Stable concepts,Footnote 1 together with a shared understanding of the analytic frameworks they establish, are routinely viewed as an essential foundation of research communities. Yet ambiguity, confusion, and disputes about concepts are common in the social sciences. One important source of this difficulty is the quest for generalization. As scholars seek to apply their models and hypotheses to more cases in the effort to achieve broader knowledge, they must often adapt their concepts to fit new contexts.
One of the most incisive treatments of this challenge is Giovanni Sartori’s influential article “Concept Misformation in Comparative Politics” (Reference Sartori1970). In this and subsequent publications (Reference Sartori and Sartori1984) he analyzed conceptual traveling, that is, the application of concepts to new cases; and conceptual stretching, that is, the distortion that occurs when a concept does not fit the new cases.
This is an old debate, and it might appear that this problem was superseded by new analytic and statistical approaches. However, this is not the case. Scholars accustomed to the language of variables will recognize that issues raised here are related to problems of establishing the validity of observation and measurement across cases. For example, analysts who have carefully derived and tested a set of hypotheses about political participation will commonly wish to probe the generality of their findings by examining the same hypotheses in additional cases. To do so, they must first establish that political participation has a sufficiently similar meaning in the new cases. An excessive concern with the difficulties of establishing equivalence among contexts of analysis can, of course, lead to the abandonment of the comparative enterprise altogether. The merit of Sartori’s approach is that it encourages the scholar to be attentive to context, yet without abandoning broad comparison.
Interest in the challenge of applying concepts across diverse contexts, and correspondingly in Sartori’s widely cited article, was stimulated by the rise of the school of comparative-historical analysis beginning roughly in the 1960s,Footnote 2 and subsequently by the comparative politics literature on authoritarianism and corporatism in the 1970s and on democratization in the 1980s and 1990s.Footnote 3 It is evident from these bodies of scholarship that broad comparison requires a use of concepts that is sensitive to context. Further, the historical depth in many of these studies is a useful reminder that the problem of conceptual stretching can arise not only from traveling across cases but also from change over time. Consequently, the challenge of achieving the virtue of conceptual traveling without committing the error of conceptual stretching remains very much with us today.
We shall examine here how concepts change – or should change – as they are applied to new cases. Sartori’s original framework is based on the assumptions of what is sometimes called a classical hierarchy, in which the relation among concepts is understood in terms of a taxonomic array of successively more general concepts, each of which encompasses concepts lower in the hierarchy (Sartori Reference Sartori1970: 1038). Each concept has clear boundaries, as well as defining properties shared by all the corresponding cases, that serve to locate it in the hierarchy. As one moves down the hierarchy, each successive concept is a “kind of” in relation to the concept above it, such that it may be called a kind hierarchy.
However, linguistic philosophy and cognitive science have presented a fundamental challenge to this understanding, arguing that in many contexts concepts follow different patterns. This challenge might seem to undermine Sartori’s approach, but we show that these alternatives can be treated in a way that is distinct from, yet complementary to, Sartori’s framework.
To provide a baseline against which these alternative perspectives can be evaluated, we first review Sartori’s procedure for modifying concepts, and then explore the distinctive issues that arise when conceptual structures do not fit Sartori’s classical pattern. We examine concerns that arise with Wittgenstein’s family resemblance concepts. This discussion suggests that Sartori’s procedure can be applied too strictly, causing analysts to abandon a concept prematurely when it initially does not appear to fit additional cases. We then consider the radial pattern analyzed by Lakoff, which suggests that concepts can be modified in distinctive ways as they are adapted to new cases.Footnote 4 We conclude by suggesting that these alternative approaches, far from being in conflict, can be used together.
Sartori’s Framework
A central element in the classical view of concepts, which provides the underpinning for Sartori’s approach, is the understanding of extension and intension (Sartori Reference Sartori1970: 1041; Sartori Reference Sartori and Sartori1984: 24). The extension of a concept is the set of cases to which it refers; the intension is the set of meanings or attributes that define the concept and establish membership.
Two complementary patterns in the relation between extension and intension are of concern here, namely, the occurrence of (1) more specific concepts with more limited extension and greater intension and (2) more general concepts with greater extension and more limited intension. Some philosophers have held that this reflects a pattern of inverse variation (Angeles Reference Angeles1981: 141).Footnote 5 In a conceptual hierarchy, these more specific and more general concepts occupy subordinate and superordinate positions, with the extension of the subordinate concepts contained inside that of the superordinate ones. This approach assumes strictly bounded concepts,Footnote 6 and each subordinate concept can be understood as a “kind of” in relation to the one above it. The hierarchy represented by these sets of terms can be called, adapting Sartori’s label, a ladder of generality.Footnote 7
An example illustrates these patterns. Max Weber’s well-known typology can be understood as involving consecutive pairs of concepts. Thus, patrimonial authority is a subtype of traditional authority; which is one of his three overall types of authority or legitimate domination; which is a subtype within the broader concept of domination (Reference Weber, Roth and Wittich1978: 212–15, 226, 231). In each successive pair of concepts, the first is a subtype, the second overarching. In relation to each subtype, the corresponding overarching concept contains a less specific meaning and covers more cases; it has greater extension and less intension.
This classical understanding of concepts helps address the problem of conceptual stretching. When scholars take a concept developed for one set of cases and extend it to additional cases, the new cases may be sufficiently different that the concept is no longer appropriate in its original form. If this occurs, they may adapt the concept by climbing the ladder of generality, thereby following the pattern of inverse variation. Thus, as analysts seek to increase the extension, they can reduce the intension to the degree necessary to fit the new contexts.
For example, scholars engaged in a comparative study of patrimonial authority might add cases that only marginally fit this concept. To avoid conceptual stretching, they could move up the ladder of generality and refer to the larger set of cases as instances of traditional authority.
This framework helps researchers proceed with greater care when addressing a basic challenge of comparative research: the effort to achieve broader knowledge through analyzing a wider range of cases. The value of this framework merits emphasis, especially in light of the recurring concern that broad comparison is difficult. Political and social reality is heterogeneous. Applying a concept in a given context requires detailed knowledge of that context, and it is easy to misapply concepts. The ladder of generality offers a specific procedure to address these issues.
Hence, Sartori’s method has deservedly served as a benchmark for analysts who wrestle with the challenge of extending concepts to new cases.
Family Resemblance
The ladder of generality assumes the clear boundaries and defining attributes of classical conceptual structures. Wittgenstein’s idea of family resemblance concepts, which entails a different principle of concept membership, suggests that this assumption should sometimes be relaxed (Wittgenstein Reference Wittgenstein1968: nos. 65–75; see also Hallett Reference Hallett1977: 140–41, 147–48; and Canfield Reference Canfield1986). The label derives from the fact that we can recognize members of a human genetic family by observing distinctive attributes they share to varying degrees, as contrasted with nonfamily members who may have few of them. The commonalities may be quite evident, even though there may be no trait that all family members, as family members, have in common. Notwithstanding the attributes that are not shared, these family members are nonetheless seen as fitting the concept. Given individuals will almost certainly have different degrees of resemblance vis-à-vis other family members, and some might therefore be considered to be a diminished instance of this resemblance, an idea that is central to the discussion below.
A similar pattern often appears in the social sciences. A concept, defined in a particular way, may fit a number of cases reasonably well, but on close examination it can become clear that for most cases the fit is not perfect. Nonetheless, the concept captures a set of commonalities the researcher considers analytically important.
This pattern is found, for example, in the literature on corporatism, which generally presents a series of defining attributes, usually without the expectation that the full set of attributes would be found in every instance (Schmitter Reference Schmitter1974; Malloy Reference Malloy1977). Fully developed cases were found in fascist Europe between the two world wars. Yet in the literature of the 1970s, a given case did not have to match these key examples to be discussed as an instance of corporatism, and the concept was not treated as being sharply bounded. For example, over many decades during the twentieth century, it was reasonable to characterize state–labor relations in Argentina, Brazil, Chile, and Mexico as corporative, despite contrasts in the structuring, subsidy, and control of labor groups found in the four cases (Collier and Collier Reference Collier and Collier1991).Footnote 8
What would happen if we applied Sartori’s method to a family resemblance concept? Let us consider a simplified hypothetical exercise in comparative analysis, based on the idea that every case lacks only one attribute that is shared by all the others. Suppose (1) the analyst begins with a case study yielding a new concept of theoretical interest, initially appearing to have five defining attributes; (2) the initial case is one of six cases that share a family resemblance; (3) the family resemblance turns out to entail six shared attributes; and (4) each case possesses a different combination of only five of these. No attribute is shared by all six cases.
Using this illustration (Table 1.1), we examine the consequences if the analyst rigidly applies the ladder of generality. If the original research were done on Case 1, the analyst might begin to formulate a concept that encompassed Attributes B–F, and Attribute A would be lacking.
| Cases | Attributes | |||||
|---|---|---|---|---|---|---|
| 1 | B | C | D | E | F | |
| 2 | A | C | D | E | F | |
| 3 | A | B | D | E | F | |
| 4 | A | B | C | E | F | |
| 5 | A | B | C | D | F | |
| 6 | A | B | C | D | E | |
Note: Gaps in the matrix indicate which attribute (A to F) is lacking for each case (1 to 6). For example, attribute A is not found in case 1.
Upon adding Case 2 to the analysis, subsequent researchers might note that Attribute B was lacking. They could seek to avoid conceptual stretching by climbing the ladder of generality to a concept that encompassed both cases (1 and 2) and whose intension was reduced to Attributes C–F. Adding Case 3 could lead to a further step up the ladder of generality to a still more general concept that encompassed only Attributes D, E, and F. As can be seen in the table, when this iterated process finally reached Case 6, the final step up the ladder would bring the elimination of the final trait, leaving a concept with no attributes. Hence, the analyst might abandon the concept prematurely.
The basic point is straightforward: In the course of applying a concept to additional cases, it is potentially counterproductive to insist on eliminating those attributes not held in common by all cases under consideration. One way to avoid this problem is to look at the larger set of cases simultaneously, so that the commonalities evident in Table 1.1 would be recognized. Yet because every case is missing one attribute, a researcher accustomed to thinking in terms of classical hierarchies might still conclude that this is a weak concept that should be abandoned.
A possible response is to emphasize that the concept is an analytic construct that the researcher should not presume to be a perfect description of each case. A well-known example of this kind of construct is the ideal type, of which specific cases are expected to be only a partial approximation.Footnote 9 A parallel perspective could be that of quantitative researchers, who would likewise assume that cases are only partial approximations of their concepts – in this instance the concepts measured by their variables. Here, of course, the key task is to formulate these concepts, in the spirit of Sartori’s famous dictum “concept formation stands prior to quantification” (Reference Sartori1970: 1038; italics in the original).
To reiterate the overall point of this section, when the analyst encounters a family resemblance pattern, two priorities must be addressed. First, in assessing the attributes empirically, one must avoid an application of the ladder of generality that is so strict as to result in the inappropriate rejection of a potentially useful concept. Second, it is essential to explore the underlying analytic relationship among the attributes that constitute the family resemblance, thereby establishing the justification for retaining the concept. Whereas with some concepts this justification may rest on shared recognition of key cases that anchor the concept, with family resemblances such cases may or may not exist. Rather, the concept is anchored in a larger constellation of similarities across a number of cases.
Radial Structure
Another departure from the classical framework is the radial structure,Footnote 10 insightfully explored by cognitive linguist George Lakoff (Reference Lakoff1987: chap. 6). As with family resemblance, it is possible that two cases strongly associated with the concept will not share all of what may be seen as the defining attributes. In contrast to the family resemblance, here the overall meaning of a concept is anchored in a “best case,” or prototype. The prototype functions as a gestalt, in that it is constituted by a bundle of traits that are learned together, understood together, and readily recognized when found together. To use a term standard in political science, the subtypes are variants of the prototype that do not necessarily share defining attributes with each other but only with the prototype.
One of Lakoff’s ordinary-language examples is “mother” (Reference Lakoff1987: 83–84). Here the prototype is an individual who, in the context of conventional gender relations in the US, is often considered a true mother – that is, an individual who (1) is a woman, (2) contributes half the child’s genetic makeup, (3) bears the child, (4) is wife of the father, and (5) nurtures the child. The subtypes arise when the component elements are taken singly. In this example, familiar types emerge: genetic mother, birth mother, stepmother, and nurturing mother.Footnote 11 These types are called radial because they can be understood as branching out in different directions from the prototype. Crucially, in this example the prototype in our society has a strong, positive normative valence. As discussed later, a parallel positive valence is a central feature of discussions of democracy.Footnote 12
This radial structure shares an important feature with family resemblance, in that it builds on the idea of partial membership in a concept and thereby raises the idea of a part–whole relationship. It differs, however, in that the radial structure is routinely anchored by a central prototype, whereas with a family resemblance concept it routinely is not. It is certainly possible that one or two individuals might to an unusual degree exemplify the shared pattern of attributes. However, the concept is anchored in the overall constellation of similarities.
In comparison with classical conceptual structures, radial structures differ in key ways. As noted, the variants that branch out within a radial structure such as mother might be viewed as subtypes of the overall concept. Yet instead of being a kind of in relation to the overall concept, they are a part of this concept. They do not share the full complement of attributes by which we would recognize the overarching concept, as they do with kind hierarchies. Rather, they divide them, and they are diminished instances of the concept. Thus, they may be viewed as diminished subtypes. Further, because the subtype is only a partial instance of the overarching concept, this could be called a part–whole hierarchy.Footnote 13 We argue in this chapter that the contrast between kind hierarchies and part–whole hierarchies has important implications for addressing the problem of conceptual stretching.
Authoritarianism versus Democracy: Contrasting Patterns of Conceptual Innovation
Let us apply these ideas to two examples of conceptual traveling. During an earlier period of wide interest in bureaucratic authoritarianism, that concept was at times extended to cases that did not closely fit the original meaning (Collier Reference Collier1979, Reference Collier and Krieger1993). Using the ladder of generality, scholars sometimes avoided conceptual stretching by shifting to the broader concept of authoritarianism – thus moving up a kind hierarchy.
A parallel problem arose beginning in the 1970s with efforts to apply the concept of democracy to new regimes in Central America, Eastern Europe, and the former Soviet Union. In some of these cases, leaders were selected in competitive elections, yet many institutions and practices often associated with democracy were absent. The problem of conceptual stretching was addressed, given the radial structure of the concept, by making the more modest claim that these were electoral democracies – thereby abandoning the implication that they were true democracies.
The possibility of encompassing marginal cases through use of diminished subtypes can allow for considerable flexibility. Though this is often desirable, it can also generate scholarly debates, given the positive normative valence entailed in the prototypical ideal of democracy.Footnote 14 By contrast, if a classical kind hierarchy was indeed the appropriate framework for analyzing bureaucratic authoritarianism, a parallel debate might not occur about whether the cases of bureaucratic authoritarianism were instances of true authoritarianism.Footnote 15
The contrast that emerges here must be kept in mind as scholars seek to avoid conceptual stretching. In the case of bureaucratic authoritarianism, this is averted by moving up a ladder of generality from a subtype to the overarching concept. In the case of democracy, this outcome is sometimes avoided by moving away from the root concept to employ a subtype. Table 1.2 summarizes this contrast.
| How is the problem of stretching addressed? | Related changes discussed at various points in the text | ||||||
|---|---|---|---|---|---|---|---|
| Changed position in hierarchy | Adjective added or removed | Shift in terms | Intension: Number of defining attributes | Extension: Number of cases encompassed by revised concept | Conceptual boundaries of root concept preserved | ||
| Kind hierarchy | By moving up one rung on ladder of generality to concept with fewer defining attributes | One step up | Often removed | Occasionally | Decreases | Increases | Yes |
| Part–whole hierarchy | By dropping one or more attributes from root concept | One step down | Often added | Occasionally | Decreases | Generally decreases, but it could increase or remain the same | No |
Two further points may be noted about avoiding conceptual stretching with kind hierarchies versus part–whole hierarchies. First, an important difference is evident in how the formal label is modified. With both forms of hierarchy, it often (though not always) occurs that an adjective is added to the root concept to form a subtype. Thus, bureaucratic authoritarianism is a subtype in relation to authoritarianism, and electoral democracy is a subtype in relation to democracy. This similarity in turn points to a crucial difference in how we move to a broader set of cases with classical, as opposed to part–whole, hierarchies. In a classical hierarchy involving bureaucratic authoritarianism, this is done by dropping an adjective. By contrast, in the part–whole hierarchy involving democracy, it is routinely done by adding an adjective. Thus, the analyst seeking to avoid conceptual stretching will use adjectives in opposite ways.
Second, a similarity may be noted. Quite apart from the adjective, a shift in the term employed may sometimes occur. For example, in Weber’s kind hierarchy (referred to earlier), one type of domination is legitimate domination (adding an adjective), which is also called authority (shifting the term). In parallel, following Møller and Skaaning (Reference Møller and Skaaning2010: 271), in a part–whole hierarchy, a liberal democracy that lacks the rule of law is a polyarchy (shifting the term), and a polyarchy that lacks civil liberties is an electoral democracy (shifting the term back). Thus, electoral democracy is definitely a diminished subtype of polyarchy, and polyarchy is a diminished subtype of liberal democracy, even though at both iterations the term employed shifts (see again Table 1.2).
Further Illustrations from Discussions of Democracy
Analyses of democracy by Terry Karl and Philippe Schmitter illustrate some of the concomitants of the structure of this concept (Karl Reference Karl1990: 2; Schmitter and Karl Reference Schmitter and Karl1991: 76–82; Schmitter and Karl Reference Schmitter, Karl and Volten1992: 52). Karl and Schmitter focus on issues associated with participatory democracy and liberal democracy. Summarizing schematically, they are concerned with four elements: “(1) contestation over policy and political competition for office; (2) participation of the citizenry through partisan, associational, and other forms of collective action; (3) accountability of rulers to the ruled through mechanisms of representation and the rule of law” (Karl Reference Karl1990: 2; emphasis added); to which we would add (4) protection of rights essential to meaningful contestation, participation, and accountability.Footnote 16
Karl explicitly notes what we see as an essential component in the structure of this concept. In a discussion of subtypes of democracy, she observes that they “are characterized by different mixes and varying degrees of the chief dimensions of democracy: contestation, participation, [and] accountability” (Reference Karl1990: 2). Thus, the subtypes divide up the component elements of the central concept (democracy), and they may vary in how closely they resemble it.
This pattern also appears in the subtypes developed jointly by Schmitter and Karl (Reference Schmitter, Karl and Volten1992: 56–58). They identify corporatist democracy and populist democracy in part by the shared attribute that the dominant center of power is located in the state. Clearly, this attribute mitigates the weight of other components in their understanding of democracy, such as citizen participation and accountability of rulers. Hence, in their framework these subtypes are less democratic than what might be deemed true democracies. This comes out clearly in Schmitter and Karl’s empirical analysis of twenty-four cases of democratization. Of the eight countries they assign to the subtypes of populist and electoralist democracy, they treat six as marginal cases, either because they have “not yet crossed the minimal democratic threshold” or because they “are not yet consolidated into a recognizable type of democracy” (68).
These studies bring us back to our argument about conceptual traveling. It would appear that one of their goals was to introduce a broad range of empirical cases into the debate on democratization, yet without stretching the concept. The authors seek to do this by creating subtypes (e.g., corporatist and populist democracy) that refer to cases observers might hesitate to call true democracies. These subtypes serve to increase the extension of the overall concept without distorting it. In this way, the authors bring these cases into the framework of a general discussion of democracy, without having to claim that they are all truly democracies.
Conclusion
Our goal has been to suggest new guidelines for researchers concerned with conceptual traveling and conceptual stretching. We conclude that Sartori’s framework for addressing these problems deservedly remains a benchmark, yet caution and refinement are in order. Examination of family resemblances reminds us that an overly strict application of classical principles of concept formation can lead to the premature abandonment of potentially useful concepts. This problem can be avoided by self-consciously thinking in terms of ideal types or adopting other techniques that do not depend on the assumption that members of a concept share a full set of defining attributes.
The effort to avoid conceptual stretching likewise takes a distinct form when one is dealing with radial structures. This is because the subtype, for example electoral democracy, tends to divide up the constituent elements of the concept of democracy. By contrast, with a classical pattern the subtype, for example bureaucratic authoritarianism, contains additional elements beyond those of authoritarianism. Relatedly, with classical hierarchies one may often avoid conceptual stretching by removing an adjective, whereas with radial structures one may often avoid conceptual stretching by adding an adjective.
We also argue that because the subtypes often divide up elements of a concept such as democracy, the formation of subtypes creates both an opportunity and a problem. It creates an opportunity for broader and more flexible application, allowing incorporation of additional cases. Yet because the flexibility abandons the well-bounded character of the concept, this very flexibility can lead to major scholarly disputes about whether this is an appropriate application.
A final observation may be made about this central issue of the fit between concepts and cases. Insights into the structure of concepts certainly do not tell us everything we need to know about how to apply them in research. Rather, this application depends on substantive expertise regarding the cases under analysis. We have suggested the example of a debate on whether a particular case should be called an instance of patrimonial, as opposed to traditional, authority. Though our methodological understanding of concepts can frame such a debate, its resolution requires case knowledge. In this sense, the arguments about concepts that have been our focus play the useful role of bringing us back to our own detailed understanding of the political settings we study.
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