American Political Science Review (2017) 111, 2, 237–255 doi:10.1017/S0003055416000733 c American Political Science Association 2017 The Political Violence Cycle S. P. HARISH New York University ANDREW T. LITTLE Cornell University lections are often violent affairs, casting doubt on the canonical claim that democracy makes societies more peaceful by creating nonviolent means to contest for power. We develop a formal E argument to demonstrate that this conclusion is incorrect. Holding elections has a direct effect of increasing levels of violence close to the voting, as this is when electoral violence can influence political outcomes. Precisely for this reason, elections also have an indirect effect of decreasing levels of violence at all other times, as parties can wait for the election when their efforts are more likely to succeed. The direct and indirect effects generate a “political violence cycle” that peaks at the election. However, when the indirect effect is larger, politics would be more violent without elections. When elections also provide an effective nonviolent means to contest for power, they unambiguously make society more peaceful while still generating a political violence cycle.

Sick of elecshun [sic] related violence and terror attacks. Each panel shows yearly counts of violent events in Can’t wait for elecshuns to be over and get non-elecshun a country from the Social Conflict Analysis Database related violence back. (SCAD) for 1990–2010 (Saleyhan et al. 2012) with ver- —A tweet from the satirical and pseudonymous tical lines illustrating years with elections where the @majorlyp during the 2013 Pakistani elections chief executive office was at stake (Hyde and Mari- nov 2012). Kenya illustrates the pattern we seek to prominent argument for democracy centers explain starkly: in three out of four years with elec- around the fact that elections allow political tions, there were more violent events than the years A groups to compete via ballots rather than bul- before and after. Ghana experienced similar spikes in lets. However, elections are often violent affairs. Con- violence around elections in 2000 and 2008, though the flict surrounding the 2007 elections in Kenya led to most violent year was the one preceding an election around a thousand deaths and hundreds of thousands (1995). In Burkina Faso, the largest spike of violence displaced. Similarly, dozens were killed in the May 2013 occurred in the year following an election, while in election-related violence in the Philippines. More gen- Nigeria patterns in violence seems unrelated to election erally, electoral violence is not a new phenomenon nor years. limited to nascent democracies, but a problem “virtu- A clearer view of this “political violence cycle” ally all states have experienced” (Rapoport and Wein- emerges when aggregating across countries and taking berg 2000, 42). As many Western governments and a more fine-grained time window. Figure 2 presents the NGOs at least nominally encourage other countries to average daily level of violence from a month before to a hold elections, the question of whether doing so in- month after election day, for elections where the office cites violence is of great practical as well as theoretical of the incumbent leader was (left panel) and was not importance. (right panel) at stake, using the full sample of SCAD That elections are a necessary condition for elec- (which includes Latin America in addition to Africa). toral violence is tautological; of greater interest is how Two patterns readily stand out: first, there is a cyclical elections affect patterns of political violence more gen- pattern with a clear spike in violence around the day of erally. Still, recent empirical studies have found that the election for both types of elections. Second, there various forms of political violence sometimes do spike is a higher (average) level of violence around elections around elections (e.g., Aksoy 2014; Hafner-Burton, when the incumbent leader’s office was in contention. Hyde, and Jablonski 2014;Newman2013). Figure 1 (See the Appendix for a complete description of the illustrates this pattern for several African countries in data and procedures that generate these graphs.) a way that will relate closely to our theoretical model. Motivated by patterns like this and the association between elections and violence more generally, some have suggested that promoting elections could be dan- S. P. Harish is Ph.D. Candidate, Department of Politics, New York University ([email protected]). gerous in certain contexts (Brancati and Snyder 2012; Andrew T. Little is Assistant Professor, Department of Govern- Collier 2009; Flores and Nooruddin 2012). More fre- ment, Cornell University ([email protected]). quently, scholars of the relationship between elections Previous versions of article were presented at the European Po- and violence do not advocate against holding elections, litical Science Association 2014 Annual Meeting, the International but do express a clear unease that their results could be Studies Association 2015 Annual Meeting, the Midwest Political Sci- 1 ence Association 2015 Annual Meeting, and the Berkeley Center used to make such an argument. And these fears are for Political Economy. Many thanks to audience members at these seminars, Deniz Aksoy, Tiberiu Dragu, Patrick Kuhn, Tom Pepinsky, Mike Miller, Arturas Rozenas, Ignacio Sanchez-Cuenca, Inken von 1 For example, Chenoweth (2010, 28) succinctly summarizes this Borzyskowski, four anonymous referees, and the editors of the APSR notion in the context of terrorism, noting that “Most studies that for helpful comments and discussion. All remaining errors are ours. establish a positive relationship between terrorism and democracy Received: June 5, 2016; revised: August 19, 2016; accepted: find themselves in awkward positions because of the implications September 14, 2016. of their results—namely, that undermining democracy may also

237 S. P. Harish and Andrew T. Little

FIGURE 1. Counts of Violent Events for Select African Countries by Year, with Vertical Lines at Years with Elections where the Office of the Incumbent was Contested

Kenya Ghana Violent Events Violent Violent Events Violent 035 012

1990 1995 2000 2005 2010 1990 1995 2000 2005 2010 Year Year Burkina Faso Nigeria 11 Violent Events Violent Events Violent 0 089

1990 1995 2000 2005 2010 1990 1995 2000 2005 2010 Year Year

FIGURE 2. Average Counts of Ongoing Violent Events by the Number of Days to the Closest Election for Full Sample of SCAD

Incumbency at Stake Incumbency not at Stake 0.3 0.6 Avg Violent Events Violent Avg Events Violent Avg 0.0 0.3 0.6 0.0 −30 0 30 −30 0 30 Days to Election Days to Election not unfounded: those writing for more general audi- gument is that elections affect incentives to use vio- ences have used this association to discourage democ- lence to further political objectives not only leading racy promotion, e.g., calling elections or democracy up to and directly after the voting, but at all times. more broadly a “curse” (Economist 2013) or “among In particular, the presence of an election in the future the causes of both the Rwandan and Yugoslavian geno- can decrease incentives to commit violence today pre- cides” (Chua 2004, 12). cisely because violence—as well as nonviolent political We provide a simple and general formal argument action—become more effective during electoral peri- which demonstrates that spikes of violence during elec- ods. That is, making electoral violence a more effective tions cannot be used as evidence that elections make tool to change political outcomes has a direct effect of politics more violent on average.2 The crux of our ar- increasing violence surrounding elections, but this can be partially if not fully offset by an indirect effect of de- creasing violence in the periods between elections. So, undermine terrorism.” Hafner-Burton, Hyde, and Jablonski (2014, we cannot conclude from this evidence that elections— 175) note that “scholars and pundits may be tempted to interpret the or more consequential elections—make politics more fact that leaders sometimes use political violence to manipulate elec- tions as confirmation that elections are necessarily ‘bad’ for countries violent. without a history of elections and democracy,” though they caution Our theoretical argument has important implica- against this conclusion. Even those criticizing a universal push for tions for the empirical study of electoral violence. early elections warn that “our findings justify neither authoritarian The strategic use of violence around elections and leadership in postconflict countries nor the automatic postponement of postconflict elections” (Flores and Nooruddin 2012, 568). 2 We always use the average level of violence as our metric of how levels of violence as measuring things like the number of people peaceful society is. This is the natural statistic when thinking about killed.

238 The Political Violence Cycle associated temporal dynamics makes empirical as- ticularly in less-than-democratic countries (Daxecker sessment of how elections affect total violence levels 2012; Rozenas 2012; Hyde and Marinov 2014). extremely difficult, since it involves constructing the Finally, we conduct two additional extensions to counterfactual of a world with less consequential elec- demonstrate that the central arguments of the arti- tions or none at all. For example, when observing a cle apply to violence committed by different actors country where violence increases during elections, it and with different goals. First, we allow the incumbent is tempting to conclude that politics would have been to commit violence, which shows that our model can more peaceful without elections. However, the increase also capture the (often more empirically relevant) in- in violence could be driven by the direct effect or indi- cidence of violence perpetrated by government forces. rect effect described above (or both). Similar results hold even if the incumbent commits the To allow for such counterfactual comparisons (al- vast majority of violence. Second, we consider violence beit theoretically), we develop a series of formal mod- used to attain more incremental political objectives els which generate dynamics similar to the empirical than taking over office, which also leads to a similar cy- record with elections, and then ask what would hap- cle of violence around elections that can make society pen were elections to become less consequential or more or less peaceful on average. In sum, the models nonexistent. In our main model, two parties compete suggest that political violence committed by any actor over the spoils from holding office, and the party in for any purpose can follow a cyclical pattern peaking opposition commits violence in an attempt to oust the at election time without implying that there would be incumbent.3 To set up a “hard case” for elections to less violence of this form without elections. have a pacifying effect, we take it as a given that vio- lence is more effective in electoral periods, in the sense that a marginal increase in the opposition’s violent effort has a higher impact on their chance of taking RELATED WORK over office. Consistent with Figures 1 and 2, this simple setup generates a political violence cycle, where conflict Holding regular elections is central to democracy since peaks in electoral periods. However, the presence of it provides a mechanism through which societal differ- elections decreases the amount of violence in nonelec- ences are peacefully resolved and voters can hold their toral periods compared to a baseline where elections representatives accountable for their actions (Prze- never happen. When the indirect effect of reducing worski 2005; Przeworski, Stokes, and Manin 1999; violence in nonelectoral periods outweighs the direct Schumpeter 1942). However, a growing literature on effect of increasing violence during electoral periods, when and why violence is used during elections has the average level of violence is lower in a society with challenged this idea by showing the link between the elections than in the counterfactual without elections. central instrument of democracy and conflict. So, our first main result is that even when assuming The existing theoretical literature on electoral vi- that the only thing elections do is periodically make olence primarily analyzes how elites use violence violence more effective, the overall impact of elections around elections to improve their chances at the polls. can be to make politics more peaceful. For example, Ellman and Wantchekon (2000) present Our second main result is that a similar cyclical pat- a model on how threats of violence influence pol- tern of violence can arise if elections also provide a icy choices of different parties. Similarly, Chaturvedi nonviolent means to contest for power and unambigu- (2005) shows how elites use violence to influence both ously make society more peaceful. To demonstrate this, voter turnout and vote choice. In a similar vein, Collier we allow the opposition to also take nonviolent actions and Vicente (2012) argue that in situations where vio- to increase their chance of taking office during electoral lence is effective in swaying swing voters, some types periods (e.g., campaigning). Providing this alternative of incumbents and challengers will use repression and means of contesting for power lowers the level of vio- terrorism, respectively. However, these models do not lence in electoral periods as well as the periods leading examine how elections affect incentives to commit vi- up to elections for a similar reason described above; olence in nonelectoral periods or what would happen there is less incentive to commit violence leading up to in the absence of elections, so they tell us little about an electoral period when parties can wait until they are how elections affect patterns of political violence more able to contest for power peacefully. If the relative cost generally. of nonviolent political activity is sufficiently low, there Other recent game-theoretic work compares levels will always be less violence in a political system with of violence in a game with and without elections, but elections; in fact, there may be less violence in every pe- only in a single period (Cox 2009;Little2012). In riod compared to a baseline without elections. Further, many existing formal models, elections always reduce when the nonviolent activity is sufficiently effective, violence as—loosely speaking—voting or elections act peaks of violence can occur after the election, consis- as substitutes for fighting (Fearon 2011; Przeworski, tent with the prevalence of postelection protest, par- Rivero, and Xi 2012), the election fully alleviates the uncertainty that can cause bargaining to break down (Cox 2009), or reducing antigovernment violence is the 3 As discussed below, we allow only the opposition to commit vio- lence in the first model to illustrate our argument in a simple fashion, goal of elections (or democratizing) and hence they but later show the conclusions hold when the incumbent commits are only held when serving this end (Acemoglu and violence as well. Robinson 2000; Little 2012).

239 S. P. Harish and Andrew T. Little

A considerable empirical literature supports the the difference between violence in electoral and non- more skeptical theoretical models. For instance, electoral periods is large. Hafner-Burton, Hyde, and Jablonski (2014) show that Finally, our argument is also related to models de- incumbents will use violence during electoral periods veloped to answer how electoral rules can be obeyed when she fears losing power or when there are insti- in the shadow of force, which argue that the results of tutionalized constraints, but that this may also lead elections can be followed and substitute for conflict if to risky postelection violence (Hafner-Burton, Hyde, losers prefer the potential to contest for power again and Jablonski 2015).4 Similarly, Aksoy (2014) shows in future elections to fighting today (Przeworski 1991; that electoral violence is more likely in places with low Przeworski 2005; Przeworski, Rivero, and Xi 2012). On “electoral permissiveness.” Both Wilkinson (2004) and the other hand, Bates (2008) argues that the prospect of Brass (2003) describe how Indian elites use violence to losing power via competitive elections makes leaders increase the turnout of their supporters and decrease less patient and more apt to act in a predatory manner that of the challengers. Using data from Africa, Dax- towards their citizens (see also Bates, Greif, and Singh ecker (2012) argues international monitoring of flawed 2002). Both of these approaches focus on conditions elections can raise the salience of fraud and conse- under which there is an equilibrium with no conflict or quently the risk of postelection violence, and Kasara predation, while our model has a unique equilibrium (2015) shows how violence may also influence future that makes precise predictions about patterns of vio- (and not just upcoming) elections in Kenya. Elections lence over time. That is, rather than describing a society may be particularly dangerous in countries that have that is in perpetual conflict or peace, the equilibrium recently transitioned from an autocracy to a democracy to our model has cycles of violence and peace around (Cederman, Hug, and Krebs 2010; Collier 2009), or elections, as in the empirical record. that have recently recovered from conflict (Brancati and Snyder 2012; Flores and Nooruddin 2012; Reilly THE BASELINE MODEL 2002).5 Most directly related to our model is a burgeoning We first present a simple model of political violence in a empirical literature which focuses specifically on spikes repeated setting. There are two parties competing for in violence, repression, and terrorism during electoral office. The game proceeds over T > 1 time periods.6 periods (Bekoe 2012; Goldsmith 2014;Newman2013; In each period, one party is the incumbent, the other Norris, Frank, and Martinez i Coma 2015; Staniland in opposition. The parties are symmetric, in the sense 2015). The types and perpetrators of violence may also that the actions and period payoffs assigned to the in- change surrounding elections: e.g., Straus and Taylor cumbent and opposition do not depend on which party (2012) show that incumbents tend to inflict violence holds which role. As a result, we refer to decisions before the vote and challengers are more likely to be made by the incumbent party and opposition party involved in postelection violence. even though the actor in these roles may alternate.7 While this empirical literature has highlighted po- The incumbent takes no actions and earns rents tential ways in which elections may incite violence, the from office ψ>0. The party in opposition in time research designs employed cannot speak directly to t chooses violence level vt ≥ 0, incurring a cost c(vt). the theoretically and policy-relevant counterfactual of Assume c is increasing and convex, with c(0) = 0. That what would happen in the absence of elections, or if is, the first unit of violence is “free,” and the marginal elections had lower stakes. Studies that compare levels cost of violence is increasing.8 of violence cross-nationally face the well-known prob- The benefit to committing violence is that it increases lems of identifying causal effects from observational the chances of taking over as incumbent in the next data. More subtly, studies that compare levels of vi- period. In particular, the probability of taking over olence closer and farther from elections within coun- tries could more plausibly identify the causal effect of 6 elections if nonelectoral periods can serve as “control” Picking a finite time horizon allows for a straightforward character- ization of a unique equilibrium which holds for any arbitrary large periods for times closer to elections. Our models show number of periods and set of exogenous parameters, which would this inference is dangerous, since the “treatment” of not be possible in the analogous infinite horizon model. having (competitive) elections affects incentives to use 7 To be more precise, we could define the game as between two violence at all times. In fact, we find that in some cases parties, A and B, one of which starts the game as the incumbent. In each period, vJ,t is the amount of violence party J would choose elections lead to less violence overall precisely when if in the opposition role in period t, and the probability of taking office when party J in the opposition is p(vJ,t; kt). Since we identify a unique equilibrium and the objective function for the party in 4 However, violence may sometimes decrease during elections, es- opposition does not depend on their label, it must be the case that pecially if they are strategic substitutes (Davenport 1997; Dunning both sides always choose the same level of violence. 2011). 8 We do not assume there is a budget constraint as this complicates 5 There is a wide literature that examines whether democracy in the analysis by raising the possibility of boundary conditions when general is associated with civil conflict and other forms of violence the opposition spends their entire budget on on violence. If anything, (Collier and Hoeffler 2004; Fearon and Laitin 2003; Hegre et al. 2001; adding budgets would make our results stronger, as it could lead to Hegre and Sambanis 2006). Similarly, a large number of studies have a “cap” of how much violence can spike during elections. Further, focused on the use of political repression in different types of regimes if the budget does not perfectly reset every period there would be and have generally found that strong democratic institutions are intertemporal substitution more directly baked into the model as any associated with lower levels of repression and human rights violations unit of violence used during an election would have to come from (Davenport and Armstrong 2004; Poe and Tate 1994). another period.

240 The Political Violence Cycle

office is given by p(vt; kt), which is continuous and comes and holding office is the only outcome parties twice-differentiable in both arguments. We assume that care about. Again, we later present extensions to the the chance of taking over office is strictly increasing in model which loosen these assumptions without chang- ∂ the violence choice ( p > 0) with diminishing marginal ing our core conclusions. Before getting to these more ∂vt 2 realistic models, we illustrate our core point about the ∂ p < ∈ , returns ( 2 0). The kt [0 1] parameter represents ∂ vt intertemporal substitution of violence in our simple the effectiveness of violence in period t. To formalize baseline model. ∂ ∂2 this, we assume that p > 0 and p > 0, meaning the ∂kt ∂vt∂kt probability of taking office and the marginal effect of Solution committing more violence are always increasing in kt. To preview, when applying the model to cycles of vio- Our solution concept (formally defined below) re- lence around elections we assume that kt is higher in quires that the level of violence chosen in each pe- electoral periods, but first provide the solution to the riod maximizes the opposition expected payoff for the general model. rest of the game given the future equilibrium violence Formally, the period payoff to a party is given by choices.11 To compute the optimal violence choice in period t, the party in opposition has to compare the ψ as incumbent expected payoff for the remainder of the game entering ut = −c(vt) as opposition. the next period as incumbent or opposition. In the last period, this is relatively straightforward, as the values of ending the game in either role are the exogenously The payoff for the entire game is the discounted sum π∗ + π∗ + of the period payoffs and a “continuation value” for given I (T 1) and O(T 1). So, the payoff for the ending the game in each role. For consistency with later party that is the opposition in the final period as a notation, we write the value of ending the game as the function of their violence choice is π∗ + π∗ + incumbent I (T 1), and as the opposition O(T − 9 T 1 1). We assume it is better to end the game as the t−1 T−1 ∗ ∗ δ u − δ c(v ) incumbent: π (T + 1) >π (T + 1). t T I O t=1 Both parties discount future payoffs at rate δ ∈ (0, 1]. period T payoff So, the total payoff for a party that attains period pay- past payoffs ,... offs u1 uT and ends the game as party J is + δT{ π∗ + + − π∗ + } p(vT; kT) I (T 1) [1 p(vT; kT)] O(T 1) T continuation value δt−1 + δTπ∗ + . ut J (T 1) t=1 Since the past payoffs are fixed, when characterizing the optimal level of violence it is simpler to work with This setup is deliberately simple to highlight our core the net present value of the game starting in period t, argument in a clear fashion.10 An inevitable drawback which only considers the payoffs beginning in period t and normalizes by the discount rate. So, for the last to this simplification is that some aspects of the model 12 are prima facie at odds with how much violence unfolds period this is given by in actual elections. For example, we assume that only π , =− + δ{ π∗ + the opposition uses violence despite the fact that much O(T vT) c(vT) p(vT; kT) I (T 1) if not most electoral violence is committed by or on be- + [1 − p(v ; k )]π∗ (T + 1)} half of the incumbent regime. We choose to have only T T O one actor commit violence in the baseline model as this To be sequentially rational, the violence level in the greatly streamlines the presentation. Further, assuming π , the actor committing violence is trying to change rather last period must maximize O(T vT). Taking the first than maintain the status quo leads to cleaner intuitions, order condition, an interior optimal violence choice in and in this context that is the opposition. Importantly the vT solves for connecting our model to the empirical literature, we ∂ later extend the model (in Section 4) to allow violence p(vT; kT) δ π∗ + − π∗ + =  . ∂ [ I (T 1) O(T 1)] c (vT) (1) by both actors, and find that our central results hold. vT Two other particularly consequential assumptions discounted value of taking over Pr(take over) are that violence is the only tool to affect political out-

9 π∗ + π∗ + 11 The probabilistic nature of who enters each period as the incum- While the specific values chosen for O(T 1) and I (T 1) can have a large impact on the equilibrium levels of violence in the final bent means this is a game with incomplete information, so subgame periods, when the game is long (i.e., T is large), the continuation val- perfection does not apply. We do not introduce extra notation for ues at the end have little effect on the behavior for most of the game. the beliefs held by the parties since the uncertainty is symmetric and In our illustrations we set the continuation values to avoid changes the probability of taking office function is a primitive of the model. in behavior due to the game ending; see the Online Appendix for a 12 That is, the payoff for the entire game for the party in opposi- derivation of this stationary value. tion for any time t given the future violence choices can be written 10 t−1 δi−1 + δt−1π , See Little and Pepinsky 2016 for a more general discussion of the i=1 ui O(t vt). Since the past payoffs are not a function role of simplification in models of comparative politics. of vt, optimizing this equation is equivalent to optimizing πO(t, vt).

241 S. P. Harish and Andrew T. Little

∗ > The left-hand side of equation (1) is the marginal As long as t+1 0—which means it is better to en- benefit to committing more violence in period T, which ter the next period as the incumbent rather than as the is equal to the change in the probability of ending the opposition—this optimization problem has a unique ∗ + game as the incumbent times the discounted difference interior solution vt . If it is better to enter period t 1 between ending the game as the incumbent versus as as the opposition rather than as the incumbent, there opposition. The right-hand side of this equation is the is no benefit to violence and hence it is optimal to pick ∗ = 14 marginal cost to committing more violence. Since there vt 0. So: are diminishing returns to committing more violence Proposition 1 The baseline model has a unique equilib- and an increasing marginal cost, this equation has a ∗ ∗ ∗ rium where v solves equation (6) when  + > 0 and unique solution v where the marginal benefit equals ∗ t t 1 T v = 0 otherwise. the marginal cost.13 t The optimal violence choice in every period has this Proof. Follows from the above analysis; see the Ap- general form: the opposition commits the level of vi- pendix for details.  olence where the marginal cost of committing more Next we analyze how changing the effectiveness of violence equals the marginal benefit via increasing the violence in a given period affects the pattern of violence chance of taking over office in the next period. The throughout the game. For simplicity we only consider only complication—which will drive the intertemporal the plausibly realistic case where it is better to enter as substitution effects we aim to model—is that the ben- ∗ > the incumbent in every period (i.e., when t 0for efit of taking over office in the next period depends on all t); see the Online Appendix for discussion of how the future effectiveness of violence. However, once we loosening this restriction affects the results. know the violence level in period T (derived above), The direct effect of increasing the effectiveness of we can compute the net present value of entering pe- violence in period t is that by increasing the marginal riod T as incumbent versus opposition, which gives the effect of v on taking over office, the marginal benefit to − t optimal level of violence in period T 1. This gives the violence increases, leading to a higher choice in period net present value of entering the next to last period t. Formally, implicitly differentiating equation (6) gives in each role, and hence the optimal violence level in ∂ ∗ vt > that ∂ 0. period T − 2, etc. kt To formalize the indirect effect, consider how mak- Formally, the opposition objective function  π , ∗ ing violence more effective in future periods (i.e., t > t) ( O(t vt)), optimal violence choice (vt ), and the net present values for entering period t in each role (π∗ (t) affects behavior in period t. (By sequential rationality, ∗ O  < and π (t)) can be defined recursively as violence levels in previous periods t t do not affect I the choice in period t.) Referring back to equation (6), ∗ this will depend on how the future effectiveness of vi- πO(t, vt) = c(vt) + δ{p(vt; kt)π (t + 1) I olence changes the relative value of entering the next ∗ ∗  + [1 − p(vt; kt)]π (t + 1)}, (2)  = + O period as the incumbent ( t+1). When t t 1, the re- sult is straightforward: making violence more effective ∗ v ∈ arg max πO(t, vt), (3) in the next period unambiguously makes the opposi- t ≥ vt 0 tion better off and the incumbent worse off entering π∗ = π , ∗ , this period. This reduces the relative value of entering O(t) O(t vt ) (4) the next period as the incumbent, so there is less vi- olence in period t. For periods t > t + 1 the technical π∗ = ψ+ δ{ ∗ π∗ + I (t) p(vt ; kt) O(t 1) analysis is more subtle, but for all of the examples we ∗ ∗ present in our illustrations, reducing the effectiveness + [1 − p(v ; k )]π (t + 1)}. (5) t t I of violence at any future period decreases the level of violence today (see the Online Appendix for exam- An equilibrium to the model is characterized by ples where this does not hold). Intuitively, as long as it ∗ π∗ π∗ is better to enter each period as the incumbent, and sequences vt , O(t), and I (t) that solve equations (2)–(5)fort = 1,...,T. It is also convenient to write taking control of the government by force is rare, any- the difference between the net present value of thing that makes doing so easier in the future reduces entering period t as the incumbent versus the as the incentives to commit violence today. Formally: ∗ ≡ π∗ − π∗ opposition as t I (t) O(t). So, the first order Proposition 2 The equilibrium level of violence in time condition for an interior level of violence vt is period t1 is (i) increasing in k , ∂ t1 p(vt; kt) ∗  + δ  = . (ii) decreasing in kt1 1, and t+1 c (vt) (6) ∂ ∗ ∂ ∗ vt  ∗ vt (iii) provided δ[1 − 2p(v ; kt)] > 3 ∗ c (v ) for t ∈ t ∂ + t { ,... − } > t 1 + t1 t2 1 , decreasing in kt2 for t2 t1 1. 13 More precisely, since p is concave and bounded above by one, the left-hand side is positive, decreasing, and approaches zero as 14 One way this can happen is if violence is extremely effective in vT →∞. Since c is convex and equal to zero at vT = 0, this ensures a period t + 1 but less effective after that, meaning is better to enter unique intersection, which by the concavity of the objective function period t + 1 as the opposition in order to take control before violence is the unique global maximizer. becomes less effective again.

242 The Political Violence Cycle

Proof. See the Appendix.  A simple microfoundation for this assumption is that While the model has not yet explicitly addressed the opposition can commit “nonelectoral” violence in elections, this result formalizes the central intuition any period, but electoral violence is only possible (or about the direct and indirect effects of making vio- only useful) in electoral periods. So, in electoral peri- lence more effective in a given period. The obvious ods, the opposition—and, as formalized in Section 4, direct effect is that there is more violence in this period. other actors—have multiple ways to influence politi- However, making violence more effective in period t cal outcomes with violence. While electoral violence has an indirect effect of decreasing violence in periods can look much different than other forms of violence, t − 1, and potentially in all periods prior to period t. for our purposes adding a new violent technology dur- The idea that political actors time their actions is ing elections is equivalent to assuming that violence fairly well documented, especially in the terrorism liter- is more effective in electoral periods (see the Online ature. For instance, the Boston Marathon bombers had Appendix for a formal statement of this point). More initially planned their attack for the July 4 festivities broadly, we make this seemingly unusual assumption (Boston 2013), and the so-called “underwear bomber” because our primary goal is to show how elections can had timed his attack for Christmas Day (Hudson 2013). reduce violence even if fighting peaks around elections. Such violent actors are also known to specifically wait So this assumption constitutes a “hard case” for our for elections so that their attacks would have a greater aims.16 impact. A recent prominent example of such an ap- As demonstrated by Proposition 2, introducing elec- proach is the the 2004 train bombings in Madrid that tions in this manner has a direct effect of increasing the took place three days before the Spanish voters went level of violence in electoral periods but also an indi- to the ballot, and is now known to have been timed rect effect of decreasing violence in the periods before specifically to influence the election outcome (Rich- elections, and potentially all nonelectoral periods. To burg 2004). Other similar instances include the Kur- show that either effect can be larger, we present several = 2 distan Workers’ Party (PKK) attacking Turkish secu- illustrative cases. For all of these examples, c(vt) vt −1 rity forces to sway the electorate in April 2015 (Aksoy and p(vt; kt) = kt[1 − (1 + vt) ]. 2015), and intelligence reports indicating that Pakistani Figure 3 presents a comparison of violence levels in terrorists planning suicide attacks timed for the Indian two societies that only vary in the presence of elections. elections (Shukla 2014). Violence (including but not In both societies, there are 20 periods, and the effec- limited to terrorism) may also be more prevalent dur- tiveness of violence in nonelectoral periods is kn = 0.3. ing seasons when it is easier to recruit fighters, for Without elections (the grey line), all periods are non- example because wages are lower outside of harvest electoral, and the equilibrium violence choice is con- seasons (Guardado and Pennings 2015).15 stant.17 In the second society (black curve), there are Proposition 2 indicates that this intuition can apply elections in periods 6, 12, and 18 (the vertical lines), to the incentives to commit violence to gain political where the effectiveness of violence increases to ke = 1. power. While some of these examples are from groups The horizontal black line represents the average vio- with no stated aspiration to actually take control of the lence level with elections. government, in Section 4 we further argue that the logic The black curve presents a similar (if tidier) pattern applies to a wide class of political violence committed as shown in the cases of Kenya and Ghana in Figure 1 by various actors and various aims. with spikes in levels of violence in electoral periods (or years). While we cannot directly know what the coun- ELECTIONS IN THE BASELINE MODEL terfactual level of violence would be without elections using observational data, with the theoretical model we With this general solution in place we now examine can make this comparison by looking at violence levels how periodic elections change aggregate levels of vio- in an otherwise identical society with no elections. In lence under the assumption that violence is more ef- this case, the black line is below the grey line, indicat- fective in electoral periods. For simplicity, we begin ing that the spikes in electoral periods are more than with a stark comparison between patterns of violence offset by the decrease in violence in nonelectoral peri- in a society with no elections versus one with periodic ods, leading to less fighting on average.18 This example elections. We then turn to the question of how mak- ing elections more consequential and other more fine- grained changes affect patterns and aggregate levels of 16 In terms of arguing whether elections are “good” or not, we are political violence. also setting aside other positive benefits of democracy such as giving citizens a voice in how they are governed. 17 This requires setting the continuation values at the end of the game A Simple Example such that the different between the expected payoff for entering each period in each role is stationary; see the Online Appendix. Suppose in a society without elections, the effective- 18 A subtle difference between the pattern of violence from the the- ness of violence is kt = kn for all periods. In a society oretical model and the empirical evidence is that in Figure 3 violence is decreasing throughout the nonelectoral period, reaching its lowest with elections, the effectiveness of violence is ke > kn points right before the electoral periods. This is because the violence- in electoral periods and kn for other periods. deterring effect of future elections is strongest when the election is near. That is, there is less incentive to wait for the election when it is 15 As these examples indicate, elections are not the only times when far away. However, this disconnect is not inherent to the model itself, violence could become more effective. but to the fact that electoral violence is only available in the electoral

243 S. P. Harish and Andrew T. Little

FIGURE 3. Comparison of Levels of Violence with No Elections (grey line) and Elections (black line)

No Elections 0.4 0.8

Violence Level Violence Elections 0.0 5101520 Time Period illustrates the first main result of the article in a sim- The right panel shows how this affects the average ple fashion: the existence of a political violence cycle levels of violence (solid line) and the difference be- does not imply societies would become more peaceful tween the average level of violence in electoral periods without elections.19 versus nonelectoral periods (dotted line). While mak- Next, we consider how general this example is by ex- ing violence slightly more effective in electoral peri- amining how changing various parameters of the model ods increases the average amount of violence, making affects patterns and aggregate levels of violence. Un- violence much more effective leads to less violence fortunately, analytic results on this relationship in the overall. However, increasing the effectiveness of vio- baseline model prove very difficult (stronger results lence unambiguously increases the difference between along these lines emerge in the model with nonviolent violence levels in electoral versus nonelectoral periods. actions in the next section). However, it is straightfor- So, for part of the parameter space, making electoral ward to simulate the model for a wide range of param- period violence more effective leads to bigger spikes of eters and functional forms for the c and p functions to violence in electoral periods but less violence overall. explore how this affects average levels of violence. The While this effect is just from one set of simulations Online Appendix contains an extensive analysis of how (again, see the Online Appendix for an illustration changing individual parameters affects violence levels of how this relationship changes for random draws of for randomly drawn values of the other parameters. In the other parameters) and the changes in the average the main text, we focus on several results from this ex- violence level are not large, this illustration has im- ercise that are of substantive interest and are generally portant empirical and policy consequences. First, it is robust to varying other parameters. interesting in light of empirical findings that competi- tive elections outside of consolidated democracies tend Consequential/Competitive Elections to be particularly violent (Hafner-Burton, Hyde, and Jablonski 2014; Straus and Taylor 2012), as well as the First, Figure 4 shows a counterintuitive and empirically sharper spike of violence in elections where the chief relevant example of how the degree to which violence executive is at stake shown in Figure 2. is more effective during elections affects the average Elections with higher stakes can be directly inter- 20 level of violence. The left panel illustrates the per pe- preted as ones where ke is higher. Connecting the riod violence levels with increasingly dark lines as ke competitiveness of elections to this parameter is less increases. Increasing the effectiveness of violence in the straightforward. However, when elections are close electoral periods leads to bigger spikes of violence dur- there can be a higher marginal return to any political ac- ing the election, but also larger decreases in violence tivity that will lead to more votes, including violence.21 in nonelectoral periods. So, in that sense, we might expect that competitive elec- tions are ones where the marginal returns to violence are high, which is precisely what we mean by ke being period itself, while some electoral violence occurs in the months high. Under this interpretation, it is the competitive- leading up to the election. As shown in the Online Appendix, when ness of the election that depresses violence before the assuming that violence is also somewhat more effective in the period before the election, a more smoothly cyclical pattern of violence arises. 20 19 It is possible that higher volatility in violence is itself bad. This See Durant and Weintraub (2014) for a discussion on how to reduce the stakes in postconflict elections. could be formalized by specifying a society welfare function that 21 sums up some convex function of the period violence choices. In For example, if a party only cares about winning the majority general this will make elections less beneficial from a welfare per- of votes, and their vote share is equal to a costly action a plus spective, though in the model with substitution elections can lead to a normally distributed variable with mean m and standard devia- σ ∂ { + − . /σ }= less violence in every period. Further, concentrating the times when tion , then the marginal return to a is ∂a [(a m 0 5) ] political actors have incentives to commit violence may also make it σ−1φ[(a + m − 0.5)/σ] where  and φ are the CDF and PDF of a easier for international actors to more effectively monitor and deter standardized normal random variable. For the first marginal unit of violence in at-risk countries (Matanock N.d.). a,thisismaximizedatm = 0.5, i.e., a perfectly competitive election.

244 The Political Violence Cycle

FIGURE 4. The Effect of Making Elections more Consequential on Average Levels of Violence

0.4 Increase in Violence During Elections

Avg Violence

Violence Level Violence with Elections Average Violence Level Violence Average 0.0 0.4 0.8 0.3 0.1 0.4

5101520 kn 2kn 3kn Time Period Election Period Effectiveness election: there is less of an incentive to commit violence are more spoils to fight over. When there is already a today if the opposition has a real chance to take office high level violence in the nonelectoral baseline, the in an upcoming election. marginal effect of making violence more effective in On the policy end, given that nearly every country electoral periods is relatively low compared to poten- holds some kind of election and few argue they should tial to decrease violence by making it more effective in be abolished entirely, the comparison between more the future. or less consequential elections is more relevant than Finally, the right panel examines the frequency of the contrast between elections and no elections at all. elections. When elections are extremely frequent, they Interestingly, this simulation suggests that to reap the lead to more violence, as there is not enough time benefits of elections in terms of peace it may not be between elections for the indirect effect of making enough to have elections that are only slightly conse- nonelectoral periods more peaceful to outweigh the quential. Conversely, this example raises the possibil- direct effect. When elections are very rare, they lead to ity that making elections less consequential will lead slightly less violence since it takes a long time to wait to smaller spikes in violence during elections but also until the next election, weakening the indirect effect. more violence overall. So, the optimal election timing is intermediate, where nonelectoral periods are short enough that the indirect Other Simulations effect matters for the entire time between elections, but long enough that the indirect effect adds up to matter Figure 5 shows how changing several other parame- more than the direct effect. ters affects the difference in average levels of vio- lence with and without elections. The left panel ex- amines the effect of the discount rate. Changing δ EXTENSIONS has a nonmonotone effect. When the parties are ex- tremely impatient (δ → 0) the optimal violence choice Several simplifying assumptions utilized so far raise is always zero since the benefits of taking over of- doubts about the scope conditions for the model. fice do not accrue right away. So if parties are com- First, by assuming that elections only increase the pletely impatient, there is no violence at all regardless effectiveness of violence, we cannot yet say how provid- of whether elections are held. For moderate levels of ing nonviolent means to contest for power affects the patience there can be more violence with elections, patterns we describe. Second, much if not most politi- and the parties are patient enough to get a benefit cal violence is perpetrated by the government and their from using violence but not patient enough for the agents, not just the opposition as in the baseline model. prospect of future elections to outweigh the direct ef- Third, so far we have only modeled violence committed fect. When δ gets large, the indirect effect becomes to take over the government, while political violence stronger and elections lead to less violence overall.22 often has other (and more incremental) goals. As our For this particular parameterization, a discount rate of goal is to assess how elections affect broad patterns of 0.88 is where elections go from promoting to preventing political violence, it is important to check that similar violence. results can come out of models with more realistic and The middle panel examines the value of holding of- general assumptions. fice (ψ). For this parameterization (and, as shown in the Fortunately, the results are robust and often even Online Appendix, the majority but not all of our simu- stronger when extending the model in several ways. In lations), increasing ψalways leads to elections having a particular, we address these concerns with three modifi- more pacifying effect. A potential explanation for this cations to the model that allow for nonviolent political is that there will be more violence in general when there technology, multiple actors committing violence, and violence to obtain goals other than taking over office. 22 The requirement that actors be patient in order to accept peace- Doing so also provides more detailed empirical insights ful allocation of power also shows up in (Przeworski 1991, 2005; about when certain political actors are more or less apt Przeworski, Rivero, and Xi 2012). to commit violence.

245 S. P. Harish and Andrew T. Little

FIGURE 5. Comparative Statics on Change in Violence with Elections by the Discount Rate (left panel), Value of Office (middle panel), and Frequence of Elections (right panel) 0.00 0.04 0.06 −0.02 0.02 −0.02 0.00 0.02 Change in Violence Change in Violence Change in Violence −0.04 −0.04 0.00 −0.06

0.0 0.2 0.4 0.6 0.8 1.0 0246810 2 4 6 8 10 12 Discount Rate, (δ) Value of Office (ψ) Frequency of Elections

Bullets and Ballots parameter reflects the increased effectiveness of po- litical activity in general. To simplify the analysis, we A central idea in the literature on democracy is that assume that nonviolent political action is not available elections allow parties to compete for power with non- or ineffective in nonelectoral periods. violent means. Further, there are a number of empirical In addition to the cost c(vt) paid to take violent ac- examples where armed groups have either delayed or tions, the opposition also pays a partial cost c(x )/β for renounced violence in the presence of nonviolent al- t t the nonviolent actions, for some βt > 0. So, βt reflects ternatives. For example, the Irish Republican Army the relative cost of violent political activity in period t: (IRA) agreed to give up arms in Northern Ireland when βt > 1 violent activity is more efficient and when in 2005 when its political arm, Sinn Fein, made in- 24 βt < 1 nonviolent action is more efficient. roads in Northern Ireland and in the Irish Republic Our solution concept (formalized in the Appendix) (Lavery and Cowell 2005). Similarly, the Free Aceh is analogous to the main model, except now the joint Movement (GAM) in Indonesia give up violence as choice of violent and nonviolent action must be sequen- part of an agreement that included Indonesia allow- tially rational. Following standard optimization pro- ing regional political parties to participate in national cedures, the first order condition for the opposition’s elections (Simanjuntak 2008). choice in period t is now the (v , x ) that jointly solve To combine our argument with the canonical claim t t that elections reduce violence by providing an alter- ∂ p(x + v ; k ) native means to contest for power, we present an ex- δ t t t ∗ =  , ∂ t+1 c (vt) (7) tension where the opposition can also use nonviolent vt ∂ + actions. In short, we find that this leads to a substitution δ p(xt vt; kt)∗ =  /β , away from violence that can make society substantially t+1 c (xt) t (8) ∂xt more peaceful even though there is still a cycle of vio- lence around elections. ∗ where t+1 is again the difference between the net To formalize this, suppose that in an electoral period, present value of entering period t + 1 as the incumbent the opposition party can also choose to take nonviolent  ∗ =  ∗ /β versus opposition. This implies c (vt ) c (xt ) t, actions to increase their probability of becoming the which by the convexity of c ensures a unique pair incumbent following the election. Let xt represent the ∗, ∗ (xt vt ) meeting these conditions. So, by an identical amount of nonviolent activity in period t, which could argument to the baseline model, there is a unique represent campaigning, mobilizing voters on election equilibrium level of violence and nonviolent activity day, or other less desirable but nonviolent tactics like ∗, ∗ (vt xt ) in each period characterized by Equations (7) vote buying. Let the probability of taking office in an ∗ > ∗ = ∗ = ∗ ≥ and (8) when t 0 and vt xt 0 when t 0. electoral period be p(xt + vt; kt) with the same func- 23 Figure 6 illustrates the impact of nonviolent activity tional form assumptions as above. So, now the kt on how much violence is chosen in equilibrium, with

23 That is, p is increasing and concave in its first argument, and the 24 This parameter could also reflect how easy it is to attain political cross partial with respect to the two arguments is positive. power through normal institutional channels.

246 The Political Violence Cycle

FIGURE 6. The Effect of Introducing Nonviolent Technologies on the Level of Violence

Expensive Nonviol 0.4 Tech No Elections Elections

Cheap

Violence Level Violence Nonviol Tech Average Level of Violence Level Average 0.0 0.2 0.15 0.25 5 10152025 012345 Time Period Relative Cost of Violence

=− 2 + = − + + −1 c(vt) vt and p(vt xt; kt) kt[1 (1 vt xt) ]. (i) the level of violence in electoral period t is decreas- As before, the flat line in the left panel is the level of ing in the relative cheapness of nonviolent technology violence with no elections. The dotted curve represents (βt), and the level of violence chosen where nonviolent technol- (ii) when the nonviolent technology becomes ex- ogy is very expensive, and the spike in violence is large tremely cheap in period t, the level of violence ap- β →∞ ∗ → during the election is large relative to the dip in vio- proaches zero (as t ,vt 0). lence in no-electoral periods, resulting in more violence Proof. See the Appendix.  on average with elections despite some substitution to In other words, with substitution to non-violent tech- nonviolent activity. nology the direct effect in the baseline model is weak- In the solid curve, the nonviolent technology is β β ened if not reversed, potentially leading to less violence cheaper (high t, set to a constant for all electoral in electoral periods. The logic of the indirect effect periods), leading to a stronger substitution away from of reducing violence in non-electoral periods remains, using violence during electoral periods. The availability and so elections can unambiguously reduce violence of effective nonviolent technology also augments the on average and even in every period (as in Figure 6). intertemporal effects of the baseline model, as there is less reason to commit violence when it is possible to contest for power peacefully in future electoral periods. Incumbent and Opposition Violence As a result, the level of violence is not only lower on average, but lower in every period than it would be Next, we analyze a case where both the incumbent without elections. The substitution effect is so large and opposition can commit violence. In this section, we assume the probability that the opposition becomes that violence peaks after the election, when (1) the + nonviolent technology is not available, but (2) the next the incumbent in period t 1 as a function of their vio- lence choice (now vO,t ≥ 0) and the incumbent violence election is far enough away that it is worth commit- ≥ ting violence to try and take over office. This pattern choice (vI,t 0) is matches the case of Burkina Faso in Figure 1; we revisit v , the relationship between this example and several the- k O t v , + v , > 0 t v , +v , O t I t p(vO,t, vI,t; kt) = O t I t oretical and empirical papers on postelection protest in p0 vO,t + vI,t = 0 the discussion. Still, the presence of elections induces a cyclical pattern of violence that, without thinking of ∈ , ∈ , + = the proper counterfactual, could erroneously lead to for some kt [0 1] and p0 (0 1). (The vO,t vI,t 0 conclusions that elections encourage violence. case is to avoid division by zero, and the exact value of The right panel of Figure 6 plots the average level p0 has no impact on the analysis.) This functional form meets all of the assumptions with respect to vO,t and of violence as a function of the relative cost of violent > actions (β). Unlike the previous graphs, making the kt in the baseline model as long as vI,t 0 (which will nonviolent action cheaper (higher β) has an unambigu- always be true in equilibrium). ous and large effect in decreasing the average levels Let the opposition cost for committing violence level vO,t be exactly vO,t, and let the cost of committing vi- of violence. In this parameterization, elections would γ <γ< lead to more violence in the absence of a nonviolent olence for the incumbent be vI,t for some 0 1. technology (β → 0), but as long as the nonviolent tech- That is, we assume that violence is “cheaper” for the in- cumbent, or, equivalently, the incumbent gets a higher nology is less than twice as expensive as violence the 25 presence of elections will decrease the average level of return to violence. violence.

25 Some of the results require more caveats analogous to those in part (iii) Proposition 2 without this assumption. In this section the Proposition 3 The model with non-violent technology cost function is not convex (and c(0) > 0) as this is not necessary to has a unique equilibrium, where: ensure interior solutions when both actors choose violence.

247 S. P. Harish and Andrew T. Little

The rents for being the incumbent are again ψ.So, Proposition 4 In the two actor model, the level of vio- actor J ’s net present value of committing violence level lence committed by both actors in period t is increasing  vJ,t in period t (given the future violence choices) is kt and decreasing in kt for all t < t. Proof. See the Appendix.  π , =− + δ , π∗ + O(t vO,t; vI,t) vO,t [p(vO,t vI,t; kt) I (t 1) The intuition for the opposition violence choice is + − , π∗ + , similar to the main model: if violence will be more [1 p(vO,t vI,t; kt)] O(t 1)] effective in the future (e.g., because of an election), the π , = ψ− γ + δ , π∗ + I (t vO,t; vI,t) vI,t [p(vO,t vI,t; kt) O(t 1) opposition invests less in violence anticipating it will ∗ be more effective later. The fact that violence will be + [1 − p(vO,t, vI,t; kt)]π (t + 1)]. I more effective in the future also leads the incumbent to choose less, as even if they are ousted they will have Our solution concept now requires that the violence an opportunity to take power back during the election. choices are mutual best responses given future violence Another intuition for the incumbent violence choice choices (see the Appendix for a formal statement) By a is that they are reacting to anticipated violence choices π∗ + >π∗ + standard analysis, whenever I (t 1) O(t 1) the by the opposition, and increasing the violence choice equilibrium violence choices are given by: by the opposition gives the incumbent an incentive to commit more violence to counteract this. Formally, the δ π∗ + − π∗ + marginal benefit for the incumbent violence choice is ∗ kt [ I (t 1) (t 1)] v = O , (9) increasing in v , as long as v , < v , , which is always O,t + γ−1 2 O t O t I t (1 ) true in equilibrium. That is, making violence more ef- fective for the opposition during elections can lead to γ−1 δ π∗ + − π∗ + ∗ kt [ I (t 1) O(t 1)] more incumbent violence. During elections, this can v , = (10) I t (1 + γ−1)2 lead to a spiral effect where the incumbent reacts to opposition violence with even more of their own. π∗ + <π∗ + However, there is a similar but peaceful spiral effect in and if I (t 1) O(t 1) both actors choose no vio- π∗ + > nonelectoral periods: since the opposition would rather lence (see the Appendix for detail). Since I (T 1) π∗ + wait to use violence, the government has less reason to O(T 1), the level of violence chosen in the last pe- ∗ > repress them. riod is positive for both actors: vJ,T 0. It immediately follows from equations (9) and (10) Continuous Policy Outcomes that the level of violence chosen by both actors in pe- riod t (when strictly positive) is increasing in the effec- Finally, a drawback of the models so far is that they tiveness in period t. Further, since γ<1, the incumbent only consider violence committed to take control of the always chooses more violence than the opposition, and government, while much political violence has more hence always remains the incumbent with a probability incremental goals. To show that the logic of our model greater than 1/2. As γ → 0, the incumbent commits applies to this more general class of political violence, far more violence than the opposition, indicating this we briefly present a variant of the model where a single extension can capture cases where the vast majority is political actor chooses a level of violence to affect a committed by government forces. continuous policy outcome. Unlike before, there is only Using these violence levels to compute the net one actor and no “incumbency”; i.e., the same actor present value for entering period t as each party, the chooses a violence level in each period to influence the difference between these payoffs is policy in their preferred direction. Formally, the actor chooses violence level vt in each of T > 1 periods. The policy in period t + 1is k ∗ = π∗(t) − π∗ (t) = ψ+ δ 1 − 2 t ∗ . t I O + γ−1 t+1 1 yt+1 = (1 − kt)yt + ktvt, (11) where kt ∈ [0, 1]. That is, the policy in each period is a γ< ∗ ∗ Since 1, whenever + is positive, t is positive as weighted average of the past policy and the efforts of ∗ t 1 well, so by induction t is positive for all t and hence the political actor. When kt is higher, violence will be both actors choose a strictly positive level of violence more effective in period t, or, equivalently, the status ∗ in each period. Further, t is decreasing in kt: when quo is “less sticky.” The period utility as a function of violence is more effective in period t, the difference the policy and violence choice is between entering this period as the incumbent versus = − 2 opposition decreases. So, there will be less violence ut yt cvt committed in period t − 1askt increases. ∗ The same inductive argument then implies that t−1 and the payoff for the entire game is ∗  < ∗ is decreasing in kt,asis t for any t t, and hence vJ,t−1 is decreasing in kt for both J = I and J = O. Combined T i−1 T with the fact that the violence levels in period t are δ ui + aδ yT+1, increasing in kt: i=1

248 The Political Violence Cycle where a > 0 represents the relative importance of the after the election. (Of course the regime may respond policy at the end of the game. to these protests with violence of their own; see e.g., The main insight from this model is that violence Arriola 2014). committed in period t increases the policy in every Most theorizing about postelection protest is back- future period. However, the impact on periods be- ward looking, in the sense that groups are motivated yond the next one is diminished by the fact that future to protest the process or outcome of the election (Dax- policies are also shaped by future violence choices. In ecker 2012; Hyde and Marinov 2014; Rozenas 2012). particular, a marginal increase in violence in period t This idea can be incorporated in our model by inter- − increases yt+1 bykt, yt+2 by kt(1 kt+1), and for any preting the time immediately after the voting as part τ> + τ−1 − of the electoral period, and postelection protest con- t 1, yτ by kt i=t+1(1 ki). So, the total return to violence today is increasing in kt and decreasing in the tributing to violence being more effective in electoral effectiveness of violence in every future period: periods. Our approach also highlights a more nuanced Proposition 5 In the continuous policy model, the and forward-looking explanation for why opposition amount of violence committed in period t is groups turn to violence after elections. Violence is par- (i) increasing in kt, ticularly attractive to electoral losers in times just after  (ii) decreasing in kt for all t > t. defeat for several reasons. First, if parties are more apt to use violence when the status quo is unfavorable, par- In addition to demonstrating that the results in the ties losing elections will have more to gain by turning baseline model extend to “policies” other than who to violence. Second, as demonstrated in the extension controls the government, this model provides an alter- with substitution, violence can peak after elections be- native intuition for why elections may reduce violence cause this is a time when nonviolent political activity is overall. When committing violence today, political ac- relatively ineffective (compared to electoral periods) tors are not just attempting to change the status quo for and it is the time when the opposition has the longest the “next period,” whether that be a day, year, or elec- to wait until nonviolent technologies become available toral cycle. Since policy tends to be sticky, the marginal (and violent actions more effective) at the next elec- benefit to violence today is a discounted sum of how tion. That is, when a party has to wait a long time to violence today affects policy for every future period. affect policy via elections they are more apt to turn to The effective discount rate for the future is not just violence to affect the status quo in the short term. a function of patience, but whether whatever political Our argument also provides insight into studies gains made today could be reversed in the future. So, about what institutional contexts are most prone to if elections increase the chance that any political gains spikes of violence around elections. Aksoy (2014) finds may be reversed, there is less reason to commit violence that terrorism in democracies tends to cluster around in nonelectoral periods. elections in systems with lower “electoral permissive- ness,” meaning it is harder for small parties to have a DISCUSSION formal role in politics. This can be interpreted in light of the model with violent and nonviolent technology. The central conclusion from all of the models is that If low electoral permissiveness means that nonviolent comparisons between levels of violence in electoral technologies are not effective, marginalized groups versus nonelectoral periods using observational data resort to violence during the election as that is their can lead to misleading conclusions about the efficacy only choice and the most effective time to do so. of elections for reducing the overall amount of violence What does our model have to say in terms of novel in society. Put another way, that elections are violent is predictions for future empirical work? We view the theoretically consistent with the general result that so- generality and small number of parameters in the cieties with more meaningful elections generally have model as a feature which provides confidence that the lower levels of conflict (Cheibub and Hays 2016, Gled- core of our argument holds across many political set- itsch and Ruggeri 2010; Hegre et al. 2001; Poe and Tate tings. However, this also means there are few compar- 1994). ative static predictions about how different institutions More specifically, the models also provide insight or other political and economic variables affect how into several recent empirical studies of when certain much violence will be used during elections or the types of elections in certain contexts are particularly difference between violence levels in electoral versus violent. First, several recent studies examine the preva- nonelectoral periods. So, one way to push the litera- lence of postelection protests (Daxecker 2012; Hyde ture forward both theoretically and then empirically and Marinov 2014; Rozenas 2012), and Straus and would be to write models that combine the forces we Taylor (2012) find that in Africa most violence is per- introduce here with political institutions to generate petrated by regimes, but the relative share of vio- comparative static predictions on variables which we lence perpetrated by opposition groups is higher af- could map to data. ter elections. Figure 7 shows this differential pattern Perhaps more importantly, future empirical work from the SCAD data used before for progovernment could aim to examine our more general contention and antigovernment violence. While progovernment that the ability to attain political goals during elections, violence tends to be higher leading up to and during whether with violence (parts (ii) and (iii) of Proposition election day, antigovernment violence is highest just 2) or other nonviolent tactics (part (i) of Proposition 3)

249 S. P. Harish and Andrew T. Little

FIGURE 7. Patterns of Pro- and Antigovernment Violence Around Elections

Pro−Government Anti−Government 0.2 0.4 Avg Violent Events Violent Avg Avg Violent Events Violent Avg 0.0 0.00 0.05 0.10 −30 0 30 −30 0 30 Days to Election Days to Election makes politics more peaceful in nonelectoral periods. tution when thinking through the broader implications Isolating variables that only change the effectiveness of their findings. in electoral periods (but not elsewhere) could prove difficult. One potential avenue for doing so would be to examine how (preferably exogenous) changes to ex- APPENDIX pectations about how competitive future elections will Data be affect violence in time periods after this revelation but before the election. Another potential empirical Figure 8 shows how the patterns we identify are less stark avenue would be to examine the effect of elections in but still clear when looking at wider time windows around places that hold both scheduled and early elections, elections. and analyze whether it leads to a political violence cy- For this and the graphs in the main text, we use two main cle similar to the available evidence on budget cycles data sources to examine the empirical patterns of violence (Khemani 2004). around elections. Violence data are obtained from the Social Conflict Analysis Database (SCAD), Version 3.0 (Hendrix and Salehyan 2012). This dataset provides information on CONCLUSION different types of violent events (protests, riots, strikes, and Elections play an important role in democracies but other social disturbances) in Africa and Latin America from they are often accompanied by violence against both 1990 to 2012. The main source of these events are based on the Associated Press and Agence France Presse news wires, candidates and voters. We have shown that the spike 26 in conflict levels around elections does not necessarily indexed by the Lexis-Nexis news service. Election dates imply that elections cause more political violence in and characteristics are from the National Elections Across general. When elections are the central means to con- Democracy and Autocracy (NELDA) Dataset (Hyde and Marinov 2012). This dataset provides information on election test for political power, they may also become the most 27 effective times to use political violence. It is precisely events for all countries during the period 1945–2010. the expectation of the ability to use violence effectively To generate these figures, we first reshape the SCAD data in a future electoral period that results in relatively into a “country-day” unit of analysis. Second, for each coun- lower levels of violence in nonelectoral periods. When try and each day we determined the distance to the nearest elections also provide a nonviolent means to contest election using the NELDA data. For example, if the previous election in a country was 200 days ago and the next is in 201 for power, there is even less reason to commit vio- − lence both during electoral and nonelectoral periods. days, the distance to election variable is 200. In the next day Elections can be peaceful for two reasons: either they when the previous election was 201 days ago and the next is in are not a serious means to contest for power, or they 200 days, the distance variable becomes 200. Figures 2, 7,and provide such an effective nonviolent means to contest 8 plot the average levels of violence levels by this distance to for power that violence is no longer a useful tool. election variable, sometimes for subsets of the data identified More generally, the model highlights cycles of any by other characteristics. political activity surrounding elections, whether fiscal For Figure 2, we distinguish between elections when the policy, repression, or interest group attempts to influ- incumbent leader’s office was in contention versus when it ence policy do not mean these activities would be more was not. This was done using the variable in the NELDA or less prevalent if elections were less consequential. dataset that captured whether the office of the incumbent When the actions spiking around elections are “bad” leader was contested in a given election. it is easy to associate elections with negative conse- quences, but concentrating the time window in which 26 these bad actions are most effective may leave citizens For more information on the search methodology and the coding procedure, see the Social Conflict Analysis Database, Version 3.0 better off in the long term. So, empirical work examin- codebook. ing how elections affect patterns of any political activity 27 For more information on what constitutes an election, see the must keep in mind the effects of intertemporal substi- NELDA codebook.

250 The Political Violence Cycle

FIGURE 8. Violence Around Elections for Wider Time Windows

Incumbency at Stake Incumbency not at Stake 0.3 0.6 Avg Violent Events Violent Avg Events Violent Avg 0.0 0.0 0.3 0.6 −180 0 180 −180 0 180 Days to Election Days to Election Incumbency at Stake Incumbency not at Stake Avg Violent Events Violent Avg Avg Violent Events Violent Avg 0.0 0.3 0.6 0.0 0.3 0.6 −365 0 365 −365 0 365 Days to Election Days to Election

∗ For Figure 7, distinguished between pro- and antigovern- The effect of increasing kt on vt−1 is determined by how ∗ ∗ ment violence around elections, progovernment violence was increasing kt affects t , which in turn affects vt−1. Formally, identified using the variable in the SCAD dataset that cap- tures “distinct violent events waged primarily by government ∗ ∗ ∗ ∂ ∂π (t) ∂π (t) authorities, or by groups acting in explicit support of govern- t = I − O . k k k ment authority, targeting individual, or ‘collective individ- t t t ual,’ members of an alleged opposition group or movement.” π∗ Antigovernment violence was identified using whether the The effect of increasing kt on I (t) is entirely through the fact ∗ “central government the target of the event,” and whether that doing so increases p(vt ; kt), both directly by increasing 28 ∗ any of the issue areas involved elections. kt and indirectly by increasing vt .So

Proof of Proposition 1 ∂π∗(t) dp(v∗; k ) Equation (3) has a unique solution for t = T, which gives I =−δ∗ t t < 0. ∂ t+1 π∗ π∗ kt dkt unique values of O(T)and I (T), which then implies the ∗ optimal vT−1 by equation (6). Further, if there is a unique π∗ π∗ ∗ O(t)and I (t), this leads to a unique vt−1, which is given For the change in the value of entering as the opposition the ∗ ≤ by equation (6) when t 0 and equal to zero other- analogous calculation has more terms as they incur a higher wise. So, by induction there is a unique triple of sequences cost to commit more violence, but by the envelope theorem π∗ ,π∗ , ∗  ( I (t) O(t) vt ) which solve equations (2)–(5)forallt. this effect drops out, giving Proof of Proposition 2 ∂π∗ (t) ∂v∗ dp(v∗; k ) Figure 9 illustrates the logic of how how changing k affects O =− t  ∗ + δ∗ t t t c (vt ) t+1 ∂kt ∂kt dkt the violence choices and relative value of incumbency for ∂ ∗ ∂ ∗ periods up to t. vt  ∗ ∗ p(vt ; kt) =− −c (v ) + δ + The most direct effect of increasing kt is to increase the ∂ t t 1 ∂ ∗ kt vt level of violence in period t, which can be demonstrated by ∗ ∗ ∂ p(v ; kt) implicitly differentiating equation (6) with respect to kt: + δ t t+1 ∂kt ∗ ∂2 ∂ ∂ ∗ − p(vt;kt) ∗ ∗ p(vt ; kt) v ∂v ∂k t+1 = δ + > 0. t = t t > 0, t 1 ∂k ∂2p(v ;k ) ∗ t ∂kt t t  −  ∗ 2 + c (v ) ∂ vt t 1 t ∗ ∂π (t) ∂π∗ ∂∗ O > I (t) < t < Since ∂ 0and ∂ 0, 0. Since there is less where the inequality is true because the numerator is negative kt kt kt ∗ benefit to entering period t as the incumbent, this decreases and the denominator is negative at vt sinceitisatalocal the incentives to commit violence in period t − 1: maximum.

∂ ∂∗ ∗ p(vt;kt) t ∂v − ∂ ∂ t 1 =− vt kt < 0. ∂2p(v ;k ) ∗ 28 ∂kt t t  −  For more information on these variables, see the SCAD codebook. 2 + c (vt) ∂ vt t 1

251 S. P. Harish and Andrew T. Little

Equilibrium Definition for Extension with FIGURE 9. Illustration of Proposition 2 Nonviolent Action ∗ kt An equilibrium to the model with nonviolent action is a xt , ∗ π∗ π∗ vt , O(t), and I (t) that solve + π (t, v , x ) = c(v ) − c(x )/β + δ{p(v + x ; k )π∗(t + 1) ... ∗ ∗ ∗ O t t t t t t t t I vt−2 vt−1 v − t + − + π∗ + }, [1 p(vt xt; kt)] O(t 1) − + − + − ∗ ∗ (v , x ) ∈ arg max πO(t, vt, xt), t t , ... Δ∗ Δ∗ Δ∗ (vt xt) t−2 (+)t−1 (+) t π∗ = π , ∗, ∗ , O(t) O(t vt xt ) π∗ = ψ+ δ{ ∗, ∗ π∗ + I (t) p(vt xt ; kt) O(t 1) + − ∗, ∗ π∗ + } [1 p(vt xt ; kt)] I (t 1) The effect on even earlier periods is more nuanced. As  < − shown in Figure 9, how kt affects violence in t t 1, de- for t = 1,...,T. The main difference between this and the ∗ ∗ pends on how k affects   , which in turn depends on how k t t t main model is that there are two optimizing choices vt and ∗ ∗ affects   .Thisisgivenby t +1 xt . Proof of Proposition 3 ∗ ∂   ∂  The idea of the proof is to show that if the level of violence ∗ p(vt ;kt ) t +1 ∂v  ∂  ∂ β t =− vt kt , is nondecreasing in t, then the opposition must use strictly ∂2p(v ;k ) ∗ β ∂kt t t  −  more non-violent technology as t increases, which lowers the ∂2 t+1 c (vt) vt marginal value of using violence, contradicting the violence choice being nondecreasing. Formally, consider any β1 >β2, ∂∗ 1, 1 2, 2 + ∗ and let (xt vt )and(xt vt ) be the equilibrium decisions with t 1   which has the same sign as ∂k . To sign this, first write t 1 ≥ 2 t these two values of beta. Suppose vt vt .Sincec is increas- as  1 ≥  2  i =  i /β ing, this implies c (vt ) c (vt ), and since c (vt) c (xt) i,  1 /β ≥  2 /β β >β c (xt ) 1 c (xt ) 2. Combined with 1 2, this requires  1 >  2 1 > 2 ∗ = ψ− ∗ + δ − ∗ ∗ . c (xt ) c (xt ) and hence xt xt . But the equilibrium con- t c(vt ) [1 2p(vt ; kt)] t+1 ditions for the violence choice for both levels of βt and the concavity of p(·) imply that: So ∂ p(x1 + v1; k ) ∂ p(x2 + v2; k )  1 = t t t δ∗ < t t t δ∗ =  2 c (vt ) t+1 t+1 c (vt ) ∂xt ∂xt ∂∗ ∂v∗ t =− t c(v∗) ∂∗ ∂∗ t t+1 t+1 which contradicts v1 ≥ v2.So,v must be strictly increasing in t t t ∗ ∗ β ∂ p(v ; k ) ∂v t, proving part i. + δ − ∗ − ∗ t t t  ∗ [1 2p(vt ; kt)] 2 t+1 ∗ ∗ For part ii, it follows from part i that c (v ) is decreasing in ∂v ∂ t t t+1 β  ∗ /β β t,soc (xt ) t must be decreasing in t as well. If this fraction ∗ ∗  ∗ ∂v  ∗ ∗ ∂ p(v ; kt) approaches zero as β →∞,thenc (v ) → 0, which implies = t −c −  t t t ∂∗ (vt ) 2 t+1 ∂ ∗ ∗ →  ∗ /β β →∞ t+1 vt vt 0. If c (xt ) t does not go to zero as t ,thenit ∂ ∗+ ∗ →∞ p(xt vt; kt) → ∗ must be the case that x , which implies ∂ 0 + δ[1 − 2p(v ; k )] t vt t t and hence v∗ → 0. ∂ ∗ t =− vt  ∗ + δ − ∗ , 3 ∂∗ c (vt ) [1 2p(vt ; kt)] (12) t+1 Equilibrium Definition for Extension with Incumbent Violence where the last line follows from the period t equilibrium An equilibrium to the model with incumbent and opposition ∂∗ t > ∗ ∗ ∗ ∗ condition (equation (6)). Rearranging, ∂∗ 0 if and only violence is a v , , v , , π (t), and π (t) that solve t+1 O t I t O I if π , , = + δ{ , π∗ + O(t vI,t vO,t) c(vO,t) p(vI,t vO,t; kt) I (t 1) ∂v∗ + − , π∗ + }, δ − ∗ > t  ∗ . [1 p(vI,t vO,t; kt)] O(t 1) [1 2p(vt ; kt)] 3 ∂∗ c (vt ) (13) t+1 π , , = + δ{ , π∗ + I (t vI,t vO,t) c(vI,t) p(vI,t vO,t; kt) O(t 1) + − , π∗ + }, [1 p(vI,t vO,t; kt)] I (t 1) ∂∗ t From part (ii) we know that < 0, and if equation (13) ∗ ∗ ∂kt ∈ π , , , ∂∗ vI,t arg max I (t vI,t vO,t) ,..., − t−1 > vI,t holds for all t t 1, then ∂∗ 0 for each of these ∗ t ∗ ∗ ∂v  ∈ π , , , t < vO,t arg max O(t vI,t vO,t) periods, and hence by induction 0. v , ∂kt O t

252 The Political Violence Cycle

π∗ = π , ∗ , ∗ , O(t) O(t vO,t vI,t) Proof of Proposition 5 π∗ = ψ+ δ{ ∗ , ∗ π∗ + An equilibrium to the continuous policy outcome model is I (t) p(vI,t vO,t; kt) O(t 1) ∗ a sequence of violence choices where each vt maximizes the + − ∗ , ∗ π∗ + } [1 p(vI,t vO,t; kt)] I (t 1) expected payoff for the remainder of the game given the future violence choices. So, in period T, the actor chooses v to maximize for t = 1,...,T. The main difference between this and the T main model is that the incumbent and opposition choices − δT−1 2 + δT − + , must be mutual best responses, rather than the opposition yT cvT a [(1 kT)yT kTvT] violence choice being optimal in isolation. Derivation of equations (9)and(10) and Proof of giving first order condition, Proposition 4

The first order conditions if both actors choose a strictly pos- 2cvT = δakT, itive level of violence are ∗ = δ / ∗ and hence vT akT 2c. v , − 1 = k δ[π∗(t + 1) − π∗ (t + 1)] I t , In period T 1, the actor picks vT−1 to maximize t I O + ∗ 2 (vO,t vI,t) ∗ T−2 2 T−1 v δ cv − + δ [(1 − k − )y − + k − v − ] γ = δ π∗ + − π∗ + O,t . T 1 T 1 T 1 T 1 T 1 kt [ I (t 1) O(t 1)] ∗ ∗ + 2 T ∗ (vO,t vI,t) + δ { − − + + }. a (1 kT)[(1 kT−1)yT−1 kT−1vT−1] kTvT

π∗ + <π∗ + If I (t 1) O(t 1) there can be no solution to these Giving first order condition, equations: the objective functions are always decreasing in ∗ = vJ,t, so in any equilibrium both actors choose vJ,t 0. = δ + δ2 − . π∗ + >π∗ + 2cvT−1 kT−1 a [kT−1(1 kT)] If I (t 1) O(t 1) and both actors chose no violence, there is an upward discontinuity in the probability of taking over office at vJ,t = 0, so it is always better to choose an in- More generally, taking the discounted sum of the returns crementally small level of violence to no violence. If only one (including the continuation value at the end of the game) actor chose a strictly positive level of violence, the other actor gives could always deviate to a lower violence level and have the ⎛ ⎞ same probability of being the incumbent in the next period. + δ T i T1 π∗ + >π∗ + ∗ kt ⎝ ⎠ So, when I (t 1) O(t 1) both violence levels must be v = 1 + δ(1 − k ) + a δ(1 − k ) . t 2c j j interior, and by the preceding system of equation, this implies i=t+1 j =t+1 j =t+1 ∗ = γ−1 ∗ vI,t vO,t. Since violence is cheaper for the incumbent, they choose more in equilibrium. This also implies that in The result follows from differentiating this equation with equilibrium the probability of a transition of power in each   >  kt respect to kt and any kt for t t. period is 1+γ−1 . The net present values for entering in each role in period t when choosing the equilibrium level of violence is SUPPLEMENTARY MATERIAL To view supplementary material for this article, please ∗ ∗ kt ∗ visit https://doi.org/10.1017/S0003055416000733. π (t) =−v , + δ π (t + 1) O O t 1 + γ−1 I k + 1 − t π∗ (t + 1) , (14) References 1 + γ−1 O Acemoglu, Daron, and James A. Robinson. 2000. “Why Did the West Extend the Franchise? Democracy, Inequality, and Growth ∗ ∗ kt ∗ in Historical Perspective.” The Quarterly Journal of Economics π (t) = ψ− γv , + δ π (t + 1) I I t 1 + γ−1 O 115 (4): 1167–99. Aksoy, Deniz. 2014. “Elections and the Timing of Terrorist Attacks.” k The Journal of Politics 76 (4): 899–913. + 1 − t π∗(t + 1) (15) 1 + γ−1 I Aksoy, Deniz. 2015. “Terrorist Attacks are Linked to the Timing of Elections, but Only in States Where it is Difficult to Influence the Political Process.” Accessed 24 Sep 2015. http://blogs.lse.ac. ∗ uk/europpblog/2015/05/19/terrorist-attacks-are-linked-to-the- and the formula for t follows from subtracting these. For the proposition, part (i) follows immediately from timing-of-elections-but-only-in-states-where-it-is-difficult-to- influence-the-political-process/ equations (9)and(10). For part (ii), consider what happens  Arriola, Leonardo R. 2014. “Suppressing Protests During Electoral when violence becomes more effective in some period t .By Crises: The Geographic Logic of Mass Arrests in Ethiopia.” ∗  Manuscript. equation (11), t is decreasing in kt, which then implies that ∗ ∗   Bates, Robert H. 2008. When Things Fell Apart: State Failure vJ,t−1 and t−1 are both decreasing in kt . This in turn implies ∗ ∗ in Late-century Africa. Cambridge, UK: Cambridge University   that vJ,t−2 and t−2 are decreasing in kt . More generally, Press. ∗ ∗ ∗ ∗ vJ,t−j and t−j decreasing implies that vJ,t−j −1 and t−j −1 Bates, Robert, Avner Greif, and Smita Singh. 2002. “Organizing are decreasing. The result then follows by induction.  Violence.” Journal of Conflict Resolution 46 (5): 599–628.

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