the actor engages in related to his goals). For example, one can have a goal of following God’s will (Belief Type 4, “I believe that my goal is to follow God’s will”) underlying one’s praying. One can also have a goal of stopping the government from attacking its citizens (Belief Type 1, “I believe that my goal is to stop the government from attacking its citizens”) underlying one’s leaving a demonstration. Or one can have a goal of fulfilling a certain desire, such as the goal to be happy (Belief Type 5, “I believe that my goal is to be happy”) underlying one’s going on vacation.
Goals are beliefs about what the subject considers the desired consequence of his action, so that action → goal achieved. This is opposed to performing the action for the sake of performing the action, so that action → action achieved. This structure underlines that people do not take up arms for the mere purpose of engaging in violence. Rather, their actions involve certain goals. It is important to note that whether one’s goals are achieved can be evaluated only after the action has been performed. As a result, goals imply a forward-looking dimension that transcends both decisions and actions.
Conclusion and Outlook
This section and the previous ones introduced decisions to engage in certain behavior, such as political violence, and the beliefs connected to such decisions. The following discussion applies these ideas by modeling political violence as decisions to take up arms based on chains of interconnected beliefs. In the next chapters, I identify these chains of beliefs by coding the actors’ direct speech for decisions to take up arms, as well as for other beliefs related to these decisions. Based on this, I construct cognitive maps that make visible the complex belief systems underlying political violence. I then analyze the maps and identify different types of belief chains that motivate decisions, which sheds light on the complex microlevel mechanisms underlying political violence.
Part II. Formalization and Counterfactuals
Formalizing Cognitive Maps into Directed Acyclical Graphs
Cognitive maps typically contain large numbers of beliefs and inferences. Therefore, it is impossible to systematically analyze them by hand. To cope with this problem, it is helpful to formalize cognitive maps. As shown by Axelrod (1984),27 formal models make traceable processes that would otherwise not be analyzable, or only be analyzable on a much smaller scale. They allow the researcher to systematically explore the reasoning processes represented by cognitive maps.
Based on the literature in graph theory28 and computer science, cognitive maps can be formalized into directed acyclical graphs (DAGs). This offers new possibilities for studying human behavior via the cognitive mapping approach. DAGs are often used in computer science to study structures of variables that are directed and limited (Koller and Friedman 2009; Pearl 2000). The reasoning processes represented by cognitive maps are also directed by involving antecedent and consequent beliefs. They are also limited by involving traceable chains of beliefs that end in decisions. As a result of this similarity, formalizing cognitive maps into DAGs offers a convenient basis for an automated analysis.
In the following, I explain how cognitive maps can be formalized into DAGs. Specifically, I do so by drawing on Judea Pearl’s theory of causality. This formalization also offers new possibilities for the study of counterfactuals, and allows me to explore alternative worlds in which individuals would not have decided to take up arms (see Chapter 6).
Directed Acyclical Graphs
According to Pearl (2000), DAGs are graphs with a particular structure. Graphs are structures with two components:
V = set of variables of vertices
E = set of edges connecting the vertices
DAGs differ from other graphs by being directed and not containing cycles or self-loops (see Figure 9). Directedness means that each edge in the graph is an arrow pointing from one vertex to another. Not containing directed cycles or self-loops means that there are no relationships such as A → B, B → A (cycle), or A → A (self-loop). In this structure, it is possible to trace paths between vertices that are separated by more than one arrow by following the direction of the edges between these vertices (see Figure 9).
According to Pearl (2000: 12), the following labels, taken from graph theory, describe the major components of DAGs:
• All vertices are called parents or children. Parents are the starting points of arrows. Children are the ending points of arrows.
• Vertices that do not have parents are called roots.
• Vertices that do not have children are called sinks.
• Indirect connections between vertices are called paths.
This structure corresponds to the structure of cognitive maps. The similarity between DAGs and cognitive maps is indicated by the terminology used to describe both structures. In particular, Pearl’s graph theory terminology corresponds almost exactly to the belief system terminology introduced in the previous sections. This shows that, although cognitive maps are considered belief systems rather than graphs, it is possible to think of them as DAGs. Table 8 gives an overview. Figure 10 visualizes these elements. The upper part is a cognitive map, the lower part is a DAG.
Figure 9. Structure of a directed acyclical graph.
Table 8: Compatibility of DAGs and Cognitive Maps
Cycles and Self-Loops
In spite of these similarities, there is a feature of DAGs that does not necessarily correspond to cognitive maps in particular, or to the nature of reasoning processes more generally: the absence of cycles or self-loops. Specifically, humans may reconsider certain beliefs before/if reaching a decision. Such reconsiderations may be represented as cycles or self-loops. Nevertheless, recall that all reasoning processes represented by cognitive maps end in decisions. Because of this, they are directed toward decisions, even if they contain cycles or self-loops. Cycles or self-loops in cognitive maps therefore represent reconsiderations only within reasoning processes that end in decisions. They do not change decisions. Based on this, it is possible to formalize cognitive maps into DAGs.29
Figure 10. Compatibility of directed acyclical graphs and cognitive maps. (2 graphs)
Counterfactuals
Following Pearl, formalizing cognitive maps into DAGs allows the researcher to intervene on the actors’ belief systems and explore when they would not have made certain decisions. In Chapter 6, I use this approach to study worlds in which the individuals I interviewed for this research would not have decided to take up arms.
Studies exploring whether people would have behaved
