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Abstract

Most writers on political science methods seem to suggest that explanation means causal explanation. Certainly, many explanations in the political sciences are causal. However, natural science often provides non-causal explanations, while non-causal explanations are recognized by philosophers of science. Causal inference, in itself, is not a causal explanation; it explains alongside theory. In this paper, we defend explanatory pluralism, arguing that many important explanations in political science are not causal in nature. We identify two important types of non-causal explanation – constitutive explanation (CE) and explanation by constraint (EC) – providing examples from the political sciences literature. We conclude by outlining what we believe non-causal explanation can contribute to political science.

Keywords

causal explanation causal inference constitutive explanation explanation explanation by constraint

Explanation is a crucial goal of political science. Yet few social scientists discuss what explanation is and how it relates to another key desideratum, causation. It is often claimed that ‘real explanation is always based on causal inferences … “non-causal explanation” is confusing terminology; in virtually all cases, these arguments are about causal explanation or are internally inconsistent’ (King et al., 1994: 75).

This view – with some notable exceptions – pervades method textbooks. Van Evera (1997: 15), for example, argues that ‘A good explanation tells us what specific causes produced a specific phenomenon and identifies the general phenomenon of which this specific cause is an example’. George and Bennett (2005: 135), who promote causal mechanisms rather than laws, mentions in a brief footnote that they ‘focus here on (causal) mechanism-based accounts without ruling out that some mechanisms may be of such a general character that they can provide unification type accounts of diverse phenomena’, while later process-tracing accounts more explicitly claim causal explanation (see discussion in Dowding, 2023). Barbara Geddes (2003) attacks simple regression models, listing all causal factors contributing to an outcome, but does not attempt to discuss non-causal models, suggesting only that careful theory can turn causal speculation into cause and effect. Gschwend and Schimmelfennig (2011) distinguish factor-centric from outcome-centric research design: the former is primarily interested in the explanatory power of causal factors, the latter in explaining outcomes by discovering causes. They do not mention any other form of explanation. Clarke and Primo (2012) want to divorce explanation from causation, but they recognize that the dominant perspective in political science is that explanation must rest on causation.¹

In this paper, we offer a clear definition of explanation and show how to distinguish causal from non-causal explanations. We then defend non-causal forms of explanation in political science, before outlining what non-causal explanation can add to political science and how it can work in tandem with causal explanation. In doing so, we distinguish causal explanation from causal inference.² We do not, in any sense, deny the importance of causal explanation nor the value of causal inference. Nor do we claim there are different types of causation. We follow the mainstream view that causation is best defined in counterfactual terms (Woodward, 2003). However, identifying a causal effect is not the same as providing a causal explanation.

We define an explanation as an answer to an open or ‘content’ question. In this, we follow standard lexicographical usage. The Oxford English Dictionary defines the verb ‘to explain’ as ‘To describe or give an account of in order to bring about understanding, to explicate; to give details of, enter into details respecting. Occasionally with indirect question as object’. Webster's definition is ‘To make plain or understandable; to show the logical development or relationships of’.

Simply demonstrating an effect is not explanation, and the dictionaries make clear that explanations do not have to be causal. It might be thought that scientific explanations are causal, but in the natural sciences, much provided by way of explanation is not causal. Natural science provides many descriptions and identity statements: the internal structure of matter, the constitution of energy, the nature of gravity. These provide understanding and demonstrate the nature of relationships, but they are not causal explanations. To be sure, descriptions of the structure of, say, chemical compounds or natural laws enter causal explanation, but that does not make such descriptions causal explanations themselves.

However, the distinction we are drawing matters. If, as we claim, such descriptions enter causal explanation but are not coterminous with it, then the evidence which we require to establish their truth value is different from that of standard causal identification. It is the methodological rather than the philosophical issue that motivates our arguments. What is important is that those descriptions constitute answers to the questions that led to their discoveries and that they are not themselves making causal claims.

Political science is undergoing a ‘credibility revolution’. Increasingly, a strong identification strategy for a causal effect is the golden ticket for young researchers (Ashworth et al., 2021). For researchers making causal claims, this is laudable. Yet finding these causal effects only constitutes explanations given the description of the invariant generalizations that bring understanding as to why these effects occur. However, often, the mechanism is not obvious. Second, taken to the limit, this leaves little or no place for explanations which do not invoke causation. This would be a major loss for political science, as non-causal explanations are often key components of theory building, helping to narrow the search space for explanatory theories, both by eliminating implausible or impossible candidate theories and by pointing the way to likely candidates. This helps efficiently focus the discipline's efforts and mitigates the ‘curse of dimensionality’ – that is, for any X, there are an infinite number of models by which one could, in principle, estimate a significant effect on some Y.

We first ask what constitutes ‘an explanation’ and then ask why causation tends to be privileged in political science. We discuss two general forms of non-causal explanation – constitutive and constraint (each has several subcategories) – before outlining why these distinctions matter for political science methodology.

What is explanation?

Philosophical accounts of ‘explanation’ agree that, minimally, an explanation is an answer to a question (Hempel, 1965; Van Fraassen, 1980). The main point of dispute between them is how wide is the set of questions to which the answer can be classified as an explanation.

A favourite trope is that scientific explanations are answers to ‘why’ questions (Achinstein, 1983), which then define those answers as causal, while answers to ‘what’ questions are considered descriptive. But not all legitimate answers to ‘why’ questions are causal. The answer to the question ‘why can’t I divide 23 strawberries equally between 4 people?’, for instance, does not have a causal answer, as we shall see below. Following Achinstein (2001), we define explanation more broadly as a ‘complete content-giving proposition with respect to a content question’ with a complete content-giving proposition being a noun phrase with a verb or verb derivative including a that-clause, an infinitive phrase and other clauses.

A content question is one answered by a complete content-giving proposition.³ For example, ‘Why did Donald Trump win re-election in 2024?’ is a content question for which ‘One reason [content noun] is the rise in inflation [verb derivative] after the Covid-19 pandemic’ is a complete content-giving proposition and hence an explanation. Achinstein's definition thus also allows answers to ‘how’ or ‘what’ questions to count as explanations. His account, however, does not countenance answers to ‘closed-ended’ questions as explanations in themselves. For instance, ‘Do you approve of President Trump?’ could be answered with a simple yes or no (not a verb or verb derivative) and thus fails Achinstein's definition.⁴

Achinstein's broader definition captures what most people would understand by ‘explanation’. Cognitive psychologists Brewer, Chinn and Samarapungavan, for instance, argue that
in everyday use, an explanation provides a conceptual framework for a phenomenon (e.g., fact, law, theory) that leads to a feeling of understanding in the reader or hearer. The explanatory conceptual framework goes beyond the original phenomenon, integrates diverse aspects of the world, and shows how the original phenomenon follows from the framework. (Brewer et al., 1998: 119)
Most social scientists would surely accept as legitimate political science explanation answers to questions like ‘How does the filibuster work?’ or ‘What was the role of the podesteria in Renaissance Italian city-states?’ (Greif, 2006). Familiarity with the answer does not make them any less explanatory. To claim these are mere descriptions rather than explanations is to beg the question that all explanation must provide causes. Thus, we adopt Achinstein's definition of an explanation as a complete content-giving proposition with respect to a content question.

Can the definition of an explanation be made more concrete? Achinstein argues that it cannot, because any universal criteria for the construction of good explanations will be subject to counterexamples where the criteria are satisfied, but we agree the purported explanation does not hold. This is because a good explanation must be sensitive to the interests, beliefs and information of the audience. A correct explanation is one where the propositional members of the ordered pair are true: that is, the propositions relating the explicanda and the explicans (in some explanatory form) are true. However, correct explanations are not good ones unless they are comprehensible to the audience given their current knowledge state. Consider Nash's (1950) explanation of why every game with finite strategies and players has at least one mixed-strategy equilibrium. His explanation is a correct one – the propositions are true, and his conclusion follows from them. However, it is a ‘good’ explanation only for those who understand Kakutani's fixed-point theorem, the definitions of closedness, convexity and so on. For others, it would not be a ‘good’ explanation unless coupled with further relevant clarification.⁵

Political science certainly strives for correct explanations. It should also strive for good explanations, and to some extent, what constitutes a good explanation depends upon the nature of the question being posed, which in turn depends on the interests of the questioner. For instance, Clarke and Primo (2012) note that the question ‘Why did Germany invade Poland in 1939?’ can yield multiple valid explanations, depending on which part of the question is emphasized: (a) ‘why did Germany invade Poland in 1939?’; (b) ‘why did Germany invade Poland in 1939?’; (c) ‘why did Germany invade Poland in 1939?’. A political scientist interested in the causes of war and conditions for peace might be most interested in question (a) – why invasion rather than negotiated settlement – whereas a scholar of military strategy or decision-making might be more interested in questions (b) or (c) – why Poland and not some other country, or why in 1939 rather than wait until 1940?

Causation and explanation

The dominant model of causation in political science is the potential-outcome framework (Rubin, 1974, 2005).⁶ Briefly, the potential-outcome framework argues that a given unit u has an outcome with respect to the response variable Y given that its actual value with respect to the treatment variable X of x′, $Y_{x = x^{'}} (u)$ , and a potential outcome $Y_{x = x^{″}} (u)$ , which it would have attained had X been x″ instead (where x′ and x″ are distinct values of X) and all other causes of Y are held constant. If the absolute value of the difference between the actual and potential outcome is greater than zero, then we say that X causally affects Y. Since a unit cannot simultaneously take on two different values of a treatment variable, causation is never established beyond doubt. Rather, causation is estimated with varying degrees of credibility, as a function of the extent to which the ‘control’ group approximates the value of Y of the treatment group without treatment.

The counterfactual element rules out explanatory irrelevances. Counterfactual considerations also rehabilitate low-probability causes: as long as $P (Y = y | X = x^{'}) \neq$ $P (Y = y | X = x^{″})$ , it matters not whether both probabilities are low (or high). Canada and the United States would have a low risk of going to war even if their mutual trade was small, but trade can still have a causal effect on war so long as it affects the probability of their going to war with each other.

How does the potential-outcome definition of causation relate to the definition of explanation given above? Here, it is crucial to explore in more detail the nature of causal explanation and the difference between causal explanation and causal inference. A causal inference question is one which seeks to credibly establish the causal effect of one variable on another. To cite some recent examples from political science journals: ‘Do commodity price shocks cause armed conflict?’ (Blair et al., 2021), ‘Does property ownership lead to participation in local politics?’ (Yoder, 2020), ‘Does political affirmative action work and for whom?’ (Gulzar et al., 2020).

While these are undoubtedly important questions, they are closed-ended: their answers are ultimately ‘yes’, ‘no’ or perhaps ‘yes under some conditions, no under other conditions’ or a regression coefficient assumed to represent the average causal effect with associated uncertainty measures. These answers are not, therefore, explanations by themselves but must be joined with other information (e.g. the classification of an individual or token case as an example of the operation of two variables which have a causal relationship with one another) to yield an explanation. ‘State s experienced an armed conflict at time t because “yes”’ or ‘because x%’ is not an explanation. However, ‘State s experienced an armed conflict at time t because it exports a commodity which experienced a shock at time t₁, and commodity shocks on average increase the risk of subsequent conflict by x%’ is an explanation. By establishing the credibility of the causal relationship, causal inference is a crucial part of this explanation, but neither causation nor causal inference is synonymous with causal explanation.

Instead, a causal explanation is an explanation which depends upon a causal relationship. Formally, our definition of causal explanation closely follows that of Woodward (2003): a causal explanation for why Y takes on a specific value y consists of the following:
a generalization G (a causal relationship) relating changes in Y to changes in X;

a statement of initial conditions that the variable X takes on the value x;

an implication of G that Y would take on the value y if X took on the value x; and

an implication of G that Y would take on a different value $y^{'}$ if X took on a different value $x^{'}$ .
This definition makes clear the difference between causal inference (which is designed to establish the truth value of G above) and causal explanation. Moreover, this definition is broad in that it makes no assumptions about the functional form of the relationship between x and y, which need not be linear, nor about potential interaction effects between X and other variables in the system. Nor does it require that G be clearly identified via an experimental or quasi-experimental method. In tune with the Achinstein analysis, it can connect the causal inference to theoretical propositions that link the relationship into the set of laws and mechanisms that enter into causal explanations. However, there are several good explanations in the natural and political sciences which do not meet this definition of causation and hence cannot be classed as causal, as we now explore.

Non-causal explanation

There are numerous accounts in the philosophy of explanation that constitute non-causal explanations. Some, such as the unification account (Kitcher and Salmon, 1989), attempt to provide a general account of scientific explanation; however, we do not seek to reduce causal explanation in this manner. Other accounts suggest that some forms of explanation are non-causal. These include constitutive explanation (Ylikoski, 2013), descriptive explanation (Gerring, 2012), explanation by constraint (Lange, 2017), equilibrium explanation (Sober, 1983) or even a functional explanation (Kincaid, 2006). These authors do not all agree with each other on the nature of what constitutes causal explanation nor on the demarcation lines separating different forms of non-causal explanation. We do not comment on these debates here.⁷

We demarcate two general categories of non-causal explanation: constitutive explanation and explanation by constraint. The former includes descriptive and conceptual explanations; the latter, equilibrium.⁸ In order to define non-causal explanation, we counterpose it to causal explanation as defined above. Note that implicit in the definition of causal explanation above are three conditions.
X and Y must be ‘separate existences’ (Ylikoski, 2013).

There must be a plausible counterfactual value of X – $x^{'}$ – different from its current value x.

There must be a plausible counterfactual value of Y – $y^{'}$ – which Y would assume if X were to assume the value $x^{'}$ .

It follows that any explanation not depending upon a causal relationship defined by these three criteria is a non-causal one. In some cases, either X or Y may have no plausible or even logically possible counterfactual condition (hence failing conditions 2 and/or 3); in others, X may be the constituent components of Y, hence failing condition 1. In the former case, we have explanation by constraint; in the latter, constitutive explanation. We comment on the relationships between explanation by constraint and constitutive explanation to causal explanations in our concluding section.

Constitutive explanation

Constitutive explanation is sometimes referred to as descriptive explanation. Gerring (2012) invoked descriptive explanations as arguments – which others call conceptual analysis – since much of his argument discusses how we conceptualize democracy in terms of the best measures for describing democracy. His example, ‘global inequality is increasing’, is a description; and hence the grounding for the truth of the claim depends on whether you think the measures provide a correct description. Gerring argued that constitutive explanations, or descriptive arguments, are necessarily prior to engaging in causal explanation. This is uncontroversial, but the importance of Gerring's claims is that a large part of political science does not provide causal analysis but is nonetheless valuable. There is no sense in which it is not scientific. A large part of the natural sciences engages in constitutive explanation, whether it be identifying the atomic qualities of the elements, the chemical qualities of compounds, the structure of the atom, the diversity of the biosphere and so on.

Constitutive explanations suggest that by understanding the nature of things, we can come to understand their causal capacities. Ylikoski (2013) said that ‘Constitutive explanations explain how things have the causal capacities they have by appealing to their parts and organization’. For him, causal explanation and constitutive explanation track different types of dependency, thus explaining different aspects of the world. They both map networks of counterfactual dependence, but constitutive counterfactuals are of a different nature. In causal explanation, a counterfactual change in X would result in a counterfactual condition for Y. In constitutive explanation, by contrast, a change in the constituent elements of Y, or in their organization, results in a change in Y, perhaps to some other Y′ or in the causal capacities of Y.

We should note that saying that understanding the causal capacities through constitutive explanation is not to smuggle causation into constitutive explanation. Describing the nature of objects of a certain type is to provide a type-level explanation of their form. It is this form that leads objects of that type to have their causal capacities, but they enter causal relationships only under certain conditions – conditions that will typically be the intervention. Causation occurs at the token level, where actual events lead to other actual events. The analysis is counterfactual, for the analysis requires us to judge under what conditions the outcome would not have occurred. This involves the type-level description of the type that the token falls under. While causation is token level, causal explanation might be at the type or token level. Type-level descriptions, when applied to token situations, enter the causal explanation of the outcomes of those token cases; however, the description or theorization of the mechanism itself is not a causal explanation, any more than the description of the lattice structure of water molecules is a causal explanation of why pure water does not conduct electricity but ionized water does – though the nature of the lattice explains this. Nonetheless, some type-level descriptions are of causal processes.

For example, an enquiry into the dispositional properties of an object requires a constitutive explanation. What makes democracies less likely to go to war with each other than autocracies with each other is an enquiry into the constitution of democracies and autocracies. There are different candidate constitutive features. This question is not answered by causal inference, though constitutive explanations may have testable implications, as do causal claims. One account of the ‘democratic peace’ claims that democracies are less likely to fight because they have legislatures which can impose audience costs on democratic leaders bluffing in international disputes (Schultz, 2001). This is a constitutive and not a causal claim: legislatures are part of what makes a democracy a democracy, not a ‘treatment’ applied to democracies.

To put it another way, to rephrase the above claim in a causal manner would be to claim that the possession of a legislature is a causal mediator between democracy and peace. The implied counterfactual is that the probability of peace given democracy and a legislature is greater than the probability of peace given democracy and no legislature: $P r (P e a c e = 1 | D e m o c r a c y = 1 & L e g i s l a t u r e = 1) >$ $P r (P e a c e = 1 | D e m o c r a c y = 1 & L e g i s l a t u r e = 0)$ . Yet the second part of the previous expression is conceptually incoherent; by most, if not all, conceptions of democracy, there is no such thing as a democracy without a legislature. However, constitutive explanations often have testable implications, like those of causal explanations. The constitutive argument above, for instance, has the testable implication that non-democracies which have some means of imposing visible audience costs on their leaders should behave similarly to democracies in international disputes (Weeks, 2008).⁹

Constitutive relationships are often identity relationships, which is why some think they provide only trivial or circular explanations. However, correct, and good, explanation provides complete content-giving propositions (the ‘argument’ in Gerring's terms) as answers to questions. For example, $H_{2} 0$ is the identity of water, but the precise structure of the molecular bindings explains why water is the only known natural compound whose liquid form has higher density than its solid form, which is an important aspect entering into all sorts of causal relationships involving water. Propositions about its characteristics explain other propositions about its characteristics. To be sure, we have more fully grounded predictions in the natural than in the political sciences around such descriptions, but the logic of the purported explanations is the same.

In political science, social network theories provide constitutive explanations in this manner. The primary goal of social network analysis is to explain the causal capacities of different networks by virtue of the organization of their parts. Granovetter's (1973) seminal strength-of-weak-ties argument demonstrates that, under certain conditions, a network composed of multiple ‘weak ties’ has a high capacity for collective mobilization because weak ties provide ‘bridges’ that help spread information between the denser cliques in which most agents are situated. This explanation is constitutive because the explicans relates to the network's organization and the explicandum to its causal capacity – explicans and explicandum are thus not ‘independent existences’ and fail condition 1 for a causal relationship. Both have a counterfactual condition: a network W composed of multiple weak ties would, if differently constituted (e.g. via multiple dense but unconnected cliques), have a lower capacity for collective mobilization. It is the description of the network that provides us with the explanation: that is, the answer to the question of why one network performs differently from another. The description of the network is not a causal explanation, but it provides the theoretical understanding that turns a causal inference into a causal explanation.

Alternatively, consider Oatley et al.'s (2013) work on the network organization of international finance. They argued that the hierarchical organization of international finance – while most countries have financial relationships with only a small number of other countries, a small number of central hubs (i.e. the US and UK) have financial relations with many other states – produces a bifurcated causal capacity. That is, the global financial system is robust to crises in peripheral countries such as Mexico or South Korea but highly vulnerable to crises in its Anglo-American core. Again, the explicans is the internal organization of the system, and the explicandum, the system's causal capacities.

Explanation by constraint

Constitutive explanation often involves identity statements and, in this form, invokes necessity. Explanation by constraint also involves necessary relationships, some of which are logically necessary, while others involve nomic or metaphysical necessity. EC constrains the possible outcomes. These constraints can take several forms.

Lange (2017) offered an influential account of explanation by constraint.¹⁰ He gives an everyday example of why one cannot divide 23 strawberries evenly among three children with no remainder. The answer, of course, is that 23 is a prime number and prime numbers can be divided evenly only by themselves and 1. This is not a causal explanation, as there is no logically conceivable counterfactual in which 23 is evenly divisible by some integer other than itself. The proposition that 23 cannot be divided evenly by any other integer follows logically from the definitions of ‘divide’, ‘evenly’ and ‘integer’ and could not, even in theory, be otherwise. That is why Lange referred to such explanations as ‘explanations by constraint’. They are constrained by necessity since ‘23 is divisible by k’ means that there must exist some integer n which, when multiplied by k, gives 23. As there is no such integer, 23 cannot be divisible by k (other than by itself). There is no possible intervention.

The mathematical constraint explains why 23 is not divisible by 3. It also provides the explanation of why one fails to divide 23 strawberries among three children on a given occasion. The type-level fact explains the token-level failure. At the token level, one might say that the fact causes the failure; however, the failure is necessary given the fact. Lange argued that there is a ‘pyramid of necessity’ into which explanation by constraints fit. At the top of this pyramid are logical and mathematical truths. Further down are physical laws, such as those that state that momentum is conserved where the Euler–Lagrange equation holds or that the Lorentz transformations hold if the space–time interval is invariant and so on. Explanations at one level of the pyramid constrain the set of explanations which may hold at lower levels (the laws of physics cannot violate logic and mathematical truths, the laws of chemistry cannot violate the laws of physics and so on). Now, many social scientists might accept that this type of explanation exists and is relevant for other disciplines but doubt whether it has any application to political science. Surely relations in the political sciences can only be probabilistic, not deterministic?

Can one conceive of a similar ‘pyramid of necessity’ in political science? Certainly, we can see type-level necessities. A type-level explanation outlines why social systems in general fail to satisfy a set of normatively desirable criteria, which then explains why a token social system fails to satisfy them. When Arrow (1951)'s theorem and its corollaries are applied to decision mechanisms such as voting systems, they demonstrate that certain types of (generally undesirable) outcomes are possible, given the constraints on how decision mechanisms must work. Nash's (1950) theorem is also an explanation by constraint. The fact that all finite games have an equilibrium where mixed strategies are allowed follows logically from the definition of the key terms – ‘finite’, ‘equilibrium’, ‘mixed strategies’ and so on. There exists no counterfactual manipulation that implies the existence of a finite game with no equilibrium in either pure or mixed strategies.

Note that this is not simply stipulating possibilities, but rather demonstrating constraints on the set of relevant possibilities. They constrain the space of possible outcomes (Taagepera, 2008). As demonstrations, they perform an explanatory role. Of course, how any specific outcome emerges is caused by the decisions input into the specific mechanism (an electoral system, say). This is the proximate causal explanation of that outcome. The explanation by constraint gives conditions under which possible outcomes might emerge. The research field of mechanism design is dedicated to examining the set of possible outcomes that can emerge under different types of mechanism. Explanation by constraint reduces the set of possible outcomes. As such, there are logically fewer explanations by constraint than causal explanations, since the latter are constrained by the former but not vice versa. By the same token, however, explanation by constraint provides more ‘bang for one's buck’ than a causal explanation, since it rules out potential causal explanations a priori, helping the focus on the search for causal relationships.

However, political science contains many explanations obtained at a lower level than mathematical and logical truths, but which constrain the set of explanations holding at even lower levels. One higher-level constraint is the demand that equilibria must be incentive-compatible. Theories should not rest on the assumption that actors play strongly dominated strategies nor assume that non-strategy-proof equilibria hold in games of asymmetric information nor that market actors will systematically miss opportunities to make a risk-free profit via arbitrage. Constraints on individual preference orderings such as transitivity can be seen in the same light.¹¹

Consider, too, the intuitive criterion of equilibrium selection (Cho and Kreps, 1987). This is a method of choosing equilibria from a signalling game where there are many (often picking pooling equilibria). It does so by providing further restrictions to off-the-path beliefs since such beliefs are not restricted by perfect Bayesian equilibrium. The motivation is that equilibria which fail the intuitive criterion should not be considered and are only equilibria as an artefact of an imperfect solution concept which precludes restricting off-the-path beliefs. In the canonical beer–quiche game inspiring the criterion, any pooling equilibrium where both ‘tough types’ and ‘wimps’ order beer, but the sender orders quiche, the receiver assigns zero probability that the sender is a tough type, since a tough type could not improve his payoff relative to the pooling equilibrium regardless of which best response the receiver chooses in return. The intuitive criterion constrains the receiver's response to 0 but the constraint is not a logical necessity (it is logically conceivable that the sender could be a tough type). Of course, when applied to token examples, these constraints enter into the causal explanation of that example. Nevertheless, they are not themselves causal explanations. The general type-level analysis provides constraints on potential causal explanations.

One way of thinking about the relationship between constraint or structure and causation is to consider the level at which questions are posed. When we ask what caused a factory fire, we do not consider the presence of oxygen on the planet to be a cause. We might consider whether the number of fire doors designed to restrict the spread of fire is part of the cause of its intensity. We might think the cause of a given fire in a factory was an electrical fault, but the reason for, or cause of, a number of fires destroying factories in two different countries is the result of fire-safety laws governing the number of fire doors. What is considered a cause is often a result of the question being asked (Dowding, 2016: ch. 6). This is also the case in qualitative research, where which issues should be ‘backgrounded’ and which ‘foregrounded’ may be disputed (Dowding, 2023). Nonetheless, supplying type-level explanations of constraints does not itself provide causal explanations of token events; at best, they provide conditions that enter causal explanations.

Equilibrium explanation

We see equilibrium explanations as a form of explanation by constraint with lower-level necessity. In this, we follow Sober, who defines an equilibrium explanation as
where causal explanation shows how the event to be explained was in fact produced, equilibrium explanation shows how the event would have occurred regardless of which of a variety of causal scenarios actually transpired. (Sober, 1983: 202)
In other words, equilibrium accounts provide explanations demonstrating self-consistent sets of variables. Given the conditions, they cannot be otherwise. Sober's example is Ronald Fisher's account of the sex ratio in a population, determined by population genetics.¹²

An equilibrium explanation should not be confused with explanations of why one equilibrium would be present but not another. Comparative statics are best described as producing causal explanations. Instead, equilibrium explanations in the political sciences are ones which explain an event by showing that it is a self-reinforcing or stable equilibrium – an attractor point with a large basin of attraction. This is sometimes called equifinality, since any starting point will reach the same end point; the proximate casual path to the end point is irrelevant to the explanation of why we end up at that point (Dowding, 2016). In this sense, as in Fisher's sex ratio example, any intervention in the system within that basis of attraction will eventually result in returning the system to the attractor point.

Kuran's (1995) analysis of ‘corner equilibria’ in belief propagation is an example of this kind of system. In Kuran's model, individuals have both private and public preferences, which may diverge if one believes one's private preferences are not widely shared, and penalties exist for expressing unpopular views. If the number of dissenters from the current consensus c is large enough (above some threshold value t), however, society rapidly shifts to a different consensus c, then individuals privately preferring c can openly express this preference, while individuals who privately prefer c shift to expressing a public preference for c. Kuran's model provides an equilibrium and so a constraint explanation of why many belief systems are stable even where they appear to impose active costs on many members of society. If people publicly expressing belief in c, where the consensus belief is c, are punished by the rest of society, including c* private believers who think there are not enough fellow believers to make it safe to publicly express support for c, public c believers either will be wiped out or revert to a public expression of c. This is the corner equilibrium.¹³ Thus, at least on a local interval where the number of dissenters is somewhere between 0 and t, the explicandum has no counterfactual (it always eventually returns to universal adherence to c), and hence, the explanation is not causal. The constraint here is weaker than that of Arrow's theorem – it is not logically necessary that small bands of public dissenters will not survive for long in a society punishing dissent. It is simply highly unlikely given weak assumptions about preferences.

Likewise, the tendency of some systems to move back to one of a set of multiple stable equilibria are explanations by constraint. The Mundell–Fleming ‘Unholy Trinity’, for instance, posits that a state cannot simultaneously fix its exchange rate to that of another currency (or commodity such as gold) and control its interest rates without also imposing capital flow controls (Fleming, 1969; Mundell, 1963). Why not? Suppose country c has free capital flows and a fixed-exchange-rate regime pegging its currency at value v. Now suppose
the central bank reduces interest rates from equilibrium to stimulate output;

market actors now borrow in country c and lend overseas;

these actors sell c's currency; then

the value of c's currency falls below v.

Thus, in the long run, there is no intervention in the system which could leave the country with a durable regime of fixed exchange rates, free capital movement and control over interest rates. There is no counterfactual and hence no causal answer to the question above.

One response is that the constraint is the summation of sets of causal relationships. That is, the constraints in the model act as incentives for actors to behave in such a manner that any attempt to fix exchange rates, have control over interest rates and allow free capital movement will not last long. The constraint explains why they fail. Governments might anticipate this failure and so not attempt the trinity. Here, the constraint is an element, but only one element in the full causal story. But what provides ‘the explanation’ of the universal empirical generalization is the constraint. To be sure, we could tell individual token stories for any given country at any given point in time as to why it had, say, flexible interest rates, an open capital account and floating exchange rates as opposed to, say, flexible interest rates, capital controls and fixed exchange rates. Those stories will be about government decisions regarding interest rates, exchange rates and capital flow rules where constraints, in some form, enter the causal story. However, the type-level explanation is the constraints themselves which allow no plausible counterfactual, so no possible set of actions can lead to any other end point. Even at the token level, moreover, the set of possible outcomes does not include one in which a given state has the option of flexible interest rates, an open capital account and a fixed exchange rate. Hence, the answer to the question ‘why can’t a state have flexible interest rates, an open capital account and a fixed exchange rate at the same time?’ cannot yield a causal explanation.

The value of non-causal explanation

Political science increasingly rewards young scholars for credible causal identification. Most proponents of the ‘credibility revolution’ understand that good theory remains important (Ashworth et al., 2021). Yet if political science seeks only to reward credible identification of causal effects, young scholars have few incentives to ask questions where causality cannot credibly be identified – and thus will ignore many important questions (Mearsheimer and Walt, 2013). Because of this incentive structure, we find many weird, unusual and apparently causal effects,¹⁴ while big questions remain understudied.

Dunning (2012) identified eight different types of ‘natural experiments’ in the political science literature: lotteries, programme rollouts, policy interventions, jurisdictional borders, electoral redistricting, ballot order, institutional rules and historical legacies – and we might add weather events. Given how many of these types of events occur around the world (and how many ‘treatments’ they might be exogenous to), researchers might trawl through this large space simply to identify the causal effect of something. The bigger the space, the more likely we are to find false positives.

Looking for ‘explanations by constraint’ reduces the set of potential theories prior to empirical testing. This is not a trivial gain. In addition to false positives, the danger is also that the vastness of the space of possible ‘effects’ means that we will miss many true effects (Van Rooij and Baggio, 2020). Finding true effects requires significant investment in data collection, experiments (if applicable) and so on. Hence, we must devise a means to narrow the search space before empirical examination. One of Van Rooij and Baggio's main proposals is that researchers first ensure that their candidate theories are compatible with many a priori constraints. Another solution is to theorize the logical space on which data points might lie and which is standard model construction in physics (Taagepera, 2008).

Constitutive explanations perform a complementary function – ruling in theories as promising candidates for further exploration. Consider the SARS-Covid-19 vaccination. The vaccination discovery process was based on understanding the composition of the Covid-19 virus – especially the protein spikes which allow the virus to attach to the hosts’ cells. The first step was to provide a constitutive answer to the question ‘Of what is the SARS-Covid-19 virus composed?’. Modelling the virus allowed researchers to develop effective vaccinations, training the immune system to recognize and combat these protein spikes. Of course, the vaccines had to be evaluated via randomized controlled trials prior to large-scale rollout, but it was constitutive knowledge of the virus structure that allowed researchers to identify the most plausible set of candidate vaccines for testing.

Are there equivalents in political science? The increasing use of network analysis in international relations (IR) is one example. Network analysts critique more traditional quantitative IR scholarship (both theoretical and empirical) for mis-specifying the international system (Cranmer et al., 2012; Cranmer and Desmarais, 2016). Past work assumes (mostly for convenience) that the international system is composed of a set of dyads and that states’ interactions within a dyad are not affected by the interactions of states in any other dyads. Network theorists propose that dyads are tightly interconnected (if the US goes to war with Iraq, for example, the UK is likely to follow). To bring the point home, the argument made by the network theorists is a constitutive one: it is about the composition of the international system. By examining this constitutive question, network proponents have opened new and promising vistas for IR research.

Conclusion

The political science tide towards all explanations being causal is leading major journals to insist upon analyses establishing causal inference. This does not accord with natural science practice. Many scientific explanations are not causal.

Constitutive explanations often precede causal analyses, sometimes by several decades of research. Constitutive explanation can also follow from causal analysis, as elements of a causal process are recognized as necessary components of a social kind. Explanation by constraint is a type of explanation that reduces the set of possible outcomes. It specifies boundary conditions on the set of contingent facts or events that causal processes can reach. These constraints need not reduce the set of possible outcomes to a single outcome. In which case, why the precise outcome x* from the set X will require a causal explanation. However, science is generally about explaining types or universals rather than tokens or particulars. In other words, it is about explaining why type X will result rather than specific token examples of X, each of which will have unique features. Only if we are interested in the unique features (and admittedly in the political sciences we often are) do we need to know the precise causal process. Equilibrium outcomes are perhaps the most obvious type of explanation by constraint in political science, though many results from cooperative game theory and social choice theory also provide logical constraints on possible outcomes. These constitute strong explanations for certain types of results, even if they never explain the precise token outcomes we see.

A political science discipline explicitly recognizing and promoting non-causal explanations can reap many benefits. By narrowing the search space for potential true theories (through explanation by constraint) and directing it to the most promising areas (via constitutive explanation), non-causal explanation can help us formulate high-verisimilitude theories which can be properly tested and then contribute to the common good.

Footnotes

Funding

The authors received no financial support for the research,authorship,and/or publication of this article.

ORCID iDs

Keith Dowding

Charles Miller

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Explanatory pluralism in political science

Abstract

Keywords

What is explanation?

Causation and explanation

Non-causal explanation

Constitutive explanation

Explanation by constraint

Equilibrium explanation

The value of non-causal explanation

Conclusion

Footnotes

Funding

ORCID iDs

References