1. Introduction

A number of authors have argued for incorporating a distinction between default and deviant states into the formalism of causal models.Footnote ¹ A central motivation for this has been the Problem of Isomorphism (Hall Reference Hall2007; Halpern and Hitchcock Reference Halpern and Hitchcock2015). This problem arises from pairs of target systems that supposedly have isomorphic causal models but give rise to different judgments of actual causation. The idea is that the different judgments are explained by assumptions about particular values that variables typically or normally take on. These assumptions are taken to be captured by the default/deviant distinction.

However, Blanchard and Schaffer (Reference Blanchard, Schaffer, Beebee, Hitchcock and Price2017) have argued that key instances of the problem can be solved by revising one of the involved models such that it gives a more appropriate representation of the corresponding target system. They also suggest a generalization of this strategy, which I will call the adjust-the-model argument. They argue that, when confronted with an instance of the Problem of Isomorphism, we should suspect that at least one of the involved models is not an appropriate representation of its target system. They state that defaults “come close to a free parameter in an otherwise so precise and objectively constrained formalism, which basically gives the theorist leeway to hand-write the result she wants” (192). Thus, according to Blanchard and Schaffer, the default/deviant distinction does more damage than good to the formalism of causal models.

In this article I provide a more nuanced account of the benefits of the default/deviant distinction. I grant that Blanchard and Schaffer’s criticism of defaults as a solution to the Problem of Isomorphism is right. However, there is another problem that is far less prominent: the Problem of Disagreement. I will show that this problem gives rise to a genuinely new argument for incorporating the default/deviant distinction.

The Problem of Disagreement has been introduced by Halpern and Hitchcock (Reference Halpern and Hitchcock2015). It arises from cases in which agents disagree in their causal judgment even though they make the same assumptions about the underlying causal model. The Problem of Disagreement is related to well-known examples of disagreement over what is ‘the cause’ of a given effect as discussed, for example, by van Fraassen (Reference van Fraassen1980). The main difference is that the Problem of Disagreement involves the explicit assumption that the disagreeing agents base their causal claims on the same underlying causal model. Halpern and Hitchcock take this to indicate that the agents’ causal judgments depend not only on assumptions about causal structure but also on a distinction between default and deviant behavior.

I will show that this argument allows two readings. First, it can be read as involving descriptive claims about how agents do reason about causal models in contexts where they disagree. This reading seems to be vulnerable to a version of Blanchard and Schaffer’s adjust-the-model argument. If two agents disagree about judgments of actual causation, we should expect that they also disagree about the underlying causal model. Second, the argument can be read as involving prescriptive claims about how agents should reason about causes when they disagree. Here the adjust-the-model argument does not apply. I will argue that it would be wrong to require that the agents support their conflicting causal judgments with different models. Instead, causal models should be understood as a representative tool that helps express causal claims that go beyond causal judgments that are based on potentially idiosyncratic normative presumptions. If understood in this way, they can help resolve disagreement over causes by giving a framework for disentangling normative and epistemic dimensions of disagreement. This function can only be fulfilled if models incorporate the default/deviant distinction. I will illustrate this claim with an example that concerns the causal role of search-and-rescue missions (SARs) in the Central Mediterranean with regard to increasing numbers of deaths through shipwreck in 2015 and 2016.

In section 2 I introduce Blanchard and Schaffer’s arguments against defaults. In section 3 I introduce the Problem of Disagreement and I point out that Halpern and Hitchcock’s way of employing it as an argument for defaults is vulnerable to a version of Blanchard and Schaffer’s criticism. In section 4 I question what the function of extended causal models should be in instances of disagreement. Using the example of SARs (sec. 5), I argue that defaults help us clarify disagreement over causes (sec. 6).

2. The Adjust-the-Model Argument

Blanchard and Schaffer put forward three main lines of criticism against incorporating the default/deviant distinction. First, defaults are unnecessary. Instances of the Problem of Isomorphism arise only because one of the involved models does not provide an appropriate representation of the underlying target system. Instead of incorporating defaults, we should adjust the models, adhering to generally accepted aptness constraints. These aptness constraints are rules for selecting a set of variables 𝒱 that constitutes the causal model, and in what follows I focus on the rule that “variables should not be allotted values that we are not willing to take seriously” (Blanchard and Schaffer Reference Blanchard, Schaffer, Beebee, Hitchcock and Price2017, 182). Blanchard and Schaffer take this aptness constraint to help us deal with cases like the gardener/queen example: some flowers would not have died if either the gardener or the Queen of England had watered them, and it needs to be explained why we tend to identify only the gardener as an actual cause.Footnote ²

Figure 1A gives a representation of the gardener/queen case. Blanchard and Schaffer argue that this is not an apt model because $Q=1$ represents a scenario that we are not willing to take seriously. Thus, they suggest eliminating variable Q, which leads to the simpler model in figure 1B, which reproduces the plausible verdict that only the gardener is an actual cause of the flowers’ death.

Figure 1.

Flowers survive if they are watered by the gardener or by the queen.

Second, Blanchard and Schaffer argue that the default/deviant distinction is unclear. Most proponents of defaults relate them to an underlying theory of typicality or normality that involves a range of possibly conflicting standards. Blanchard and Schaffer worry that the unclarity associated with these notions spoils the otherwise precise theoretical framework of causal models.

Third, Blanchard and Schaffer criticize that incorporating the default/deviant distinction is psychologically implausible. Proponents of defaults assume that the judgments evoked by thought experiments like the gardener/queen case reflect judgments that arise from the competent use of a norm-laden notion of actual causation. Instead, according to Blanchard and Schaffer, the fact that causal reasoners ascribe a higher relevance to norm-violating factors is to be explained by biases that interfere with the correct use of a norm-free notion of actual cause.

There is an important tension between the first line of criticism and the other two. Suppose I am a proponent of the idiosyncratic view that the queen is in charge of watering the flowers and that the gardener is not supposed to water them. According to the adjust-the-model strategy, I am supposed to represent only those scenarios that I take to be serious possibilities. Thus, I will provide a model in which variable Q is the only cause of variable F. But this is a problem. Now my idiosyncratic view spoils not only my judgments of actual causation but also the corresponding causal model.

The underlying point is this. Blanchard and Schaffer argue that the default/deviant distinction is unclear and reflects biases. But they also suggest to solve cases like the gardener/queen example by adjusting the models on the basis of considerations about what scenarios are to be taken seriously. But this, presumably, depends on ideas regarding normality that are similar to those affecting defaults—otherwise it would be easy to generate counterexamples to the strategy. This means that the constraint on models is no less unclear. In fact, exploiting constraints on 𝒱 makes the problem even worse. For now the unclarity is not confined to defaults, and they infect the whole model. My argument in this article is that there are situations in which normality considerations should not affect the choice of variables in 𝒱 . If there is unclarity, then defaults are a better place for it.

3. The Problem of Disagreement

Consider a variation of the gardener/queen case provided by Halpern and Hitchcock: “while a homeowner is on a vacation, the weather is hot and dry, her next-door neighbour does not water her flowers, and the flowers die. Had the weather been different, or had her next-door neighbour watered the flowers, they would not have died” (Reference Halpern and Hitchcock2015, 414–15). Halpern and Hitchcock argue that since the flowers’ death depends on both the weather and the neighbor’s omission it seems like a counterfactual theory of causation cannot distinguish between these factors. Yet, according to some authors (e.g., Moore Reference Moore2009) the weather is a cause of the flowers’ death but not the neighbor’s omission to water them because omissions generally cannot be considered to be causes. Halpern and Hitchcock flag this as the “problem of isomorphism.” But, they claim, there is “an even deeper problem. There is actually a range of different opinions in the literature about whether to count the neighbour’s negligence as an actual cause of the flowers’ death. … Prima facie, it does not seem that any theory of actual causation can respect all of these judgments without lapsing into inconsistency” (Reference Halpern and Hitchcock2015, 415). This is the Problem of Disagreement.

The Problem of Disagreement arises when the following two conditions hold. First, there are two (or more) agents who have conflicting judgments of actual causation with regard to the same target system. For example, theorists like Moore argue that only the weather is an actual cause because they think that omissions cannot be actual causes. They disagree with theorists like Lewis (Reference Lewis2000) who think that the neighbor’s negligence is also an actual cause, because they think that omissions are genuine causes. Second, the opposing agents agree on the underlying causal model. In the flower case Halpern and Hitchcock take this to be a model with a graph like the one in figure 1A, and a structural equation such that the flowers die if the weather is hot and the neighbor fails to water them.

What exactly do the agents disagree about in such cases? According to Halpern and Hitchcock, the disagreement concerns the actual cause of the outcome. But would this not imply an implausible metaphysical view according to which actual causation is subjective? Halpern and Hitchcock admit that actual causation is a subjective and context-dependent notion that is to be distinguished from an underlying and objective notion of causal structure. Yet such a notion has an important function because it indicates targets of intervention that are particularly suited from the pragmatic perspective of the agent (Hitchcock and Knobe Reference Hitchcock and Knobe2009).

Let us see how Halpern and Hitchcock account for this case of disagreement. The idea is that defaults give rise to a normality ordering over the worlds that can be represented by the model. Actual causes are those factors that fulfill Halpern and Pearl’s (Reference Halpern and Pearl2005) definition of actual causation plus a normality criterion. The normality criterion requires that the possible world that is needed to show that the effect depends on the cause be at least as normal as the actual world. Halpern and Hitchcock argue that “those who maintain that omissions are never causes can be understood as having a normality ranking where absences or omissions are more typical than positive events,” and Halpern and Hitchcock take this to reflect “a certain metaphysical view: there is a fundamental distinction between positive events and mere absences, and in the context of causal attribution, absences are always considered typical for candidate causes” (Reference Halpern and Hitchcock2015, 437–38). This assumption of typicality gives rise to the judgment that the only actual cause of the flowers’ death is the weather.

An advocate of the view that omissions are always causes can be understood as subscribing to an alternative normality ordering. Here the worlds in which the flowers do not die are equally normal, and they are taken to be at least as normal as the world where the flowers die. Consequently, both the weather and the neighbor’s negligence fulfill the normality criterion and qualify as actual causes of the flowers’ death.

There are two problems with this reconstruction of the disagreement. First, it seems implausible that Moore would agree that absences are generally more normal than positive events. In fact, according to each of the many dimensions of normality, there seem to be clear counterexamples. Living humans more frequently breathe than not, and we are legally and morally required to help those whose lives are in danger. The kind of metaphysical point that Moore (Reference Moore2009) makes with regard to the causal status of omissions is independent of claims regarding the normality of omissions. Thus, it seems Halpern and Hitchcock have chosen an example in which defaults do not do the explanatory work that they expect them to do.

Second, suppose there is an agent who believes that absences are always considered typical and, thus, never can be causes. Moreover, suppose that the agent complies with the constraint that causal models should only represent scenarios that are to be taken seriously. According to the agent’s beliefs, it is a very far-fetched possibility that omissions like the one of the neighbor are causes. Thus, the rules of appropriate modeling command that she leave out the variable representing the neighbor’s negligence. But if this is the case, then this agent disagrees with the proponent of absences as causes already at the level of standard causal models.

So, it seems like Halpern and Hitchcock’s argument faces similar difficulties as the argument from the Problem of Isomorphism. In particular, there is not really a problem in the first place if we choose what seem to be the most plausible representations of the agents’ actual beliefs.

4. What Is the Function of Extended Causal Models?

In the remainder of the article I argue that there is an alternative reading of the Problem of Disagreement that involves prescriptive claims about how disagreeing agents should use extended causal models. I will argue that the alternative reading shows that in some cases defaults are a useful extension.

What is the function of extended causal models? Halpern and Hitchcock “envision a kind of conceptual division of labour where the causal model … represents the objective patterns of dependence that could in principle be tested by intervening on the system, and [the normality ordering] represents the various normative and contextual factors that also influence judgments of actual causation” (Reference Halpern and Hitchcock2015, 435). Thus, causal reasoning involves considerations that are located at two distinct levels. First, there is the level of standard causal models. These represent the objective patterns of counterfactual dependence. Second, there is the level of judgments of actual causation. These judgments are influenced by the normality ordering that reflects normative and contextual considerations.

However, the conceptual division of labor does not work as straightforwardly. First, the causal model itself is not completely objective. Objectivity on this level means that “once a suitable set of variables has been chosen, there is an objectively correct set of structural equations among those variables” (Halpern and Hitchcock Reference Halpern and Hitchcock2015, 431–32). But the choice of the set of variables (and their possible values) is likely to be governed by criteria that are sensitive to normative and contextual factors (such as in Blanchard and Schaffer’s treatment of the gardener/queen case). Second, even the judgments of actual causation need to have some objective core. Otherwise they could hardly help us “identify appropriate targets of corrective intervention” (432).

If causal models (plus information about the variables’ actual values) and claims of actual causation are so similar, could we just make do with one of them? No. Claims of actual causation are highly selective. This has the advantage that they can guide agency very straightforwardly by indicating the best targets of intervention. Presumably, causal models are somewhat closer to the objective structure because they allow representing larger chunks of it. They express complex counterfactual dependencies that are not captured by a simple claim of the form ‘ $X=x$ is an actual cause of $Y=y$ .’ These larger chunks still depend on norms, but do so to a lesser degree, for selection does not have to be constrained so narrowly.

In what follows we see that the Problem of Disagreement helps to indicate one distinctive advantage of causal models, understood along these lines: they can help us provide a representation of disagreement of causes that is more conducive to resolving the disagreement than bare claims of actual causation. Moreover, I will argue that this function is sometimes (but not always) crucially facilitated by incorporating the default/deviant distinction.

5. An Example: Search-and-Rescue Missions

According to Frontex, the European Border Control Agency, nongovernmental organization search-and-rescue missions (NGO SARs) are an actual cause of the increase of fatalities in the Central Mediterranean from 2015 to 2016.Footnote ³ Yet, it has been argued that NGO SARs are only one factor acting within a complex causal structure and that it is erroneous to describe NGO SARs as the cause of the increase. I will look at a study performed by Forensic Oceanography and show that the most natural way to understand their criticism of Frontex’s claim is to see it as an attack on Frontex’s assumptions about the causal model.Footnote ⁴

Let us begin with a closer look at the claims put forward in the Frontex report. The report states that

The presence of SARs (both NGO and state-led operations) near the Libyan coastline is said to give a sense of security that encourages migrants and refugees to risk their lives. This has two effects. First, smugglers can offer crossings that are more risky. Second, there is an overall increase in attempted crossings.

The report also states that “closely related issues are the safety of migrants and refugees and, most significantly, the increasing number of fatalities” (Frontex 2017, 32). After reporting estimates of the fatalities in 2016, the report states that “the increasing number of migrant deaths, despite the enhanced EUNAVFOR Med/Frontex surveillance and NGO rescue efforts, seems paradoxical at first glance” (33). But then the report relates the increase of fatalities to a change in the smugglers’ tactics: “the rising death toll mainly results from criminal activities aimed at making profit through the provision of smuggling services at any cost” (33).

It seems fair to assume that the above quoted passages can be summarized by the causal model displayed in figure 2A. In the model, S represents the presence of SARs, C is a factor that represents the risk level of the individual crossing and the number of attempted crossings, and D represents the number of deaths. It is claimed that an increase in S leads to an increase in C, that an increase in C leads to an increase in D, and that an increase in S also leads to a direct decrease in D. The narrative does not allow a more detailed quantification of these relations. But there is a possible reading of the narrative according to which the increase of deaths via the route 〈S, C, D〉 is larger than the decrease via the route 〈S, D〉.

Figure 2.

Simple model of the pull-factor narrative. A, Frontex; B, Forensic Oceanography.

The Forensic Oceanography report (2017) identifies the pull-factor claim as part of a toxic narrative within a “de-legitimisation and criminalisation campaign” directed at NGO SARs. The aim of the report is an empirical assessment of the claims put forward by Frontex. The report can be understood as challenging the structural relation between S and C as stated by Frontex and suggesting to add a variable X that feeds into C and that explains the increase in risk level and number of attempted crossings from 2015 to 2016 (see fig. 2B). Relevant factors, among others, are the availability of seaworthy vessels and involvement of Libyan militia and Libyan Coast Guard.

The Forensic Oceanography report (2017) also describes NGO SARs as a continuation or replacement of preceding state-led SARs. In particular, the report claims that “aiming to deter migrants from crossing the Mediterranean, the EU and its member states pulled back from rescue at sea at the end of 2014, leading to record numbers of deaths. Non-governmental organisations (NGOs) were forced to deploy their own rescue missions in a desperate attempt to fill this gap and reduce casualties.” That is, whereas the Frontex report suggests that there is a new kind of SARs that explains the increase, the Forensic Oceanography report describes SAR activity in the Mediterranean as a default condition.

6. The Role of Defaults

The disagreement between the Frontex report and the Forensic Oceanography report concerns the question whether the presence of SARs led to an increase in the number of deaths. The underlying question is: Why are refugees willing to risk their lives? The presence of SARs (and stories about how they guarantee safety on sea) is considered to be one factor. However, there are at least three further kinds of factors: (i) the situation in the home country, (ii) the hope for a better life in the European Union, and (iii) the absence of alternative pathways into the European Union (legal pathways or simply pathways that are not as risky).

Suppose each of these factors corresponds to a variable in a causal model such that a variable describing the willingness to risk one’s live depends on these variables. The disagreement about the causal role of SARs involves agents who have opposing views about which of these variables represent possible scenarios that are to be taken seriously—for functional, legal, and moral reasons. For example, there is disagreement about the moral and legal feasibility of cutting back life-saving missions on sea.

How should this disagreement be represented? One way would be to require that the involved agents agree on a set of variables 𝒱 by including all variables that are at stake in the debate and represent their disagreement on the level of the default/deviant distinction. From a humanitarian perspective, for example, life-saving missions would be the moral and legal default state. By contrast, certain opposing agents might want to describe the absence of SARs as the default state. But both kinds of agents would be required to include a variable representing SARs.

Alternatively, one could require the views to be expressed by different standard causal models that reflect the individual views about what scenarios are to be taken seriously. This is what is suggested by the adjust-the-model strategy. The advantage is that such models do not incorporate the default/deviant distinction, which is considered unclear. The disadvantage, however, is that now the unclarity occurs in a disagreement about which scenarios are to be represented by the model in the first place.

The problem with this strategy is that it leaves unclear whether agents disagree for normative or for epistemic reasons. Suppose agent A ₁ does not include a particular variable X in her standard causal model even though agent A ₂ thinks that X is a cause of Y. Does agent A ₁ claim that a change in X would merely amount to a scenario that is not to be taken seriously? Or does agent A ₁ claim that a change in X would not make a difference to Y? Extended causal models fare better in this kind of context. They provide formal resources that help the involved agents to point out where disagreement arises for normative reasons and where it arises for epistemic reasons. Agent A ₁ would be required to include X into the model and clarify whether she takes Y to be independent of X or merely considers X to represent scenarios that from her particular point of view are highly abnormal.

This is particularly important in cases in which it is likely that disagreement arises not only about norms but also about the underlying counterfactual dependencies. The core of Frontex’s pull-factor claim is the counterfactual dependency of C on S. This claim is difficult to assess. It involves nontrivial assumptions about refugees’ dispositions to risk their lives. Frontex supports the pull-factor claim by a comparison of the risk levels in 2015 and 2016 and relates this to an increase of the NGO SAR activity over this period. But this argument is valid only if all other potential causes for an increased risk level remain constant over this period. In Frontex’s selective causal model it looks like this is the case. A more encompassing model such as the one provided by the Forensic Oceanography report, however, suggests that Frontex’s claims are unwarranted. In order to warrant the pull-factor claim in the context of such a more encompassing model, the Frontex report would have to show that the influence of these other factors is irrelevant.

7. Conclusion

The adjust-the-model strategy gives rise to a powerful objection to existing arguments for defaults that are based on the Problem of Isomorphism and the Problem of Disagreement. In this article I have suggested a prescriptive reading of the Problem of Disagreement that provides a new argument for defaults that is not undermined by the adjust-the-model strategy. In cases of disagreement, extended causal models should represent assumptions about the underlying causal structure that are shared by the involved agents, while the defaults should account for the normative disagreement. This helps keep normative disagreement apart from disagreement about the underlying counterfactual structure.