Violent and Non-Violent Strategies of Counterinsurgency

Responses to insurgency include both a large-scale societal reform directed at improving the lives of civilians and a direct military response with no additional programs to improve civilian welfare. In this paper, we ask, what is the optimal combination of aid and military response from the viewpoint of the state? Using a computationalmodel, we evaluatewhatmix of these two strategies helps the government defeat an insurgency more quickly. Our model yields that aidmay boost amilitary strategy that avoids civilian casualties, but it may not compensate for a military strategy that targets civilians indiscriminately.


Introduction
. As the United States continues to find itself engaged in military action against non-state actors in places such as Afghanistan and Syria, understanding the e ectiveness of alternative strategies available to insurgents and counterinsurgents remains an important area of study.Policymakers (Guide to the Analysis of Insurgency ; Nagl ; Petraeus ; Sepp ; Counterinsurgency: The U.S. Army/Marine Corps Field Manual.FM -.MCWP -. ) and academics (Berman et al. , ; Galula [ ]) agree that a government's peaceful interaction with the population is critical in defeating insurgency.Such observers fear that governments can be their own worst enemies when they use violence indiscriminately to try to defeat an insurgency.The advocates of a more peaceful approach emphasize that providing security and aid to the population will increase the support of communities for the government rather than insurgents.But while governments may understand that providing aid to a population in order to sway popular sentiment is a good idea, doing so may be expensive and di icult under violent conditions.And in practice, even proponents of an aid strategy acknowledge that some military action to stop insurgents will be necessary when those insurgents are engaging in e ective violence.The US government explicitly notes that both military and economic means will be necessary to defeat insurgency (Counterinsurgency: The U.S. Army/Marine Corps Field Manual.FM -.MCWP -. , p. -).However, while we understand that states must mix aid and military strategies, it is less well-understood how di erent mixtures of these strategies might succeed or fail at defeating an insurgency.If establishing security and providing public goods are both important in defeating an insurgency, then what is their relative contribution to achieving the desired outcome for the government?In practical terms, how should states allocate their finite resources when designing counterinsurgency campaigns? .
Two findings in the counterinsurgency literature suggest desired elements of a successful counterinsurgency strategy.First, counterinsurgency campaigns that target civilians indiscriminately increase support for insurgency among civilians (e.g., Condra & Shapiro ).Second, small-budget, well-designed, local aid programs that improve civilians' lives increase support for the state among civilians (e.g., Berman et al. ).Based on these findings, a reasonable counterinsurgency campaign would avoid targeting civilians and would provide aid to civilians.Governments frequently face constraints on the total resources available for providing aid or for developing precisely-targeted military campaigns.This leads us to ask: what is an e ective balance between these approaches?Could su icient investment in one strategy overcome the lack of investment in another strategy? .
The military approach may be carried out using either selective or indiscriminate violence, which have opposite e ects on the dynamics of insurgency.Selective state violence punishes based on individual behavior, targeting only rebels or individuals who aided rebellion.Intuitively, such violence has a suppressive e ect on insurgency, as it makes participation in rebellion costlier relative to neutrality or loyalty to the state.The use of selective violence thus deters civilians from joining or aiding the rebellion (Kalyvas ).
. In contrast, indiscriminate state violence punishes civilians based on their a iliation with a group, e.g., their village or ethnic group, regardless of whether individuals took up arms or assisted rebels in any way.Indiscriminate violence makes loyalty to the state costly, sometimes even costlier than neutrality, which means it e ectively encourages civilians to join the rebellion (Kalyvas & Kocher ).Even when civilians do not join the rebels they can assist them by providing or withholding information from the government about the rebels.In particular, when civilians are aggrieved at the government because of indiscriminate state violence, they are more likely to withhold private information about the rebels from the government, thus preventing the government from using selective violence.This leads to further growth of the insurgency (Berman et al. ; Condra & Shapiro ).Empirically, this logic has been supported by multiple studies, and practitioners of COIN have also recognized the importance of avoiding state indiscriminate violence (Counterinsurgency: The U.S. Army/-Marine Corps Field Manual.FM -.MCWP -. ; Petraeus ; Sepp ). .
Given the counterproductive e ect of indiscriminate violence, it is puzzling why states use it.Possible reasons include lack of intelligence (Kalyvas ), bad discipline (Humphreys & Weinstein ), or its ability to drive a wedge between insurgents and civilians (Lyall ).We do not focus on the reasons why a government chooses to use indiscriminate or selective violence, leaving these decisions exogenous in our model, instead focusing on the consequences of these decisions. .Following Bennett ( ), we model both selective and indiscriminate types of violence.The military strategy has two features: (i) state soldiers' ability to identify and capture the target, i.e., intelligence about who the insurgents are and ability to remove insurgents from the population (e ectiveness), and (ii) the extent of collateral damage if any, i.e., how many civilians are hurt during the operation (accuracy).Thus, following Bennett ( ), our model may represent a range of military approaches from pure indiscriminate violence to pure selective violence.
. What is the aid approach?An aid strategy relies on "carrot" operations to persuade civilians to support the central government by delivering political, economic, and development benefits that come in the form of direct aid, employment, medical care, infrastructure, and other non-violent projects (U.S. Government Counterinsurgency Guide , pp. -).We use "aid" as a short cut to describe any services provided to civilians aimed at improving their welfare. .Not every aid program is created equal.Some programs increase support and cooperation from civilians, which in turn allows the government to decrease insurgent attacks.Other programs seem to have no impact on insurgency dynamics.For instance, in the Iraq war, scholars compared the large-scale infrastructure building projects managed by USAID and small-scale programs managed by battalion commanders designed to provide local public goods.They concluded that small-budget programs designed to address specific local needs of communities were more e ective at increasing civilians' support and cooperation than large-budget programs that were attempting to a ect change beyond one local district (Berman et al. , ).Intuitively, among small-budget programs, those designed by groups of specialists with diplomatic, reconstruction, and military expertise were more e ective at garnering civilians' cooperation than programs designed without expert input (Berman et al. ). .
Given these results, we do not focus on global aid programs that could theoretically improve the welfare of the entire civilian population in our model.Instead, we model localized e ects of the aid approach.Since some local programs may be designed without any expert feedback, we allow for the e ects of the aid strategy to vary with respect to the number of civilians recruited at a time and the intensity with which civilians' attitudes change.The state aid approach varies across two dimensions in our model: (i) the number of civilians a ected by an interaction and (ii) the intensity of change in the a ected civilians' attitudes.As a result, a well-designed small-scale program would increase the approval of the government among more civilians than a poorly-designed program. .
Insurgents may also use non-violent recruitment strategies to increase their ranks of fighters and their support among civilians.Sometimes, insurgent organizations fill the void of governance and provide both public goods and law enforcement services to the population.For instance, Al-Qaeda in the Arabian Peninsula distributed water to families in Southern Abyan during summer heat, installed electric lines to communities that never had electricity before, and helped carry out investigations about stolen property (Johnsen , p. ).In other cases, insurgent organizations invest less in communities, instead seeking new recruits through individual monetary benefits or emphasis on one's group identity.For instance, the Taliban has focused its recruitment e orts on providing attractive salary packages combined with appealing to Pashtunwali cultural notions of honor (European Asylum Support O ice ).To use Olson's ( ) terminology, in our model, both the state and the insurgents are acting partially as "stationary bandits" as we model the struggle between the two political organizations to increase their territorial control over a given locality.It thus makes sense for insurgents as well as the state soldiers to provide some services to the population and avoid stealing % of the civilians' profits to extract greater returns in the longer term. .
In short, both sides of the conflict use non-violent means to win the approval of the population, eventually controlling it.While no empirical work has systematically studied the quality of insurgent use of the aid strategy, we assume that some e orts of the rebels' non-violent methods of recruitment work better than others.Thus, we model the quality of the rebel aid approach as varying across the same dimensions as the government aid: the number of civilians a ected by an interaction and the intensity of change of civilians' attitudes. .Why model these two approaches simultaneously?Recent empirical work in the counterinsurgency literature has concluded that it is the synergy between a government's aid and military strategies that is key to suppressing an insurgency (Berman et al. ).In other words, we should expect that a combination of the military action that targets insurgents without harming civilians and small-scale aid programs that address a specific local need will have a better chance at defeating an insurgency than state e orts that harm civilians and employ large-scale projects that bypass local community needs.It is less clear how di erent mixtures of these strategies might succeed or fail at defeating an insurgency.If the military and aid approaches are both important, then what is their relative contribution to achieving the desired outcome for the government?The use of a computational model allows us to compare various combinations of strategies by insurgents and counterinsurgents and determine which approach plays a more important role in defeating an insurgency.

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Our model does not represent counterinsurgency comprehensively.Rather, following Epstein ( ), it illuminates one element of this phenomenon, the relative contribution of non-violent and violent methods to the success of counterinsurgency.Previous models captured the relative weight of selective vs. indiscriminate targeting of insurgents (e.g. ).The complete pseudo code is included in the Appendix.The model parameters and their default values are listed in Table . .
Time: In the course of each simulation model run, the interactions among agents (the actors in the model) may develop into a defeat of insurgency (all insurgents are removed which terminates the run) or a sustained insurgency (if the simulation reaches , ticks, it terminates the run).The sequence within each tick is described in the following subsections and is represented graphically in Figure .Each tick includes an action sequence by a randomly selected insurgent, followed by an action sequence by a randomly selected soldier.A selected insurgent probabilistically decides between attacking a soldier, which always triggers a counterattack by a soldier, and peacefully recruiting civilians, which probabilistically triggers a counterattack by a soldier.Then, during state turn, a selected soldier probabilistically decides between attacking an insurgent and peacefully recruiting civilians (providing aid).One may think of a model's tick as an hour or perhaps a day.While time units are not defined in this model, it makes sense to think of a tick as a rather short period of time. .

Agents:
The model assumes two core types of agents: civilians, who may become rebels/insurgents, and soldiers, who never change their identity.We make no assumptions about social groupings among civilians, continuing to rely on "light" agents, as Bennett ( ) does.
. Civilians represent the bulk of a population.Individual civilians are characterized by a degree of anger at the government, a degree of fear of the government, and a violence threshold, i.e., a propensity to use violence under the right circumstances.A rebel/insurgent is a civilian who is willing to engage in violence against the government, and specifically against a nearby soldier (who represents the government).Insurgents in turn may be latent, i.e., willing to engage in violence, or active, i.e., having actually done so.Growth of insurgency occurs in the model when ordinary civilians turn into insurgents.A civilian becomes a latent insurgent when the civilian is angrier at the government than afraid of it (anger it > f ear it ), and if their anger passes an individual threshold propensity to use violence (anger it > violence threshold it ).If a latent insurgent is within a defined range of a soldier and is given an opportunity, then the latent insurgent will conduct an attack and become an active insurgent. .The insurgents' assumed goal is to convert more civilians into insurgents.Each tick, a randomly selected latent insurgent either attacks a nearby soldier (if P IR is less than a random draw from a uniform distribution) or uses the aid strategy to peacefully recruit nearby civilians (if P IR is greater than or equal to a random draw).The general activity of "peaceful recruitment" covers many specific actions on the ground that a civilian could use to express his or her anger at the government, including secretly recruiting followers, participating in a protest to express displeasure, writing or blogging or posting, or using many other specific activities designed to create attention and draw followers to the insurgents' cause. .Soldiers' assumed goal is to remove all of the latent insurgents from the world, thereby defeating the insurgency.Soldiers target insurgents to pursue this goal.Each tick, a randomly selected soldier either attacks an active nearby insurgent if there is any (if P GR is less than a random draw from a uniform distribution) or uses the aid strategy to peacefully recruit nearby civilians (if P GR is greater than or equal to a random draw).By default, soldiers are placed on the grid. .Space: We did not alter the simulation space from Bennett's ( ) model, thus the space in the model is simulated by a two-dimensional grid (not a torus) of rectangular cells (by default, the size of the grid is by cells).Agents interact only with their neighbors, where neighbors are defined as all actors within a specified Moore distance ( cells by default).We may think of this space as a city district, or a city, or a country.Each agent occupies one grid cell, and only one agent can occupy one cell.The agents do not move.) model, on which we based our COIN model.P IR , represents the probability that an insurgent will recruit, i.e., employ the aid strategy, this turn.p i+n represents a simple draw from a uniform distribution.P IEW R represents the probability that an insurgent is exposed when it recruits.P GR represents the probability that a solder will recruit, i.e., employ the aid strategy, this turn.P IR , P IEW R , and P GR are among the systematically varied parameters of the simulation.For details, see Equations , a, b and Tables -. .World Map Display: We also did not alter the display of agents from Bennett's ( ) model.Agents are displayed in the space via di erent colors and shapes.Civilian agents may be green (anger<fear<violence threshold), yellow (anger>fear and fear<violence threshold), orange (latent insurgents, i.e., anger>fear>violence threshold), or red (active insurgents, i.e., a latent insurgent that carried out an attack).Soldier agents are represented by blue squares, outlined in red when soldiers are attacked by active insurgents.

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Modeling the military approach: As Figure shows, there are three circumstances in which soldiers may use the military action: (i) during a soldier's turn, a soldier may probabilistically determine to attack, given that there is an active insurgent in the neighborhood; (ii) during an insurgent's turn, a soldier responds to an insurgent attack with a counterattack; (iii) during an insurgent's turn, a soldier responds to an insurgent's use of aid, if an active insurgent is detected during peaceful recruitment.While a significant portion of violence in civil conflicts is remote, e.g., the use of improvised explosive devices by the rebels or the use of drones by the government, here we only model direct violence.Future research should explore the consequences of remote violence on duration of insurgency.
. A soldier executes the military action by removing (capturing or killing) an insurgent with a probability equal to the soldier's level of e ectiveness, i.e., P(Soldier Removes Insurgent)=e ectiveness.This parameter captures soldiers' ability to identify who the insurgents in the population are and target them.In other words, it is uncertain if soldiers will be able to identify who the insurgent is a er observing an attack occur.The e ectiveness parameter is supposed to capture the di iculty of obtaining intelligence about who the insurgents are in a population.
. The probability that a soldier's counterattack inflicts collateral damage on each civilian in the neighborhood of the targeted insurgent is parameterized by the soldier's level of accuracy, i.e., each nearby civilian is injured with probability P(Soldier Injures Civilians)= −accuracy.Furthermore, multiple civilians may be hurt in the soldier's counterattack creating a temporary variable Number of Civilians Injured, which records the number of hurt civilians for a current instance of soldier counterattack.When any civilian is hurt, his or her level of fear of the government increases (a deterrent e ect), as shown below each civilian i in tick t + 1: In addition, a civilian's level of anger also increases.Furthermore, anger increases in proportion to the total number of civilians injured by the soldier's attack and the amount of increase accounts for whether a soldier was provoked by an insurgent, as follows: where for each civilian i in tick t+1, anger level will be updated following Equation a, if a soldier was provoked and counterattacks during an insurgent's turn.By contrast, civilian anger will be updated following Equation b if a soldier attacks during a soldier's turn without being provoked.In other words, we assume that civilians will not get as angry by soldiers' harming bystanders if the soldiers were responding to an insurgent attack.All civilian characteristics are bounded between and , such that if any value exceeds these boundaries it is reset to a boundary level.When anger and fear change, new latent insurgents may be created, or an insurgent could potentially be pushed back to being a regular civilian.
. Consider an example.Two civilians got injured during a soldier's counterattack.Civilian A had fear of .and anger of ., while civilian B had fear of .and anger of . .Civilian A's fear will update to ., while civilian B's fear will update to ., showing the "diminishing return" in fearfulness to reflect that over time it takes more extreme actions to provoke the same response in human beings (Bennett , .).Similarly, civilian A's anger will update from . to ., while civilian B's anger will update from . to . .If civilians A and B were injured in an unprovoked attack by a soldier, then their fear in tick t + 1 would have been the same as a er a counterattack, but their anger levels would have been .and .respectively.

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The model assumes that soldiers do not die.In addition, the supply of civilians is e ectively infinite: although insurgents die and are removed, they are always replaced with a randomized civilian (not necessarily a new insurgent) placed somewhere in the world grid.
. Modeling the aid approach: Both soldiers and rebels probabilistically decide between attacking their opponents and employing aid to recruit nearby civilians peacefully.The probability of each action is set exogenously, and globally (one value for all soldiers, one for all civilians).This exogenous, centralized probability setting provides direction across agents.If a central government or other command structure were to dictate (and rigorously enforce) that one option was always to be followed, the probability of one action would be set to % or %.Alternatively, as agents have more discretion/freedom, the probability will be closer to %.In other words, we are specifying that the proclivity to carry out aid projects is set centrally, but communication, impact, and reaction come from local gains/visibility of these projects.A future project could expand the spread of information by expanding the radius of interaction/view around any action.We suspect that this would accelerate the dynamics of the model rather than make a fundamental change, but fully exploring the implications of global communication/information remains for further work. .
If a soldier chooses to use the aid strategy during his or her turn, then the soldier will gain support decrease the anger of a Number of Recruitable Civilians by Soldier by a given increment Anger Change Given Soldier Recruitment.Both parameters are varied systematically in the model, as described in Table .The Number of Recruitable Civilians by Soldier takes on values of , , and civilians.The increment by which civilians' anger declines varies as -. , -. , and -. .The recruited civilians' anger in the following tick is updated as: For example, civilians A and B, whose anger levels were .and .respectively in tick t, were recruited by a soldier that was assigned to recruit civilians decreasing their anger by . .In tick t + 1, A's anger will become (-.would be updated to ) and B's anger will become . .If the soldier was able to decrease civilians' anger only by ., then updated anger levels would be .
for A and .for B.
. When a rebel chooses to use aid, she or he is assumed to increase the anger of a Number of Recruitable Civilians by Insurgent (systematically varied in the simulation between , , and ) by a certain increment, Anger Change Given Insurgent Recruitment (systematically varied between ., ., and .).The a ected civilians' anger in the following time unit will be: For instance, the same civilians A and B, whose anger levels were .and .respectively in tick t, were recruited among the other civilians by a rebel.The rebel was able to increase civilians' anger by . .In tick t + 1, A's anger will become .and B's anger will become . .If the soldier was able to decrease civilians' anger only by ., then updated anger levels would be .
for A and .for B.
. As with the attacking insurgents, detection of peacefully recruiting insurgents is uncertain.When insurgents attack, in the simulation code, they are revealed to soldiers, but soldiers may have low ability to identify and remove insurgents, i.e., low e ectiveness, thus we say that identifying true insurgents is uncertain, as the probability of their capture varies.The probability of insurgent exposure when recruiting, P IEW R , is varied between , ., and . .This modeling choice leads to insurgent attacks always triggering soldiers' counterattack (that may or may not remove the insurgent or injure innocent bystanders), while peaceful recruitment triggers soldier counterattack with probability P IEW R .This modeling choice reflects the underlying reality that violent action is easier to detect and justify a response to.While perfect detection of peacefully recruiting rebels is unrealistic, we investigate this scenario to understand whether the gains from intelligence are linear.They are not, as explain in the analysis section.

Example Runs
. Each run of the simulation produces an entire history of interactions between soldiers and rebels, and continues either until the insurgency is defeated (no latent insurgents remain in the world), or , ticks are reached (loosely indicating a self-sustaining insurgency).

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We illustrate the dynamics of the simulation by showing the termination state display output for nine individual runs in Figures , , and   .The central display titled "Actors" shows the counts of actors and events in the simulation run over time.The y-axis shows a simple count of agents and instances of events; one unit on the y-axis represents agents/instances.The x-axis represents time; one unit of the x-axis represents , ticks.In all nine runs, this display shows that the simulation has civilians at all times (shown in blue), because we replace each killed insurgent with a randomly placed civilian.In addition, the central display tracks the number of active insurgents (shown in red), number of latent insurgents (green), cumulative number of insurgents killed (black), and the number of recent attacks (orange).The rightmost display "Anger/Fear" shows the average levels of anger and fear among civilians over time.Both anger and fear are bounded between and and so is the y-axis of the rightmost display.The x-axis represents time; one unit of the x-axis represents , ticks.
. presents scenarios in which soldiers use a well-designed aid program % of the time, but insurgents never use aid.Anecdotal evidence suggests that most rebel groups provide at least some public goods to the local communities, so this scenario is unrealistic.Yet, it is useful as a hypothetical best-case scenario for the government.Finally, panel (c) shows scenarios in which both soldiers and insurgents employ well-designed aid programs % of the time.By "welldesigned" aid programs we mean those that a ect nine civilians at a time and decrease/increase civilians' anger by the greatest increment of -. (for soldiers) and .(for insurgents). .
Finally, we used the random seed of for each of the nine runs to ensure comparability among the nine runs.
. The role of aid for soldiers of low accuracy and e ectiveness.Consider Figure , which shows scenarios of soldiers with low accuracy and e ectiveness (both .), a "nightmare scenario for most governments. . .[that] might fit the case of fighting an urban counterinsurgency campaign, where insurgents have many places to hide, and where noninsurgent civilians are densely packed" (Bennett , .).All three scenarios ( a, b, and c) are forced to stop at the , th tick, indicating that an insurgency spreads throughout the entire population and becomes established in a given territorial unit.
. Compared to scenario a, the introduction of soldiers' aid strategy ( b) lowers the average level of anger in the population, as shown in the Anger/Fear display.In scenario a, it takes only ticks for soldiers to create a hostile population (at tick , average anger exceeds than average fear and remains close to or above .for the rest of the model run).When only soldiers employ aid ( b), the average anger never surpasses average fear; it takes , ticks for the average anger to reach .for the same inaccurate and ine ective soldiers (in a the average anger of .was reached at ticks ).When both rebels and soldiers employ aid ( c), the average anger approaches but never surpasses average fear and it takes , ticks to reach the average anger of . .

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Introducing aid gives soldiers fewer opportunities to remove insurgents, thus, the cumulative number of killed insurgents declines from , in scenario a with no aid to in b and in c.Recall that soldiers target insurgents as a response to insurgent attack and during soldier turn (on patrol).This is why introducing soldier aid strategy % of the time does not cut the number of removed insurgents in half.Furthermore, if rebels recruit civilians peacefully ( c), they further reduce soldiers' opportunities to counterattack and remove insurgents from the population as insurgent exposure when they recruit is probabilistic.

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Fewer opportunities to attack, combined with insurgents raising civilians' anger in addition to soldiers' angering civilians by creating collateral damage, leads to % of the population becoming active insurgents by the end of run c.This large number of active insurgents is also shown by clusters of red circles in world map display in panel c.By contrast, only % and % of civilians constitute active insurgent at the , th tick of runs a and b respectively, implying that if the runs a-c were not interrupted at the , th tick, scenario c would have lasted much longer than a and b.

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In summary, soldiers that miss insurgent targets and injure civilians % of the time cannot defeat an insurgency at its early stages, even when they employ aid.While relying on aid helps slow the speed of growth of insurgency, aid cannot compensate for the dangerous e ects of ine ective and inaccurate military action.
. The role of aid for soldiers of medium accuracy and e ectiveness.Consider Figure , which depicts end-state output from three scenarios of soldiers with medium accuracy and e ectiveness (both .).Scenario a is consistent with Bennett's ( ) finding that once soldiers capture targets and avoid hurting civilians at % of the time or more, an average duration of insurgency drops considerably.Scenarios a, b, and c end before the , th tick, indicating that an insurgency does not become sustained in a given territorial unit.Adding aid strategy creates a wide variation in the duration of insurgency: the a run with no aid ends at the , th tick, the b run with soldiers' aid ends a er ticks, and the c run with both sides' aid ends at the , th tick. .Relative to scenarios a and b, the c run describes a more realistic situation of both sides employing aid.Allowing aid on both sides extends insurgency more than twofold compared to the a run and more than twelvefold compared to the b run.This is due two reasons: (i) soldiers go on patrols % less, since they recruit half the time, thus they can remove half of insurgents in a given time period, and (ii) insurgents that peacefully recruit civilians are not always detected by soldiers.
. In the cases with medium accuracy and e ectiveness, average anger in the population never surpasses average fear.In scenario a, the highest level of average anger is ., while introducing soldiers' aid in b lowers the highest level of anger achieved to . .When both rebels and soldiers employ aid ( c), the average anger reaches the .level at about the same time as the peak anger is reached in the a run with no aid (around the th and th tick respectively).
. Lower levels of average anger among civilians also mean that the runs in Figure end with lower proportions of latent insurgents than the runs in Figure .In the c run, insurgents raise civilians' anger at the government via aid, making .% of civilians latent insurgents.This proportion is still much lower than half the population being latent insurgents by the end of the scenario c.
. In summary, soldiers that miss insurgent targets and injure civilians % of the time defeat an insurgency at its early stages regardless of the aid approach.It is important to note that for the cases of soldiers' medium levels of accuracy and e ectiveness, the set-up of the aid strategy may extend the duration of insurgency more than twice when both soldiers and insurgents peacefully recruit.).Scenario a is consistent with Bennett's ( ) finding that once soldiers capture targets and avoid hurting civilians at % of the time, an insurgency is defeated swi ly (in just ticks in the a run).Among scenarios a, b, and c, the latter depicts the longest insurgency that ends a er ticks, still a very short insurgency compared to the runs of Figure .This further demonstrates that the levels of accuracy and e ectiveness of soldiers' military action are the primary determinants of the duration of insurgency.This is not to say that the aid strategy does not matter.For instance, letting both soldiers and insurgents recruit half the time in the c run extends an insurgency more than nine-fold relative to scenario a. Yet, even this extended duration is very short when compared to runs with low/medium e ectiveness and accuracy.

Analysis of Repeated Simulations
. The duration of insurgency is an emergent feature of our model, such that if the soldiers have no latent insurgents in their range, the insurgency is considered defeated.Alternatively, reaching , ticks terminates a run, loosely indicating a self-sustaining insurgency.We evaluate the output of the simulation, assuming that government actors prefer insurgencies that are shorter and rebel actors -longer.

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Table specifies the discrete values of key initialization parameters and details the total number of unique combinations of parameter values: parameters were varied across discrete values, while parameters were varied across values, resulting in (10 4 )(3 5 ) = 2, 430, 000 unique combinations of parameter values.Since the model has stochastic elements, we analyze summaries of multiple histories generated from the starting value sets to determine reliable trends that appear across multiple iterations of the model, rather than examining a single run which might not be representative.million simulation runs were recorded and collapsed into a dataset of . million observations, such that each observation is an average of to runs of the model at each unique combination of parameter values.
. Baseline e ect of the quality of the military approach.Figure shows the duration of insurgency varying as a function of the quality of the military strategy for those cases when neither side uses aid strategy (also see row in Table .for more precise mean and variance values).
. We use this surface as a baseline for comparison with the scenarios discussed below.In this and subsequent graphs, the height represents duration of insurgency (bounded between and , , where the maximum point represents the cuto , at which we assume that insurgency cannot be defeated).Length and depth of the graph represent soldiers' e ectiveness and accuracy (both bounded between .and .), two features that define the quality of the military strategy. .
Figure shows a reverse relationship between the quality of the military strategy and the duration of insurgency: insurgencies are longest when accuracy and/or e ectiveness are low and shortest when those levels are high.If soldiers miss targets more than % of the time (e ectiveness< .), it takes a high level of accuracy to defeat an insurgency (accuracy> .).If soldiers create collateral damage more than % of the time (ac-curacy< .), improvements in e ectiveness lead to shorter insurgencies.If both accuracy and e ectiveness improve above %, insurgencies can be defeated rapidly.
. Baseline e ect of the quality of aid: Both sides (soldiers and rebels) may employ the aid strategy.  .The main takeaway of Figure is unsurprising: one's decision to abandon the aid strategy benefits the opponent.As panel a shows, if insurgents never employ aid, while state soldiers use well-designed development programs % of the time, then even militarily inaccurate and ine ective soldiers will defeat insurgency (all cases of insurgency end under , ticks, thus not one case becomes a sustained insurgency).Similarly, if soldiers never employ the aid strategy, yet rebels are able to a ect multiple civilians at a time, then whether insurgents will succeed at reaching , ticks depends entirely on how accurate and e ective the soldiers are.If soldiers locate targets at least % of the time (e ectiveness≥ .) and avoid hurting civilians at least % of the time (accuracy≥ .) they will be able to remove all insurgents before it reaches , ticks.Furthermore, if soldiers' e ectiveness and accuracy≥ ., they defeat insurgency very quickly (in under , ticks).While these scenarios are unrealistic, they help illustrate that even when soldiers ignore aid, they still can defeat an insurgency if their military response relies on intelligence and avoids hurting civilians.

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Is the military or aid approach more important in defeating insurgency?Our model yields that, for soldiers to defeat an insurgency, improvements in accuracy and e ectiveness are more important than improvements in the two features of the aid strategy: the number of recruitable civilians by soldier and anger change given soldier recruitment.In other words, if the model's assumptions capture insurgency dynamics adequately, it is more critical for soldiers to invest in their ability to acquire intelligence about who the rebels are (parameterized by e ectiveness) and do so without hurting bystanders (parameterized by accuracy), than to invest in designing such economic development programs that would improve the welfare of more civilians.
. Table .presents average durations of insurgency by the features of the aid strategy and by the features of the military approach.Horizontal scenarios are numbered from to .Each scenario contains five rows to present durations of insurgency as the average, standard deviation, th percentile, median, and th percentile.
The scenarios are labeled as high, medium, and low quality of the aid program's design, parameterized by the number of recruitable civilians by soldier/insurgent and the anger change given soldier/insurgent recruitment.In addition, each scenario contains three columns that represent high, medium, and low levels of accuracy and e ectiveness of soldiers' military action respectively.
. For each scenario presented across rows of Table ., improvements in the quality of the military approach lead to greater reductions in duration of insurgency than improvements in the quality of aid.In other words, di erences across columns of Table .are greater than di erences across rows.The e ect of aid quality is especially small in the rightmost column of cases with inaccurate and ine ective military approach: with one exception (discussed in the following subsection), all average durations are less than a standard deviation away from a sustained insurgency ( , ticks).In our simulation, it is possible for soldiers to defeat rebels when soldiers' aid strategy a ects only a few civilians but their military strategy is e ective and accurate.In contrast, it is impossible for a government to defeat an insurgency if soldiers a ect a lot of civilians through aid programs but cannot identify rebels or capture them without hurting bystanders.  .Could the use of aid ever compensate for a low-quality military strategy?The simulation suggests that a government may not avoid a sustained insurgency under an ine ective and inaccurate military strategy by relying on aid.The only exception to this trend is described in the dark-gray column of scenario of Table .: the average, median, and th percentile durations of insurgency under scenario are , ., , ., and , .respectively, i.e., this is a long insurgency.In this scenario, inaccurate and ine ective soldiers a ect nine civilians through aid programs at a time, while insurgents influence only one civilian through aid at a time.] We assume that this scenario is unrealistic, because in practice, insurgents would be better o either increasing their peaceful recruitment e orts or forgoing recruitment altogether, letting the inaccurate and ine ective military action by soldiers backfire even more (since insurgent attacks always trigger soldier counterattacks, while a counterattack a er insurgent recruitment is based on the probability that an insurgent is exposed given it recruits, P IEW R ).

.
In contrast, under a more realistic set-up in which both sides rely on e ective aid strategy, the simulation yields that soldiers cannot defeat insurgents with an ine ective and inaccurate military approach (see scenariosof Table .).Specifically, scenario of Table represents a case of both soldiers and rebels employing a welldesigned aid strategy, i.e., both types of agents a ect nine civilians at a time and change civilians' anger by the amount of -. for soldiers and .for insurgents.Under scenario , consider the low quality of military response scenario that summarizes durations of insurgency for the ine ective and inaccurate military approach (soldiers miss targets and injure civilians more % of the time).The median insurgency under these conditions lasts , .ticks and the th percentile insurgency is considered self-sustaining, interrupted at , ticks.
. In fact, with the exception of the aforementioned scenario , all median insurgencies under the conditions of inaccurate and ine ective military approach exceed , time units, i.e., represent prolonged conflicts.Given that the , th tick cut-o point is arbitrary, we should not put too much weight on the di erence between insurgencies that end just short of , and those that are interrupted at the , th step.
. Finally, our model suggests that when both sides use the aid strategy, insurgencies survive much longer -even for the most accurate and e ective military operations -than in the cases when the aid strategy is omitted.Compare all cases of using aid % of the time on both sides (scenario of Table .) to the baseline scenario of no aid on either side (scenario of Table .).The average duration of insurgency in scenario is on average .times greater than in the scenario .The di erences are especially pronounced when comparing the scenarios of more e ective and accurate military action: insurgencies last on average ticks in scenario vs. ticks in scenario for the soldiers that capture targets and avoid collateral damage > % of time.Furthermore, an average insurgency lasts ticks in scenario vs. ticks in scenario for soldiers that capture targets and avoid collateral damage -% of time.At the same time, when comparing the militaries of low accuracy and e ectiveness across the recruitment scenarios, the di erences are negligible.This is an artificiality introduced by the arbitrary cut-o point of , ticks.Future research may want to consider other cut-o points to investigate whether all inaccurate and ine ective military strategies are equally bad for the government.In summary, our main finding that emerges from Table .is that inaccurate and ine ective military approach cannot be compensated for by a well-designed aid program.The role of intelligence.Our simulation further yields that collection of intelligence is critical to soldiers' success.We model intelligence collection though two parameters: the probability of locating and removing the attacking insurgents (e ectiveness) and the probability of locating the peacefully recruiting insurgents (P IEW R ).
In those scenarios when both of these probabilities approach , soldiers cannot defeat insurgency.
. That is, if soldiers have no information about the peacefully recruiting insurgents, but locate the attacking insurgents and avoid collateral damage at least % of the time (e ectiveness and accuracy both at .), then an average insurgency lasts more than , ticks, very long but finite.In contrast, if soldiers obtain intelligence about the peacefully recruiting insurgents % of the time (Figure b) and locate the attacking insurgents and avoid collateral damage % of the time, then an average insurgency lasts about , ticks.That is, even when soldiers can detect peacefully recruiting rebels % of the time, they still cannot target them e ectively and accurately.This di erence is much more pronounced between Figures a and b, as high accuracy and e ectiveness of soldiers' military approach can be further improved by greater detection of the peacefully recruiting rebels (note the maximum duration of insurgency of only , ticks in b, as opposed to , in a). Figure a shows there exists a narrow scenario in which even the soldiers that avoid collateral damage and capture insurgents at least % of the time cannot prevent an insurgency from becoming a self-sustaining one.This happens if soldiers obtain no intelligence on peacefully recruiting rebels and rebels use the aid strategy % of the time, implying that only % of the time they attack, revealing themselves to the soldiers.

.
Are there any cases when greater reliance on aid is undesirable for counterinsurgents?The model further suggests that -from the viewpoint of soldiers -a well-designed aid strategy is always preferable for accurate and e ective military operations, while being futile for the inaccurate and ine ective military campaigns.ticks.Under inaccurate and ine ective the military strategy the shorter insurgencies occur when insurgents recruit at most % of the time and soldiers recruit -% of the time.This hypothetical case -albeit unlikely -underscores the importance of somehow limiting rebel use of the aid strategy when no opportunity to limit civilian casualties exists.
. In contrast, under an accurate and e ective military strategy when soldiers miss their targets and cause collateral damage less than % of the time (shown in graphs a-b), rebels rarely achieve a self-sustaining insurgency (compared to Figures a-b).Under these circumstances, a higher rate of soldiers' use of aid reduces the average duration of insurgency.
. Finally, obtaining any intelligence about rebels' use of aid is more important for soldiers than obtaining perfect intelligence.We have also graphed the surfaces in Figures and with soldiers' ability to detect peacefully recruiting rebels perfectly, i.e., P IEW R = .(the graphs are omitted for space).While some intelligence makes a big di erence for the accurate and e ective soldiers (the di erence between a and b), perfect intelligence does not provide as much gain in reducing the duration of insurgency for the state. .In summary, a greater reliance on aid only helps soldiers if they avoid collateral damage more than % of the time and obtain at least some intelligence about who the recruiting insurgents are.This conclusion underscores how critical the assumption that civilians trade intelligence for aid is (Berman et al. , ; Condra & Shapiro ).Table .and Figures , , demonstrate that neither side undermines its cause by employing a (well-designed) aid strategy, yet, soldiers cannot compensate for an ine ective and inaccurate military action by using peaceful recruitment.The relative weight of military strategy (compared to aid) is greater when considering how both COIN strategies a ect the duration of insurgency.

Limitations and Future Work
. This work does not exhaust the possible modeling choices with respect to how states and insurgents implement the aid and military strategies.Future work could consider, for instance, an adaptive value for soldiers' probability of employing the aid strategy.While we have modeled the government's strategy to employ aid programs as an externally given value, we could allow governments to adapt their strategy in response to the perceived number of insurgents, perceived level of civilian anger, or insurgent strategy.Strategy adaptation could be applied to the insurgents' probability of using aid (as opposed to violence) as well.
. There are also fundamentally di erent ways that action sequences could be modelled in a simulation of insurgency.For example, the model could be restructured such that instead of one insurgent and one soldier engaging each tick, all insurgents and all soldiers act in each tick.This modeling choice would ensure that none of the available soldiers stays unengaged, which could theoretically happen in the current version of the model, as it is conceivable that a soldier is not randomly picked throughout the entire run.We believe that this restructuring would have the primary e ect of speeding up the simulation as multiple actions have e ects at once; it could also remove the possible e ect of sequential activity and path dependence.It is possible that a similar e ect could be obtained in the current sequence by expanding the reach of "media" in the simulation so that actions have less-localized e ects on civilians' anger and fear.For instance, if civilians in a nearby province are made aware of either a successful local aid project or of an attack killing civilians, the e ects of the action will spread more rapidly.
. We could also explore di erent types of resource constraints on governments.Our model considers the limitation of state resources only to an extent: there are soldiers at all times in our model and if the state employs the aid strategy % of the time, then a er, say, ticks (if insurgency survives until then) on average soldiers will have engaged in peaceful recruitment of civilians and soldiers will have employed military action.The current model represents the tradeo between aid and military action only in the number of soldiers available and each soldier's inability to do both actions during the same tick.An alternative representation of a tradeo that governments face could involve consideration of the cost of aid vs. military action, and the cost of deploying (soldier) agents to implement those strategies.

Conclusion
. Recent arguments in the counterinsurgency literature suggest the importance of using peaceful aid strategy in conjunction with, or in place of, the military strategy when seeking to defeat an insurgency.To understand the relative importance of each strategy and to evaluate the reasonable balance between the aid and military approaches, we developed a computational model of insurgent and soldier interactions in which both types of agents can either peacefully recruit civilians or undertake military attacks on the opponent.A series of computational experiments established four major implications of our model.First, a high-quality military strategy, i.e., attacking insurgents without harming civilians, is more important for defeating an insurgency than aid.Second, aid cannot compensate for a low-quality military strategy.Third, investing in obtaining at least some intelligence is critical for the government; however, the gains in improving from imperfect intelligence to perfect intelligence are not as dramatic.Finally, soldiers benefit from a greater reliance on aid only if they can obtain some intelligence about the insurgents' aid activity and soldiers avoid collateral damage during military engagement at least half the time.
. When it comes to evaluating the best strategies for insurgents, our model suggests that when facing a poorly trained army, increasing recruitment activities is unnecessary for insurgents, as government troops create more rebels than they kill by their inaccurate and ine ective attacks.In contrast, when insurgents face a well-trained military operation, they are better o avoiding attacks altogether.In this case, recruiting civilians in as much secrecy as possible yields better results for insurgents.
. The first two takeaways may be combined into a testable hypothesis: greater amounts of aid provided to those regions where military strategy avoids civilian casualties are expected to suppress insurgent attacks.In contrast, investing in areas where military operations abuse loyal civilians is expected to be counterproductive.I f t h e r e i s an exposed i n s u r g e n t i n t h e i r neighborhood , s o l d i e r p r e e m p t i v e l y t a r g e t s an exposed i n s u r g e n t A .G i v e n t h e a t t a c k , t h e s t a n d a r d c a p t u r e / c o l l a t e r a l damage / update sequence i s f o l l o w e d B .
Because t h e s o l d i e r c o u n t e r a t t a c k was not i n r e s p o n s e t o an i n s u r g e n t , a n g e r i n c r e a s e s a t a h i g h e r r a t e ( d ) I f s o l d i e r −s e l e c t e d a c t i o n i s t o r e c r u i t ( by d o i n g good works i n t h e neighborhood ) i .I f t h e r e i s a c i v i l i a n i n t h e s o l d i e r ' s neighborhood , i t may be r e c r u i t e d , up t o a number s p e c i f i e d i n a model parameter A .R e c r u i t e d c i v i l i a n s e x p e r i e n c e an a n g e r d e c r e a s e B .No worry about c o l l a t e r a l damage .Repeat from s t e p u n t i l no l a t e n t o r a c t i v e i n s u r g e n t s remain , o r t i c k s a r e r e a c h e d .

Notes
Our focus on these strategies does not deny that many scholars have investigated the importance of multiple other factors in influencing the course of an insurgency or civil war.E.g., we could consider (i) the absence of di icult terrain and the absence of natural resources that could fund a rebel organization (Collier & Hoe ler ; Fearon & Laitin ; Ross ), and (ii) ethnic sorting and cleansing (Agnew et al. ; Weidmann & Salehyan ).Our simulation ignores these other independent factors for the moment; it could be expanded in the future if we would expect these factors to confound our results.
The most interesting dynamic of Bennett's ( ) model emerges at low rates of soldiers capturing targets, which could approximate situations of soldiers having no intelligence about who the individual insurgents are in the population.For instance, in a scenario of soldiers capturing targets % of the time, militaries can never defeat an insurgency if they avoid collateral damage % of the time or less, while gains in avoiding collateral damage beyond % of the time will generate dramatic reductions in insurgency duration (Bennett , . ).This e ect is replicated in Figure .Other common labels include "enemy-centric" (Guide to the Analysis of Insurgency ) or "hard-power" (Rineheart ).
For instance, see ) for divergent findings.
An important caveat to these findings is that empirically, aid disbursements in Iraq seemed to suppress insurgent attacks only in those areas that a government controls, while actually increasing insurgent attacks in areas of split control (Sexton ).Since government / insurgent control over territory is an emergent characteristic of our model, we cannot directly compare the underpinnings of our model to Sexton's ( ) findings.However, our model's result that the military approach is important at defeating insurgency is consistent with Sexton's ( ) findings: first, soldiers need to secure an area, then, work on increasing support for the government.
The simulation was programmed in Java.
While one might think of plausible alternative distributions for initial fear, initial anger, and violence threshold in the population, in this version, we follow Bennett's ( ) default values for these parameters to make comparisons with the baseline model more straightforward.
While we do not separate these activities (e.g.protest vs. quiet action) explicitly, a future version of the model could expand the action set, or by focusing on additional subsets of civilians, like those whose anger is greater than fear, yet the violence threshold has not been met.
The precise means by which a soldier attacks an insurgent (or vice-versa) is le undefined in the model, it is possible that an actor could be using some method of violence that is not face-to-face.
We also analyzed additional emergent features of the simulation, notably speed of growth (measured as the time until % of the population become latent insurgents), peak number of latent insurgents, and peak number of active insurgents.Analyses of these features support the same conclusions as presented here.For details, see   The exception being a scenario in which the insurgents recruit % of the time and there is no exposure of the recruiting insurgents (see Figure a).
The exception being a scenario in which insurgents do not recruit at all (see Figure b).Across all levels of aid quality in Table ., Figure approximates the average between the columns "low" and "medium" quality of the military approach and Figure approximates the average between the columns "medium" and "high" quality of the military approach in Table . . ) communicate these same takeaways in finer detail in a series of D graphs.
A narrow exception is discussed in the previous subsection.

Figure :
Figure : The flowchart of the COIN model's single tick.Note: *The soldier counterattack and attack sequences are shown in Figure .The portions of the flowchart in white represent Bennett's () model, on which we based our COIN model.P IR , represents the probability that an insurgent will recruit, i.e., employ the aid strategy, this turn.p i+n represents a simple draw from a uniform distribution.P IEW R represents the probability that an insurgent is exposed when it recruits.P GR represents the probability that a solder will recruit, i.e., employ the aid strategy, this turn.P IR , P IEW R , and P GR are among the systematically varied parameters of the simulation.For details, see Equations , a, b and Tables -.

Figure :
Figure : The flowchart of the soldier counterattack/attack sequence.Note: This flowchart details the soldier counterattack/attack sequence; see Figure for the flowchart of the full single tick of the COIN model. .
Figure describes the display output for three runs, all of which had highly inaccurate and ine ective military action by soldiers (e ectiveness= .and accuracy= .), i.e., soldiers miss targets and injure bystanders % of the time.Figure presents the display output for three runs, in which soldiers had medium levels of accuracy and e ectiveness ( .each). Figure shows the output from the three runs, in which soldiers were highly accurate and e ective (e ectiveness= .and accuracy= .), i.e., soldiers miss targets and injure bystanders % of the time.

Figure :
Figure : Various aid scenarios for e ectiveness= .and accuracy= . .Scenario (a), on top: No aid, simulation reaches , ticks, i.e., sustained insurgency.Scenario (b), in middle: Soldiers use aid % of the time, number of recruitable civilians by soldier= ; anger change given soldier recruitment=-., insurgency reaches , ticks, i.e., sustained insurgency.Scenario (c), on the bottom: Soldiers use aid % of the time, number of recruitable civilians by soldier= ; anger change given soldier recruitment=-., insurgents use aid % of the time, number of recruitable civilians by insurgent= ; anger change given insurgent recruitment= ., insurgency reaches , ticks, i.e., sustained insurgency.
Panels (a), (b), and (c) of Figures -di er by how the actors employ aid.Panel (a) replicates the model in Bennett ( ) without letting soldiers or insurgents use any aid option.Panel (b)

Figure :
Figure : Various aid scenarios for e ectiveness= .and accuracy= . .Scenario (a), on top: No aid, simulation ended a er , ticks, i.e., insurgency is defeated.Scenario (b), in middle: Soldiers use aid % of the time, number of recruitable civilians by soldier= ; anger change given soldier recruitment=-., simulation ended a er ticks, i.e., insurgency is defeated.Scenario (c), on the bottom: Soldiers use aid % of the time, number of recruitable civilians by soldier= ; anger change given soldier recruitment=-., insurgents use aid % of the time, number of recruitable civilians by insurgent= ; anger change given insurgent recruit-ment= ., simulation ended a er , ticks, i.e., insurgency is defeated.

Figure
Figure : accuracy = .and e ectiveness = . .Scenario (a), on top: No aid, simulation ends a er ticks, i.e., insurgency is defeated.Scenario (b), in middle: Soldiers use aid % of the time, number of recruitable civilians by soldier= ; anger change given soldier recruitment=-., simulation ended a er ticks, i.e., insurgency is defeated.Scenario (c), on the bottom: Soldiers use aid % of the time, number of recruitable civilians by soldier= ; anger change given soldier recruitment=-., insurgents use aid % of the time, number of recruitable civilians by insurgent= ; anger change given insurgent recruitment= ., simulation ended a er ticks, i.e., insurgency is defeated.
Figure presents highly stylized scenarios in which only one side does so (only soldiers provide aid in a and only insurgents -in b).In both panels of Figure actors employ a well-designed aid strategy, i.e., soldiers and insurgents a ect to civilians, whose anger is changed by larger anger increments (-. and -. for soldiers' aid strategy and .and .for insurgents' aid strategy).

Figure :
Figure : Duration of insurgency by accuracy and e ectiveness.No aid.

Figure :
Figure : Duration of insurgency by accuracy and e ectiveness.Various aid scenarios.Scenario (a), on the le : Rate of government recruitment P GR = .; number of recruitable civilians by soldier= , ; anger change given soldier recruitment=-.,-. ; no insurgent recruitment, P IR = . .Scenario (b), on the right: Rate of insurgent recruitment P IR = .; number of recruitable civilians by insurgent= , ; anger change given insurgent recruitment= ., .; no soldier recruitment, P GR = . .

Figure :
Figure : Duration of insurgency by accuracy and e ectiveness.Both sides provide aid.Varying probability of soldiers detecting the peacefully recruiting insurgents.Scenario (a), on the le : Rate of government recruitment P GR > .; number of recruitable civilians by soldier= , ; anger change given soldier recruitment=-., -. ; rate of insurgent recruitment P IR > .; number of recruitable civilians by insurgent= , ; anger change given insurgent recruitment= ., .; probability of insurgent exposure when it recruits P IEW R = . .Scenario (b), on the right: Same, but P IEW R = . .

.
Figure plots insurgency duration as a function of soldiers' e ectiveness and accuracy, when both soldiers and rebels use well-designed aid programs that recruit multiple civilians at a time and change their anger levels by moderate and high increments.The two panels in Figure di er in soldiers' ability to detect peacefully recruiting rebels (P IEW R = in a and . in b).When rebels can peacefully recruit undetected by soldiers (Figure a), insurgency duration depends on whether soldiers acquire intelligence about the attacking insurgents (e ectiveness) and whether soldiers can avoid collateral damage during their response operations (accuracy).

Figure :
Figure : Duration of insurgency duration by the probability soldiers and insurgents employing the aid strategy.Low accuracy and e ectiveness of the military action.Varying probability of insurgent exposure when insurgents recruit.Scenario (a), on the le : Soldier e ectiveness= .to .; soldier accuracy= .to .; number of recruitable civilians by soldier= , ; anger change given soldier recruitment=-. to -. ; number of recruitable civilians by insurgent= to ; anger change given insurgent recruitment= .to .; probability insurgent exposed when it recruits, P IEW R = . .Scenario (b), on the right: Same, but P IEW R = . .
Figures and di er in the soldiers' military action: low levels of accuracy and e ectiveness in Figure vs. high levels in Figure .When soldiers miss their targets and cause collateral damage -% of the time (shown in graphs a-b), the region of self-sustaining insurgencies is overwhelming (the median duration of insurgency in Figure a is , .ticks).Even when defeated, the th percentile duration of insurgency in Figure a is , .

Figure :
Figure : Duration of insurgency duration by the probability soldiers and insurgents employing the aid strategy.High accuracy and e ectiveness.Varying probability of insurgent exposure when insurgents recruit.Scenario (a), on the le : Soldier e ectiveness= .to .; soldier accuracy= .to .; number of recruitable civilians by soldier= , ; anger change given soldier recruitment=-.,-. ; number of recruitable civilians by insurgent= , ; anger change given insurgent recruitment= ., .; insurgent exposure when it recruits, P IEW R = . .Scenario (b), on the right: Same, but P IEW R = . .
s u r g e n t t u r n ( a ) A random i n s u r g e n t ( l a t e n t o r a c t i v e ) i s s e l e c t e d ( b ) The i n s u r g e n t s e l e c t s ( p r o b a b i l i s t i c a l l y ) one o f two a c t i o n s : r e c r u i t o r a t t a c k ( c ) I f i n s u r g e n t −s e l e c t e d a c t i o n i s a t t a c k :i .I f a s o l d i e r i s i n range , i n s u r g e n t a t t a c k s a s o l d i e r : A .I n s u r g e n t i s exposed f u l l y B .The t a r g e t e d s o l d i e r c o u n t e r a t t a c k s : C .I f t h e s o l d i e r c o u n t e r a t t a c k s , t h e s t a n d a r d c a p t u r e / c o l l a t e r a l damage / update sequence i s f o l l o w e d : − P r o b a b i l i s t i c a l l y ( based on e f f e c t i v e n e s s ) , t h e i n s u r g e n t i s k i l l e d and removed from s i m u l a t i o n − I f removed , a new c i v i l i a n i s added t o t h e s i m u l a t i o n a t a random l o c a t i o n and w i t h random c h a r a c t e r i s t i c s − P r o b a b i l i s t i c a l l y ( based on a c c u r a c y ) , c i v i l i a n s s u r r o u n d i n g t h e i n s u r g e n t a r e wounded − Anger and f e a r i s updated f o r c i v i l i a n s who were wounded − Because t h e s o l d i e r c o u n t e r a t t a c k was a r e s p o n s e t o an i n s u r g e n t , a n g e r i n c r e a s e s m o d e r a t e l y ( d ) I f i n s u r g e n t −s e l e c t e d a c t i o n i s r e c r u i t : i .I f any c i v i l i a n i s i n range , i n s u r g e n t r e c r u i t s one o r more c i v i l i a n s , up t o a number s p e c i f i e d i n a model parameter A .I n s u r g e n t i s exposed w i t h a c e r t a i n p r o b a b i l i t y ( s p e c i f i e d by t h e parameter P ( I n s u r g e n t Exposed G i v e n i t R e c r u i t s ) B .R e c r u i t e d c i v i l i a n s e x p e r i e n c e a moderate a n g e r i n c r e a s e C .I f t h e i n s u r g e n t i s exposed , nearby s o l d i e r s can make a c o u n t e r a t t a c k / ' ' a t t a c k o f o p p o r t u n i t y ' ' on i n s u r g e n t s ( r e s p o n d i n g w i t h s o l d i e r ' s r e s p o n s e p r o b a b i l i t y , c u r r e n t l y .) − G i v e n a c o u n t e r a t t a c k , t h e s t a n d a r d c a p t u r e / c o l l a t e r a l damage / update sequence i s f o l l o w e d − Because t h e s o l d i e r c o u n t e r a t t a c k was a r e s p o n s e t o an i n s u r g e n t , a n g e r i n c r e a s e s m o d e r a t e l y .S o l d i e r t u r n ( a ) A random s o l d i e r i s s e l e c t e d ( b ) The s o l d i e r s e l e c t s ( p r o b a b i l i s t i c a l l y ) one o f two a c t i o n s : r e c r u i t o r a t t a c k ( c ) I f s o l d i e r −s e l e c t e d a c t i o n i s a t t a c k :i .
Figures a through b and Table of the web appendix.The figure parallels Bennett's ( ) results.See Figure in Bennett ( ), as all of the results presented in this paper are the runs with replacement and no neighborhood influence.This same point is illustrated in greater detail by a series of D graphs in the web appendix.Compare Figures a-b and Figures a-b.Also, refer to Figures (p. ) and a-b (p.-) and a note on a narrowly constructed scenario of when the aid strategy may compensate for an incompetent military strategy (p. ) of the web appendix.

Figures a and
Figures a and b in the web appendix (pp.-) communicate this point in greater detail through a series of D graphs.
Figures a-b of the web appendix (pp.- Our model contributes to this line of research by allowing counterinsurgents to use various combinations of the military and aid approach by also focusing on the specific features of each approach.because he allows for a full range of military strategies from highly indiscriminate to highly selective.Bennett ( ) omits the aid strategy altogether, a gap that we fill.See Figure for a graphical representation of how our model di ers from Bennett's (

Table : test Quality of aid response Quality of military response Type of cell entry
High quality of state aid: probability of soldiers employing aid P GR = .;angerchange given soldier recruitment=-.; number of recruitable civilians by soldier= .Medium quality of state aid: P GR = .;angerchange given soldier recruitment=-.; number of recruitable civilians by soldier= .Low quality of state aid: P GR = .;angerchange given soldier recruitment=-.; number of recruitable civilians by soldier= .High quality of insurgent aid: probability of insurgents employing aid P IR = .;angerchange given insurgent recruitment=-.; number of recruitable civilians by insur-gent= .Medium quality of insurgent aid P IR = .;angerchange given insurgent re-cruitment=-.;number of recruitable civilians by insurgent= .Low quality of insurgent aid: P IR = .;angerchange given insurgent recruitment=-.; number of recruitable civilians by insurgent= .High quality of soldiers' military action: accuracy> .; e ectiveness> ..Medium quality of soldiers' military action: accuracy≥ .and≤.; e ectiveness≥ .and≤.;Lowquality of soldiers' military action: accuracy≤ .; e ectiveness≤ ..See Tableand Figure of the web appendix for an extended analysis of insurgency duration, and also peak of latent and active insurgents.