Point of Departure: Scale Types and Measurement

A basic point of reference here is the familiar framework of nominal, ordinal, interval, and ratio scale types. We add two further types: the partial order, which has order among some but not all the categories (Davey and Priestley Reference Davey and Priestley2002: chap. 1);Footnote ¹ and the absolute scale, which is an enumeration of the individuals or entities in a given category – for example, the number of voters in different electoral districts.Footnote ²

The controversy over scale types is focused on four alternative criteria for evaluating their desirability and utility. First, traditional distinctions between lower and higher levels of measurement are anchored in the idea that the latter contain a higher level of information, which is formalized in the idea of mathematical group structure.Footnote ³ This perspective provides valuable distinctions, yet closer examination reveals that the relationship between scale types is complex. For example, the meaning of higher levels of measurement depends on lower levels, as we will show later.

A second criterion is permissible statistics – that is, the statistical procedures that can and should be employed with each scale type. Higher levels of measurement were traditionally seen as amenable to a greater range of procedures, which led many scholars to consider categorical variables less useful. However, some of these earlier distinctions have broken down, and complex forms of statistical analysis are now routinely applied to nominal scales.

Third, alternative definitions of measurement are crucial in evaluating scale types. A classic, highly influential, and very narrow definition, dating back at least to the physicist N. R. Campbell (Reference Campbell1920), treats measurement as the quantification of physical properties. Measurement in this sense can be achieved with a yardstick (Michell Reference Michell1999: 121). In this framework, “measurement” corresponds to the standard understanding of ratio scale, thus privileging order, plus a unit of measurement, plus a real zero.

Alternatively, measurement has been defined as “the assignment of numerals to objects or events according to rules” (Stevens Reference Stevens1946: 677; 1975: 46–47).Footnote ⁴ Such assignment corresponds to standard practice with higher levels of measurement, where scores are expressed numerically and provide a true “metric.” According to this alternative definition, if each category in a nominal or ordinal scale is designated with a numeral, this also constitutes measurement. In typologies, of course, the categories are routinely designated not with numerals, but with terms that evoke the relevant concepts. In our view, the idea of measurement should not be reified, and this naming of types could also be considered measurement. The real issue is whether the differentiation along dimensions or among cases serves the goals of the researcher. We are convinced that typologies do serve these goals.

A fourth criterion concerns the cut point between qualitative and quantitative measurement. Some analysts (Vogt Reference Vogt2005: 256) consider a scale qualitative if it is organized at a nominal level, and quantitative if the level is ordinal or higher – thereby privileging whether order is present. By contrast, others (e.g., Young Reference Young1981: 357; Duncan Reference Duncan1984: 126, 135–36; Porkess Reference Porkess1991: 179) treat ordinal versus interval as the key distinction, thus focusing instead on whether categories, as opposed to a unit of measurement, are employed. An even more demanding cut point – strongly embraced by some social scientists – derives from the tradition of Campbell and requires both a unit of measurement and a real zero.

As we will see, contention over these criteria is central to debates on typologies.

The Critiques

Both some recent commentaries, and an older generation of methodologists, have sharply criticized categorical variables and typologies.Footnote ⁵ Yet many of these critiques reflect an outdated understanding of scale types.

Gill’s (Reference Hibbs2006: 334) mathematics textbook for political scientists states that nominal scales have the least “desirability” among levels of measurement. Similarly, the Encyclopedia of Measurement and Statistics (Salkind Reference Peterson2007: 826, 683) adopts the fairly standard line that the ratio level of measurement “provides the richest information about the traits it measures”; among the scale types, “nominal is considered the ‘weakest’ or least precise level of measurement … and one should use a more precise level of measurement whenever possible.” Teghtsoonian (Reference Teghtsoonian2002: 15106) asserts that “contemporary theorists find the nominal sale of little interest because it imposes no ordering on the measured entities.”

Some of the earlier critiques by prominent scholars are exceptionally harsh. In his seminal article, Stevens (Reference Stevens1946: 679) argues that nominal scales are “primitive.” Blalock (Reference Blalock1982: 109–10) maintains that “one of the most important roadblocks to successful conceptualization in the social sciences has been our tendency to … rely very heavily on categorical data and discussions of named categories.” He argues that scholars who work with nominal scales suffer from “conceptual laziness,” and he expresses dismay that so much attention has been given to “categorical data and classificatory schemes.” Young (Reference Young1981: 57) is similarly harsh in the opening sentence of his presidential address for the Psychometric Society, published as the lead article in Psychometrika: “Perhaps one of the main impediments to rapid progress in the development of the social, behavioral, and biological sciences is the omnipresence of qualitative data,” by which he means data involving nominal or ordinal scales. He thus groups nominal and ordinal together.

Duncan (Reference Duncan1984: 126), a pioneer in the development of path analysis and structural equation modeling, likewise rejects nominal and ordinal scales on the grounds that they are not a form of measurement, given that “the purpose of measurement is to quantify” and the goal is to establish “degrees.” He considers the argument that classifications are in any sense a type of measurement to be “obfuscatory” (135). Furthermore, Duncan argues that with many presumably ordinal scales, the demonstration of order is questionable, and if one applies a strong standard, there are many fewer meaningful ordinal scales than is often believed (136).

Skepticism about nominal scales also derives from the concern that they obscure multidimensionality and fail to produce unidimensional measures, which are seen as critical to good research. Blalock (Reference Blalock1982: 109) states that a key obstacle to adequate conceptualization is the failure to “grapple with the assessment of dimensionality” and the overreliance on categorical scales, often identified simply by proper names. Shively (Reference Shively1980: 31; also Shively Reference Shively2007: chap. 3) emphasizes that terms and concepts from ordinary language, which are routinely used in designating the categories in nominal scales, are especially likely to hide multidimensionality. Jackman (Reference Jackman1985: 169) similarly states that the variables employed in research “are supposed to be unidimensional”; and Bollen (Reference Bollen1980) and Bollen and Jackman (Reference Bollen and Jackman1985) likewise underscore the importance of arriving at unidimensionality, arguing that if multiple dimensions are hidden, then measurement is inadequate and causal inferences are misleading.

Some critics of categorical variable specifically criticize typologies as well. Duncan (Reference Duncan1984: 136), for instances, laments sociologists’ “addiction to typology.” In their widely noted book, King, Keohane, and Verba (Reference Leonard, Leonard and Marshall1994: 48, emphasis in original) are less emphatic, though still dubious: “[T]ypologies, frameworks, and all manner of classifications, are useful as temporary devices when we are collecting data.” However, these authors “encourage researchers not to organize their data this way.”

The Achilles’ Heel of Quantitative Measurement: Meeting the Assumptions

Interval and ratio scales are often considered more valuable because, in principle, they contain more information than nominal and ordinal scales. They are also seen as more amenable to achieving unidimensional measurement. However, these advantages depend on complex assumptions about the empirical relationships present in the data, assumptions that may not be valid for a given application. Political and social attributes are not always quantifiable, and there is often the temptation to treat data as if they contain information that may not be there. Of course, categorical data also depend on assumptions, but because these “lower” levels of measurement posit less complex empirical relationships, the assumptions are simpler.

Psychometricians have devoted great attention to the problem of assumptions. Michell (Reference Michell2008: 10) suggests that in his field, “the central hypothesis (that psychological attributes are quantitative) is accepted as true in the absence of supporting evidence. … Psychometricians claim to know something that they do not know and have erected barriers preserving their ignorance. This is pathological science.” Barrett (Reference Barrett2008: 79) points out that, paradoxically, maintaining the pretense of a higher level of measurement can distort – rather than enhance – the information about the real world contained in data at a lower level of measurement.

These questions about assumptions are highly salient for political science, given both the wide influence of psychometrics in political research (Poole Reference Poole, Brady and Collier2008) and the common presumption that political phenomena are indeed quantifiable.

Such questions about assumptions arise, for example, in discussions of structural equation modeling with latent variables (SEM-LV) – an analytic tool intended to establish higher levels of measurement and remove measurement error. This technique can build on ordinal or dichotomous nominal data to estimate unobserved quantitative variables.

Unfortunately, given the large number of untestable or hard-to-test assumptions that go into SEM-LV, many scholars question its contribution.Footnote ⁶ These assumptions include ideas about the distributions of unobservable variables, the number and dimensionality of such variables, the structure of measurement relations among the observable variables, and the causal relations among the unobservable variables.

Item response theory (IRT) emerged as an alternative to SEM-LV for creating indicators at a higher level of measurement and removing measurement error. Notwithstanding differences in emphasis and procedure, the two families of techniques have fundamentally similar assumptions (Takane and de Leeuw Reference Takane and de Leeuw1987; Reckase Reference Reckase, van der Linden and Hambleton1997; Treier and Jackman Reference Treier and Jackman2008: 205–6). Hence, IRT likewise raises concerns about assumptions in quantitative measurement.

In sum, quantitative scholars’ hopes and expectations about these tools may surpass actual accomplishments. These researchers face major challenges in meeting the critiques of quantitative measurement advanced by scholars such as Michell.

Higher Levels of Measurement Rest in Part on a Foundation of Nominal Scales

Some critiques of nominal scales imply that scholars who work with higher-level scales escape the confines of this lowest level of measurement. That is incorrect. In their effort to give conceptual meaning to higher levels of measurement, scholars routinely build on nominal dichotomies.

Establishing an absolute scale requires a nominal dichotomy to identify the specific entities counted by the scale. As noted earlier, the need for this dichotomy is illustrated by the challenge of counting the number of voters in different electoral districts. Performing such a count depends on a dichotomous understanding of which voters are in each district and which are not, and also on a dichotomy that identifies the subset of people who count as voters. This points to a pivotal observation: Working with the highest level of measurement requires the lowest level of measurement. Nominal scales are crucial here.

In seeking to establish ordinal, interval, and ratio scales, scholars sometimes simply create an indicator without careful conceptualization, and then proceed to treat the indicator as if it satisfied the corresponding level of measurement. Yet giving conceptual content to the indicator requires establishing what it means for the phenomenon being measured to be “absent”; this establishes what Goertz (Reference Goertz2006: 30–35) calls the negative pole of the concept (also see Satori 1970; Collier and Gerring Reference Douglas2009). This stands in contrast to being “present,” and as the analyst works with the entire scale, this dichotomy of present–absent provides a foundation for reasoning about “More of what?” Obviously, present–absent is a nominal dichotomy, and we thus see the interplay between the full range of values on the scale and this simple nominal distinction.

As an example, take Sniderman’s (Reference Schmitter1981) ordinal measure of government support, in which the lowest category is “disaffection.” It is essential to establish here whether disaffection is simply the absence of government support or if it includes active opposition – which is very different. Again, a dichotomous understanding of the presence or absence of support is essential to addressing this issue.

Overall, scholars do indeed sometimes follow poor measurement practices and construct “indicators” (i.e., specific procedures for scoring cases) without carrying out this conceptual work. They proceed to treat the resulting variable as if it were at one or another of these levels of measurement. Yet indicators should be constructed to measure something, and careful conceptual work is essential to establish what that something is. Nominal scales are indispensable to the reasoning required, and this key contribution is another reason why it is inappropriate to denigrate nominal scales.

Revised Norms for “Permissible Statistics”: Nominal Scales in Quantitative Analysis

A significant source of concern about nominal scales had been their presumed incompatibility with regression analysis and, more broadly, the conviction that fewer statistical tools are appropriate for nominal/typological variables than for higher-level variables.

However, this norm has in important respects been superseded. Nominal scales are now routinely used in regression analysis as independent variables – that is, with the use of dummy variables. Under the rubric of “categorical data analysis” (see, e.g., Agresti Reference Agresti2002), a broad set of tools for treating such data as the dependent variable have been developed. Among these tools, logit and probit models are particularly well known. Often these nominal scales are simple dichotomies, but multinominal scales (i.e., multicategory nominal scales) are also used. In political science and sociology, a count of articles in leading journals shows that logit and probit were little used in the 1970s and had become widespread by the 1990s – a trend that has subsequently continued.

In working with logit, probit, and dummy variables, scholars in practice often do not worry about dimensionality. When dichotomies are entered into regression analysis (e.g., party identifiers versus independents), the researcher routinely does not do a scaling analysis to test whether the dichotomy taps an underlying dimension. This seems perfectly reasonable. Even though party identification is a multifaceted and multidimensional concept, it is still valuable to learn if age cohorts differ in their party identification. In this context, the quest for unidimensionality may well be subordinated.

Other tools for quantitative causal inference also rely on nominal variables, and, here again, attention to dimensionality is often not a central concern. Matching methods, for example, attempt to estimate the causal effect in observational data of two alternative “treatments” by comparing cases drawn from two groups that are as similar as possible on a set of conditioning variables (Rubin Reference Rubin2006). These techniques essentially require that the causal variable of interest be categorical; if it is continuous, the definition of treatment groups is ambiguous and some sort of threshold or cut point (i.e., dichotomization) must be imposed.

This use of categorical independent variables echoes the best-practices design for causal inference, the randomized experiment. While experiments can use randomization to assign different values of a treatment, measured as a continuous variable, by far the more common approach in the social sciences is to employ discrete treatments based on a categorical variable. As with matching methods and the models discussed in the previous paragraph, discussions of the dimensionality of treatment assignment in experimental designs are rarely at the center of attention.

Placing Multidimensionality in Perspective

One of the earlier criticisms of typologies and nominal scales was that they often failed to address multidimensionality. Skeptics charged that, lurking behind what might appear to be clear concepts and compelling classifications, one too often finds multiple dimensions and poor measurement. These analysts saw higher levels of measurement as far more capable of achieving unidimensionality.

This critique needs to be rebalanced. First, the construction and refinement of typologies has made sophisticated contributions to addressing multidimensionality. This is “conceptual work,” and it should become clear later that carefully crafted typologies contribute decisively to this task. Hence, far from obstructing the careful treatment of dimensions, typologies can play a critical role in that endeavor.

Second, dealing with dimensions in quantitative research often proves more complicated, ambiguous, and inconclusive than was previously recognized. Jackman’s mandate (noted earlier) that “variables are supposed to be unidimensional” represents an admirable goal in many forms of analysis, yet it routinely is not achieved. This is partly because, as discussed previously, some of the most promising tools for extracting dimensions have fallen well short of their promise.

Third, unidimensionality is not a well-defined “end state” in research. It is better understood as involving a series of iterations and approximations that emerge as research proceeds. Consider standard measures of political democracy. These may include (1) free and fair elections, (2) respect for political rights and civil liberties, (3) universal suffrage, and (4) whether elected leaders to a reasonable degree possess effective power to govern (Collier and Levitsky Reference Collier and Levitsky1997: 433–34). Some scholars combine these attributes by creating simple additive measures of democracy, and others use a spectrum of alternative tools.

Yet each of these component indicators can hide multidimensionality. For example, the concept of civil liberties is certainly multidimensional, including freedom of expression – attributes that do not necessarily vary together. One component, freedom of expression, is multidimensional, given that it includes freedom of the press, freedom of broadcast media, uncensored use of the internet, and other aspects of freedom to express political views. Each of these components, in turn, is certainly multidimensional as well. Furthermore, an indicator that appears to yield unidimensional measurement for a given set of cases may not do so with additional cases. These problems involve basic ideas about the contextual specificity of measurement validity, which have received substantial acceptance in psychology.Footnote ⁷

The issue, therefore, is not that quantitative analysis arrives successfully at unidimensionality and qualitative analysis has great difficulty in doing so. Moving beyond multidimensionality is an issue at all levels of measurement, and for higher levels it is not necessarily resolved by complex scaling techniques. The challenge for both qualitative and quantitative measurement is to find the scope of comparison and level of aggregation – that is, the degree to which indicators are broken down into their constituent elements – best suited to the analytic goals of the study.

Concept Formation

Conceptual typologies make a fundamental contribution to concept formation in both qualitative and quantitative research. Developing rigorous and useful concepts entails four interconnected goals:Footnote ⁸ (1) clarifying and refining their meaning, (2) establishing an informative and productive connection between these meanings and the terms used to designate them, (3) situating the concepts within their semantic field, that is, the constellation of related concepts and terms, and (4) identifying and refining the hierarchical relations among concepts, involving kind hierarchies.Footnote ⁹ Thinking in terms of kind hierarchies brings issues of conceptual structure into focus, addresses challenges such as conceptual stretching, and productively organizes our thinking as we work with established concepts and seek to create new ones.

A Five-Step Template

Building on these ideas, we now propose a template for constructing typologies. We illustrate our framework with Nichter’s (Reference Murillo2008: 20) typology of the allocation of rewards in electoral mobilization (Table 7.2), which forms part of his larger quantitative analysis of clientelism. While our template might appear straightforward, the literature in fact lacks a clear, didactic presentation of the building blocks in the template. Moreover, scholars too often limit the value of their typologies – and sometimes make serious mistakes – by failing to follow this template.

Table 7.2Targeting rewards and electoral mobilization

Source: Nichter Reference Nichter2008

The building blocks of typologies may be understood as follows:

1. (1) Overarching concept: This is the concept measured by the typology. In Nichter, the overarching concept is the targeting of rewards. This concept should be made explicit and should be displayed as the title in the diagrammatic presentation of the typology. Occasionally, the title instead names the variables that are cross-tabulated (e.g., Dahl Reference Dahl1971: 7); in other cases, the matrix simply lacks a title (O’Donnell and Schmitter Reference O’Donnell and Schmitter1986: 13). It is better to state the overarching concept directly.

2. (2) Row and column variables: The overarching concept is disaggregated into two or more dimensions, and the categories of these dimensions establish the rows and columns in the typology. These dimensions capture the salient elements of variation in the concept, so the plausibility and coherence of the dimensions vis-à-vis the overarching concept are crucial. In Nichter, the row variable is whether the prospective recipient of the reward is inclined to vote; its component categories define the rows. The column variable is whether the prospective recipient favors the party offering the reward. It merits note that row and column variables in a typology need not be limited to nominal or ordinal scales, but may also be interval or ratio.

3. (3) Matrix: Cross-tabulation of the component categories of these dimensions creates a matrix, such as the familiar 2 by 2 table employed by Nichter. The challenge of creating a matrix can push scholars to better organize the typology, tighten its coherence, and think through relations among different components.

4. (4) Incorporating three or more dimensions: One option here is to present the familiar 2 by 2 matrix twice, once for each of the two subgroups of cases that correspond to the third dimension. See, for example, Table 9.4 in this volume, Chapter 9. Other examples are Leonard (Reference Leonard, Leonard and Rogers Marshall1982: 32–33) on decentralization and Vasquez (Reference Vasquez1993: 320) on war. Alternatively, one of the categories in a row and/or column variable may be further differentiated into subcategories. Additional dimensions can also be introduced through a branching tree diagram – as in Gunther and Diamond (Reference Gunther and Diamond2003: 8) on political parties; or as a cube, with the cell types placed at different locations in the cube. Figure 0.1 in the Introduction to this volume provides an example of a cube; see also Linz (Reference Linz, Greenstein and Polsby1975: 278) on authoritarianism.

5. (5) Cell types: These are the concepts and associated terms located in the cells. The cell types are “a kind of” (see footnote 10) in relation to the overarching concept measured by the typology. The conceptual meaning of these types derives from their position in relation to the row and column variables, which should provide consistent criteria for establishing the types. In Nichter’s typology, the terms in each cell nicely capture the constellation of attributes defined by the intersection of each row and column variable: rewarding loyalists, vote buying, turnout buying, and double persuasion.

Even when the typology is based on interval or ratio variables, scholars may identify cell types. These may be polar types located in the corners of the matrix, or intermediate types.Footnote ¹⁰

Sometimes the analyst does not formulate a concept that corresponds to the cell types; rather, the names of the categories in the corresponding row and column variables are simply repeated in the cell. For example, in a typology that cross-tabulates governmental capacity and regime type, the terms in the cells are “high-capacity democratic,” and so on. Here, the typology is valuable, but this potential further step in concept formation is not taken.Footnote ¹¹

Organizing Theory and Concepts

Scholars use typologies to introduce conceptual and theoretical innovations, sometimes drawing together multiple lines of investigation or traditions of analysis.

For example, the typology of “goods” in public choice theory synthesizes a complex trajectory of research. Goods are understood here as any objects or services that satisfy a human need or desire. Samuelson’s (Reference Pierson1954) classic article introduced the concept of “public good,” and later scholars have extended his ideas, adding new types such as the “club good” (Musgrave Reference Musgrave, Brown and Solow1983). With slight variations in terminology (see Mankiw Reference Mankiw1998: 221; as opposed to Ostrom, Gardner, and Walker Reference O’Donnell and Schmitter1994: 7), the idea of a good is now routinely conceptualized in two dimensions: rivalrous, according to whether consumption by another individual precludes simultaneous consumption by another individual; and excludable, according to whether the good can be extended selectively to some individuals, but not others. Cross-tabulating these two dimensions yields public, private, club, and common goods (the last also known as common-pool resources).

The joining of two analytic traditions is found in Kagan’s (Reference Kullberg and Zimmerman2001: 10) typology of “adversarial legalism.” He draws together (1) the idea of an adversarial legal system, which has long been used to characterize Anglo-American modes of legal adjudication, and (2) the traditional distinction between legalistic and informal modes of governance. He integrates these two theoretical approaches in a typology that posits four modes of policy implementation and dispute resolution: adversarial legalism, bureaucratic legalism, negotiation or mediation, and expert or political judgment.

Schmitter’s (Reference Remmer1974) analysis of interest representation bridges alternative analytic traditions while also illustrating the ongoing process of refining a typology. He connects what was then a new debate on the concept of corporatism to ongoing discussions of pluralism as well as prior understandings of monism, anarchism, and syndicalism. He shows how corporatism should be taken seriously as a specific type of interest representation that can be analyzed in a shared framework vis-à-vis these other types. Schmitter later introduces a further refinement, making it clear that the overarching concept in a typology is not necessarily static. Based on his recognition that he is conceptualizing not just a process of the representation, but a two-way interaction between groups and the state, he shifts the overarching concept from interest “representation” to interest “intermediation” (Schmitter Reference Schmitter1977: 35n1).Footnote ¹⁴

Conceptualizing and Measuring Change

Ongoing scholarly concern with mapping political transformations and empirical change is an important source of innovation in typologies. An example is the evolving conceptualization of party systems that occurred in part as a response to the historical changes in their bases of financial support. Duverger (Reference Duverger1954: 63–64) initially proposes the influential distinction between “mass” and “cadre” parties, which are distinguished – among other criteria – on the basis of financial support from a broad base of relatively modest contributions versus reliance on a small set of wealthy individual contributors. Subsequently, Kirchheimer (Reference Kirchheimer, LaPalombara and Weiner1966: 184–95) observes that in the 1960s, many European parties moved away from the organizational pattern of the mass party. They are replaced by “catch-all” parties that cultivate heterogeneous financial bases. Subsequently, Katz and Mair (Reference Katz and Mair1995: 15–16) conclude that parties have begun to turn away from financial reliance on interest groups and private individuals (whether wealthy or not), developing interparty collaboration to obtain financing directly from the state – thereby creating the “cartel” party.

The influence of political change can also be reflected in choices about dimensions in typologies. For instance, Dahl (Reference Dahl1971) maps out historical paths to modern polyarchy; hence, his dimension of inclusiveness centrally involves the suffrage, and given the historical depth of his analysis this dimension ranges from restrictive to universal. By contrast, Coppedge and Reinicke (Reference Coppedge and Reinicke1990: 55–56), focusing on data for 1985, declare polyarchy unidimensional and argue that Dahl’s dimension of inclusiveness can be dropped. As of that year, the movement to universal suffrage was nearly complete and was no longer a significant axis of differentiation among cases.Footnote ¹⁵

Free-Floating Typologies and Multiple Dimensions

Some of the most creative typologies may appear unidimensional, yet this may mask multiple dimensions and/or the dimensions may be ambiguous. These “free floating” typologies lack explicit anchoring in dimensional thinking. Such typologies may often be refined by teasing out the underlying dimensions.Footnote ¹⁶

For example, Hirschman’s (1970) “exit, voice, and loyalty” has provided a compelling framework for analyzing response to decline in different kinds of organizations – a topic inadequately conceptualized in prior economic theorizing. Yet as Hirschman (Reference Hirschman1981: 212) points out, these are not mutually exclusive categories. Voice, in the sense of protest or expression of dissatisfaction, can accompany either exit or loyalty. Hirschman’s typology can readily be modified by creating two dimensions: (1) exit versus loyalty and (2) exercise versus nonexercise of voice. This revised typology would have mutually exclusive categories, thereby responding to a standard norm for scales and typologies and making it possible to classify cases in a more revealing way.

Another example is Evans’ (Reference Hale1995) conceptualization of alternative state roles in industrial transformation. Evans presents what appears to be a nominal scale with four categories: midwifery, demiurge, husbandry, and custodian. On closer examination, however, two dimensions are present: (1) key state actors may see entrepreneurs’ ability to contribute to development as malleable or fixed, and (2) the role of the state vis-à-vis entrepreneurs may be supportive or transformative. Evans’ four original types fit nicely in the cells of this 2 by 2 typology, and the result is a more powerful conceptualization of the state’s role.

Typologies Generate Scales at Different Levels of Measurement

Typologies also refine measurement by creating categorical variables that are distinct scale types.

• Nominal scale. Nichter’s (Reference Murillo2008) analysis of targeting rewards yields the cell types discussed earlier: rewarding loyalists, turnout buying, vote buying, and double persuasion. These categories are collectively exhaustive and mutually exclusive, but not ordered; they form a nominal scale.

• Partial order. In Dahl’s (Reference Fish1971: chap. 1) 2 by 2 typology of political regimes, there is unambiguous order between “polyarchy” and the other three types, and also between “closed hegemony” and the other three types. Yet between the two intermediate types – competitive oligarchy and inclusive hegemony – there is no inherent order, and Dahl’s categories are a partial order.

• Ordinal scale. In their analysis of issue voting, Aldrich, Sullivan, and Borgida (Reference Aldrich, Sullivan and Borgida1989: 136) tabulate (1) small- versus large-issue differences among candidates against (2) low- versus high-salience and accessibility of the issues. One cell corresponds to a low effect, while a second cell corresponds to a high effect of the opposing issues being voted on. The other two cells are given the same value: “low to some effect.” A three-category ordinal scale is thereby created.

Conceptual Typologies as Building Blocks in Explanations

Typologies likewise contribute to formulating and evaluating explanatory claims. Conceptual typologies routinely constitute the independent, intervening, and dependent variables in explanations. Political scientists take it for granted that standard quantitative variables play this role, and it is essential to see that conceptual typologies do so as well. Conceptual typologies do not thereby become explanatory typologies. Rather, they map out variation in the outcomes being explained and/or in the explanation of concern, and in contrast to an explanatory typology, the outcomes and the explanation are not placed in the same matrix.

The typology as an independent variable is illustrated by Dahl’s (Reference Fish1971: chap. 3) analysis of the long-term stability and viability of polyarchies. Here, his types of political regimes define alternative trajectories in the transition toward polyarchy. Moving from closed hegemony to polyarchy by way of competitive oligarchy is seen as most favorable to a polyarchic regime, whereas the paths through inclusive hegemony and from a closed hegemony directly to polyarchy are viewed as “more dangerous” (Dahl Reference Dahl1971: 36).

Typologies serve as the dependent and intervening variables in research on interactions between women’s social movements and the state in advanced industrial democracies. Mazur (Reference Mazur2001: 21–23) conceptualizes the dependent variable – the state response – on two dimensions: the state’s acceptance of women’s participation in the policy process and whether the state response coincides with the goals of the movement. Four types of state response emerge in the typology: no response, preemption, cooptation, and dual response. The dual response is of special interest because it constitutes the most complete achievement of the movement’s objectives, involving both “descriptive” and “substantive” representation.

A key intervening variable is a typology of “policy agency activities” in the women’s movement. These agency activities are analyzed on two dimensions: whether they successfully frame the policy debate in a gendered way and whether the goals of the movement are advocated by the particular agency. Cross-tabulating these dimensions yields four types of agency activities: symbolic, nonfeminist, marginal, and insider. The cell type of insider constitutes the most complete achievement of both advocating the movement’s goals and gendering the policy debate (Mazur Reference Mazur2001: 21–22).

Typologies in Quantitative Research

The introduction of typologies can be a valuable step in causal inference within a quantitative study. A typology can provide the conceptual starting point in a quantitative analysis, as with Nichter’s study of the targeting of rewards in electoral competition, discussed earlier. It may also delineate a subset of cases on which the researcher wishes to focus, overcome an impasse in a given study, or synthesize the findings. In other instances, researchers use quantitative analysis to assign cases to the cells in a typology.

• Delineating a subset of cases. In Vasquez’s (Reference Weyland1993: 73) quantitative study of war, a typology helps to identify a subset of cases for analysis. He argues that prior research yielded inconsistent findings because researchers failed to distinguish types of war. He then identifies eight types by cross-tabulating three dimensions: (1) equal versus unequal distribution of national power among belligerent states, (2) limited versus total war, and (3) number of participants. Vasquez uses this typology to focus on a subset of cases, that is, wars of rivalry.

• A typology likewise serves to identify a subset of cases in Mutz’s (Reference Montgomery, Cheema and Rondinelli2007) survey experiment on news media and perceived legitimacy of political opposition, in this case involving a four-category treatment. Subjects are shown a recorded political debate in which the content is held constant across treatments, but two factors are varied: the camera’s proximity to the speakers (close or moderate) and the civility of the speakers (civil or uncivil). One cell in the resulting 2 by 2 typology, with a close camera and uncivil speakers, is singled out for special causal attention and is conceptualized as “in-your-face” television. The typology thus frames the categorical variable on which the analysis centers.

• Overcoming an impasse. Introducing a typology may also help overcome an impasse in quantitative research. Hibbs’ (Reference Karl1987: 69) study of strikes in eleven advanced industrial countries introduces a 2 by 2 matrix at a point where quantitative analysis can be pushed no further. He uses bivariate correlations to demonstrate that increases in the political power of labor-based and left parties are associated with lower levels of strikes in the decades after World War II, and he hypothesizes that the role of public sector allocation serves as an intervening factor. Hibbs argues that as labor-left parties gain political power, the locus of distributional conflict shifts from the marketplace to the arena of elections and public policy, thereby making strikes less relevant for trade unions.

• Yet the multicollinearity among his variables is so high that it is not feasible to sort out these causal links, especially given the small number of cases. Hibbs then shifts from bivariate linear correlations to a 2 by 2 matrix that juxtaposes the level of state intervention in the economy and alternative goals of this intervention. For the period up to the 1970s, he analyzes cases that manifest alternative patterns corresponding to three cells in the typology: relatively high levels of strikes directed at firms and enterprises (Canada, US), high levels of strikes which serve as a form of pressure on the government (France, Italy), and a “withering away of the strike” that accompanies the displacement of conflict into the electoral arena (Denmark, Norway, Sweden). This typology allows him to push the analysis further, notwithstanding the impasse in the quantitative assessment.

• Placing cases in cells with probit analysis. Carmines and Stimson’s (Reference Carmines and Stimson1980) study formulates a 2 by 2 typology of issue voting: easy issue voting, based on a deeply embedded preference on a particular issue; constrained issue voting, based on a deeply embedded preference on a second issue that further reinforces the vote choice; hard issue voting, based on a complex decision calculus involving interactions and trade-offs among issues; and non-issue voting, based more on party identification than on issue preferences. The study tests hypotheses about the relationship between political sophistication and the role of issue preferences in the vote. The authors place respondents in these four cells using probit analysis and then examine the contrasts among the types with regard to political sophistication.

• Synthesizing findings. In studying the impact of foreign policy platforms on US presidential candidates’ vote share, Aldrich, Sullivan, and Borgida (Reference Aldrich, Sullivan and Borgida1989: 136) use a typology to synthesize their findings. They explore which campaign messages resonate with voters – specifically, which campaign issues are (1) “available,” in the sense that an opinion or position on a given issue is understood, and (2) “accessible,” or perceived as relevant, by voters. Although much of the article employs probit analysis to predict the victory of specific candidates, the authors seek to characterize broader types of elections in their conclusion. To do so, they introduce a 2 by 2 matrix to classify presidential elections according to whether there are small versus large differences in candidates’ foreign policy stances and according to the low versus high salience and accessibility of foreign policy issues raised in each election.

In sum, typologies thus contribute to quantitative research in diverse ways.