Negative Case Selection: Justifications and Consequences for Set-Theoretic MMR

Abstract

The combined usage of qualitative comparative analysis (QCA) and process tracing (PT) in set-theoretic multi-method research (MMR) holds great potential for reaching valid inferences. Established views of case selection after QCA hold that studying negative cases provides lessons about the causes of an outcome in a limited set of circumstances. In particular, recommendations focus on negative cases only if they contradict the analysis or if suitably similar positive match cases exist to leverage comparisons. By contrast, I argue that set-theoretic MMR can gain from studying negative cases even when these conditions do not hold. First, negative cases can give insights into why an outcome fails to occur. Second, they can help guard against theoretical inconsistency between explanations for the outcome and its absence. Third, they can ensure that the mechanisms producing the outcome and its absence are not too similar to be logically capable of resulting in different outcomes. Following these arguments, I recommend that studies of negative cases in set-theoretic MMR focus on failure mechanisms in carefully bounded populations, search for theoretical inconsistency among mechanisms, and focus in part on the mechanism proposed to produce the outcome.

Keywords

multi-method research qualitative comparative analysis process tracing case selection negative cases

Introduction

There is much to be gained by mixing different methods in pursuit of valid inferences about the social and political worlds. In particular, because of their common focus on set theory, the sequential application of qualitative comparative analysis (QCA) and process tracing (PT) in set-theoretic multi-method research (MMR) holds great promise (Beach and Rohlfing 2015; Rohlfing and Schneider 2013; 2015; Schneider and Rohlfing 2013, 2014; Schneider and Wagemann 2012; for applied examples, see Beach 2015; Casal Bértoa 2015; Samford 2010).¹ QCA links combinations of conditions (or causes) to outcomes, all conceptualized as sets (Ragin 2008). PT links start-up conditions (causes) to outcomes through mechanisms comprising mechanism elements. In recent methodological work, conditions, outcomes, mechanisms, and mechanism elements in PT are all also conceptualized as sets (e.g., Beach and Pedersen 2013). Set-theoretic MMR on sufficiency, which is the focus of this article for reasons I will explain, proceeds in three steps. First, QCA is used to establish the sufficient conditions for an outcome. Subsequently, QCA results are used to select cases for PT. Finally, PT is used to examine the mechanisms linking conditions to outcomes.²

However, the application of set theory and QCA raises some approach-specific issues. In this article, I address one such issue: Which, if any, gains for the analysis of an outcome can come from PT in negative cases in set-theoretic MMR? By negative cases, I simply mean cases where the outcome does not occur.

Researchers using PT often refer to negative cases when arguing why their perspectives on positive cases are valid. For instance, in her study of the “nuclear taboo” in American foreign policy, Tannenwald (1999:442-43) discusses the decision to bomb Hiroshima and Nagasaki (a negative case of nuclear nonuse). She shows that—while some protested using nuclear weapons against Japan—moral arguments did not play the role they did in later nonuse decisions.

In another well-known example, Skocpol (1979) uses cases where social revolutions did not happen to support her study of the French, Russian, and Chinese revolutions. For instance, she examines why the Meji Restoration in Japan did not result in a revolution, even though it resulted in a political crisis resembling the crisis of prerevolutionary France. She argues that Japanese bureaucratization and the absence of a powerful landed upper class meant that Meji reforms were not met with the resistance and peasant rebellions that fueled the revolution in France (see especially Skocpol 1979:99-103, 109-11).

As these examples illustrate, researchers in the applied PT literature invoke negative cases. Yet, two characteristics of set-theoretic approaches complicate the discussion in set-theoretic MMR significantly.

First, set-theoretic causation is asymmetric.³ As a consequence, the causes of an outcome Y are not necessarily the reverse of the causes of its negation or absence ∼Y (read: “not Y.” For a discussion of asymmetry, see Schneider and Wagemann 2012:81-83). This means that researchers may hesitate to invoke negative cases, since some differences and similarities between positive and negative cases can be ascribed to asymmetry. Second, because QCA often assigns cases to qualitatively different categories (or configurations), comparing cases across configurations does not lend much direct analytical leverage (e.g., Schneider and Rohlfing 2013:575).⁴

These two characteristics mean that established case selection procedures only consider negative cases useful in two instances. First, when they contradict the analysis (i.e., when they are negative but the analysis predicts that they should be positive) and hence present a problem in need of a solution. Second, when they can be matched and compared with nearly identical positive cases. The aim of the matching procedure is to approximate Mill’s Method of Difference, permitting (symmetric) identification of the difference a cause makes for an outcome (e.g., Schneider and Rohlfing 2014:12). These procedures are sound, but they are overly limiting. In particular, they are limiting because suitably similar match cases will often not be available.

In this article, I will argue that established procedures underutilize the leverage negative cases can provide. In particular, I argue that what I term nondeviant negative cases—negative cases that are typical of the sufficient conditions for the absence of an outcome—can be of great value.

My main message is this: When QCA is mixed with PT, studies of nondeviant negative cases are analytically useful both with and without positive match cases. Contrary to current recommendations, I argue that it is not necessary to approximate a Method of Difference design to gain from studying these cases.⁵

I will present three reasons, or “justifications,” why studies of nondeviant negative cases are worth engaging post-QCA. I will show what their use can mean to conclusions both about negative cases and about positive ones. None of my justifications hinge on method-of-difference style comparisons with available positive match cases. Table 1 summarizes my arguments (using Y to signify an outcome).

Table 1.

Overview of the Argument.

Justification	Basic Argument	Recommendation (Consequence)
Inferential	To understand processes in negative cases, we need to study them in cases where Y could have occurred	Focus on failure mechanisms in processes leading to ∼Y
Theoretical	The theoretical models leading to Y and ∼Y must include the same fundamental elements	Search for theoretical disagreement in processes leading to Y and ∼Y
Logical	The mechanisms leading to Y and ∼Y cannot be illogically similar	Study elements of the mechanism leading to Y in negative cases

The first justification is inferential: Precisely because set-theoretic MMR involves asymmetric claims and qualitative distinctions, there are limits to how much an analysis can claim about negative cases without studying them. However, in carefully bounded populations, negative cases are interesting both for their own sake and because they can show how an explicitly possible outcome fails to come about. Consequently, studies of negative cases may focus on what one might call “failure mechanisms.” In addition to creating knowledge about negative cases, this may highlight a need to refine mechanisms proposed to produce the outcome in positive cases.

The second justification refers to theory: Processes leading to different outcomes are likely to be more diverse than processes leading to the same outcome. This diversity can expose theories to conditions under which their assumptions become contradictory or unexplored factors prove to be relevant. Consequently, studies of negative cases should be attentive to the assumptions behind the processes claimed to produce outcomes in positive cases. If these assumptions contradict or differ in positive and negative cases, the analysis highlights a need to refine the hypothesized processes in order to align them.

The final justification is logical: Studies of negative cases can ensure that the mechanism proposed to produce the outcome in positive cases is not at work in the negative cases as well. Consequently, studies of negative cases should focus, at least in part, on the mechanisms proposed to produce outcomes in positive ones. If mechanisms producing an outcome and its absence are illogically similar, the mechanism must be either rejected or refined.

As is clear, the approach I propose assumes that the researcher has specified a mechanism producing the outcome (set-theoretic MMR does not necessarily require this, see Rohlfing and Schneider 2015). However, this does not mean that negative cases are only useful when positive cases are also studied. All that is required is a hypothesis, which could be based on theory or on previous work. This means that full-fledged theory-building PT (Beach and Pedersen 2013), where the researcher induces mechanisms from data largely without the guidance of theory, should at least begin with positive cases. But in theory-testing PT (Beach and Pedersen 2013), I propose negative cases, and nondeviant negative cases in particular, as useful sources of leverage.⁶

The article proceeds as follows. In the second section, I discuss nondeviant negative cases and case selection in set-theoretic MMR on sufficiency. Here I also explain why I focus on sufficiency only (and hence ignore necessity). In the third section, I present an exemplary study of social pacts, which I will refer to throughout (Avdagic 2010). In the fourth through sixth sections, I outline the inferential, theoretical, and logical gains from studying nondeviant negative cases one by one. In each section, I emphasize what each justification means to how we should study negative cases in set-theoretic MMR. Additionally, I apply the guidelines I emphasize to Avdagic’s (2010) study. I conclude in the seventh section.

Set-Theoretic MMR and Nondeviant Negative Cases

In this section, I first argue why I focus on sufficiency, as opposed to necessity, in the remainder of this article. Second, I detail what the focus on sufficiency means for how we can approach mechanisms. Finally, I show what nondeviant negative cases are and how currently recommended case selection strategies in set-theoretic MMR use them.

I will focus on sufficiency for two reasons. First, a focus on sufficiency aligns with QCA as its core results pertain to sufficiency. Concisely, QCA treats cases as configurations of conditions and attempts, using Boolean minimization, to determine which combinations of these conditions are sufficient for an outcome. The resulting combinations are referred to as the solution. If multiple combinations are sufficient for an outcome, each is referred to as a term (for an extensive introduction to QCA, see Schneider and Wagemann 2012). As I will be operating with separate solutions for outcomes and their absence, I refer to the sufficient solution for an outcome Y as the Y-solution and the sufficient solution for the absence of Y as the ∼Y-solution.

Second, a focus on sufficiency also aligns with PT. To see this, let us conceive of mechanisms as what causes their associated causes to cause their associated outcome (Goertz and Mahoney 2012:100). And let us adopt the idea that mechanisms produce their associated outcome (e.g., Beach and Pedersen 2013:chapter 3). On these two premises, mechanisms in set-theoretic MMR must be sufficient for their associated outcomes. Sufficient conditions ensure that their outcomes occur as they constrain cases to be positive in their presence. They produce outcomes. Necessary but insufficient conditions do not produce outcomes. Instead, necessary conditions constrain cases to be negative in their absence but permit that anything can happen in their presence. Hence, considering mechanisms as necessary but not sufficient for outcomes is unattractive. Insufficiency would permit the outcome not to occur in the presence of the mechanism.

Similarly, considering conditions in a QCA as necessary but insufficient to initiate a mechanism is not attractive. This would mean that the conditions do not produce the outcome through the mechanism. Instead, the conditions would permit anything to happen in their presence.

Thus, if we conceive of mechanisms as I have outlined, conditions must be sufficient for a mechanism, which is sufficient for an outcome (see also Mikkelsen 2015; Rohlfing 2012:152; Rohlfing and Schneider 2015).⁷

Within a mechanism, each mechanism element, or part of the mechanism, must have these same characteristics. It must have a sufficient cause, comprising either one or more other conditions or mechanism elements. And it must be a sufficient cause, either individually or jointly with other conditions or mechanism elements, of one or more mechanism elements or the outcome. If this is not the case, the productive continuity of the mechanism can break down since insufficient mechanism elements permit anything to happen in their presence. This is unattractive. Thus, to ensure productive continuity, PT in set-theoretic MMR involves mechanisms comprising sufficiency chains (Mikkelsen 2015). A focus on sufficiency accommodates this. A focus on necessity would not.⁸

Next, I fully introduce nondeviant negative cases. Set-theoretic MMR on sufficiency distinguishes between five types of cases (see Schneider and Rohlfing 2014):

Typical cases that are consistent with a solution and members of both solution and outcome.

Deviant cases for consistency in degree that are not fully consistent with a solution but are members of both solution and outcome.⁹

Deviant cases for consistency in kind that are members of the solution but not the outcome and hence qualitatively contradict the solution.

Deviant cases for coverage that are members of the outcome but not the solution and hence are not explained by the solution. These cases always deviate in kind.

Individually irrelevant (IIR) cases that are members of neither solution nor outcome.

Figure 1 shows an enhanced XY plot used for case selection in the existing literature (e.g., Schneider and Rohlfing 2013:579). The figure plots membership in a Y-solution against membership in Y. Cases above the diagonal are fully consistent with the Y-solution. Cases above the horizontal line are members of Y. Finally, cases to the right of the vertical line are members of the Y-solution. In the figure, I present case types for the Y-solution in normal font and case types for the ∼Y-solution in boldface (I refer to deviance in kind simply as deviance).

Figure 1.

Enhanced XY plot with positive and negative case types. Note: Y-solution case types in normal font. ∼Y-solution case types are in boldface. Case types in zones 4 and 5 are identical.

Figure 2.

Identifying nondeviant negative cases.

A basic principle that guides the types cases is: The solutions for Y and ∼Y cannot be the same. If they were, the solutions would create simultaneous subset relations with Y and ∼Y. Simultaneous subset relations occur when the same condition(s) are deemed sufficient for both outcome and its absence. This occurrence is not logically feasible (Schneider and Wagemann 2012:237-44).

Cases in zone 1 are typical of the Y-solution, whereas cases in zone 2 are deviant for consistency in degree from the Y-solution. Because they are members of the Y-solution, neither of these two types of cases can be members of the ∼Y-solution. Additionally, they are members of Y. Hence, they are IIR cases for the ∼Y-solution.

Cases in zone 3 are deviant for consistency in kind. They are negative when the Y-solution expects them to be positive. But since they are members of the Y-solution, they cannot be members of the ∼Y-solution. Hence, these cases do not contradict the ∼Y-solution but are also not explained by it. They are deviant for coverage from the ∼Y-solution.

Cases in zone 6 that are deviant for coverage from the Y-solution may or may not be members of the ∼Y-solution. If they are members, they are deviant for consistency in kind from the ∼Y-solution as they are positive when this solution predicts that they should be negative. If they are not members, they are IIR cases for the ∼Y-solution.

Finally, cases in zones 4 and 5 are IIR cases for the Y-solution. Since they are not members of the Y-solution, they may or may not be members of the ∼Y-solution. If they are not members of the ∼Y-solution, they are deviant for coverage for this solution. If they are members of the ∼Y-solution, they may or may not be fully consistent with this solution. If they are not fully consistent, they are deviant for consistency in degree for the ∼Y-solution. If they are fully consistent, they are nondeviant negative cases.

Thus, I can now provide a definition of nondeviant negative cases as cases that are typical for the ∼Y-solution. They are a, possibly exhaustive, subset of IIR cases for the Y-solution. Figure 2 summarizes how nondeviant negative cases can be identified as negative cases that are members of and fully consistent with the ∼Y-solution. In addition, the figure shows how other types of cases (marked in bold) relate to the ∼Y-solution.

Existing case selection recommendations highlight three uses for negative cases. These are best illustrated with reference to the zones in Figure 1. First, cases in zone 3 can be examined either alone or in comparison with cases in zone 1 to find why they contradict the Y-solution. Second, cases in zones 4 and 5 can be compared with cases in zone 6 to develop new explanations for Y. This requires that the selected cases are identical on the conditions included in the analysis. The analysis of the selected cases then searches for conditions that can distinguish the cases from each other. Such conditions would account for why cases in zone 6 are positive. Third, cases in zone 1 can be compared to cases in zone 5. This strategy requires that the selected cases are similar on all conditions in the relevant term but one. The strategy thus creates a comparison following the logic of Mill’s method of difference (Schneider and Rohlfing 2014). The aim is to identify how the one difference between the selected cases account for their different outcomes. I am concerned with this third strategy in particular. I argue that studying cases in zone 5, and zone 4, is useful even when no cases in zone 1 are similar enough to satisfy the one-difference requirement. So long as a researcher has a working hypothesis concerning the mechanism producing Y, I argue, cases in zones 4 and 5 can even be analyzed by themselves. That is, I argue that IIR cases are not always, in fact, individually irrelevant.

I will argue that nondeviant negative cases are particularly worth studying. Some of my recommendations will extent to other types of negative cases as well. However, since the ∼Y-solution proposes a consistent account of why nondeviant negative cases are negative, I view them as more fruitful targets for analyses than other types of negative cases.

Before introducing my example, let me make a point to avoid misunderstanding. Much has been written on how doing case study research without negative cases either results in selection bias (Geddes 1990) or may be outright impossible (King, Keohane, and Verba 1994:129-30). In PT, these claims do not hold. Here, studies of only positive cases are both possible and valuable (Beach and Pedersen 2013; Collier, Mahoney, and Seawright 2004; George and Bennett 2005; Goertz and Mahoney 2012). I do not claim that studying negative cases is necessary for causal inference. I do claim it is highly useful for set-theoretic MMR. This is merely to prevent the reader from thinking that I am rehearsing variations over well-known themes from “the statistical worldview” (McKeown 1999). I am not.

The Empirical Example: Social Pacts in Europe

In this section, I introduce Avdagic’s (2010) study of social pacts in Europe. I will use her study as an example throughout. However, I am not attempting to question her contribution or contribute to her field. The aim is solely the example.

Avdagic (2010) provides an analysis of why some Western European countries responded to economic internationalization by relying on social pacts. Her analysis includes the outcome “reliance on social pacts as a strategy of economic adjustment during the 1990s” (SOPC) and four conditions: “Maastricht imbalance” (MAAS), the members of which do not fulfil the European Union convergence criteria, “high unemployment” (UNEM), “intermediary union centralization” (MEDC), and finally “electorally weak governments” (MING).¹⁰ Table 2 depicts the SOPC-solution.¹¹

Table 2.

Avdagic’s SOPC-Solution.

Solution for SOPC	Consistency	Raw Coverage	Unique Coverage	Cases with Membership > .5
MAASMEDCMING +	0.961	0.423	0.423	Portugal, Italy, Spain
∼MAASUNEMMEDC*∼MING +	1.00	0.154	0.154	Ireland
∼MAASUNEM∼MEDC*MING	1.00	0.192	0.192	Finland

Note: Conditions: {MAAS, UNEM, MEDC, MING}, inclusion cutoff = 0.8. There are no deviant cases. MAAS = Maastricht imbalance; MEDC = intermediary union centralization; MING = electorally weak governments; SOPC = reliance on social pacts as a strategy of economic adjustment during the 1990s; UNEM = high unemployment.

The SOPC-solution fits the data well (solution consistency is 0.978 and solution coverage is 0.769) and does not result in any deviant cases for either consistency in kind or coverage. Spain deviates in degree for consistency. This means that all negative cases are IIR for the SOPC-solution. I will show below that most are in fact nondeviant negative cases.

Next, I reverse the outcome and derive the ∼SOPC-solution using the same conditions as in Table 2. I show the result in Table 3. Once again, the solution fits the data well (solution consistency is 0.927 and solution coverage is 0.864). As the table reveals, a number of cases are jointly covered by several terms (they feature joint coverage indicated by jc in the table). The ∼SOPC-solution leaves no deviant cases for consistency in kind and leaves one case, Greece, as deviant for coverage.

Table 3.

∼SOPC-Solution for Avdagic’s Data.

Solution for ∼SOPC	Consistency	Raw Coverage	Unique Coverage	Cases with Membership > .5
∼MEDC*∼MING+	0.910	0.585	0.114	Germany, Austria^jc, the Netherlands^jc, Belgium^jc, France^jc, United Kingdom^jc
MAAS*∼MEDC +	0.933	0.636	0.165	Austria^jc, the Netherlands^jc, Belgium^jc, France^jc, United Kingdom^jc, Sweden
∼MAASMEDCMING	1.00	0.114	0.114	Denmark

Note: Conditions: {MAAS, UNEM, MEDC, MING}, inclusion cutoff = 0.8. Greece is deviant for coverage. ^jc = joint coverage; MAAS = Maastricht imbalance; MEDC = intermediary union centralization; MING = electorally weak governments; SOPC = reliance on social pacts as a strategy of economic adjustment during the 1990s; UNEM = high unemployment.

All positive cases are IIR for the ∼SOPC-solution. In fact, they have to be IIR as they are positive and are members of the SOPC-solution. Most IIR cases for the SOPC-solution are nondeviant negative cases. Only Belgium and the Netherlands deviate in degree for consistency from the ∼SOPC-solution.

The exhaustive list of typical cases is thus Finland, Ireland, Portugal, and Italy. The exhaustive list of nondeviant negative cases is Austria, Denmark, France, Germany, the United Kingdom, and Sweden.

Applying Schneider and Rohlfing’s (2013:581) principle of maximum set membership to the SOPC-solution results in a recommendation to select Italy, Ireland, and Finland.¹² But as I am making the case for studying negative cases, I will focus on only one case from the term covering the most cases and focus attention on the ∼SOPC-solution. Thus, I focus on Italy as a typical of the term MAAS*MEDC*MING and SOPC.

Applying the principle of maximum set membership to the ∼SOPC-solution, along with the recommendation to avoid selection of jointly covered cases (Schneider and Rohlfing 2013:567), results in a recommendation to select Germany, Sweden, and Denmark.¹³ I select Sweden as typical of the term MAAS*∼MEDC and ∼SOPC.

It will be useful to explicate how Avdagic (2010) theorizes the mechanisms leading to SOPC. Consider in particular the term MING*MAAS*MEDC, which covers Italy. I have depicted the mechanism associated with this term in Figure 3. The boxes in the figure are conditions, mechanism elements, and the outcome. The arrows are sufficiency links, indicating that the element at their tail is sufficient for the element at their head. Multiple-tailed arrows indicate that the elements at their tails are jointly sufficient for the element at their head (I signify these using ●; see also Goertz and Mahoney 2005; Mikkelsen 2015).

Figure 3.

Avdagic’s Argument.

Avdagic’s (2010) argument for the MING*MAAS*MEDC term is the following. MAAS creates an economic problem needing a solution. Social pacts become a solution to this problem (denoted PAC.SOL in Figure 3) as labor unions are centralized enough to be capable of effectively implementing a social pact but not centralized enough to make the necessary adjustments by themselves (MEDC). Politically, weak governments (MING) need extra-parliamentary political support for to make their solution viable (POL.SUP in the figure). Thus, MING produces a need for political support whereas the combination of MAAS and MEDC produces an economic problem that social pacts could viably address. Subsequently, the combination of this economic problem and the need for political support produces engagement of social partners by governments (ENGAGE). This produces agreement (AGREE) and, finally, social pacts (SOPC; Avdagic 2010:648).

I will not engage deeply with the positive Italian case as my emphasis is on negative cases in set-theoretic MMR. It suffices for my purposes that Regini and Colombo’s (2011) analysis of social pacts in Italy accords well with Avdagic’s expectations. Indeed, Avdagic notes the “perfect” account of the Italian case (Avdagic 2010:648-49). Weak governments had both political and economic reasons to invite social partners to the negotiating table, and they did on several occasions. I return to Avdagic’s (2010) study and the negative Swedish case in particular after each of my three “justifications,” which I present one by one in the following three sections.

Inferential Gains

My first argument concerns the inferential gains for set-theoretic MMR from studying negative cases and nondeviant negative cases in particular. The argument proceeds in two steps. First, I argue that, given a properly constituted population or universe of cases, negative cases are of interest simply because they are negative. This is particularly relevant for nondeviant negative cases because QCA provides sufficient conditions for why the cases are negative. Second, I argue that, again given a properly conceived population of cases, the PT component of set-theoretic MMR ought to study how mechanisms in negative cases fail to produce a positive outcome.

Clearly, a proper constitution of the population of cases is important. In particular, researchers need to select negative cases with care. Identifying relevant negative cases is often neither obvious nor a one-time choice. Rather, which cases should be analyzed is determined in the course of a back and forth between theory and evidence. In this process, the scope of inquiry is limited to relevant negative cases (Ragin 2000).

A commonplace recommendation in the literatures on both QCA and PT is to restrict attention to negative cases that resemble the positive ones enough to be plausible candidates for the occurrence of the outcome. The reason is what philosophers refer to as “the Raven Paradox.” Mahoney and Goertz (2004:653) explain:

The paradox begins with the hypothesis that “all ravens are black.” The positive cases which clearly support the hypothesis are black things that are ravens and ravens that are black. The paradox arises from the logical fact that all nonblack, nonraven things also support the hypothesis. We intuitively feel that most—though probably not quite all—nonblack, nonraven things are not very useful in testing this hypothesis.

In order to arrive at a useful testing ground for finding causes of an outcome (i.e., one without too many nonblack nonraven things), researchers ought to select cases in which the outcome either is present or could plausibly have been present. The constitution of the population of cases is subject to a “possibility principle” (Mahoney and Goertz 2004). This is good practice in QCA as well (Berg-Schlosser and De Meur 2009; Ragin 2000).

The possibility principle is the reason, for instance, why studies of the democratic peace thesis focus on crises that could have been wars (Owen 1994) and why Skocpol (1979; as also argued by Mahoney and Goertz 2004:660) chooses cases of nonrevolution where revolution could have happened. Negative cases are only included when the positive outcome could plausibly have occurred but did not.¹⁴

Within the scope of the possibility principle, the corollary of this view is that the absence of an outcome ∼Y becomes of interest for set-theoretic MMR since the outcome Y is explicitly possible for all cases. That is, there is reason to examine the negative cases simply because they are negative. This argument applies in particular to nondeviant negative cases since the ∼Y-solution presents a reason for them being negative. Studying these cases can help the research uncover whether the ∼Y-solution is corroborated by within-case evidence.

Let me take the argument a little further. Because the included instances of ∼Y could have been instances of Y, focus can shift from studying causes of ∼Y to studying why mechanisms producing Y fail in the negative cases. Because Y could have emerged, mechanisms pushing to produce Y may be in motion in all cases, and studying negative cases can help illuminate why these processes break down. In this endeavor, nondeviant negative cases are particularly useful. Since the ∼Y-solution proposes why these cases are negative, it can help guide the examination of the reasons why Y fails to emerge.

The example I have already provided from Tannenwald’s (1999) study of nonuse of nuclear weapons shows how this approach works. Her study of the decision to bomb Hiroshima and Nagasaki emphasizes that some actors involved in the decision-making process protested the use of nuclear weapons against Japan. However, these voices were eventually ignored because their arguments did not resonate with a “nuclear taboo” the way similar arguments would later.

Similarly, in her analysis of the “revolutionary events” in Prussia/Germany in 1848–1850, Skocpol (1979:144-47) notes how revolutionary upheavals spread across Europe at the time. However, the Prussian/German upheavals failed to become a social revolution. The reason was that they did not result in the dissolution of the army as they had in France, and as they later would in Russia (see also Skocpol and Somers 1980). Thus, like Tannenwald, Skocpol uses a failure mechanism in a negative case to emphasize the importance of the breakdown of state structures for social revolutions to occur.

By studying failure mechanisms in this way, researchers can come to a better understanding of mechanisms in both positive and negative cases. This may be particularly useful, for instance, when policy trends or administrative fashions seemingly occur in waves across a range of cases (e.g., Lah and Perry 2008), or when external political (e.g., Vachudova 2005) or economic (e.g., Avdagic 2010) pressures put strains on existing behavior and institutions across a range of cases.

Turning to the social pact example, the constitution of Avdagic’s (2010) population is based on economic conditions. Specifically, the 14 European Union member states she includes are all welfare states subject to constraints from economic internationalization and the Economic and Monetary Union’s convergence criteria (Avdagic 2010:629). Thus, given that these factors were present throughout the European Union of the 1990s, the outcome (SOPC) is possible in all cases in question (as well as in some cases she leaves out, see also Regini 2000:6-8).

Thus, among the 14 countries, Avdagic (2010) studies ∼SOPC is of interest as it is puzzling why countries like Denmark or Sweden did not rely on social pacts when facing the challenges from economic internationalization. Additionally, as an inspection of Tables 2 and 3 will show, there is more to gain from an inferential standpoint in selecting Germany or Sweden rather than cases from the Y-solution terms not covering Italy (i.e., selecting Ireland or Finland). The former would be informative on more cases simply because there are more countries like Germany or Sweden.

Beyond this, a study of a negative case can focus on how some European welfare states handle economic internationalization and convergence criteria without relying on social pacts. Given the pressure from economic internationalization, studying how Swedish governments handled economic constrains without social pacts is both interesting and informative for the study of social pacts.

In the Swedish case, economic problems rooted in internationalization were overwhelming in the 1990s and reflected themselves in a Swedish Maastricht imbalance (MAAS). Governments and social partners were hardly passively facing these problems. However, they did not successfully pursue social pacts. Instead, governments responded to the crisis of the Swedish welfare state with austerity. As I will discuss further in coming sections, the social pact solution was attempted in Sweden. Eventually, the attempts failed. The social partners disagreed too much on the solutions to Sweden’s economic problems and indeed on the need for and benefits of central bargaining (cf. Huber and Stephens 1998:380-82). The disagreement was partly rooted in the historical dominance of the highly centralized Swedish unions (∼MEDC), which made them take a tough negotiating stance and made organized business view them as unattractive bargaining partners (Blyth 2001; see also Baccaro and Simoni 2008). Hence, the Swedish case can show how Sweden’s term (MAAS*∼MEDC) is linked to ∼SOPC. Additionally, the failure mechanism in the Swedish case points to the importance of the social partners’ interests aside from the interests of governments emphasized in Figure 3. Below, I will return to this argument. For now, let me turn to the theoretical gains.

Theoretical Gains

The theoretical gains I will discuss pertain to a demand for theoretical consistency. Specifically, within the confines of a single study, it must be demanded that assumptions on human motivation, decision making, and similar theoretical bases should be the same in all cases. The actual motivating factors may differ across cases, but the assumptions about which factors can possibly motivate must be invariant. In this respect, negative cases constitute a valuable source of differentiated processes, which heighten the risk of uncovering theoretically inconsistent claims. Since outcomes are different, processes must be different, but human beings must remain the same.

Before elaborating on this point, a brief discussion on the nature of mechanisms is worthwhile as it is consequential for how theoretical consistency can be interpreted. I approach mechanisms on three analytical levels: empirical, theoretical, and ontological. At the empirical level, mechanisms focus on the predictions of how empirical cases behave if causes produce outcomes through specified mechanisms. Much methodological work has already discussed how evidence may be linked to these predictions (e.g., Beach and Pedersen 2013:chapters 6 and 7; Bennett 2008; Mahoney 2012; Rohlfing 2012:chapters 6 and 7). The way in which analyses evaluate evidence is of little consequence for my current purposes. Hence, I leave the empirical level aside for now.

On the theoretical level, mechanisms entail some informed idea of why their different parts relate to each other. Mechanisms detail how conditions shape actors’ beliefs, the constraints they face, and ultimately how their behavior shapes outcomes (see, e.g., Hedström and Swedberg 1996; Hedström and Ylikoski 2010). As I have argued, to be feasibly producing outcomes through a mechanism in set-theoretic MMR, conditions must be sufficient for a mechanism, which is sufficient for its associated outcome. The theoretical level of the mechanism details the reasons why these relations occur (Beach and Pedersen 2013:chapter 4).

Finally, the theoretical ideas about why a mechanism would operate are underpinned by an ontological level. This level embeds assumptions about how the world “works,” how human beings are motivated and make decisions. Behind theoretical ideas are invariant principles, which drive the causal force that makes the mechanism productive (Waldner 2010). One well-known example of a set of such principles is rational actor models, built on the assumption that human decision making and motivation is based on weighing gains and losses according to exogenous preferences.

Moving from empirical predictions to invariant principles, theoretical consistency becomes increasingly important. At the ontological level, invariant principles within a single study must be just that: invariant. This raises two potential issues, both of which negative cases can help expose.

First, there is a risk of outright theoretical incommensurability. Social science theories do not all rest on similar assumptions and some might be contradictory (Harvey and Cobb 2003; Smith 2003). Of course, the borders between “paradigms” are porous and plenty of cross-cutting work is possible. However, there are real limits to the compatibility between perspectives. Crosscutters often need to engage in serious—but often highly informative—tampering with models, ideas, and assumptions (Lichbach 2009; Sil and Katzenstein 2010).

The study of negative cases can help expose problems with models by forcing them to engage with differentiated processes leading to different outcomes. If commensurability is threatened in the process, there is a need to adjust the model’s principles.

However, requiring commensurability does not go far enough. The second potential issue arises, even in commensurate models, when different principles are important for producing different outcomes. The assumptions on human motivation and decision making must be identical in all cases in a study.

As an example, consider a study approaching its cases from the perspective of a modified (bounded) rational actor model. Such a model can permit that an outcome did not occur in a negative case because the attention of core actors were not directed at the interests that would have made them desire that outcome. However, this raises the question of why similar actors in positive cases did focus their attention this direction. Actors in both types of cases must face the same limitations on their decision making that makes attention important in the negative case. Alternatively, the model must provide an account for why the environment in the positive cases facilitated more (or differently) informed decision making than in negative ones.

Thus, invariant principles do not necessarily entail that all outcomes must be accounted for by the same motivational factors. They simply entail that the “model of man” applied to account for one case, or set of cases, is applied to all cases. The study of negative cases presents a possibility to examine this requirement by differentiating the processes and mechanisms that are studied.

In sum, negative cases provide leverage by allowing the researcher to examine differentiated processes within the frame of one study. This will expose propositions to a heightened, and preferable, risk of uncovering theoretical inconsistency. Precisely because their outcomes diverge, processes at work in negative cases are likely to diverge more from processes in positive cases than processes in different types of positive cases from each other.

The consequence of this second justification is to direct attention to the assumptions underlying accounts of the Y-solution when examining cases covered by the ∼Y-solution in set-theoretic MMR. The study of negative cases should be attentive to, indeed search for, theoretical disagreement between the account given for instances of Y and that given for instances of ∼Y. The study of nondeviant negative cases is particularly helpful. The ∼Y-solution suggests reasons why these cases are negative, which means that the ∼Y-solution can guide the examination of nondeviant negative cases and make processes in these cases easier to trace.

In her study of social pacts, Avdagic (2010) clearly views the configurations in Table 1 as providing the reasons and means for rational actors to pursue social pacts in order to find solutions to their problems. Her “bargaining model” relies on the gains and losses of social partners and, particularly, governments considering social pacts. The conditions in her solution shape the actors’ strategic situation and consequently their decisions. As indicated, this accords with the actions of the Italian governments and social partners.

However, the case for Sweden is less clear. Swedish governments in the 1990s did pursue social pacts, but they failed. They failed not because labor unions by themselves made the adjustments needed to fulfill the convergence criteria. Nor because governments saw no need for social concertation. Instead, Swedish pact attempts failed because the social partners did not see social pacts as a viable solution. Particularly the Employers’ Confederation saw deregulation and flexibility rather than coordination as the solution (Huber and Stephens 1998; Pestoff 2002). As noted, the historical dominance of Sweden’s highly centralized organized labor (∼MEDC) helped drive this view.

The Employers’ Confederation revolted against union dominance throughout the 1980s and early 1990s. As it did, the Swedish corporatist infrastructure eroded (Lindvall and Sebring 2005). Corporatist bargains were replaced by market-friendly guiding principles for policy (Regini 2000) and by liberal economic ideas championed by the Employers’ Confederation (Blyth 2001; Pestoff 2002). Hence, when economic problems piled up, some of the central actors did not see social pacts as a viable solution. Social partners could not find common ground in important policy areas (Lindvall and Sebring 2005). In particular, the Employers’ Confederation was rejecting the idea of centralized bargaining. It no longer believed that bargaining served as a vehicle for wage moderation (Huber and Stephens 1998:380-82). In Sweden, the zeitgeist, at least until 1998, was “hostile to the very idea of social negotiations” (Pestoff 2002:303).

These observations raise interesting questions for both positive and negative cases. Most importantly, the evidence that the Swedish Employers’ Confederation’s beliefs and ideas were hostile to social pacts raises questions: Were Swedish pacts halted in their infancy because the preferences of the Swedish social partners were different from the preferences of their Italian counterparts? Did different preferences rather than different strategic situations result in different outcomes? Why did preferences diverge across countries?

One framework useful to understand these observations is Culpepper’s (2008) “common knowledge” model. This model makes bargaining partners’ views on what will further their aims endogenous to their ideas about how the economy operates. Preferences are no longer fixed. Instead, they can vary in different settings.

The common knowledge model and Avdagic’s (2010) perspective are not theoretically incommensurate. Nevertheless, the endogenous preferences proposed by Culpepper (2008) suggest a need to tweak the bargaining model. If ideas influence bargaining preferences in Sweden, they must potentially be able to shape preferences everywhere including in Italy (for evidence that they did shape preferences in Italy, see Culpepper 2008:18-26).

My point with respect to negative case selection is this: Avdagic’s (2010) argument may account for the Italian case. However, the evidence from the negative Swedish case suggests an additional reason the Italian governments and social partners could agree on social pacts. Their views on how the economy operated aligned in a way their Swedish counterparts’ did not.

Hence, Avdagic’s (2010) argument could fruitfully be supplemented by including how social partners come to share common views on potential solutions to economic problems (see Culpepper 2008). This would help account for why Swedish social partners could not find common ground and for why the Italian social partners could. Thus, endogenizing preferences adds a theoretical layer to the analyses of both positive and negative cases. It helps refine the mechanism I depicted in Figure 3.

In the subsequent section, I proceed to the most consequential justification for negative case selection in set-theoretic MMR: the logical gains.

Logical Gains

As the final justification, I argue that PT analysis of negative cases can ensure that the mechanisms producing an outcome Y and its absence, ∼Y, are not illogically similar. I will argue that mechanisms leading to different outcomes cannot be the same. Furthermore, extending this point, I will argue that only a limited class of elements of a mechanism suggested to produce a positive outcome can be present in a negative case. Specifically, no element proposed to directly or indirectly produce outcomes in a positive case must be present in a negative case.

To fix ideas, consider the hypothetical mechanisms depicted in Figure 4. In panel (a), I depict a simple causal chain connecting a condition A to an outcome Y through a mechanism M_a comprised two elements m_a ₁ and m_a ₂. Hence, this mechanism holds that A is sufficient for M_a , which is sufficient for Y. Or, including the individual elements, A is sufficient for m_a ₁, which is sufficient for m_a ₂, which is sufficient for Y.

Figure 4.

Some exemplary mechanisms.

The mechanism I illustrate in panel (b) is somewhat more complex. It links the combination of two conditions B and C to Y through a mechanism M_b . If this mechanism’s conditions B and C are to produce their associated outcome Y, the following must hold (see Mikkelsen 2015):

B is sufficient for m_b ₁;

C is sufficient for m_b ₂;

m_b ₁ and m_b ₂ are jointly sufficient for m_b ₃;

m_b ₂ is sufficient for m_b ₄;

m_b ₃ and m_b ₄ are jointly sufficient for Y.

I will use these mechanisms to illustrate the logical gains from studying negative cases in two steps. First, I will discuss the mechanisms in the figure as wholes (i.e., M_a and M_b ). Subsequently, I will unpack the mechanisms and discuss their mechanism elements.¹⁵

The basic driver of the logical gains I will discuss is avoiding simultaneous subsets. Any condition, conditions, or mechanism sufficient for an outcome Y cannot also be sufficient for the absence of that outcome ∼Y (Schneider and Wagemann 2012:237-44).

The first conclusion I will draw from this is the following: The same mechanism cannot be operating in both cases of Y and ∼Y. If the mechanism in panel (a) of Figure 4 is correct, two conclusions follow. First, A cannot be featured in cases of ∼Y. The reason is that, if A is a feature of a case and the mechanism in panel (a) is correct, A would produce M_a , which would produce Y rather than ∼Y.

Second, M_a cannot be featured in cases of ∼Y either. Because of asymmetry, this does not necessarily follow from the prior conclusion. The presence of A will ensure the presence of M_a . But M_a can occur for other reasons than A. However, if the mechanism is correct, whenever M_a occurs, Y occurs. Hence, M_a cannot occur in negative cases.

When I discussed theoretical gains, I noted that the invariant principles of a mechanism must be identical across positive and negative cases. The point I am currently making is that the reverse holds for another level of the mechanism. At the empirical level, mechanisms in positive and negative cases cannot be identical. If a study finds that they are, it follows that the mechanism proposed in the study is incorrectly specified. The logical gains of studying negative cases are acquired from examining empirically whether mechanisms that must logically be different are, in fact, different.

Next, I unpack mechanisms into their constituent parts. This expands the possibilities for simultaneous subsets considerably. Consequently, the gains from negative case selection are expanded as well. Consider the mechanism in panel (b) of Figure 4. This mechanism, if correct, entails that the conjuncture of B and C should not occur in negative cases. If B and C were both present, they would produce M_b , which would produce Y rather than ∼Y. Additionally, as I have argued, the proposed mechanism entails that M_b and ∼Y should not be observed in the same case.

However, the mechanism entails a lot more. To see exactly what, one can move backward (i.e., against the direction of the arrows) in the figure and apply the same logic as before. The conclusion for panel (b) of Figure 4 is threefold. First, m_b ₃ and m_b ₄ cannot both be present in negative cases. If they were, they would produce Y rather than ∼Y. Either m_b ₃ or m_b ₄ may be present, since they are jointly rather than individually sufficient for Y (as indicated with the ●). However, both cannot be present simultaneously if the mechanism is correct. Second, following the same line or argument, maximally one of m_b ₁ and m_b ₂ can be present in negative cases. If both were present, they would jointly produce m_b ₃, m_b ₂ would produce m_b ₄, and m_b ₃ and m_b ₄ would jointly produce Y rather than ∼Y. Finally, as already noted, maximally one of conditions B and C can be present in negative cases if the mechanism is correct.

Thus, only a limited class of mechanism elements can be observed in negative cases if a mechanism proposed to produce an outcome is true. The logical gains of negative case selection lie in the provision of an opportunity to find if mechanism elements proposed to link a solution to an outcome are present in negative cases. Additionally, if some of these elements are present, negative case selection gives an opportunity to find whether their presence in the negative case is permissible by the mechanism proposed to produce Y.

Applied researchers sometimes already use this logic. Again, Skocpol’s (1979) discussion of the Meji Restoration provides an example. Like in prerevolutionary France, foreign military pressure led to a major reform of Japanese state and society and to a major political crisis. Yet, Japan did not succumb to a social revolution. As I mentioned in the introduction, the Meji example highlights that political crises alone cannot not account for social revolutions. If they could, Japan would have experienced such a revolution. Instead, the state and peasant rebellions need to be taken into account (other examples are given in Skocpol and Somers 1980).

What does one do when encountering a simultaneous subset in positive and negative cases? I will propose two ways forward. The first is to reject the proposed mechanism. Recognizing that the mechanism cannot be correct, the researcher may choose to abandon or drastically alter it.

The second way forward is to retain the mechanism but alter it to resolve the simultaneous subset problem. Recall that, when several elements of a mechanism are needed to produce another element or outcome (marked ● in Figure 4), one of the producing elements can be featured in negative cases. This provides an alternative to rejecting the proposed mechanism.

For instance, a researcher believes the mechanism in panel (a) of Figure 4 is correct but finds m_a ₁ in a case of ∼Y. A simultaneous subset occurs, implying that the mechanism is incorrect. But studying a positive case further, the researcher finds that A initiates two mechanism elements m_a ₁ and m_a ₃ that together produce m_a ₂. If m_a ₃ is not found in the negative case, the new mechanism can be correct, provided of course that it is theoretically plausible and supported by empirical evidence.

An alternative solution builds on the inferential gains I have discussed. A study of a negative case may find that ∼m_a ₃, when combined with m_a ₁, makes the mechanism depicted in panel (a) fail to produce m_a ₂. This can give rise to the same conclusion: m_a ₁ and m_a ₃ may jointly produce m_a ₂, which then produces Y. If this solution is pursued, nondeviant negative cases are particularly useful, since the ∼Y-solution can help guide the search for additional mechanism elements.

Thus, I propose two reactions to uncovering that mechanisms in cases featuring Y and ∼Y are illogically similar. Either reject the proposed mechanism or add elements to it. Adding elements works because, as Sartori (1970) famously noted, increasing the intention of a concept decreases its extension. In other words, adding attributes to a concept makes it apply to fewer empirical instances. The same is true of mechanisms (cf. Falleti and Lynch 2009:1149). Adding elements to a mechanism means that the mechanism will operate in fewer cases. If doing so excludes negative cases from being covered by mechanism elements that will produce the outcome, the simultaneous subset problem is resolved.

In this way, PT in negative cases can either reject or refine conclusions about mechanisms in positive cases. PT in negative cases can ensure that the mechanisms proposed to produce the outcome and its absence are not illogically similar. As my discussion has shown, the consequence of this justification is that studies of negative cases should focus, at least in part, on the mechanisms proposed to produce the outcome in positive cases. The purpose of this is to ensure that negative cases feature neither the whole mechanism proposed to produce the outcome, nor elements of it that would produce Y if the proposed mechanism was correct.

Let me return one last time to the social pact example. As I noted in the third section, the mechanism Avdagic (2010) proposes links Italy’s term MAAS*MEDC*MING to SOPC relies heavily on the economic and political incentives for governments to engage social partners. As I have indicated, the Italian case corroborates this link. On several occasions, minority governments sought to address Italy’s economic problems by facilitating negotiations between employer and employee organizations and reach social pacts (Regini and Colombo 2011).

The problem is that governments in Sweden also sought to facilitate this type of negotiations.¹⁶ Looking back at the argument as I depict it in Figure 3, neither AGREE nor ENGAGE should not be observed in negative cases. Additionally, negative cases may feature maximally one of the elements “weak governments needing extra-parliamentary support” (POL.SUP) and “an economic problem that a social pact can plausibly address” (PAC.SOL). However, ENGAGE did occur in Sweden.

Although the Swedish unions had been weakened as the corporatist system weakened, they remained more than intermediately centralized (∼MEDC). Yet, rather than expecting unions to solve Sweden’s economic challenges on their own accord, the Social Democratic governments worked hard on getting social partners to agree on a social pact in 1996, 1998, and 2001. All three times the negotiations ultimately collapsed as a result of rejections by unions or organized business (Hamann and Kelly 2011:94-96).

Governments in Sweden, as in Italy, sought deals with the social partners. They did invite social partners to partake in negotiations (ENGAGE), and in 1998–1999 struggled for months behind the scenes to get the failing pact negotiations back on track. But eventually they failed (Pestoff 2002:303-5).

With this observation in hand, the argument that governments’ political (POL.SUP) and economic (PAC.SOL) incentives to engage social partners suffice to result in social pacts (SOPC) does not hold. The argument faces the challenge that governments did engage social partners also in cases where social pacts did not occur. Hence, this engagement by itself cannot be the mechanism linking a term to SOPC. If it were, social pacts would have occurred in Sweden as well.

In this instance, the problematic observation suggests a plausible way forward. The proposed argument (in Figure 3) does not include the negotiations themselves but accounts only for their initiation. The reason Sweden did not experience social pacts in the 1990s was not the unwillingness of governments to facilitate negotiations. It was the unwillingness of the Swedish social partners to reach a national-level compromise. Hence, adding a mechanism element that considers the actual negotiations is the natural way to resolve the logical problem that government engagement occurred in both positive and negative cases.

One plausible solution lies in considering internal cohesion of the organizationally centralized Swedish unions. In Sweden, divisions within organized labor prevented social pacts from emerging (see Iversen 1996). For wage bargaining in the 1990s in particular, internal dissent from the export sector was important. From 1996, this sector had engaged in sector-level agreements, which both sector-level employer and employee organizations fought to protect from national-level bargains between peak organizations (Thelen and Kume 2006:14-21).

Italian union leaders met resistance to pacts in the early 1990s. The resistance was not grounded in the defense of already established agreements. Instead, radical elements in the unions refused to cooperate with business and government altogether. This resistance was overcome through member consultations and internal democracy, partly as an attempt by the unions to secure their continuing representation in the system (Baccaro and Lim 2007:33-34; Regini and Colombo 2011:119-23). In the more centralized Swedish unions (∼MEDC), this solution was not viable. Instead, diverse organized employee groups defended different interests and made internal agreement in organized labor difficult (cf. Iversen 1996).

These observations show how studying the negative Swedish case can refine claims about positive cases such as Italy. Specifically, the observations direct attention to the interests of the social partners and how these interests are shaped by the internal cohesion of organized labor (see also Baccaro and Lim 2007). The argument linking MAAS*MEDC*MING to SOPC can take account of this by including an “internally coherent unions” element in the mechanism. The revised proposition then holds that government engagement (ENGAGE) with social partners produce agreement (AGREE) and SOPC only in combination with internally coherent unions. Hence, a study of the negative Swedish case can refine Avdagic’s (2010) conclusions on positive cases from her article.

I will end the empirical discussion by emphasizing that I have focused on social pacts only as an example. None of the theoretical perspectives I have discussed are new. They have been discussed by Culpepper (2008), Baccaro and Lim (2007), and others. But they are not incorporated in Avdagic’s (2010) interpretation of her QCA results.¹⁷ I have used the nondeviant negative Swedish case to argue that cases like it can enrich the interpretation and permit it to give an improved account of both positive and negative cases. However, my main point is methodological as my conclusions will reflect.

Conclusions

A range of analytical gains may be acquired from PT in negative cases in set-theoretic MMR. This is true even when no suitably similar cases exist for comparisons. Specifically, negative case selection and PT in selected negative cases brings insight into the mechanisms driving both the outcome and its absence. The PT component of a set-theoretic MMR design can benefit significantly from negative case selection by improving proposed mechanisms to make them more consistent theoretically and more congruent with empirical evidence. Thus, I propose that examination of negative cases, and of nondeviant negative cases in particular, is both useful and consequential for research combining QCA and PT.

I have presented three arguments, or “justifications,” for negative case selection: First, inferential gains can be achieved by examining nondeviant negative cases for their own sake and by studying how mechanisms producing outcomes break down. Second, theoretical gains can be achieved by exposing the theoretical basis of mechanisms proposed to produce the outcome to differentiated processes and, consequently, a heightened risk of theoretical inconsistency. Finally, logical gains can be achieved from the insurance that the mechanisms featured in positive and negative cases are not similar at a level at which they cannot be if they are correctly specified.

There are multiple consequences of these gains. First, uncovering a failure mechanism can pose questions about the mechanism producing the outcome. Second, uncovering theoretical inconsistency can reveal that a theoretical model overlooks an important factor needed to understand why positive and negative cases diverge. Finally, uncovering that mechanisms in positive and negative cases are illogically similar may lead to rejection of a mechanism or to a refinement of it by adding elements that distinguish positive and negative cases.

Reconciling a mechanism proposed to produce an outcome with questions raised by negative cases may often entail searching for additional relevant explanations or mechanism elements. It is often necessary to engage in some examination beyond the initially hypothesized mechanism to arrive at answers that work. Depending on whether the answers introduce new conditions or new mechanism elements, the QCA part of a set-theoretic MMR design may need revisiting. Thus, negative case selection can force another round of dialogue between theory and evidence throughout both stages of the research design. This dialogue brings the analysis closer to truly consistent causal claims. Although additional work is indubitably involved, set-theoretic MMR should not permit itself to forego the gains from negative thinking.

Footnotes

Acknowledgments

I thank Derek Beach, Jens Blom-Hansen, Fernando Casal Bértoa, Jørgen Møller, Rasmus Brun Pedersen, Karin Hilmer Pedersen, Ingo Rohlfing, Svend-Erik Skaaning, and two anonymous reviewers for their helpful comments and suggestions.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Notes

References

Avdagic

Sabina

. 2010. “When Are Concerted Reforms Feasible? Explaining the Emergence of Social Pacts in Western Europe.” Comparative Political Studies 43:628–57.

Avdagic

Sabina

. 2011. “The Emergence of Social Pacts: Analysing Negotiation Processes and Bargaining Outcomes.” Pp. 45–61 in Social Pacts in Europe: Emergence, Evolution and Institutionalization, edited by Avdagic

Rhodes

Visser

. Oxford, UK: Oxford University Press.

Baccaro

Lucio

Lim

Sang-Hoon

. 2007. “Social Pacts as Coalitions of the Weak and Moderate: Ireland, Italy and South Korea in Comparative Perspective.” European Journal of Industrial Relations 13:27–46.

Baccaro

Lucio

Simoni

Marco

. 2008. “Policy Concertation in Europe: Understanding Government Choice.” Comparative Political Studies 41:1323–48.

Beach

Derek

. 2015. “Combining QCA and Process-Tracing in Practice – A Study of Congruence Between Voter Views and Governmental Positions in the EU.” Working paper, Aarhus: Aarhus University.

Beach

Derek

Rohlfing

Ingo

. 2015. “Integrating Cross-Case Analyses and Process Tracing in Set-Theoretic Research: Strategies and Parameters of Debate.” Working paper, Aarhus and Bremen: Aarhus University and BIGSSS.

Beach

Derek

Pedersen

Rasmus B.

. 2013. Process Tracing Methods: Foundations and Guidelines. Ann Arbor: University of Michigan Press.

Bennett

Andrew

. 2008. “Process Tracing: A Bayesian Perspective.” Pp. 702–21 in The Oxford Handbook of Political Methodology, edited by Box-Steffensmeier

J. M.

Brady

H. E.

Collier

. Oxford, UK: Oxford University Press.

Berg-Schlosser

Dirk

De Meur

Gisèle

. 2009. “Comparative Research Design: Case and Variable Selection.” Pp. 19–32 in Configurational Comparative Methods: Qualitative Comparative Analysis (QCA) and Related Techniques, edited by Rihoux

Ragin

C. C.

. Thousand Oaks, CA: SAGE Publications.

10.

Blyth

Mark

. 2001. “The Transformation of the Swedish Model: Economic Ideas, Distributional Conflict, and Institutional Change.” World Politics 54:1–26.

11.

Collier

David

Mahoney

James

Seawright

Jason

. 2004. “Claiming Too Much: Warnings about Selection Bias.” Pp. 85–102 in Rethinking Social Inquiry: Diverse Tools, Shared Standards, edited by Brady

H. E.

Collier

. Lanham, MD: Rowman & Littlefield.

12.

Culpepper

Pepper D.

2008. “The Politics of Common Knowledge: Ideas and Institutional Change in Wage Bargaining.” International Organization 62:1–33.

13.

Falleti

Tulia G.

Lynch

Julia F.

. 2009. “Context and Causal Mechanisms in Political Analysis.” Comparative Political Studies 42:1143–66.

14.

Fernando

Casal Bértoa

. 2015. “It’s Mostly About Money! A Set-Theoretic Multi-Method Approach to the Sources of Institutionalization in Post-Communist Party Systems.” Sociological Methods & Research. doi: 10.1177/0049124115588998

15.

Geddes

Barbara

. 1990. “How the Cases You Choose Affect the Answers You Get: Selection Bias in Comparative Politics.” Political Analysis 2:131–50.

16.

George

Alexander L.

Bennett

Andrew

. 2005. Case Studies and Theory Development in the Social Sciences. Cambridge, MA: The MIT Press.

17.

Goertz

Gary

Mahoney

James

. 2005. “Two-level Theories and Fuzzy-Set Analysis.” Sociological Methods & Research 33:497–538.

18.

Goertz

Gary

Mahoney

James

. 2012. A Tale of Two Cultures: Qualitative and Quantitative Research in the Social Sciences. Princeton, NJ: Princeton University Press.

19.

Hamann

Kerstin

Kelly

John

. 2011. Parties, Elections, and Policy Reforms in Western Europe: Voting for Social Pacts. London, UK: Routledge.

20.

Harvey

Frank

Cobb

Joel

. 2003. “Multiple Dialogues, Layered Syntheses, and the Limits of Expansive Cumulation.” International Studies Review 5:144–47.

21.

Hedström

Peter

Swedberg

Richard

. 1996. “Social Mechanisms.” Acta Sociologica 39:281–308.

22.

Hedström

Peter

Ylikoski

Petri

. 2010. “Causal Mechanisms in the Social Sciences.” Annual Review of Sociology 36:49–67.

23.

Huber

Evelyne

Stephens

John D.

. 1998. “Internationalization and the Social Democratic Model: Crisis and Future Prospects.” Comparative Political Studies 31:353–97.

24.

Iversen

Torben

. 1996. “Power, Flexibility, and the Breakdown of Centralized Wage Bargaining: Denmark and Sweden in Comparative Perspective.” Comparative Politics 28:399–436.

25.

King

Gary

Keohane

Robert O.

Verba

Sidney

. 1994. Designing Social Inquiry: Scientific Inference in Qualitative Research. Princeton, NJ: Princeton University Press.

26.

Lah

T. J.

Perry

James L.

. 2008. “The Diffusion of the Civil Service Reform Act of 1978 in OECD Countries: A Tale of Two Paths to Reform.” Review of Public Personnel Administration 28:282–99.

27.

Lichbach

Mark Irving

. 2009. “Thinking and Working in the Midst of Things.” Pp. 18–71 in Comparative Politics: Rationality, Culture and Structure, 2nd ed., edited by Lichabach

M. I.

Zuckerman

A. S.

. Cambridge, UK: Cambridge University Press.

28.

Lindvall

Johannes

Sebring

Joakim

. 2005. “Policy Reform and the Decline of Corporatism in Sweden.” West European Politics 28:1057–74.

29.

Mahoney

James

. 2012. “The Logic of Process Tracing Tests in the Social Sciences.” Sociological Methods & Research 41:570–97.

30.

Mahoney

James

Goertz

Gary

. 2004. “The Possibility Principle: Choosing Negative Cases in Comparative Research.” American Political Science Review 98:653–69.

31.

Mikkelsen

Kim S.

2015. “Fuzzy-Set Case Studies.” Sociological Methods & Research. doi: 10.1177/0049124115578032

32.

Møller

Jørgen

Skaaning

Svend-Erik

. 2015. “Explanatory Typologies as a Nested Strategy of Inquiry: Combining Cross-Case and Within-Case Analysis.” Working paper, Aarhus: Aarhus University.

33.

McKeown

Timothy J.

1999. “Case Studies and the Statistical Worldview: Review of King, Keohane, and Verba’s Designing Social Inquiry: Scientific Inference in Qualitative Research.” International Organization 53:161–90.

34.

Owen

John M.

1994. “How Liberalism Produces Democratic Peace.” International Organization 19:87–125.

35.

Pestoff

Victor A.

2002. “Sweden During the 1990s: The Demise of Policy Concertation and Social Partnership and Its Sudden Reappearance in 1998.” Pp. 295–310 in Policy Concertation and Social Partnership in Western Europe: Lessons for the 21st Century, edited by Berger

Compston

. Oxford, UK: Berghahn Books.

36.

Ragin

Charles C.

2000. Fuzzy-Set Social Science. Chicago: University of Chicago Press.

37.

Ragin

Charles C.

2008. Redesigning Social Inquiry: Fuzzy Sets and Beyond. Chicago: University of Chicago Press.

38.

Regini

Marino

. 2000. “Between Deregulation and Social Pacts: The Responses of European Economies to Globalization.” Politics & Society 28:5–33.

39.

Regini

Marino

Colombo

Sabrina

. 2011. “Italy: The Rise and Decline of Social Pacts.” Pp. 118–46 in Social Pacts in Europe: Emergence, Evolution and Institutionalization, edited by Avdagic

Rhodes

Visser

. Oxford, UK: Oxford University Press.

40.

Rohlfing

Ingo

. 2012. Case Studies and Causal Inference: An Integrative Framework. Basingstoke, UK: Palgrave MacMillan.

41.

Rohlfing

Ingo

Schneider

Carsten Q.

. 2013. “Improving Research on Necessary Conditions: Formalized Case Selection for Process Tracing after QCA.” Political Research Quarterly 66:220–35.

42.

Rohlfing

Ingo

Schneider

Carsten Q.

. 2015. “A Unifying Mechanismic Framework for Set-Theoretic Multi-Method Research.” Working paper, Bremen and Budapest: BIGSSS and Central European University.

43.

Samford

Steven

. 2010. “Averting ‘Disruption and Reversal’: Reassessing the Logic of Rapid Trade Reform in Latin America.” Politics & Society 38:373–407.

44.

Sartori

Giovanni

. 1970. “Concept Misinformation in Comparative Politics.” The American Political Science Review 64:1033–53.

45.

Schneider

Carsten Q.

Rohlfing

Ingo

. 2013. “Combining QCA and Process Tracing in Set-Theoretic Multi-Method Research.” Sociological Methods & Research 42:559–97.

46.

Schneider

Carsten Q.

Rohlfing

Ingo

. 2014. “Case Studies Nested in Fuzzy-set QCA on Sufficiency: Formalizing Case Selection and Causal Inference.” Sociological Methods & Research. doi:10.1177/0049124114532446

47.

Schneider

Carsten Q.

Wagemann

Claudius

. 2012. Set-theoretic Methods for the Social Science: A Guide to Qualitative Comparative Analysis. Cambridge, UK: Cambridge University Press.

48.

Sil

Rudra

Katzenstein

Peter J.

. 2010. “Analytic Eclecticism in the Study of World Politics: Reconfiguring Problems and Mechanisms across Research Traditions.” Perspectives on Politics 8:411–31.

49.

Skocpol

Theda

. 1979. States and Social Revolutions: A Comparative Analysis of France, Russia, and China. Cambridge, UK: Cambridge University Press.

50.

Skocpol

Theda

Somers

Margaret

. 1980. “The Uses of Comparative History in Macrosocial Inquiry.” Comparative Studies in Society and History 22:174–97.

51.

Smith

Steve

. 2003. “Dialogue and the Reinforcement of Orthodoxy in International Relations.” International Studies Review 5:141–43.

52.

Tannenwald

Nina

. 1999. “The Nuclear Taboo: The United States and the Normative Basis of Nuclear Non-Use.” International Organization 53:433–68.

53.

Thelen

Kathleen

Kume

Ikuo

. 2006. “Coordination as a Political Problem in Coordinated Market Economies.” Governance 19:11–42.

54.

Vachudova

Milada Anna

. 2005. Europe Undivided: Democracy, Leverage, and Integration after Communism. Oxford, UK: Oxford University Press.

55.

Waldner

David

. 2010. “What Are Mechanisms and What Are They Good for?” Qualitative & Multi-Method Research 8:30–34.