therefore in most research situations we can realistically only employ two or three process-tracing case studies. Yet by selecting so few cases, our ability to make stronger cross-case inferences (external validity) is impaired. Therefore, we are forced to choose between stronger internal and external validity; and when push-comes-to-shove case-based researchers usually opt for the former.

If we are not able to detect a causal mechanism between X and Y in a typical case after numerous repeated attempts, there can be two reasons for this: (1) either the case is idiosyncratic or (2) there is no causal relationship. To determine which of the two is correct requires comparing the chosen case with what we know about other typical cases, assessing the values of the case and other typical cases both on X, Y, contextual conditions, and a range of other potential causal conditions. In particular, this comparison can shed light on the contextual conditions for the functioning of the mechanism, enabling us to assess whether the bounds of the population have been set properly. This procedure is the same as used when comparing deviant cases in quadrant IV with typical cases in order to detect omitted conditions (we discuss this more below in the fifth section). However, if we cannot detect any significant differences between the chosen case and other typical cases in the population, we can make the cautious inference that there is not a causal relationship between X and Y. We would conclude that while there is a correlation between X and Y, there is no underlying causal mechanism linking the two, meaning that the postulated causal relationship is spurious.

Deviant Cases in Quadrant II—Finding New Causes (or Mission Impossible?)

Cases within quadrant II are deviant cases where existing causal theories (X) are unable to account for the outcome (Y is present). This type of deviant case can be used to find new causes of the outcome, although we are much more skeptical about whether tracing mechanisms is the most efficient methodological tool for these purposes, in contrast to the arguments found in the existing literature (e.g., Lieberman 2005:443; Rohlfing 2008:1510; Schneider and Rohlfing 2013).

The basic idea is that one traces backward from the occurrence of the outcome to find a new cause. But it is far from straightforward what one is actually tracing under these circumstances. Existing suggestions that we engage in backward tracing using case studies builds on an understanding of mechanisms that sees them as mere events. Yet tracing “events” is not the same thing as tracing causal mechanisms that can be understood as theoretical systems that can be found in multiple cases. And if we have no idea about the cause (X), we also have no clue about the mechanism(s) linking the mystery cause with the outcome, meaning that we are in effect blindly groping in the dark after a cause. We therefore claim that a comparative design or a congruence case study would be a much more efficient analytical first-step in detecting new causes (see Beach and Pedersen 2016). For example, we might compare systematically two cases that are similar in all aspects except the occurrence of the outcome (Y, ∼Y). We would then want to know what new, undiscovered X is different between the two cases. After having found this using a paired comparison, it would be possible to engage in a form of in-depth case study that focuses on this new candidate cause, attempting to discern whether the new condition is actually causally related to Y.

Deviant Cases in Quadrant IV—Why Does the Causal Mechanism between X and Y Not Work in the Case?

Cases within zone IV have two different purposes depending on whether one is theorizing that X is a sufficient cause or that X is merely a contributing cause. The following offers the first set of comprehensive guidelines that illustrate how we combine comparative and within-case methods to uncover omitted causal or contextual conditions. ²³

If we theorize that X is a sufficient cause of Y, deviant cases where X is present but where Y is not present are useful to investigate the contextual conditions that have to be present to trigger the mechanism that will produce Y. If X is not theorized as a sufficient cause, deviant cases within quadrant IV can be used to detect omitted causal conditions that together with X would be sufficient to produce Y.

In both instances, we only employ this type of design after we have positive results when tracing a mechanism in one or several typical cases within quadrant I. The argument here is that there is no reason to investigate mechanism breakdown before we are more confident about the actual existence of a mechanism linking X and Y in one or more typical cases. However, once we are confident about what is going on in typical cases, investigating this type of deviant case is very important for developing better causal theories. Using an analogy, once we are certain about the mechanisms that enable airplanes to fly, we would want to investigate accidents to develop a better understanding of the contextual conditions under which planes can fly safely.

The within-case component of a condition-centered design involves tracing a mechanism using in-depth process tracing in a deviant case until the mechanism breaks down in the case. We want to uncover when and why the mechanism failed (Anderson 2012:421-22). Existing theories of causal mechanisms that were either built or tested on typical cases within quadrant I provide the foundation for the tracing in deviant cases until mechanism breakdown. Finding out when and why a mechanism breaks down gives us clues about omitted contextual or causal conditions, although to repeat, the tracing component here is auxiliary, and the main analytical method is a systematic paired comparison of the deviant case with a typical case.

A condition-centered design therefore relies on an analytical two step, where we use a deviant case first to trace where and why the theorized mechanism breaks down. We then use these insights to inform a pairwise comparison of the deviant and typical case to uncover omitted causal and/or contextual conditions. Using as a hypothetical example research focused on studying links between economic development (X) and democratization (Y) through some form of “middle-class” mechanism that details a causal mechanism whereby the growth of the middle-class spurs democratization, we might find in a deviant case like Poland that while a middle-class was produced by economic growth (X), the next part of the mechanism was not present, with demands for democratization instead coming from elite actors. We would then compare the single deviant case (Poland) with what we know more broadly about other typical cases in the population where we know the middle-class mechanism functioned as expected (e.g., South Korea) to uncover whether there is a missing causal or contextual condition that can explain why the mechanism did not work as predicted in the deviant case. Here, we might find that when parallel state-building processes were underway as in Poland, the middle-class mechanism did not function properly, suggesting that lack of parallel state-building processes is an important contextual condition in which economic development (X) is linked to democratization (Y) through a middle-class causal mechanism. Poland would also then be reclassified as a case outside of the relevant contextual conditions, moving into quadrant III. After we have found an omitted contextual or causal condition, we would have to reclassify our cases, with previously deviant cases becoming irrelevant (they are moved to zone III), as they lack a causal condition that has to be present for Y to occur (sufficiency), or they lack a contextual condition that enables the mechanism to function properly.