to engage in certain behavior, such as political violence (see Chapter 6). At this stage, however, it is important to note that cognitive maps represent belief systems, whereas Pearl’s examples refer to physical mechanisms in the world. Therefore, it is not immediately obvious that external interventions can be applied to cognitive maps. In the following, I show that this is nevertheless the case, and that belief connections can be modeled as if they were causal.
Belief Connections Can Be Modeled as if They Were Causal
Pearl’s example about the sprinkler implies that it is principally possible to perform external interventions on cognitive maps. This is the case because the example in which he performs his external intervention can itself be considered a cognitive map: Pearl treats the vertices of this DAG as knowledge, or true beliefs. Specifically, he treats them as knowledge about what season it is; whether the sprinkler is turned on; whether it rains; whether the pavement is wet; and whether the pavement is slippery. If the vertices of this DAG can be considered true beliefs, they can also be considered beliefs; and if the vertices can be considered beliefs, the edges between the vertices can also be considered belief connections.
Pearl’s example therefore shows that one can model external interventions on cognitive maps by changing particular beliefs that are knowledge.34 However, it is not clear whether the connections between the true beliefs on which the external intervention is performed and the remaining beliefs can be considered as Pearl proposes (deleting A → C; tracing effect of C = SPRINKLER ON). This is due to two reasons: (1) the remaining beliefs of cognitive maps may not be true beliefs as in Pearl’s example, and (2) by their nature all belief connections have a subjective dimension (see section on Belief Connections), and Pearl’s treatment of edges as stable and autonomous physical mechanisms does not apply immediately.
Accordingly, it is helpful to consider the purpose of Pearl’s external intervention, which is to deal with the uncertainty of human knowledge about cause-effect relationships in the external world. Specifically, Pearl’s external intervention overcomes this uncertainty by defining certain things to be. Upon knowledge about the existence of these particular things, their causes become irrelevant for considering their consequences; and their consequences can in turn be considered from additional knowledge about the connections between the things that are defined to be (causes) to other things (effects).
Table 9: Causal and Logical Connections
Relating this to belief connections, the major issue is not whether there is uncertainty about what causes certain things in the external world. Belief connections consist of logical antecedents and consequents, and represent possibilities rather than necessities.35 These connections are by their nature less strong than cause-effect connections, but they have the same structure: both express directed relationships in which certain components depend on others (see Table 9, column “Directedness”). Based on this structural similarity, it is possible for belief connections to represent cause-effect connections, even though they are not cause-effect connections themselves—as demonstrated by Pearl’s sprinkler example, involving a DAG with vertices representing knowledge about the world. On the other hand, they may also represent purely logical connections including beliefs that are not knowledge—whose internal structure is the same.
This structural compatibility of belief-belief and cause-effect connections suggests that, although belief connections are logical, it is nevertheless possible to model them as if they were causal. In the following section, I show how this can serve the systematic study of alternative worlds in which actors would not have decided to engage in certain behavior.
Extending External Interventions to Beliefs That Are Not Knowledge
Given that cognitive maps can be modeled as if they were causal, it becomes possible to intervene on different types of beliefs, including beliefs that are not knowledge. For example, one can also intervene on religious beliefs, or on beliefs about feelings. This offers new possibilities for the study of counterfactuals by intervening on internal rather than external factors. In other words, it becomes possible to study counterfactuals that include actors with different internal worlds. This study does not pursue this avenue, as external factors are identified as mattering more than internal factors in relation to political violence. However, other studies might pursue this avenue to develop deeper insight into other phenomena.
Counterfactual Model
Based on the previous section, it is possible to extend Pearl’s external interventions to cognitive maps, and to use the cognitive mapping approach to study counterfactuals. In order to do so, it is necessary to consider the main components by which Pearl formally defines counterfactuals:
• A Causal Model that represents the entire structure on which the counterfactual will be modeled.
• A Submodel that represents only the change that is made to the model when introducing an external intervention.
• The Effect and Potential Response that represent what follows from the external intervention in the model.
• The entire structure of the Counterfactual resulting from the external intervention.
Figure 13 illustrates these components, building on my earlier presentation of external interventions. The figure is divided into two parts. The upper part illustrates a cognitive map before an external intervention (Pearl’s causal model). The lower part illustrates the cognitive map after an external intervention is performed (Pearl’s submodel, effect, potential response, and counterfactual). Note that it is only possible to identify the submodel, the effect, the potential response, and the entire counterfactual after introducing the intervention.
Pearl’s definitions for the main components of counterfactuals are presented in the Appendix. To follow the analysis in this book, however, it is not necessary to read the Appendix. Instead, I explain in Chapter 6 how the computational model developed for this research applies Pearl’s theory to model counterfactuals.
Other Theories of Counterfactuals
Pearl’s theory of counterfactuals makes a significant contribution to the existing literature on counterfactuals. As Pearl writes, using external interventions to model counterfactuals has major advantages over other theories of counterfactuals (238–40), first addressed by David Hume and later presented by John Stuart Mill, David Lewis, or Saul Kripke. Specifically, Pearl’s theory differs from the works of these authors by focusing on the processes by which counterfactuals are constructed.
Figure 13. Modeling counterfactuals. (2 graphs)
There is a vast body of literature about theories of counterfactuals, particularly in the field of philosophy, and the following paragraphs can by no means give a complete overview or analysis. Rather, my aim is to briefly present some of the main features of this literature and identify some of the major contributions offered by Pearl’s approach. Following Pearl’s own references, this section addresses Lewis’s theory of counterfactuals, to which various works in the study of political science refer (e.g., Fearon 1991; Sylvan and Majeski 1998). In addition, the section addresses Hume, because he was the first researcher to explicitly address counterfactuals, and Kripke,
