Theoretical Intuition

In this section, we provide a high-level overview of the intuition driving the choices in our theoretical model. Armed groups target civilians to extract resources from the population and to increase their likelihood of prevailing in expected conflicts with other groups (Kalyvas Reference Kalyvas2006). Civilians likewise act strategically to minimize their personal likelihood of being killed by armed groups (Arjona Reference Arjona2017; Kaplan Reference Kaplan2017). Thus, to understand when and where civilian victimization is likely to take place, we need to evaluate this complex, multi-actor strategic environment.

To do this, we estimate the relational, or network, competitiveness of the environment. If violence is concentrated around a single actor, where one actor dominates conflict initiation toward many others or receives conflict from many challengers, then civilian victimization will be less likely. If, however, all actors are likely to fight one another—in an all-against-all competition—civilian victimization will be at its highest. To investigate this, we conceptualize the overall strategic environment as a social network, wherein the nodes in this network are armed groups and the edges are battles between these groups. We formulate our concept of network competition across each conflict network as followsFootnote ²:

(1)$${\rm Network\;Competition} = 1-\mathop \sum \limits_{i = 1} N( CS_i) ^2$$

whereN denotes the number of actors and CS _i is the conflict share of actor i, which is a measure of the proportion of battles an armed actor is involved in.Footnote ³ Our measure provides us with a representation of how dispersed conflict is in the network. Figure 1 provides a conceptual illustration of a low- and high-competition scenario.

Figure 1.

Conceptual networks illustrating scenarios of low and high network competition.

Note: Network competition is low in the left panel and high on the right, while the number of conflictual events and actors stay constant.

The left-hand network exhibits low network competition. Here, conflict patterns are dominated by a single sender or receiver in the network. In this network, an armed group's strategic decision to victimize civilians is fairly straightforward—victimization takes place if the coercive effect (causing more non-supporters to reluctantly support the group in charge) outweighs the resources that could be mobilized from non-supporters. In this environment, while there may initially be low levels of victimization, we will quickly approach an equilibrium in which most civilians support the groups in control of their territory and no victimization occurs.

The right-hand network reveals a different picture. This competitive conflict network functions as a Hobbesian war of all against all, where each armed group is ready to attack each other armed group. Almost all actors are at risk of an attack, and they are at risk of an attack from multiple sources, leading to even stronger incentives toward victimization. In this case, there is likely a fluid control of territory. Frequent changes in the system increase incentives for violence against civilians, which is an assumption supported by existing research (Wood and Kathman Reference Wood and Kathman2015). Some of the most intractable and dynamic conflicts—such as the modern wars in Somalia—are likely to exhibit this network structure. Our theoretical model (explained later) builds on existing work by formalizing the competitive process in a network environment and including the strategic behavior of civilians as a key predictor of violence against civilians during war.Footnote ⁴

Civilian Victimization during War

Current research acknowledges that an armed actor's decision to victimize civilians is conditional on the conflict landscape at large, wherein the decisions of armed groups are informed by the actions of both rival armed challengers and the civilian population. As Wood (Reference Wood2010, 612) explains: “Unraveling these dynamics is particularly important if scholars wish to fully understand the dense web of interactions that guide insurgents' decisions to use violence.” While this literature has begun to uncover the intuition behind how multi-actor conflicts influence victimization, much of the theoretical mechanisms remain underspecified and measurements for complexity rest on accounting solely for the number of armed groups. We draw on the intuition from the literature that the interdependent dynamics of armed groups influence violence against civilians and use it to support each turn in our modeling decisions, described in the following. We demonstrate how unitary choices among actors can generate relational, competitive dynamics across the conflict network.

Sequential Order of Events

We depict the main stages of the game in Figures 2 and 3. In these figures, territories are represented by rectangles and rectangle size is determined by its civilian population. Territories of the same color are held by the same armed group. The beginning stages of the game are shown in Row 1 in Figure 2. In Row 2 (left panel), we illustrate an armed group's choice to attack in a given territory (if any). Civilians are arranged in the territory based on their ideological preferences (Row 2, right panel); this figure also shows civilians' decision to support an armed actor. The outcomes for both armed actor and civilian decisions are in the final row. In Figure 3, we depict how a third actor represented in this conflict environment would choose to victimize civilians. This actor's calculus depends on both whether an attack is likely and the possible consequences of victimization. In the following, we discuss the intuition behind the decision rules for each group in Figure 3 (for the explicit mathematical criterion for each choice, see Section A.1 in the Online Appendix).

Figure 2.

The choice of an armed actor to attack, and the choice of civilians to support the actor or not.

Notes: Rectangles represent territory, with territory size based on the size of the civilian population. For the solid colors, color represents the group controlling the territory. The arrows illustrate the potential territories this group can attack. A solid arrow indicates the actual choice. The diagonal lines represent the civilian population in each territory, ordered by ideology. In the two territories that are part of the battle, the civilians choose between two combatants; in the other territory, the civilians choose between supporting the blue group or supporting no one. Based on the resources from civilian support, the battle concludes with blue group's victory.

Figure 3.

Graphic illustrating the choice of an armed actor to victimize civilians.

Notes: The orange group first determines whether any of their neighbors are likely to attack. If they are likely to attack, the orange group decides whether to victimize to maximize their support and chance of winning in a battle; if they choose not to victimize, they do so to maximize the resources they gain from the territory. Victimizing can either “succeed” (by targeting a non-supporter) or “fail” (by indiscriminately targeting a supporter) based on both levels of support in the territory and random chance. If it achieves its aims, the ideological range of support for the incumbent group increases; if it fails, the range contracts.

(0) Genesis of country and actors

We begin by generating all of the relevant actors and territories. We first generate a number of territories that is at least as large as the number of armed actors in the game. The territories are connected via a random adjacency matrix that we define such that no territory is totally isolated. We then generate some number of armed actors, each with a random ideal point (x _i) and level of ideology (ϕ _i). Each armed actor is assigned a territory, and the remaining territories are given to the last group, that is, the government.Footnote ¹¹ We then generate the number of civilians in each territory, each with a random ideal point (η _i). With this foundation, we are ready to begin the game.

(1) Armed groups choose which territories to invade

When an armed actor attacks another territory, each group involved in the territory has a probability of winning based on their share of spatially weighted resources.Footnote ¹² Armed groups estimate their likelihood of victory using either their prior beliefs about the distribution of civilian preferences or the past actions taken by civilians in a territory toward a particular armed group. Specifically, the potential attacker assesses how much utility they will gain from attacking a territory compared to how satisfied they will be if they do nothing. The difference between these two factors is the payoff for attacking a given territory. Groups choose to attack a territory where there will be the biggest payoff from attacking compared to the status quo (or if none of these are positive, they attack nowhere). This decision is illustrated in Figure 2. When more distinct groups choose to attack each other, our measure of network competitiveness will be higher.

(2) Civilians choose whether to support armed groups

Civilians' decisions are conditioned not just on the characteristics of armed actors, but also on the behavior of other civilians.Footnote ¹³ When civilians choose who to support, they assume that other civilians will make support decisions probabilistically based on their proximity to armed groups (see Equation A8 in the Online Appendix). Civilians who are ideologically close to the armed group are assumed to be highly likely to support them, and civilians who are very far from the armed group will be much less likely to support them. If a group has a history of killing supporters, all civilians are perceived as less likely to support the group.

If the territory is the site of a battle, civilians will make an estimation about each group's likelihood of victory given expected levels of support and choose to support the group that has the best combination of (1) ideological congruence, (2) history of treating their supporters well, and (3) likelihood of winning the battle. If the territory is not the site of a battle, support will be based on ideological similarity and expected civilian support (as groups with larger amounts of civilian support are better able to gather information and punish non-supporters).Footnote ¹⁴

(3) Battles take place and winners are determined

If a territory is the site of a battle, one group will win probabilistically based on their share of locally weighted resources, (c) civilians in each involved territory will die, and the winning group will take control of the territory.

(4) Armed groups choose which territories to victimize

When deciding to victimize, the armed group that controls a territory will first try to ascertain whether that territory is at risk of an attack. If it is, the incumbent group will victimize if it helps them to win a potential future battle; if not, they will only victimize when it increases the amount of resources they can extract from the territory. In general, when network competitiveness is low, groups will be more tolerant of non-supporters in order to maximize how many resources they can mobilize, which will lead to a lower level of victimization.

When an armed group chooses to victimize, they know that there is some chance that they will successfully victimize a non-supporter and some chance that they will instead victimize a supporter, based both on their access to solid intelligence (a function of the number of supporters) and, in the absence of intelligence, on random chance. When a civilian is victimized, there is both a direct and indirect effect. The direct effect is that a civilian—who may be a supporter of the armed group, a non-supporter who can be coerced, or a potential supporter of a rival attacking group—is killed, meaning that the civilian's support can thereby no longer be realized. The indirect effect is that when a group targets a supporter, the range of the ideological space that supports that group contracts, and when they target a non-supporter, it expands. Thus, armed groups take both effects into account when they choose whether or not to victimize. However, when the territory is at risk of attack, the incentives to victimize are higher because the direct effect, that is, targeting potential supporters of an invading group, may be positive, whereas when there is no risk of attack, the direct effect is always a cost, and so victimization is only chosen if the indirect effect outweighs this cost. The tradeoffs for the armed group in each of these cases is illustrated in Figure 3.

(5) Civilians choose to flee

After victimization, civilians choose whether or not to flee from a territory into an adjacent territory. We have a threshold for fleeing that decreases as the conflict endures.Footnote ¹⁵

(6) Game iterates

Stages 1–6 will continue until one of three end conditions are met: (1) the government controls all the territories; (2) the government controls no territories; or (3) the game reaches the predetermined turn limit and ends in a stalemate.

Simulation Results from the Computational Model

To determine the macro-level effects of the micro-actions described earlier, we run a simulation analysis with 10,000 separate conflict scenarios. In each scenario, we chose parameters determining the conflict environment at random, each of these parameters are listed in Table 1. From the simulations, we record three main conflict statistics: the number of armed groups in the network; the overall level of violence in the network; and our measure of network competition. We also capture the frequency of civilian victimization in each run of the game.

Table 1.

Summary of the parameters in our computational model

To estimate the effect that our three statistics have in relation to civilian victimization, we employ a negative binomial regression with fixed effects on the conflict scenarios and another in which we use random effects. We depict the results of this analysis in Figure 4; the left plot shows the result with fixed effects and the right with random effects.

Figure 4.

Analysis of determinants of victimization in computational model.

Notes: The left panel visualizes coefficient estimates when using fixed effects on conflict scenarios and the right uses random effects. Points represent average values of parameters. Thicker lines represent the 90 per cent confidence interval and thinner lines the 95 per cent interval. A darker shade of red (blue) indicates significant positive (negative) values.

Here, we can see that more competitive conflict networks have a higher expected frequency of civilian victimization.Footnote ¹⁶ This finding generates our main hypothesis for empirical investigation: even when controlling for the overall level of violence, a more competitive conflict network leads to higher levels of civilian victimization.

Empirical Analysis

To investigate the implications of our computational model empirically, we use the Armed Conflict Location and Event Dataset (ACLED) developed by Raleigh et al. (Reference Raleigh2010). The ACLED collects the “dates, actors, locations, fatalities, and types of all reported political violence and protest events around the world.” Our first step is to calculate the level of network competition for countries experiencing intrastate conflict according to the battles data provided by the ACLED. Battles are defined by the ACLED as “a violent interaction between two politically organized armed groups at a particular time and location.”Footnote ¹⁷ We assume that relevant actors to our study are those actors that have been involved in a battle event as either a primary or an associated actor. Our final cross-national sample ranges from 1997 to 2020 and includes 42 countries.Footnote ¹⁸

For each country in our sample, we construct a conflict adjacency matrix, in which a value of 1 is recorded if there was a battle between an armed group in the row and column of the matrix. Given that untangling who initiated a particular battle can be difficult, the conflict adjacency matrices we construct are symmetric. Our conflict matrices also include any actor—whether listed as the primary actor or associated actor in the ACLED—involved in a given battle. The set of actors in these adjacency matrices include both rebel groups and government forces. We aggregate military and police forces from the same country into one government actor.Footnote ¹⁹ Additionally, we exclude international actors, such as peacekeepers, militaries from other countries, the United Nations, and election observers, from our analysis. Finally, we also clean the data for any “unidentified” actors. These steps help ensure that the actors in our analysis reflect groups involved in conflicts against one another at the intrastate level of analysis. In some cases, these actor-cleaning steps lead to empty adjacency matrices with no actors.Footnote ²⁰

For inclusion in our sample, we impose a restriction that a country must have at least three years of non-empty conflict adjacency matrices.Footnote ²¹ Our resulting data clearly show that intrastate conflicts are often much more complex than a war between the government and a few mobilized challengers. From 2011 onwards, the majority of conflicts involve five actors or more. The data also reveal that highly complex conflicts, where a country has ten or more active armed groups in a given year, are on the rise—as shown in the top panel of Figure 5. The bottom panel of Figure 5 depicts the distribution of network competition across our sample of countries from 1997 to 2020.Footnote ²²

Figure 5.

The number of active armed groups and distribution of network competition in countries from the ACLED between 1997 and 2020

Notes: Top panel shows the number of active armed groups in countries from the ACLED between 1997 and 2020. Dark grey represents armed conflicts with four or fewer active armed groups; light grey represents armed conflicts with five to nine active armed groups; white represents armed conflicts with ten or more armed groups. Bottom panel uses violin plots to showcase the distribution of network competition across our sample of countries over time. Thick, horizontal bars through each violin plot designate the median.

Once we have generated our set of adjacency matrices for every country-year, we then calculate the number of actors and the level of network competition in the networks. We control for the overall level of violence by counting the number of battle events a country faces in a given year. Apart from the ACLED-based data, we incorporate a number of other controls that have been argued to affect the level of civilian victimization at the country-year. For brevity, these are listed in Table 2.Footnote ²³ Importantly, we can directly measure some controls through the ACLED data, such as the number of actors in a given conflict. Other measures, such as Polity scores, population, excluded population, and the presence of peacekeepers, are measured at the country level and are thus easily adapted to our study. These measures are included as control variables to account for conditions that are known to influence the level and type of conflict in a given country. The inclusion of the excluded population variable into the model, for example, is important because the number of excluded groups is shown to affect conflict mobilization and would thus have a downstream effect on the number and strength of armed groups, as well as civilian victimization (Fjelde and Hultman Reference Fjelde and Hultman2014; Uzonyi and Demir Reference Uzonyi and Demir2020). Similarly, regime type can influence the likelihood that conflict actors victimize civilians (Eck and Hultman Reference Eck and Hultman2007; Harff Reference Harff2003).

Table 2.

Summary of data used in our empirical analysis

Notably, however, there is no annually updated available data on the attributes of armed actors that span across both space and time at the actor level. To overcome this, we rely on Cunningham, Gleditsch, and Salehyan's (Reference Cunningham, Gleditsch and Salehyan2013) “Non-state actors in civil wars” (NSA) data. The NSA data extend the Uppsala Conflict Data Program (UCDP)/ Peace Research Institute Oslo (PRIO) Armed Conflict Dataset (Themnér and Wallensteen Reference Themnér and Wallensteen2013) and cover all internal armed conflicts from 1945 to 2011.Footnote ²⁴ The NSA data contain information about rebel–government dyads and only include actor dyads that generate 25 battle-related deaths in a calendar year. We aggregate the NSA data to the country level for two reasons. First, our analysis is at the country level and we require cross-national data for our empirical models. Secondly, the NSA data are based on different event data than our study and necessarily include a number of restrictions on which actors are included in the data. This means that the actors in the NSA data do not neatly match every actor in the ACLED data. Nevertheless, we assume that these measures can still provide important information about general conflict dynamics at the country level. Specifically, we aggregate NSA measures to create country-level covariates that proxy the balance of power between armed non-state actors and governments in a given conflict. Our full aggregation strategy can be found in the replication files. To summarize, we first create binary indicators from each row of data for each category of interest in the NSA data. With these indicators, we can then summarize if, on average, rebel groups in a given country were much weaker or much stronger than the government, and if they, on average, tended to have foreign support.

While the ACLED data are available from 1997 to 2020, the availability of other data sources varies markedly. We list the last year of available data for each of the other variables in Table 2. To maximize the possible size of our sample, we run several models. First, we run a “base” model that just includes the variables we derive from the ACLED, which gives us a sample of 42 countries from 1997 to 2020.Footnote ²⁵ The next model we run includes polity, population, gross domestic product (GDP) per capita, and a measure of excluded population from the Ethnic Power Relations dataset (Cederman, Wimmer, and Min Reference Cederman, Wimmer and Min2010). The sample for this model includes 38 countries and ranges from 1997 to 2018. In the last model, we create a binary variable to indicate whether any peacekeepers are active in a given country-year based on data from Kathman (Reference Kathman and Benson2013). We also include controls from the NSA database for rebel strength relative to the government and whether rebels or governments receive support from foreign countries (Cunningham, Gleditsch, and Salehyan Reference Cunningham, Gleditsch and Salehyan2013).Footnote ²⁶ The sample for this final model ranges from 1997 to 2015 and includes 19 countries.

Our dependent variable is a count of the number of civilians killed during a country-year. We retrieve this information from the “Violence against civilians” event type in the ACLED. According to the ACLED codebook, this variable represents “violent events where an organized armed group deliberately inflicts violence upon unarmed non-combatants. By definition, civilians are unarmed and cannot engage in political violence. The perpetrators of such acts include state forces and their affiliates, rebels, militias, and external/other forces. (Raleigh et al. Reference Raleigh2021).” To model this, we utilize a negative binomial framework. We report the results for our “base” models of civilian victimization in Figure 6. The left panel shows results using fixed effects on countries and the right uses random effects.

Figure 6.

Regression results for the base model specification for 42 countries from 1997 to 2020.

Notes: The left panel visualizes coefficient estimates with country-level fixed effects and the right visualizes the results with random effects. Points represent average values of parameters. Thicker lines represent the 90 per cent confidence interval and thinner lines the 95 per cent interval. A darker shade of red (blue) indicates significant positive (negative) values.

In both cases, we find strong support for the effect of network competition on civilian victimization, even after controlling for the overall level of conflict intensity and the number of actors in the network. Next, we test the robustness of this finding by incorporating other factors that have been argued to affect civilian victimization. These models are estimated via random effects, as some of the covariates have little variation within countries over time.Footnote ²⁷ Additionally, many of the control variables that we include have a notable quantity of missing data. As detailed in Honaker and King (Reference Honaker and King2010), simply employing listwise deletion can lead to inferential issues.Footnote ²⁸ We utilize a Bayesian multiple imputation scheme to estimate a posterior of imputed datasets, run our models on ten randomly sampled datasets from the posterior, and then show the combined parameter estimates using Rubin's rules in Figure 7.Footnote ²⁹ The results from this analysis show that the effect of network competition continues to have a substantive impact on civilian victimization even after accounting for the control variables listed in Table 2.

Figure 7.

Regression results from multiply imputed datasets when pairing base specification with controls using random effects for countries.

Notes: Specification in the left panel includes 38 countries from 1997 to 2018 and the right includes 19 countries from 1997 to 2015. Points represent average values of parameters. Thicker lines represent the 90 per cent confidence interval and thinner lines the 95 per cent interval. A darker shade of red (blue) indicates significant positive (negative) values.

We visualize predicted levels of victimization for the effect of network competition using a simulation-based approach (King, Tomz, and Wittenberg Reference King, Tomz and Wittenberg2000). The results of this analysis are shown in Figure 8; each column in Figure 8 corresponds with a model from Figure 7. Irrespective of the controls included, we can see that there is considerable variation in predicted levels of victimization as network competition increases.

Figure 8.

Simulated substantive effect of our measure of network competition across each model.

Robustness Checks

We also ran a number of checks to test the robustness of our findings. We discuss these checks briefly here and invite readers to learn more in the Online Appendix. Given the difficulties in accurately measuring fatality counts from conflict (Dawkins Reference Dawkins2021), we also reestimate our model using a count of one-sided violent events in a country-year as the dependent variable. With this alternative dependent variable, we still find that our network competition measure has a positive and significant effect on the number of civilian victimization events in a given year using either a random- or fixed-effects framework. Another prominent concern is that information from various event datasets can vary widely across countries (Eck Reference Eck2012). Recognizing this, we run our analysis using information from UCDP as well. Ideally, we would like to integrate information from both data sources (Donnay et al. Reference Donnay2019), but such a task would require building a dictionary that can bridge actor-level information between UCDP and the ACLED. Nonetheless, when using information from UCDP, our network competition measure remains positive and significant.Footnote ³⁰

We also test the robustness of our network competition finding to the inclusion of a number of other controls. First, to account for potential persistence in victimization over time, we include a lagged dependent variable, and our findings remain substantively unchanged. We also examine how controlling for the geographic proximity of actors in an armed conflict affects our estimates of network competition.Footnote ³¹ A notable concern here is that high levels of victimization could be a result of actors in an armed conflict being geographically concentrated, rather than being a function of network competition. When controlling for the geographic spread of armed groups, we find that our measure of network competition still aligns with our theoretical expectations. Another potential complicating factor for estimating the effect of network competition on victimization is that low levels of victimization might occur not because network competition is low, but because a high proportion of the armed groups in the network are allied. To deal with this, we estimate a latent measure of amity between groups using the conflict data—in doing this, we are building on a number of works seeking to solve a similar problem (Cheng and Minhas Reference Cheng and Minhas2021; Dorff, Gallop, and Minhas Reference Dorff, Gallop and Minhas2021; Gallop and Minhas Reference Gallop and Minhas2021).Footnote ³² When including a measure representing how many groups are allied in a country-year, we still find the substantive implications of our network competition measure to be unchanged.

Additionally, COVID-19 may impact not only our results, but also even the reporting of conflict data in a number of ways. To ensure that our results are not being affected by this type of exogenous dynamic, we reran our analysis with only data between 1997 and 2019. With this smaller sample, our results for network competition still remain unchanged. Lastly, for the results presented in the article, the underlying sample had a requirement that a country must have at least three years of observations to be included. In the Online Appendix, we examine the results when we set no minimum year requirement and when we set a five-year requirement; in either case, the results for network competition remain robust.

Future Research

In this article, we assert that civilian decision making is central to the competitive environment in which armed groups operate. Despite our inclusion of civilian behavior into our theoretical model, our project is limited in its ability to empirically test outcomes related to civilian agency. We view this as a meaningful, yet necessary, limitation of our study in order to focus on explaining the general relationship between network competition and violence against civilians across country cases. In addition, while the theoretical implications of our model claim we should observe important civilian behaviors—like fleeing—as a response to violence, our model also suggests that a suite of behaviors are possible, such as protest or self-defense, and does not specify which type of civilian behavior we should actually observe. Thus, empirically testing these outcomes is beyond the current study. Future research, however, can build on this work by both better clarifying specific expectations of civilian behavior within this networked theoretical framework and collecting new fine-grained intrastate data to test these expectations. The study of civilians during conflict would greatly benefit from data on both collective civilian acts and the targets of civilian resistance.

In the future, additional research can better incorporate other important factors into our model, such as the ability for armed groups to endogenously enter and leave the model and the possibility that armed groups' reliance on foreign support or lootable goods influences patterns of victimization inside the conflict network. Further, additional empirical research is needed to examine how geography shapes competition in multi-actor contexts and the consequences of geography for victimization in these environments. To operationalize the role of geography within the empirical model from our study, we would require cross-national and time-varying measures of armed actors' control of geographic units. While accurately incorporating this information is beyond the scope of our study, an emerging body of research measuring the geography of armed conflict and territorial control (Anders Reference Anders2020; Haass Reference Haass2021; Kikuta Reference Kikuta2022) provides a promising next step in the accumulation of knowledge on this important topic.