toward a unified theory of causality

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2008; 41; 412 originally published online JanComparative Political StudiesJames Mahoney

Toward a Unified Theory of Causality

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412

Toward a UnifiedTheory of CausalityJames MahoneyNorthwestern University, Evanston, Illinois

In comparative research, analysts conceptualize causation in contrastingways when they pursue explanation in particular cases (case-oriented research)versus large populations (population-oriented research). With case-orientedresearch, they understand causation in terms of necessary, sufficient, INUS,and SUIN causes. With population-oriented research, by contrast, theyunderstand causation as mean causal effects. This article explores whether itis possible to translate the kind of causal language that is used in case-oriented research into the kind of causal language that is used in population-oriented research (and vice versa). The article suggests that such translationis possible, because certain types of INUS causes manifest themselves asvariables that exhibit partial effects when studied in population-orientedresearch. The article concludes that the conception of causation adopted incase-oriented research is appropriate for the population level, whereas theconception of causation used in population-oriented research is valuable formaking predictions in the face of uncertainty.

Keywords: causality; logic; probabilities; cases; populations

Comparative analysts use distinct methods and conceptualize causationin contrasting ways when they carry out explanation in particular cases

versus large populations. When analyzing individual cases, comparativistsseek to identify the specific values of variables that enabled and/or gener-ated outcomes of interest. They pursue a genetic and sequential mode ofexplanation that is implemented in part through narrative prose. By con-trast, when comparativists study large populations, they seek to estimate theaverage effects of independent variables of interest. They carry out statisti-cal analysis and report results as coefficients that apply to populations aswholes rather than particular observations.

Comparative Political StudiesVolume 41 Number 4/5

April/May 2008 412-436© 2008 Sage Publications

10.1177/0010414007313115http://cps.sagepub.com

hosted athttp://online.sagepub.com

Author’s Note: For helpful insights, I thank James Caporaso, Robert J. Franzese Jr., John Gerring,Edward Gibson, Gary Goertz, Erin Kimball, Kendra Koivu, Damon B. Palmer, Jason Seawright,Larkin Terrie, David Waldner, Erik Wibbels, and Steven I. Wilkinson. All errors are mine.




These two approaches can be called, for convenience, case-oriented andpopulation-oriented research.1 Case-oriented researchers seek to identifythe causes of particular outcomes in specific cases. They may find causalpatterns that apply broadly, but their primary concern is with causation inthe specific cases under analysis. By contrast, population-oriented researchersseek to identify typical causal effects in overall populations. They may some-times investigate whether a particular case follows a general casual pattern,but their main interest is to say something about the larger population pattern.

To illustrate these differences, consider research on democratization. Bothcase-oriented and population-oriented researchers are interested in the ques-tion, “What causes democracy?” However, they normally address this ques-tion in different ways. The case-oriented researcher pursues it by asking whatcaused democracy in certain cases, such as a set of democratic and nonde-mocratic countries that are homogeneous on contextual variables. It iscommon, for example, to ask why democracy occurred among some but notother countries of a particular region (e.g., Yashar, 1997) or a particular his-torical epoch (e.g., R. B. Collier, 1999). The analyst may explain the casesunder investigation without being able to generalize this explanation to abroad range of places and times. The population-oriented researcher, by con-trast, addresses the question by asking about the partial effects of independentvariables of interest on the distribution of democracy in a large number ofcases. For example, cross-national research on democracy is often concernedwith producing good estimates of the average effect of variables such as eco-nomic development (e.g., Londregan & Poole, 1996) or the number of politicalparties (e.g., Mainwaring, 1993). In these studies, the analyst may accuratelyreport the typical effects of particular independent variables without provid-ing a comprehensive explanation of democracy for any particular case.

Perhaps most comparativists believe that both case-oriented and population-oriented forms of research are worthy. However, their many differences arenot well appreciated, which fosters misunderstandings (Mahoney & Goertz,2006). Of these differences, perhaps the most basic one concerns concep-tions of causality. Case-oriented and population-oriented approaches divergein their fundamental understandings of causation, leaving the comparativefield without a unified theory of causality. The challenge of unificationinvolves reconciling the apparently contradictory claims about causationendorsed in the two approaches. How can causation be both a process thatenables or generates specific outcomes in cases and a statistical likelihoodthat operates probabilistically within a population? A unified theory shouldtell us why there is no contradiction here and why (and if) we need suchseemingly different understandings of causation at the case level and the

Mahoney / Causality 413




population level. It should in fact provide the tools for translating the kindof causal language that is used at the case level into the kind of causal lan-guage that is used at the population level (and vice versa).

In this article, I explore how to unify the case-oriented and population-oriented approaches to causation. The theory for unification that I propose isreductionist—it assumes that causal effects at the population level manifestthemselves only insofar as causal processes are operating in the individualcases.2 The population level does not exhibit any “emergent properties” thatcannot be reduced to (i.e., explained in terms of) processes that occur in theindividual cases. Causation at the population level is thus epiphenomenal;case-level causation is ontologically prior to population-level causation.Although to some this bottom-up approach will seem obvious, the morecommon approach to achieve unification has been top-down: Scholars try tounderstand causation at the level of the individual cases using ideas thatapply to the population level. As we shall see, this approach is fraught withproblems that are corrected by starting with a firm understanding of causa-tion at the level of the individual cases and then extending this understandingto the level of the population.

In developing a unified theory of causation, I do not explore all differencesbetween the case-oriented and population-oriented approaches. Perhaps mostnotably, I do not consider here important questions related to temporality,causal mechanisms, and the transmission of causal effects over time.Nevertheless, the issues covered in this article provide a necessary founda-tion for the further explication of these and other differences between thetwo approaches.

The Case-Oriented Approach

Case-oriented researchers seek to explain particular outcomes in specificcases. They ask questions such as, “Why did European countries developeither liberal-democratic, social-democratic, or fascist regimes during theinterwar period?” (Luebbert, 1991); “Why did the United States providegenerous benefits for Civil War veterans and their dependents?”(Skocpol,1992); and “Why did Korea and Taiwan but not Syria and Turkey experiencesustained economic development after World War II?” (Waldner, 1999). Inaddressing these questions, the researchers try to identify the values on vari-ables that actually caused the particular outcomes in the specific cases.

This research goal seems straightforward enough. But what concretelydo case-study researchers mean when they assert that a given variable value

414 Comparative Political Studies




is a cause of a particular outcome? For example, what does Skocpol (1992)mean when she argues that competitive patronage democracy was a causeof the Civil War pensions? There are different possible answers to thesequestions, some more useful than others.

Probability-Based Definitions

Perhaps the most common approach to defining causation in the indi-vidual case is to assume that it works like causation at the level of the pop-ulation. Here, causality is conceived in terms of likelihoods and probabilities.A cause is specifically a value on a variable that makes an outcome morelikely; a cause increases the probability that an outcome will take place.This definition of cause as “probability raiser” stems from the probabilitytheory that underpins population-oriented research.3

Yet at the level of the individual case, there are various problems withthe idea that causes are probability raisers. For one thing, probabilities mustbe derived from populations. And causes that increase the probability of agiven outcome in a population need not increase the probability of that out-come in any particular case. Indeed, some factors that one would want tocall “causes” of an outcome in an individual case actually decrease theprobability of the outcome in a larger population. Philosophers use stylizedscenarios to illustrate the idea,4 but students of comparative politics will beaware of examples. For instance, although much research suggests that eco-nomic development increases the probability of democracy (or democraticstability), it has long been treated as a cause of the breakdown of democ-racy and the emergence of authoritarianism in South America during the1960s the 1970s (e.g., D. Collier, 1979; O’Donnell, 1973; also see Mainwaring& Pérez-Liñán, 2003). Likewise, the election of leftist and labor-based gov-ernments historically makes the initiation of radical market-oriented reformsless likely on average, but these governments have been treated as a causeof such reforms in several contemporary developing countries (Levitsky &Way, 1998).

What is more, the very idea of viewing causation in terms of probabilitieswhen N = 1 is problematic. At the individual case level, the ex post (objec-tive) probability of a specific outcome occurring is either 1 or 0; that is, eitherthe outcome will occur or it will not. This view is consistent with nearly allinterpretations of probabilities. Thus, according to frequency probabilityapproaches: “It makes no sense to speak of a single-case probability . . . . Ona frequentist interpretation probabilities are properties of the whole ensem-ble, not of the individual events” (Appleby, 2004, p. 449). Other realist





approaches that see probabilities as objective features also treat single-caseprobabilities as meaningless (Milne, 1986). Likewise, for different reasons,Bayesian subjectivists reject the idea of single-case probabilities (seeAlbert, 2005).5 To be sure, the ex ante (subjective) probability of an out-come occurring in a given case can be estimated in terms of some fraction.But the real probability of the outcome is always equal to its ex post prob-ability, which is 1 or 0. For example, across many trials, the probability ofa craps player rolling snake eyes (1s on two six-sided dice) is 1 in 36. Yetfor any individual roll, the real probability of snake eyes at the time of therelease of the dice is equal to 1 or 0. The outcome for the particular role isaffected not only by the fact that each dye has six sides but also by initialposition, velocity, angular momentum, and so forth—factors that determineinfallibly and, in principle, predictably (not haphazardly, not quantum ran-domly) whether the dice will come up snake eyes.6

We can make these ideas more concrete with an example from compar-ative politics: the emergence of democracy in India. Scholars who work onthis question routinely note that India’s long-standing democracy is sur-prising given what we know about population-level probabilities (e.g.,Kohli, 1988, 2001; Rudolph & Rudolph, 1959; Varshney, 1998; Waldner,2006). After all, India has many features (e.g., poverty, ethnic heterogene-ity, inequality, regionalism) that are believed to severely decrease the like-lihood of democracy. Yet given that democracy did happen, the challengefor case-oriented researchers has been to explain it (as opposed to assum-ing that it was a product of random chance). Among other things, mostcase-oriented researchers point to the Congress Party as a key promoter andstabilizer of democracy. Of course, in other contexts, mass-incorporatingparties of this nature have triggered stable authoritarianism and even long-lived totalitarian regimes (Huntington, 1968). Why should the party havebeen a cause of democracy in India? Interestingly, case-oriented researcherssuggest that some of the very factors that made democracy in India so sub-jectively surprising also explain why the Congress Party promoted democ-racy. Thus, hierarchical social structures and ethnic divisions led theCongress Party to adopt a “rule-based internal functioning” in the courseof the nationalist movement (Varshney, 1998). The presence of a hetero-geneous society also encouraged elites to incorporate into the party mid-dle and rich farmers—actors who occupied a strategic position betweenlanded elites and landless workers. In turn, internal bureaucratic function-ing and a broad accommodationist alliance meant that the Congress Partywas well poised to lead a peaceful and sustainable transition to democracywith independence. The crucial point for us is that the conditions that






caused democracy in India included some of the very factors that proba-bilistically decrease the likelihood of democracy in general. Without all ofthese obstacles, India’s Congress Party may not have played its historicrole, and the country may not have developed a stable democratic regime.

Necessity and Sufficiency Definitions

Rather than thinking about case-level causes as probability raisers, wewill do better to adopt an orientation grounded in the philosophy of logic.From this orientation, it is common to define cause in the individual caseas a variable value that is necessary and/or sufficient for an outcome. Theidea that causality should be viewed as specifically necessary causation fol-lows a long tradition going back to Hume (Goertz, 2003; Lewis, 1986). Theapproach captures the intuition that a cause is something that—when coun-terfactually taken away under ceteris paribus conditions—fosters a differ-ent outcome. For instance, Moore (1966) famously quips “no bourgeoisie,no democracy” (p. 418) to highlight the idea that a strong and independentbourgeoisie was necessary for a path to democracy in early modern cases.More recently, Weyland (1998) argues that profound crises were necessaryfor leaders to initiate “shock” plans of economic adjustment in the contem-porary developing world; Tarrow (1989) asserts that deep, visible structuralcleavages and political opportunities have been necessary causes of histor-ical protest cycles; and Amsden (1992) contends that a relatively equitabledistribution of income has been necessary for successful late industrializa-tion. In these examples, the author believes that, in the absence of the cause,the outcome of interest would not have happened.

Although useful, this approach cannot accommodate sufficient causes.With sufficient causes, the counterfactual absence of the cause may notchange the outcome in an individual case and thus could be interpreted asnot exerting an effect under the necessary cause definition.7 There is in facta large philosophical literature, also going back to Hume, which definescause in terms of sufficiency rather than necessity.8 Some comparativists atleast implicitly use this approach. For instance, Goldhagen (1997) arguesthat a culture of virulent anti-Semitism was sufficient to cause Germans tobe motivated to kill Jews. Alternative causal factors, such as the rise of theNazis and Hitler, were not necessary. Germany’s anti-Semitism was enoughby itself to deliver the motivational basis for the Holocaust.

The real problem with these frameworks is not that they fail to speak ofcauses, but rather that they are not exhaustive. Individual causes do not takethe form of only necessary and/or sufficient causes. One can easily think of




examples of causes that were neither necessary nor sufficient. In each of theseexamples, one will find, the cause works together in combination with othercauses to produce an outcome. It is the larger combination that generates theoutcome; or stated differently, the values on two or more variables—not anysingle variable—are jointly sufficient (or possibly jointly necessary) for theoutcome. Let us examine these causes.

INUS and SUIN Causes

Case-oriented researchers rarely treat any single variable value as suffi-cient for a given outcome. Instead, when attempting to identify the causesthat generate a specific outcome, they usually treat individual variable val-ues as INUS causes. The acronym INUS is derived by Mackie (1965) asfollows: “the so-called cause is, and is known to be, an insufficient but nec-essary part of a condition which is itself unnecessary but sufficient for theresult” (p. 246; also see Mackie, 1980). A stylized illustration of INUS cau-sation is the idea that a building can burn down (Y1) either because of ashort circuit (A1) combined with wooden framing (B1) or because of a gaso-line can (C1) combined with a furnace (D1); that is, Y1 = (A1 & B1) v (C1 &D1), where “&” represents the Logical AND, the “v” represents the LogicalOR, and “=” represents sufficiency. There is no necessary cause for the out-come; instead, alternative combinations are each sufficient.

INUS causes are commonplace in case-oriented research. For instance,consider Moore’s (1966) argument that democratic pathways in the earlymodern world required both a strong bourgeoisie and an aristocracy thateither aligned with this bourgeoisie or was historically weakened. In theargument, there are two combinations that generate democracy: (a) a strongbourgeoisie that is allied with aristocratic elites, and (b) a strong bourgeoisieand a weak aristocracy. Although a strong bourgeoisie is a necessary cause,the bourgeois–aristocratic alliance cause and the weak aristocracy cause areINUS causes. We can summarize the argument as follows:

Y1 = X1 & (A1 v B1), (1)

where Y1 = democratic pathway; X1 = strong bourgeoisie; A1= alliancebetween bourgeoisie and aristocracy; and B1 = weak aristocracy. Neither A1

nor B1 is individually necessary or individually sufficient. Instead, they areINUS causes that combine with X1 to form two possible combinations thatare sufficient for Y1. Many other studies that use Qualitative ComparativeAnalysis (QCA) in either its dichotomous or its fuzzy-set version assume






INUS causation and seek to identify the different causal pathways to givenoutcomes.9

An alternative kind of combinatorial cause, one that is linked to neces-sity, is a SUIN cause. A SUIN cause is, to make a parallel with Mackie’sINUS cause, a sufficient but unnecessary part of a factor that is insufficientbut necessary for an outcome (Mahoney, Kimball, & Koivu, 2007). Herethe constitutive attributes of a necessary cause are treated as causes them-selves. For example, a well-known theory holds that nondemocracy (i.e., anondemocratic dyad) is necessary for war. There are various attributes thatby themselves would constitute nondemocracy, including fraudulent elec-tions, high levels of repression, and severe suffrage exclusions. By virtue ofconstituting nondemocracy all by themselves, each of these conditions is aSUIN cause of war. Fraudulent elections, repression, and suffrage exclu-sions are neither necessary nor sufficient for war, but rather factors that canconstitute nondemocracy, which in turn is necessary for war. Or consideragain Moore’s (1966) argument. We saw how a bourgeois–aristocraticalliance and a weak aristocracy are INUS causes. If we now imagine thatMoore were to treat these two factors as each examples of a third factor—politically subordinate aristocracy—then they would be SUIN causes: con-stitutive parts sufficient for a necessary cause (politically subordinatearistocracy) of democracy. We can summarize this idea as follows:

Y1 = X1 & Z1; Z1 = A1 v B1, (2)

where Y1 = democratic pathway; X1 = strong bourgeoisie; Z1 = politicallysubordinate aristocracy; A1 = alliance between bourgeoisie and aristocracy;and B1 = weak aristocracy. Here A1 and B1 are SUIN causes of a democratic path.

Logically speaking, then, there are five kinds of causes that can be used incase-oriented research. A cause may be (a) necessary but not sufficient, (b)sufficient but not necessary, (c) necessary and sufficient, (d) INUS, or (e)SUIN. This list appears to be mutually exclusive and collectively exhaustive(Mahoney et al., 2007). Of these five causes, the prototypical one is a neces-sary and sufficient cause. All other causes are derivative of a necessary andsufficient cause. In fact, the other four causes become more important to theextent that that they approach the threshold of being a necessary and suffi-cient cause (Mahoney et al., 2007; also see Braumoeller & Goertz, 2000;Goertz, 2006; Hart & Honoré, 1959; Ragin, 2006). Thus, necessary causesare increasingly important as they approach causal sufficiency. Sufficientcauses are more important as they approach causal necessity. And INUS andSUIN causes gain importance as they become closer to being individuallynecessary and sufficient.





To embrace necessary and/or sufficient causation (including INUS andSUIN causation) is to assume that the world of human beings is deterministic.10

This assumption does not of course mean that a given researcher will be suc-cessful at identifying the causes of any outcome. Nor does this assumptionmean that the researcher will achieve valid measurement or carry out goodresearch. The assumption of an ontologically deterministic world in no wayimplies that researchers will successfully analyze causal processes in thisworld. But it does mean that randomness and chance appear only because oflimitations in theories, models, measurement, and data.

The only alternative to ontological determinism is to assume that, at leastin part, “things just happen”; that is, to assume that truly stochastic factors—whatever those may be (see Humphreys, 1989)—randomly produce out-comes. The assumption of a genuinely probabilistic world finds its bestdefense with indeterministic relations in quantum mechanics. Yet whether ornot subatomic processes are truly indeterministic is still debated amongphysicists. Moreover, as Waldner (2002) suggests, quantum theorists arguethat the kinds of issues addressed in the social sciences do not work like quan-tum mechanics. Randomness at the subatomic level seems inappropriatewhen applied to the world of human beings and their objects, assuming thatthese entities function like all other known nonparticle entities.

Before concluding this section, I want to note that various methods existfor analyzing necessity and sufficiency (including INUS and SUIN causes).Indeed, all of the major small-N cross-case methods used in this field—Mill’s methods of agreement and difference, typological theories, counter-factual analysis, Boolean algebra, and fuzzy-set analysis—assume thesekinds of causes (e.g., Elman, 2005; George & Bennett, 2005; Goertz &Levy, 2007; Mahoney, 1999; Ragin, 1987, 2000). Here is not the place toreview the huge literature on these methods, including critiques of them,but the methods are out there, and they are a basic part of the tool kit ofcase-oriented research in comparative politics.

The Population-Oriented Approach

Population-oriented researchers do not have as their primary goal theexplanation of any particular case. Instead, they want to accurately estimatethe effects of variables within whole populations. They ask questions suchas, “What is the effect of presidentialism on the consolidation of democracy?”(Cheibub, 2007); “To what extent is globalization a cause of inegalitariandistribution?” (Garrett, 1998); and “Does regime type matter for economicgrowth?” (Gerring, Bond, Barndt, & Moreno, 2005). In addressing these





questions, the researchers want to generalize about the typical effects of theparticular causal factor(s) of interest.

Mean Causal Effects

The population-oriented approach in many ways parallels experimentalresearch.11 Experiments are usually not designed to provide comprehensiveexplanations of outcomes. Nor are they designed to explain particular cases.Rather, they are intended to accurately assess the typical effects of particulartreatments for populations. Experimenters want to know what difference (ifany) one or more treatments has for an outcome on average. The approach isquite consistent with the idea that causes are probability raisers. One can infact say that a treatment is a cause when its presence raises the probability ofan outcome occurring in any given case of a larger population.

The experimental template underpins the definition of causality used inthe population-oriented approach, a point well illustrated by King, Keohane,and Verba’s (1994, pp. 76-81) famous discussion of “mean causal effect” (β).They present this concept using the example of the effect of incumbency onthe vote fraction received by a candidate running for office. The meancausal effect in the example is the difference between the mean distributionof the vote fraction received by an incumbent candidate across multiplehypothetical elections and the mean distribution of the vote fractionreceived by a nonincumbent across multiple hypothetical elections. In theirnotation, β = µI

i _ µN

i , where µXi is the mean of the distribution of the depen-

dent variable under condition X and I and N are incumbent and nonincum-bent, respectively. This understanding of β as being equal to the differencebetween the means of two distributions is shared by many leading statisti-cal methodologists (Braumoeller, 2006).12

Population-oriented comparativists often identify causes by estimating βcoefficients in multivariate statistical models. They are especially concernedwith two aspects of β. The first is substantive significance, which derives fromthe size of the coefficient and may be evaluated in various ways. The secondis statistical significance, which summarizes the likelihood that the observedfinding is a product of sampling error or other random error and is affected bythe number of variables and cases used in the statistical test. For example,Gerring et al.’s (2005) argument that democratic stock is an important cause ofeconomic growth is based on the substantive and statistical significance of β forthe democracy stock variable in their multivariate models. In contemporarycomparative politics, it is worth noting, independent variables of theoretical





interest that meet a specified level of statistical significance (e.g., p ≤ .05) areoften considered important causes even if the size of their effect is modest.Indeed, the total explanatory power of most statistical models is modest whenevaluated using a measure such as adjusted R2. This underscores the experi-mental underpinning of this tradition: The goal is to assess the average effects(if any) of individual variables rather than comprehensively explain variationon an outcome.

Net Causal Effects

Causal research in the population-oriented tradition has for decades beenconcerned with distinguishing genuine causation from spurious covariation(e.g., Pearl, 2000, pp. 78-85, 173-200). When one seeks to estimate themean effect of X on Y in the context of an observational study, the questionimmediately arises as to which other variables should be held constant.Both the size and statistical significance of an effect can change radicallydepending on the other variables that are included. These other variables—known as covariates, concomitants, or confounders—must be controlled for(conditioned on) if one wishes to correctly estimate the net effect of X onY. Net effects are essentially calculated by partitioning the population intosubgroups that are homogenous on the control variables, measuring theeffect of values of X on the distribution of Y in the subgroups, and then aver-aging the results (e.g., Turner, 1997). The goal of this form of multivariateanalysis is not to deny that the control variables are causes of Y, but to ruleout the possibility that they account for the observed effect of X on Y.

Explanation in population-oriented research makes various specificationassumptions to mitigate the potential problems that arise from the use ofobservational data rather than experimental data (e.g., Shadish, Cook, &Campbell, 2002). With an experiment, of course, cases are randomly assignedto different values of an independent variable, such that in theory their priorcharacteristics are unrelated to those values. But this kind of independenceis almost never true with observational data. Hence, population-orientedresearchers need to control for variables using tools such as stratification toachieve conditional independence on average (mean conditional indepen-dence). Conditional independence is, in effect, a way of trying to meet thecounterfactual assumptions of causation embedded in this approach.

Population-oriented researchers make other familiar and related assump-tions, each of which can be justified to varying degrees, depending on thestudy in question. These include the following:




1. Stable Unit Treatment Value Assumption—the idea that influencesamong observations do not affect outcomes and the notion that a givenvalue on an independent variable is stable across cases (for an excellentrecent discussion, see Brady & Seawright, 2004).

2. Absence of endogeneity—in comparative politics, endogeneity is oftendiscussed in conjunction with the specific problems that arise from reci-procal causation. Strictly speaking, though, endogeneity arises wheneveran independent variable is correlated with the error term.

3. Temporal stability—the assumption that causal effects are stable overtime. Unrecognized differences across time can produce missing vari-able bias.

4. Measurement transience—the assumption that the act of observing casesand measuring variables does not alter causal effects or, if it does, thatthis impact can be modeled.

The proliferation of more and more advanced statistical techniques is partof an ongoing quest to meet these various assumptions. How successful con-temporary research is at doing so is debated.13 For our purposes, this debateneed not distract us any more than analogous debates over the merits ofsmall-N methods mentioned above. Rather, we need to explore how thisapproach to causal analysis, which thinks about causation in terms of proba-bility theory, can be unified with the case-oriented approach discussed above,which thinks about causation in terms of logic.

From the Cases to the Population (and Back):Toward a Unified Theory

The starting point for a unified theory is the recognition that, at the popu-lation level, causation occurs almost exclusively through INUS causes. To seewhy this is true, we need to explore the relationship between INUS causes andvariables that exert partial effects in statistical models. As we shall see, thesevariables have the effects they do because they are INUS causes.

Causation at the Population Level

If one accepts that causation at the population level derives from causationat the case level, then the five kinds of causes that can apply to individualcases—necessary, sufficient, necessary and sufficient, INUS, and SUINcauses—are the only kinds of causes that can operate at the populationlevel. Four of these five types, however, are usually not relevant when ana-lyzing populations. We saw below how two types—sufficient causes and





necessary and sufficient causes—are very infrequently used at the caselevel. As one generalizes to the population level, these types will, if any-thing, be even less common. By contrast, necessary causes are standard incase-oriented research. Yet when we shift to the population level, necessarycauses become hard to find. For example, causes that were necessary forhigh unemployment in Germany may not have been necessary for highunemployment in France; necessary causes for particular cases often do notgeneralize. Indeed, with only a few possible exceptions, such as the hypoth-esis that nondemocracy (i.e., a dyad with a nondemocratic state) is neces-sary for war, comparativists have not found many necessary causes thatapply to broad populations. Because SUIN causes work through necessarycauses, they will also not often be discovered at the population level.

This leaves INUS causes as the main type of cause that applies at the pop-ulation level. If INUS causes are present, different sets of variable values leadto a particular outcome. The presence of multiple combinations of variablevalues that produce the same outcome is sometimes called “equifinality”(George & Bennett, 2005). Although equifinality is usually associated withQCA techniques (Ragin, 1987, 2000), its emphasis on multiple paths to agiven outcome is implicitly present in most population-oriented research,including the additive linear models that comparativists frequently use. Thereare countless ways to arrive at an outcome (i.e., a particular range of valueson the dependent variable) in an additive linear model. Each independentvariable exerts its own effect, and each independent variable can potentiallycompensate for any other. One case may have the outcome of interest becauseit has high values on certain variables, whereas a different case arrives at thesame outcome because it has high values on other variables. No variablevalue is necessary, but different variable values (in conjunction with the errorterm) are sufficient to produce the outcome. Equifinality is thus omnipresentin mainstream population-oriented research (Mahoney & Goertz, 2006).

Equifinality is not the only issue to which analysts of INUS causes mustattend. Another key assumption underpinning INUS causation is that vari-ables often do not exert effects independently of one another. Instead, theeffect of one variable depends on the values of one or more other variables.Variables work together as packages, not isolated factors. Boolean algebra isthe usual way in which case-oriented researchers try to formally model thiskind of causation (Ragin, 1987, 2000). Some statistical methodologists havedeveloped broadly parallel tools such as Boolean probit and Boolean logit(Braumoeller, 2003). Moreover, the study of interaction effects, which is notuncommon (e.g., perhaps 25% of quantitative comparative articles now includeat least one interaction term), has moved statistical research in the direction






of combinatorial causation (Kam & Franzese, 2007). Insofar as statisticalcomparativists start to use saturated interaction models in which all possibleinteractions are assessed and simplified in a top-down manner, we wouldessentially see an integration of QCA techniques and statistical methods. Thekey point here is that there are various methods that can, in principle, be usedto study INUS causes and combinatorial causation across broad populations.

Indeed, some leading scholars suggest that many or most outcomes atthe population level need to be explained in terms of combinatorial causa-tion (e.g., Achen, 2005; Franzese, 2003; Hall, 2003; Ragin, 1987). If theyare right, one might wonder if thinking about causation in terms of themean effects of individual variables—the traditional focus of population-oriented research—is useful at all. Doubts are reinforced by recent writingson interaction effects in the population-oriented tradition. Methodologistshave made it clear that one should include lower order constitutive termswhen testing multiplicative interaction models, but one cannot interpret thecoefficient on these terms as an average effect (Brambor, Clark, & Golder,2005; Braumoeller, 2004; Kam & Franzese, 2007). As the number of inter-action terms increases, the idea of thinking about coefficients as reportingthe effects of individual variables starts to drop out altogether. If one wereto use a saturated interaction model, in fact, one could say virtually nothingabout the individual variables. With QCA models, analogously, the focus is onthe causal combinations, not the individual factors (with the exception ofcauses that are individually necessary or sufficient). How, then, is the notionof a mean causal effect for an individual variable—still the dominant way ofconceptualizing causation in political science—relevant to thinking aboutcausation?

Mean Causal Effects as Symptoms of INUS Causes

The answer to this question is that independent variables that exert par-tial effects in well-specified statistical models are INUS causes; they arenormally, in fact, important INUS causes. However, with only a few partialexceptions (Brady & Seawright, 2004; Marini & Singer, 1988; Shadish et al.,2002), the possibility that mean causal effects are symptoms of INUScauses has not been developed in the methodological literature.

The relationship between a mean causal effect and an INUS cause can bebetter understood if we first define an “important” INUS cause. The generalcriterion is that an INUS cause becomes more important as it becomescloser to being a necessary and/or sufficient cause; beyond this, it must alsobe a nontrivial cause.14 Borrowing from the language of probability theory,




we can say that important INUS causes are “probabilistically necessary”and/or “probabilistically sufficient” causes at the population level. Theextent to which they are probabilistically necessary or probabilistically suf-ficient can be assessed in practice with one or more available techniques(see Braumoeller & Goertz, 2000; Clark, Gilligan, & Golder, 2006; Dion,1998; Eliason & Stryker, in press; Ragin, 2000).

INUS causes that are probabilistically necessary are factors that usuallyor almost always have to be present for the outcome to occur. They are thusnormally present in the different combinations of variable values that caneach generate the outcome of interest. Arguably, smoking as a cause of lungcancer is a good example. Smoking is an INUS cause because it must com-bine with other environmental and biological factors to generate the cancer.At the same time, smoking may well be probabilistically necessary for lungcancer—that is, it is usually present in the various distinct combinations ofvariable values that generate lung cancer.15 Smoking, of course, exerts apartial effect on lung cancer in population-oriented research (i.e., it raisesthe probability of the outcome). The reason why smoking exerts this partialeffect and thus can be treated as a probability raiser is precisely because itis an important INUS cause. The causal properties of the variable (i.e., itsstatus as a probabilistically necessary INUS cause) lead it to manifest thepopulation-level statistical effect.

Probabilistically necessary INUS causes are often implicitly discussed inthe comparative politics literature as well. An example is the presence of aneconomic crisis as a cause of third wave transitions to democracy. As Bermeo(1990) remarked in her review of O’Donnell, Schmitter, and Whitehead’s(1986) Transitions from Authoritarian Rule: “It is surely not coincidental thateconomic crises accompanied every transformation reviewed here. The pat-tern suggests that economic crises might be a necessary though not sufficientincentive for the breakdown of authoritarian regimes” (p. 366). Although onecan now easily find cases of recent democratic transition without economiccrisis (e.g., Chile), it seems fair to conclude that crisis was a probabilisticallynecessary cause of a third wave democratic transition (i.e., countries rarelyexperienced transitions during economic good times; for systematic evi-dence, see Haggard & Kaufman, 1995, pp. 32-36). Statistical models thatshow an individual effect for economic crisis on democratic transition at thepopulation level (e.g., Gasiorowski, 1995) are picking up this variable’sstatus as a probabilistically necessary INUS cause.

The other kind of important INUS causes are those that are probabilisti-cally sufficient. These causes do not have to combine with many other (non-trivial) causes to generate the outcome of interest. Rather, probabilistically





sufficient causes can almost produce the outcome by themselves (but needsome help from other variables). For instance, lung cancer is probabilisti-cally sufficient for death. Most deaths do not involve lung cancer, but whenlung cancer is present, it will generate death under most circumstances(though there are some exceptions). Again, INUS causes that are proba-bilistically sufficient will manifest themselves as variables that exert partialeffects when included in correctly specified statistical models.

Probabilistically sufficient INUS causes are also readily found in the com-parative literature. For example, one of the most celebrated empirical findingsin the field concerns the relationship between economic development anddemocracy. Although the specific workings of this relationship are subject todebate, much evidence suggests that a high level of economic development isprobabilistically sufficient for either democracy or democratic stability (e.g.,Boix & Stokes, 2003; Przeworski, Alvarez, Cheibub, & Limongi, 2000). Richcountries are thus almost always democratic. There are some exceptions, andcertainly one would not want to say that wealth alone is fully sufficient fordemocracy (or democratic stability). However, when significant wealth ispresent, one can be nearly certain that democracy (or democratic stability)will also be present. Statistical results that show that economic developmenthas a significant effect on democracy (e.g., Londregan & Poole, 1996) arelikely an artifact of the probabilistically sufficient status of this variable.Again, the implication is that the variable shows up as a probability raiserbecause it is an important INUS cause.

We may conclude, then, that individual variables that reveal partial effectsin correctly specified statistical models are causes. But the effects they exhibitas summarized by a statistical coefficient are not what make them causes.They are causes by virtue of being important INUS causes (i.e., they are prob-abilistically necessary and/or sufficient for outcomes). And their exhibitedeffects are just symptoms of this underlying logical status.16

Translating Back and Forth

Treating variables that exhibit mean causal effects in statistical modelsas INUS causes is helpful in several ways. For one thing, it is substantivelyenlightening to know whether a variable exerts its effect because it isprobabilistically necessary or because it is probabilistically sufficient (orboth). For example, the finding that a higher level of economic develop-ment is almost always sufficient for democracy is of obvious substantiveimportance. It tells us that the promotion of economic growth beyond a cer-tain level nearly guarantees the promotion of human freedom. The same is





true of the finding that high levels of cumulative left governance are almostalways necessary for high levels of public day care (Stryker, Eliason, &Tranby, in press). The implication is that public day care programs will bedislodged only with a long-term shift to the right in government. Althoughthese kinds of findings are not about partial effects as traditionally under-stood, they are clearly useful if correct.

Moreover, by translating an initial statistical finding into the language ofINUS causation, the researcher can better theorize how the factor should beincluded in a subsequent model that assesses combinatorial causation. In thecase of INUS causes that are probabilistically necessary, they must beincluded in nearly all causal combinations of a QCA model (and would nor-mally need to appear in many terms in a multiplicative interaction model aswell). For example, because nondemocracy (i.e., a nondemocratic dyad) isat least probabilistically necessary for warfare, this factor must be includedas one cause in nearly all of the causal combinations of a QCA model ofinterstate warfare. INUS causes that are probabilistically sufficient, by con-trast, often do not need to be included in causal combinations. This is truebecause these causes can generate the outcome of interest almost by them-selves, needing only a little help from other (nontrivial) factors. For instance,if the presence of a large historically exploited minority group is nearly suf-ficient for initially low levels of social performance in Spanish America(Mahoney, 2003), then this cause can be analyzed reasonably well by itselfwithout including it as part of a larger causal package.

The population-oriented approach can thus help researchers locate impor-tant INUS causes. And the INUS causes can then be evaluated subsequentlywith more complex QCA or interaction models. The importance of findingthe right variables and combinations to be included in these models canhardly be overstated. Our theories in comparative politics routinely positcomplex interactions (Hall, 2003), but they are almost never precise enoughto locate all relevant INUS causes, with potentially devastating implicationsfor testing causal theories in practice (e.g., Kam & Franzese, 2007). Tools forbetter specifying our combinatorial causal models are of tremendous value.

Beyond this, of course, researchers will always be interested in tryingto estimate the mean effects of individual variables in their own right.Information about mean effects helps one make informed predictions andestimate the future impact of a given intervention. Individuals and politicalactors seek this kind of information as they maneuver in the world. Forexample, it is one thing to know that authoritarianism is a probabilisticallynecessary INUS cause of social revolution (or that smoking is a probabilisti-cally necessary INUS cause of lung cancer). This tells us that governments





can ward off social revolutions by promoting formal democratic institutions(or that we can be fairly certain to avoid lung cancer by not being exposedto tobacco smoke). Yet it is another thing to have a good estimate of the riskof social revolution a government faces by having authoritarian institutions(or the risk of lung cancer we face by smoking). The true probability of theoutcome occurring at the case level is 1 or 0. However, in the absence offull knowledge about all of the sufficiency combinations that can producethe outcome, we would like to know if the probability is more likely 1 or 0,and exactly how much more likely! We seek insight about what we canmost reasonably expect to happen in a context of limited knowledge. Thepopulation-oriented tradition can help decision makers formulate betterguesses about whether, given a particular course of action and other knownconditions in the world, the probability of a specific outcome of interestoccurring is really 1 or 0.17

These observations bring us full circle. Just as one might want to trans-late findings from population-oriented research into the causal language ofthe case-oriented tradition, so too might one wish to translate findingsabout probabilistically necessary and probabilistically sufficient INUScauses into the language of mean causal effects.

Conclusion

This article has explored the unification of case-oriented and population-oriented approaches to causality in comparative politics. The method ofunification proposed here entailed extending the case-oriented approach tothe population level, under the assumption that causal patterns at the popu-lation level must be derivative of causation that is occurring at the caselevel. With this extension, it became clear that INUS causes are really whatare indirectly studied in most population-oriented research. In particular,important INUS causes (i.e., probabilistically necessary and/or sufficientINUS causes) manifest themselves as variables that exhibit partial causaleffects in well-specified statistical models.

A basic implication of this analysis is that more comparative researchersneed to try to study INUS causes as directly as possible at the populationlevel, using statistical models with various interaction terms or the tools ofQCA. To be sure, these researchers will face daunting methodological chal-lenges in the effort to generate interpretable results given the tremendous datarequirements of these models. But this kind of complexity-sensitive analysismay be the only road, over the long run, to valid causal generalization across






many cases in comparative politics. Meanwhile, those who work on thisagenda will surely benefit from the insights of ongoing research on bothmean effects for individual variables and specific causes in particular cases.

Notes

1. Here, I modify Ragin’s (1987) terminology, which distinguishes between case-orientedand variable-oriented approaches. The distinction between these two approaches also appearsin the philosophical literature, sometimes identified as the difference between “token causa-tion” and “type causation,” or between “single-case causation” and “property causation” (see,e.g., Woodward, 2003).

2. This is known as the “singularist view” in philosophy. Its advocates include Anscombe(1971), Mellor (1995), and Woodward (1990). The rival position is known as the “superve-nience view,” and it is exemplified by Eells (1991).

3. Gerring (2005) adopts this approach for political science. Philosophers who think aboutcausation at the level of the population have also long embraced this definition. For example,“A probabilistic account—essentially the idea that a cause raises the probability of its effect—is now commonplace in science and philosophy” (Dowe & Noordhof, 2004, p. 1). Also seeCartwright (1989); Eells (1991); Eells and Sober (1983); Good (1961, 1962); Lewis (2000);Menzies (2004); Pearl (2000); Skyrms (1980); Suppes (1970).

4. For instance, “Imagine a golf ball rolling towards the cup, such that its probability ofdropping in is quite high. Along comes a squirrel, who kicks the ball away from the cup, thusreducing the chance of it going in. Then, through a series of improbable ricochets, the balldrops into the cup. How are the squirrel’s kick and the ball’s dropping in the cup related? Iwant to argue that the squirrel’s kick reduced the probability of the ball’s dropping in and thesquirrel’s kick caused the ball to drop in” (Sober, 1984, pp. 406-407). A standard objection tothis kind of example is that if one characterizes the specific causes (i.e., the squirrel’s kick andsubsequent ricochets) in great enough detail, then it will become clear that this interventiondid not really lower the probability of the ball dropping in. I agree; the real probability of theball dropping in was always equal to 1. Probabilities do not make sense for the explanation ofsingular events (as I discuss below). Also see Dowe (2004), on chance-lowering causes; andSchaffer (2000), on probability raising without causation.

5. The major attempt to defend single-case probabilities is Popper’s (1959) propensityinterpretation. But his approach is widely rejected (see Williams, 1999).

6. Seemingly random processes such as dice rolling and coin flipping are not really ran-dom (Ekeland 1988; Ford, 1983). It is true that dice rolling and coin flipping exhibit extremesensitivity to initial conditions and may be good examples of the dynamics of chaos theory.However, chaos theory is fully a deterministic approach to explanation (Waldner, 2002).

7. The problems that redundant causation (also called symmetrical overdetermination)poses for necessity definitions of cause are very well known. See Ehring (1997); Menzies(1996); Scriven (1966).

8. The Humean notion of sufficiency understood in terms of constant conjunction subse-quently became the basis for the covering-law model of causation associated with mid-20thcentury positivists (e.g., Hempel, 1965; Nagel, 1961; Popper, 1959).

9. Examples of comparative works include Amenta’s (1996) study of New Deal socialspending; Berg-Schlosser and DeMeur’s (1994) analysis of democracy in interwar Europe; Huber,Ragin, and Stephens’s (1993) work on the welfare state; Griffin, Botsko, Wahl, and Isaac’s (1991)




study of trade union growth and decline; Mahoney’s (2003) work on long-run development inLatin America; and Wickham-Crowley’s (1992) study of guerrillas and revolutions.

10. Determinism is the thesis that “there is at any instant exactly one physically possiblefuture” (Van Inwagen, 1983, p. 3). For a discussion of common misconceptions of the entail-ments of determinism, such as the incorrect notion that determinism denies free will andhuman agency, see Dennett (2003).

11. Angrist, Imbens, and Rubin (1996) assert that “causal inference in statistics . . . is fun-damentally based on the randomized experiment” (p. 444).

12. King, Keohane, and Verba (1994) follow Holland (1986) in referring to “mean causaleffect.” The same idea is varyingly called “average treatment effect” (Sobel, 1996), “averagecausal response” (Angrist & Imbens, 1995), and “average causal effect” (Dawid, 2000).

13. For some skeptical views, see Clogg and Haritou (1997); Freedman (1991); Lieberson(1985); Shalev (2007).

14. Empirically speaking, a necessary cause is trivial if it is always (or almost always) pre-sent, irrespective of the outcome. A sufficient cause is trivial if it is almost never present andthus almost never generates the outcome of interest (see Braumoeller & Goertz, 2000; Goertz,2006; Ragin, 2006; also see Hart & Honoré, 1959). For example, the presence of oxygen is atrivially necessary cause of a revolution, because it is always present in all cases. INUS causesthat are close to being trivial in this empirical sense are not important.

15. Apparently, there are relatively few cases (i.e., about 10%) of lung cancer in whichsmoking is not involved.

16. To be sure, not all INUS causes will exert mean effects in population-oriented research.For example, it is easy to write a Boolean equation in which a variable and its negation areboth INUS causes of the same outcome (e.g., Y = A&B v ∼A&D). When this is true, the vari-able and its negation may end up canceling out one another’s effect, such that the variableoverall exerts no mean effect in a population.

17. In the population-oriented tradition, a respected body of work views causation in termsof this kind of decision maker understanding (e.g., Dawid, 2000; Rubin, 1978).

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James Mahoney is a professor of political science and sociology at Northwestern University.He is the author of The Legacies of Liberalism: Path Dependence and Political Regimes inCentral America and coeditor of Comparative Historical Analysis in the Social Sciences. Hiswork also includes articles on political and socioeconomic development in Latin America,path dependence in historical sociology, and causal inference in small-N analysis.





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