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DOI: 10.1177/0010414007313115

January 20082008 41: 412 originally published online 31Comparative Political Studies

James MahoneyToward 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 contrasting

ways when they pursue explanation in particular cases (case-oriented research)

versus large populations (population-oriented research). With case-oriented

research, they understand causation in terms of necessary, sufficient, INUS,

and SUIN causes. With population-oriented research, by contrast, they

understand causation as mean causal effects. This article explores whether it

is 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 translation

is possible, because certain types of INUS causes manifest themselves as

variables that exhibit partial effects when studied in population-oriented

research. The article concludes that the conception of causation adopted in

case-oriented research is appropriate for the population level, whereas the

conception of causation used in population-oriented research is valuable for

making predictions in the face of uncertainty.

Keywords: causality; logic; probabilities; cases; populations

Comparative analysts use distinct methods and conceptualize causation

in contrasting ways when they carry out explanation in particular casesversus large populations. When analyzing individual cases, comparativists

seek to identify the specific values of variables that enabled and/or gener-

ated outcomes of interest. They pursue a genetic and sequential mode of

explanation that is implemented in part through narrative prose. By con-

trast, when comparativists study large populations, they seek to estimate the

average effects of independent variables of interest. They carry out statisti-

cal analysis and report results as coefficients that apply to populations as

wholes rather than particular observations.

Comparative Political Studies

Volume 41 Number 4/5

April/May 2008 412-436

2008 Sage Publications

10.1177/0010414007313115

http://cps.sagepub.comhosted at

http://online.sagepub.com

Authors 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.

http://cps.sagepub.com/http://cps.sagepub.com/http://cps.sagepub.com/http://cps.sagepub.com/


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These two approaches can be called, for convenience, case-orientedand

population-oriented research.1 Case-oriented researchers seek to identify

the causes of particular outcomes in specific cases. They may find causalpatterns that apply broadly, but their primary concern is with causation in

the specific cases under analysis. By contrast, population-oriented researchers

seek 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. Both

case-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 what

caused democracy in certain cases, such as a set of democratic and nonde-

mocratic countries that are homogeneous on contextual variables. It is

common, for example, to ask why democracy occurred among some but not

other 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 cases

under investigation without being able to generalize this explanation to a

broad range of places and times. The population-oriented researcher, by con-trast, addresses the question by asking about the partial effects of independent

variables of interest on the distribution of democracy in a large number of

cases. For example, cross-national research on democracy is often concerned

with producing good estimates of the average effect of variables such as eco-

nomic development (e.g., Londregan & Poole, 1996) or the number of political

parties (e.g., Mainwaring, 1993). In these studies, the analyst may accurately

report 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 are

not 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 diverge

in their fundamental understandings of causation, leaving the comparative

field without a unified theory of causality. The challenge of unification

involves reconciling the apparently contradictory claims about causation

endorsed in the two approaches. How can causation be both a process thatenables or generates specific outcomes in cases and a statistical likelihood

that operates probabilistically within a population? A unified theory should

tell us why there is no contradiction here and why (and if) we need such

seemingly different understandings of causation at the case level and the

Mahoney / Causality 413



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population level. It should in fact provide the tools for translating the kind

of 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 is

reductionistit assumes that causal effects at the population level manifest

themselves only insofar as causal processes are operating in the individual

cases.2 The population level does not exhibit any emergent properties that

cannot be reduced to (i.e., explained in terms of) processes that occur in the

individual 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 more

common approach to achieve unification has been top-down: Scholars try to

understand causation at the level of the individual cases using ideas that

apply to the population level. As we shall see, this approach is fraught with

problems that are corrected by starting with a firm understanding of causa-

tion at the level of the individual cases and then extending this understanding

to 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 most

notably, 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 the

two approaches.

The Case-Oriented Approach

Case-oriented researchers seek to explain particular outcomes in specific

cases. They ask questions such as, Why did European countries develop

either liberal-democratic, social-democratic, or fascist regimes during the

interwar period? (Luebbert, 1991); Why did the United States provide

generous benefits for Civil War veterans and their dependents?(Skocpol,

1992); and Why did Korea and Taiwan but not Syria and Turkey experience

sustained 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 concretely

do case-study researchers mean when they assert that a given variable value

414 Comparative Political Studies



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is a cause of a particular outcome? For example, what does Skocpol (1992)

mean when she argues that competitive patronage democracy was a cause

of 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 probability

theory that underpins population-oriented research.3

Yet at the level of the individual case, there are various problems with

the idea that causes are probability raisers. For one thing, probabilities must

be derived from populations. And causes that increase the probability of a

given 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 the

probability of the outcome in a larger population. Philosophers use stylized

scenarios to illustrate the idea,4 but students of comparative politics will be

aware of examples. For instance, although much research suggests that eco-

nomic development increases the probability of democracy (or democratic

stability), it has long been treated as a cause of the breakdown of democ-

racy and the emergence of authoritarianism in South America during the

1960s the 1970s (e.g., D. Collier, 1979; ODonnell, 1973; also see Mainwaring

& Prez-Lin, 2003). Likewise, the election of leftist and labor-based gov-

ernments historically makes the initiation of radical market-oriented reforms

less likely on average, but these governments have been treated as a cause

of such reforms in several contemporary developing countries (Levitsky &

Way, 1998).

What is more, the very idea of viewing causation in terms of probabilities

whenN= 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, either

the outcome will occur or it will not. This view is consistent with nearly allinterpretations of probabilities. Thus, according to frequency probability

approaches: It makes no sense to speak of a single-case probability . . . . On

a frequentist interpretation probabilities are properties of the whole ensem-

ble, not of the individual events (Appleby, 2004, p. 449). Other realist




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approaches that see probabilities as objective features also treat single-case

probabilities 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 of

a craps player rolling snake eyes (1s on two six-sided dice) is 1 in 36. Yet

for any individual roll, the real probability of snake eyes at the time of the

release of the dice is equal to 1 or 0. The outcome for the particular role is

affected not only by the fact that each dye has six sides but also by initialposition, velocity, angular momentum, and so forthfactors that determine

infallibly 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 on

this question routinely note that Indias 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 challenge

for case-oriented researchers has been to explain it (as opposed to assum-

ing that it was a product of random chance). Among other things, most

case-oriented researchers point to the Congress Party as a key promoter and

stabilizer of democracy. Of course, in other contexts, mass-incorporating

parties of this nature have triggered stable authoritarianism and even long-

lived totalitarian regimes (Huntington, 1968). Why should the party have

been a cause of democracy in India? Interestingly, case-oriented researchers

suggest 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 the

Congress Party to adopt a rule-based internal functioning in the course

of the nationalist movement (Varshney, 1998). The presence of a hetero-

geneous society also encouraged elites to incorporate into the party mid-

dle and rich farmersactors 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 Party

was well poised to lead a peaceful and sustainable transition to democracy

with independence. The crucial point for us is that the conditions that




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caused democracy in India included some of the very factors that proba-

bilistically decrease the likelihood of democracy in general. Without all of

these obstacles, Indias 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, we

will do better to adopt an orientation grounded in the philosophy of logic.

From this orientation, it is common to define cause in the individual case

as 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). The

approach captures the intuition that a cause is something thatwhen coun-

terfactually taken away under ceteris paribus conditionsfosters a differ-

ent outcome. For instance, Moore (1966) famously quips no bourgeoisie,

no democracy (p. 418) to highlight the idea that a strong and independent

bourgeoisie 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 structural

cleavages and political opportunities have been necessary causes of histor-

ical protest cycles; and Amsden (1992) contends that a relatively equitable

distribution 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 not

change the outcome in an individual case and thus could be interpreted as

not exerting an effect under the necessary cause definition.7 There is in fact

a large philosophical literature, also going back to Hume, which defines

cause in terms of sufficiency rather than necessity.8 Some comparativists at

least implicitly use this approach. For instance, Goldhagen (1997) argues

that a culture of virulent anti-Semitism was sufficient to cause Germans to

be motivated to kill Jews. Alternative causal factors, such as the rise of the

Nazis and Hitler, were not necessary. Germanys 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 of

causes, but rather that they are not exhaustive. Individual causes do not take

the form ofonly necessary and/or sufficient causes. One can easily think of



8/26

examples of causes that were neither necessary nor sufficient. In each of these

examples, one will find, the cause works together in combination with other

causes to produce an outcome. It is the larger combination that generates theoutcome; or stated differently, the values on two or more variablesnot any

single variableare jointly sufficient (or possibly jointly necessary) for the

outcome. 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) as

follows: the so-called cause is, and is known to be, an insufficientbut nec-

essary part of a condition which is itselfunnecessary but sufficientfor the

result (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 a

short 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 Logical

OR, 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 Moores (1966) argument that democratic pathways in the early

modern world required both a strong bourgeoisie and an aristocracy that

either aligned with this bourgeoisie or was historically weakened. In the

argument, there are two combinations that generate democracy: (a) a strong

bourgeoisie that is allied with aristocratic elites, and (b) a strong bourgeoisie

and a weak aristocracy. Although a strong bourgeoisie is a necessary cause,

the bourgeoisaristocratic alliance cause and the weak aristocracy cause are

INUS causes. We can summarize the argument as follows:

Y1 =X1 & (A1 vB1), (1)

where Y1 = democratic pathway; X1 = strong bourgeoisie; A1= alliance

between bourgeoisie and aristocracy; andB1 = weak aristocracy. NeitherA1norB

1is individually necessary or individually sufficient. Instead, they are

INUS causes that combine withX1 to form two possible combinations that

are sufficient for Y1. Many other studies that use Qualitative Comparative

Analysis (QCA) in either its dichotomous or its fuzzy-set version assume




9/26


INUS causation and seek to identify the different causal pathways to given

outcomes.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 Mackies

INUS cause, a sufficientbut unnecessary part of a factor that is insufficient

but necessary for an outcome (Mahoney, Kimball, & Koivu, 2007). Here

the constitutive attributes of a necessary cause are treated as causes them-

selves. For example, a well-known theory holds that nondemocracy (i.e., a

nondemocratic dyad) is necessary for war. There are various attributes that

by 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 a

SUIN cause of war. Fraudulent elections, repression, and suffrage exclu-

sions are neither necessary nor sufficient for war, but rather factors that can

constitute nondemocracy, which in turn is necessary for war. Or consider

again Moores (1966) argument. We saw how a bourgeoisaristocratic

alliance and a weak aristocracy are INUS causes. If we now imagine that

Moore were to treat these two factors as each examples of a third factor

politically subordinate aristocracythen they would be SUIN causes: con-stitutive parts sufficient for a necessary cause (politically subordinate

aristocracy) of democracy. We can summarize this idea as follows:

Y1 =X1 &Z1;Z1 =A1 vB1, (2)

where Y1= democratic pathway; X

1= strong bourgeoisie; Z

1= politically

subordinate aristocracy; A1 = alliance between bourgeoisie and aristocracy;

andB1 =weak aristocracy. HereA1 andB1 are SUIN causes of a democratic path.

Logically speaking, then, there are five kinds of causes that can be used in

case-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 and

sufficient cause. In fact, the other four causes become more important to the

extent 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 & Honor, 1959; Ragin, 2006). Thus, necessary causes

are increasingly important as they approach causal sufficiency. Sufficient

causes are more important as they approach causal necessity. And INUS and

SUIN causes gain importance as they become closer to being individually

necessary and sufficient.



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To embrace necessary and/or sufficient causation (including INUS and

SUIN 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 assumption

mean that the researcher will achieve valid measurement or carry out good

research. The assumption of an ontologically deterministic world in no way

implies that researchers will successfully analyze causal processes in this

world. But it does mean that randomness and chance appear only because of

limitations in theories, models, measurement, and data.

The only alternative to ontological determinism is to assume that, at least

in part, things just happen; that is, to assume that truly stochastic factorswhatever those may be (see Humphreys, 1989)randomly produce out-

comes. The assumption of a genuinely probabilistic world finds its best

defense with indeterministic relations in quantum mechanics. Yet whether or

not subatomic processes are truly indeterministic is still debated among

physicists. Moreover, as Waldner (2002) suggests, quantum theorists argue

that the kinds of issues addressed in the social sciences do not work like quan-

tum mechanics. Randomness at the subatomic level seems inappropriate

when 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 exist

for analyzing necessity and sufficiency (including INUS and SUIN causes).

Indeed, all of the major small-N cross-case methods used in this field

Mills methods of agreement and difference, typological theories, counter-

factual analysis, Boolean algebra, and fuzzy-set analysisassume these

kinds of causes (e.g., Elman, 2005; George & Bennett, 2005; Goertz &

Levy, 2007; Mahoney, 1999; Ragin, 1987, 2000). Here is not the place to

review 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 of

case-oriented research in comparative politics.

The Population-Oriented Approach

Population-oriented researchers do not have as their primary goal the

explanation of any particular case. Instead, they want to accurately estimate

the effects of variables within whole populations. They ask questions such

as, What is the effect of presidentialism on the consolidation of democracy?

(Cheibub, 2007); To what extent is globalization a cause of inegalitarian

distribution? (Garrett, 1998); and Does regime type matter for economic

growth? (Gerring, Bond, Barndt, & Moreno, 2005). In addressing these



11/26


questions, the researchers want to generalize about the typical effects of the

particular causal factor(s) of interest.

Mean Causal Effects

The population-oriented approach in many ways parallels experimental

research.11 Experiments are usually not designed to provide comprehensive

explanations of outcomes. Nor are they designed to explain particular cases.

Rather, they are intended to accurately assess the typical effects of particular

treatments for populations. Experimenters want to know what difference (if

any) one or more treatments has for an outcome on average. The approach isquite consistent with the idea that causes are probability raisers. One can in

fact say that a treatment is a cause when its presence raises the probability of

an outcome occurring in any given case of a larger population.

The experimental template underpins the definition of causality used in

the population-oriented approach, a point well illustrated by King, Keohane,

and Verbas (1994, pp. 76-81) famous discussion of mean causal effect ().They present this concept using the example of the effect of incumbency on

the vote fraction received by a candidate running for office. The meancausal effect in the example is the difference between the mean distribution

of the vote fraction received by an incumbent candidate across multiple

hypothetical elections and the mean distribution of the vote fraction

received by a nonincumbent across multiple hypothetical elections. In their

notation, = Ii_ N

i, where X

iis the mean of the distribution of the depen-

dent variable under conditionXandIandNare incumbent and nonincum-

bent, respectively. This understanding ofas 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 coefficients in multivariate statistical models. They are especially concerned

with two aspects of. The first is substantive significance, which derives fromthe size of the coefficient and may be evaluated in various ways. The second

is statistical significance, which summarizes the likelihood that the observed

finding is a product of sampling error or other random error and is affected by

the 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 offorthe democracy stock variable in their multivariate models. In contemporary

comparative politics, it is worth noting, independent variables of theoretical



12/26


interest that meet a specified level of statistical significance (e.g.,p .05) are

often 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 variation

on 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 the

mean effect ofXon Yin the context of an observational study, the question

immediately arises as to which other variables should be held constant.

Both the size and statistical significance of an effect can change radically

depending on the other variables that are included. These other variables

known as covariates, concomitants, or confoundersmust be controlled for

(conditioned on) if one wishes to correctly estimate the net effect ofXonY. Net effects are essentially calculated by partitioning the population into

subgroups that are homogenous on the control variables, measuring the

effect of values ofXon the distribution ofYin the subgroups, and then aver-

aging the results (e.g., Turner, 1997). The goal of this form of multivariate

analysis is not to deny that the control variables are causes ofY, but to rule

out the possibility that they account for the observed effect ofXon Y.

Explanation in population-oriented research makes various specification

assumptions to mitigate the potential problems that arise from the use of

observational data rather than experimental data (e.g., Shadish, Cook, &

Campbell, 2002). With an experiment, of course, cases are randomly assigned

to different values of an independent variable, such that in theory their prior

characteristics are unrelated to those values. But this kind of independence

is almost never true with observational data. Hence, population-oriented

researchers need to control for variables using tools such as stratification to

achieve conditional independence on average (mean conditional indepen-

dence). Conditional independence is, in effect, a way of trying to meet the

counterfactual 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 the

study in question. These include the following:



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1. Stable Unit Treatment Value Assumptionthe idea that influences

among observations do not affect outcomes and the notion that a given

value on an independent variable is stable across cases (for an excellentrecent discussion, see Brady & Seawright, 2004).

2. Absence of endogeneityin comparative politics, endogeneity is often

discussed in conjunction with the specific problems that arise from reci-

procal causation. Strictly speaking, though, endogeneity arises whenever

an independent variable is correlated with the error term.

3. Temporal stabilitythe assumption that causal effects are stable over

time. Unrecognized differences across time can produce missing vari-

able bias.

4. Measurement transiencethe assumption that the act of observing casesand measuring variables does not alter causal effects or, if it does, that

this impact can be modeled.

The proliferation of more and more advanced statistical techniques is part

of an ongoing quest to meet these various assumptions. How successful con-

temporary research is at doing so is debated.13 For our purposes, this debate

need not distract us any more than analogous debates over the merits of

small-N methods mentioned above. Rather, we need to explore how this

approach 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 see

why this is true, we need to explore the relationship between INUS causes and

variables that exert partial effects in statistical models. As we shall see, these

variables 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 causation

at the case level, then the five kinds of causes that can apply to individualcasesnecessary, sufficient, necessary and sufficient, INUS, and SUIN

causesare the only kinds of causes that can operate at the population

level. Four of these five types, however, are usually not relevant when ana-

lyzing populations. We saw below how two typessufficient causes and




14/26

necessary and sufficient causesare very infrequently used at the case

level. 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, necessary

causes become hard to find. For example, causes that were necessary for

high unemployment in Germany may not have been necessary for high

unemployment in France; necessary causes for particular cases often do not

generalize. 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 that

apply 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 lead

to a particular outcome. The presence of multiple combinations of variable

values that produce the same outcome is sometimes called equifinality

(George & Bennett, 2005). Although equifinality is usually associated with

QCA techniques (Ragin, 1987, 2000), its emphasis on multiple paths to a

given outcome is implicitly present in most population-oriented research,including the additive linear models that comparativists frequently use. There

are countless ways to arrive at an outcome (i.e., a particular range of values

on the dependent variable) in an additive linear model. Each independent

variable exerts its own effect, and each independent variable can potentially

compensate for any other. One case may have the outcome of interest because

it has high values on certain variables, whereas a different case arrives at the

same outcome because it has high values on other variables. No variable

value is necessary, but different variable values (in conjunction with the error

term) are sufficient to produce the outcome. Equifinality is thus omnipresent

in mainstream population-oriented research (Mahoney & Goertz, 2006).

Equifinality is not the only issue to which analysts of INUS causes must

attend. Another key assumption underpinning INUS causation is that vari-

ables often do not exert effects independently of one another. Instead, the

effect of one variable depends on the values of one or more other variables.

Variables work together as packages, not isolated factors. Boolean algebra is

the usual way in which case-oriented researchers try to formally model this

kind 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 not

uncommon (e.g., perhaps 25% of quantitative comparative articles now include

at least one interaction term), has moved statistical research in the direction




15/26


of combinatorial causation (Kam & Franzese, 2007). Insofar as statistical

comparativists start to use saturated interaction models in which all possible

interactions are assessed and simplified in a top-down manner, we wouldessentially see an integration of QCA techniques and statistical methods. The

key point here is that there are various methods that can, in principle, be used

to study INUS causes and combinatorial causation across broad populations.

Indeed, some leading scholars suggest that many or most outcomes at

the population level needto be explained in terms of combinatorial causa-

tion (e.g., Achen, 2005; Franzese, 2003; Hall, 2003; Ragin, 1987). If they

are right, one might wonder if thinking about causation in terms of the

mean effects of individual variablesthe traditional focus of population-oriented researchis useful at all. Doubts are reinforced by recent writings

on interaction effects in the population-oriented tradition. Methodologists

have made it clear that one should include lower order constitutive terms

when testing multiplicative interaction models, but one cannot interpret the

coefficient 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 reporting

the effects of individual variables starts to drop out altogether. If one wereto use a saturated interaction model, in fact, one could say virtually nothing

about the individual variables. With QCA models, analogously, the focus is on

the causal combinations, not the individual factors (with the exception of

causes that are individually necessary or sufficient). How, then, is the notion

of a mean causal effect for an individual variablestill the dominant way of

conceptualizing causation in political sciencerelevant to thinking about

causation?

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 are

normally, in fact, important INUS causes. However, with only a few partial

exceptions (Brady & Seawright, 2004; Marini & Singer, 1988; Shadish et al.,

2002), the possibility that mean causal effects are symptoms of INUS

causes 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 general

criterion is that an INUS cause becomes more important as it becomes

closer to being a necessary and/or sufficient cause; beyond this, it must also

be a nontrivial cause.14 Borrowing from the language of probability theory,



16/26

we can say that important INUS causes are probabilistically necessary

and/or probabilistically sufficient causes at the population level. The

extent 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 usually

or almost always have to be present for the outcome to occur. They are thus

normally present in the different combinations of variable values that can

each generate the outcome of interest. Arguably, smoking as a cause of lung

cancer 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 lung

cancerthat is, it is usually present in the various distinct combinations of

variable values that generate lung cancer.15 Smoking, of course, exerts a

partial effect on lung cancer in population-oriented research (i.e., it raises

the probability of the outcome). The reason why smoking exerts this partial

effect and thus can be treated as a probability raiser is precisely because it

is an important INUS cause. The causal properties of the variable (i.e., itsstatus as a probabilistically necessary INUS cause) lead it to manifest the

population-level statistical effect.

Probabilistically necessary INUS causes are often implicitly discussed in

the comparative politics literature as well. An example is the presence of an

economic crisis as a cause of third wave transitions to democracy. As Bermeo

(1990) remarked in her review of ODonnell, Schmitter, and Whiteheads

(1986) Transitions from Authoritarian Rule: It is surely not coincidental that

economic crises accompanied every transformation reviewed here. The pat-

tern suggests that economic crises might be a necessary though not sufficient

incentive for the breakdown of authoritarian regimes (p. 366). Although one

can now easily find cases of recent democratic transition without economic

crisis (e.g., Chile), it seems fair to conclude that crisis was a probabilistically

necessary cause of a third wave democratic transition (i.e., countries rarely

experienced transitions during economic good times; for systematic evi-

dence, see Haggard & Kaufman, 1995, pp. 32-36). Statistical models that

show an individual effect for economic crisis on democratic transition at the

population level (e.g., Gasiorowski, 1995) are picking up this variablesstatus 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




17/26

sufficient causes can almost produce the outcome by themselves (but need

some 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 partial

effects 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 findings

in the field concerns the relationship between economic development and

democracy. Although the specific workings of this relationship are subject todebate, much evidence suggests that a high level of economic development is

probabilistically sufficient for either democracy or democratic stability (e.g.,

Boix & Stokes, 2003; Przeworski,Alvarez, Cheibub, & Limongi, 2000). Rich

countries are thus almost always democratic. There are some exceptions, and

certainly one would not want to say that wealth alone is fully sufficient for

democracy (or democratic stability). However, when significant wealth is

present, 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) are

likely an artifact of the probabilistically sufficient status of this variable.

Again, the implication is that the variable shows up as a probability raiser

because it is an important INUS cause.

We may conclude, then, that individual variables that reveal partial effects

in correctly specified statistical models are causes. But the effects they exhibit

as 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 exhibited

effects are just symptoms of this underlying logical status.16

Translating Back and Forth

Treating variables that exhibit mean causal effects in statistical models

as INUS causes is helpful in several ways. For one thing, it is substantively

enlightening to know whether a variable exerts its effect because it is

probabilistically 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 substantive

importance. It tells us that the promotion of economic growth beyond a cer-

tain level nearly guarantees the promotion of human freedom. The same is




18/26

true of the finding that high levels of cumulative left governance are almost

always 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. Although

these 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 of

INUS causation, the researcher can better theorize how the factor should be

included in a subsequent model that assesses combinatorial causation. In the

case of INUS causes that are probabilistically necessary, they must be

included in nearly all causal combinations of a QCA model (and would nor-mally need to appear in many terms in a multiplicative interaction model as

well). For example, because nondemocracy (i.e., a nondemocratic dyad) is

at least probabilistically necessary for warfare, this factor must be included

as one cause in nearly all of the causal combinations of a QCA model of

interstate warfare. INUS causes that are probabilistically sufficient, by con-

trast, often do not need to be included in causal combinations. This is true

because 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 itself

without 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 subsequently

with more complex QCA or interaction models. The importance of finding

the right variables and combinations to be included in these models can

hardly be overstated. Our theories in comparative politics routinely posit

complex interactions (Hall, 2003), but they are almost never precise enough

to locate all relevant INUS causes, with potentially devastating implications

for testing causal theories in practice (e.g., Kam & Franzese, 2007). Tools for

better specifying our combinatorial causal models are of tremendous value.

Beyond this, of course, researchers will always be interested in trying

to estimate the mean effects of individual variables in their own right.

Information about mean effects helps one make informed predictions and

estimate the future impact of a given intervention. Individuals and politicalactors seek this kind of information as they maneuver in the world. For

example, it is one thing to know that authoritarianism is a probabilistically

necessary INUS cause of social revolution (or that smoking is a probabilisti-

cally necessary INUS cause of lung cancer). This tells us that governments




19/26

can ward off social revolutions by promoting formal democratic institutions

(or that we can be fairly certain to avoid lung cancer by not being exposed

to 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 the

outcome occurring at the case level is 1 or 0. However, in the absence of

full knowledge about all of the sufficiency combinations that can produce

the 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 can

most reasonably expect to happen in a context of limited knowledge. The

population-oriented tradition can help decision makers formulate betterguesses about whether, given a particular course of action and other known

conditions in the world, the probability of a specific outcome of interest

occurring 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 of

the case-oriented tradition, so too might one wish to translate findings

about probabilistically necessary and probabilistically sufficient INUS

causes 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 of

unification proposed here entailed extending the case-oriented approach to

the population level, under the assumption that causal patterns at the popu-

lation level must be derivative of causation that is occurring at the case

level. With this extension, it became clear that INUS causes are really what

are indirectly studied in most population-oriented research. In particular,

important INUS causes (i.e., probabilistically necessary and/or sufficient

INUS causes) manifest themselves as variables that exhibit partial causal

effects in well-specified statistical models.

A basic implication of this analysis is that more comparative researchers

need to try to study INUS causes as directly as possible at the population

level, 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 data

requirements of these models. But this kind of complexity-sensitive analysis

may be the only road, over the long run, to valid causal generalization across




20/26


many cases in comparative politics. Meanwhile, those who work on this

agenda will surely benefit from the insights of ongoing research on both

mean effects for individual variables and specific causes in particular cases.

Notes

1. Here, I modify Ragins (1987) terminology, which distinguishes between case-oriented

and variable-oriented approaches. The distinction between these two approaches also appears

in 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 about

causation at the level of the population have also long embraced this definition. For example,

A probabilistic accountessentially the idea that a cause raises the probability of its effect

is now commonplace in science and philosophy (Dowe & Noordhof, 2004, p. 1). Also see

Cartwright (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 of

dropping 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 ball

drops into the cup. How are the squirrels kick and the balls dropping in the cup related? I

want to argue that the squirrels kick reduced the probability of the balls dropping in andthe

squirrels kick caused the ball to drop in (Sober, 1984, pp. 406-407). A standard objection to

this kind of example is that if one characterizes the specific causes (i.e., the squirrels kick and

subsequent ricochets) in great enough detail, then it will become clear that this intervention

did not really lower the probability of the ball dropping in. I agree; the real probability of the

ball dropping in was always equal to 1. Probabilities do not make sense for the explanation of

singular events (as I discuss below). Also see Dowe (2004), on chance-lowering causes; and

Schaffer (2000), on probability raising without causation.5. The major attempt to defend single-case probabilities is Poppers (1959) propensity

interpretation. 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 extreme

sensitivity 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-20th

century positivists (e.g., Hempel, 1965; Nagel, 1961; Popper, 1959).

9. Examples of comparative works include Amentas (1996) study of New Deal social

spending; Berg-Schlosser and DeMeurs (1994) analysis of democracy in interwar Europe; Huber,

Ragin, and Stephenss (1993) work on the welfare state; Griffin, Botsko, Wahl, and Isaacs (1991)



21/26

study of trade union growth and decline; Mahoneys (2003) work on long-run development in

Latin America; and Wickham-Crowleys (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 and

human 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 causal

effect. The same idea is varyingly called average treatment effect (Sobel, 1996), average

causal 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 and

thus almost never generates the outcome of interest (see Braumoeller & Goertz, 2000; Goertz,

2006; Ragin, 2006; also see Hart & Honor, 1959). For example, the presence of oxygen is a

trivially necessary cause of a revolution, because it is always present in all cases. INUS causes

that 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 which

smoking 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 anothers effect, such that the variable

overall exerts no mean effect in a population.

17. In the population-oriented tradition, a respected body of work views causation in terms

of 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 ofThe Legacies of Liberalism: Path Dependence and Political Regimes in

Central America and coeditor ofComparative Historical Analysis in the Social Sciences. His

work 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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