Download Third Party Intervention to Prevent Atrocities

The Road to Hell?
Third Party Intervention to Prevent Atrocities
Andrew H. Kydd and Scott Straus∗
March 9, 2011
∗
Both at the University of Wisconsin, Madison, [email protected], [email protected]. The authors thank
the participants at a presentation at the Elliott School of International Affairs for their helpful comments,
in particular Holger Schmidt, Charles Glaser, Jim Goldgeier, Harris Mylonas, Jim Lebovic and Elizabeth
Saunders. The authors also received helpful comments at the International Relations Colloquium at the
University of Wisconsin, Madison, and the 2010 meetings of the American Political Science Association
1
Abstract
Preventing and stopping genocide and other large-scale atrocities have emerged as
important policy goals of the post-Cold War. However, a critical but stalled debate
exists about the effects of institutionalizing third-party commitments to halt atrocities.
From a deterrence perspective, some argue that the credible threat of intervention
increases costs on perpetrators, thereby decreasing the level of atrocities. Others argue,
invoking the economics literature on “moral hazard,” that third party intervention
may actually encourage rebellions by weak minorities that would otherwise have no
prospects of success, and hence make war and its associated atrocities more likely.
To break the impasse, we develop a new intervention game to model the effects of
third-party commitments to end atrocities. We find that the points made by both
camps have merit. However, based on the insights into the dynamics of violence that
the model provides, we derive a set of remedies to minimize the negative impacts
of increasing third-party commitments to end atrocities. We conclude that in most
situations and with the proper institutional design, the net impact of stronger thirdparty commitments to end atrocities will be to lower the expected level of atrocities.
2
Since the end of the Cold War, an important policy debate and a substantial body of
literature has emerged around the question of third-party military intervention to prevent or
stop mass atrocities, in particular genocide and mass killing (Wheeler 2003; Weiss 2007). One
important debate has focused on the legality and legitimacy of such third-party interventions,
which are often labeled “humanitarian interventions.” Such actions generally require the
coercive deployment of force by an external actor or coalition of actors, which runs contrary
to sovereignty protections in the United Nations Charter (Hoffmann 1996; Holzgreze and
Keohane 2003; Rotberg 2010; Teson 1997; Weiss 2007.) Advocates of intervention have
stressed the need to protect innocent life, while opponents have emphasized the sovereign
rights of weak states against international interference. The debate game to a head in the
context of the NATO intervention to prevent Serbian atrocities against ethnic Albanian
civilians in Kosovo in 1998-1999. In that case, strong sovereignty objections from Russia,
among other countries, blocked action in the United Nations Security Council, prompting
NATO to plan and implement the intervention (Wheeler 2003).
Advocates of intervention typically assume that it will have beneficial effects by preventing atrocities, and lament the lack of the “political will” required to intervene. Driven by
understandable normative concerns, they claim that intervention failures simply reflect weak
political commitments to risk blood and treasure in the name of protecting the human rights
of people in distant lands (Power 2002; MIGs 2009). Several recent policy initiatives are
designed to address these problems. The Responsibility to Protect (R2P) is a framework
developed within the United Nations system to clarify the sovereignty question and to provide criteria for intervention, among other third-party commitments such as reconstruction
(Evans 2008). The Genocide Prevention Task Force, also called the Albright-Cohen Report
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(2008), is a U.S. framework for building political will and developing a policy framework.
Both seek to institutionalize international rhetorical commitments to prevent and stop mass
atrocities.
However, a recent stream of literature challenges the underlying assumption that the
threat of third-party intervention will have a salutary effect. In particular, some scholars
argue that the threat of intervention encourages weak parties to a conflict to fight when
they would not otherwise do so and to provoke atrocities in order to generate bias against
their more powerful military opponents. In that way, greater institutionalization and greater
resolve to intervene in cases of mass atrocity will perversely increase the probability of war
and atrocities in war, in a grim illustration of the adage that the road to hell is paved with
good intentions. Advocates of this critique analogize the situation to the “moral hazard”
literature in economics in the sense that the threat of third-party intervention prompts
actors to engage in risky action they would not otherwise take (Crawford and Kuperman
2006; Kuperman 2008 a,b). The moral hazard position challenges the implicit deterrence
framework underlying the pro-intervention position, which assumes that stronger and more
credible commitments to intervene will increase the costs of committing atrocities thereby
creating disincentives to engage in such behavior.
This debate between advocates of intervention and their moral hazard critics has crystalized the question of what effect institutionalizing third-party commitments to end mass
atrocities would actually have, a question with clear and important theoretical and policy implications. Unfortunately, the debate cannot be resolved empirically for two reasons. First,
third-party intervention that is even purported to be motivated by stopping atrocities is historically quite rare, and usually accompanied by additional stated or unstated motivations
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like saving one’s own nationals, aiding friendly local forces or attempting to overthrow unfriendly regimes. Second, because the proposed policy change of greater institutionalization
has not happened yet, it is impossible to evaluate its effects empirically. On the theoretical
level, the debate also suffers from over reliance on argument by analogy to economic or other
strategic models, and a consequent lack of precision in understanding the strategic dynamics
of this specific problem. Third party intervention to stop atrocities is a complex enough
phenomenon, and distinct enough from the typical insurance context in which the moral
hazard literature arose, that it deserves serious strategic modeling in its own right.
In this paper we develop a game theoretic model of third party intervention to stop
mass atrocities, the first such model in which a third party, motivated by the desire to
reduce atrocities, attempts to establish a threshold on the allowable level of atrocities and
enforce this threshold by threats to intervene. The model builds on existing insights from
the literature on third-party interventions in armed conflict, but applies those insights to a
situation where one party in a conflict threatens to commit mass atrocities against civilians.
Two assumptions underlie the modeling in the paper: first, that mass atrocities are most
common in the context of armed conflict (Ulfelder and Valentino 2008; Straus 2007) and,
second, that parties to a conflict act strategically when they engage in atrocities (Kalyvas
2006; Valentino 2004).
The model clarifies a number of issues which are sometimes submerged in the existing
literature but are nonetheless central to resolving the debate. First, what should be the
criterion for evaluating whether institutionalizing a capability to intervene in the case of
atrocities is good or bad? Advocates of intervention implicitly argue that the main criterion
should be reducing the level of atrocities that occur in war, or simply, minimizing the number
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of civilians killed per war. This would seem unobjectionable, wars happen and it would be
good to make them less costly. The moral hazard critics claim, however, that this will
make war more likely by encouraging otherwise hopeless rebellions. The frequency of war is
another important variable that should be minimized. However, as our model shows, there
is a tradeoff between these two goals, because making war less costly makes it more likely in
incomplete information settings. What this tradeoff implies, however, is that we should care
not about the costs per war or the likelihood of war, but the expected costs of war over time,
which is the product of the costs per war and the probability of war. What is important
is not how many people die per war, or how many wars there are per year, but how many
people die from war per year. We therefore derive expressions for the expected costs of war
and discuss how this variable responds to various policy innovations.
Second, the model clarifies the mechanisms that underly both the good and bad effects
of intervention. Basically, our model illustrates two mechanisms by which the prospect of
intervention can affect the strategic interaction between two sides in a conflict: 1) altering
the expected outcome of the conflict and 2) reducing the costs of the conflict. The intervenor
can alter the expected outcome of the conflict, either by altering the distribution of power
between the two sides or by making outcomes preferred by the third party more likely than
they otherwise would be. Altering the balance of power between the two sides is sometimes
argued to have little impact on the likelihood of war or atrocities, since strengthening one
side should make the other side more accommodating in the negotiations. This is indeed
the case if the parties are risk neutral, but we show that if the parties are risk acceptant,
then strengthening the weaker side can precipitate war, as the moral hazard critics contend.
However, this effect is minimized if the third party has a relatively neutral ideal point, that
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is, it fights not to achieve victory for one side or the other, but to impose a compromise
settlement. Thus altering the expected outcome of war can increase the likelihood of war,
but with a neutral third party it need not.
The second mechanism, reducing the costs of war, is of course the main goal of the
pro-intervention school. This has the beneficial effect of reducing the level of atrocities
per war. However, as the moral hazard critics contend, this also makes war more likely.
The net effect on the expected level of atrocities is complex, and depends on the values
of certain parameters. However, the model also shows that the imposition of alternative
costs on the leadership of the atrocity committing side can compensate for the reduction in
costs on the part of the victims of atrocities. In effect, a well designed intervention regime
can transfer costs from the civilian victims of atrocities to the leadership of the atrocity
committing side, thereby keeping the likelihood of war fixed while reducing the cost per war
(for civilians), and so reduce the expected level of atrocities. This highlights the importance
of a multidimensional approach to the intervention problem, making use of compensating
policy tools to mitigate or eliminate undesirable consequences of imposing a threshold on
the permissable level of atrocities.
The intervention model developed in the paper contributes to breaking an intellectual
logjam about the likely effects of strengthening an international regime to prevent gross
violations of human rights. The paper also provides a theoretical foundation, rather than
simply a normative one, for developing international anti-atrocity mechanisms. Furthermore,
the findings from the model have direct policy implications. Finally, the paper puts the
formal theory literature on armed conflict and third party intervention in conversation with
the literature of genocide and mass killing, thereby helping to break down an artificial, but
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entrenched boundary.
1
The Debate
Two broad positions can be found in the literature on the effect of the prospect of intervention on the civil conflicts. What can loosely be characterized as the deterrence perspective
argues that credible threats to intervene to prevent atrocities should in fact reduce the level
of atrocities observed in war, ensuring that “never again” will the world stand by as genocide takes place. The provocation or moral hazard perspective argues that humanitarian
intervention, by reducing the costs of rebellion for weak actors and increasing their chances
of success, makes war more likely and hence causes more civilian deaths. The existing game
theoretic literature tackles portions of the question but does not provide an adequate answer.
Some models exhibit a neutrality result, in which intervention alters the balance of power
but does not affect the likelihood of war, or, implicitly, the level of civilian casualties. Others
find that the relationship between intervention and atrocities is non-monotonic.
1.1
The Deterrence Perspective
The deterrence perspective, influenced by the international relations literature on deterrence (Huth 1988, Huth 1999, Zagare & Kilgour 2000), argues that threats of third party
intervention in the event of atrocities should moderate conflict and facilitate conflict resolution, and the more credible the threats are the more effective they will be. In international
relations theory, the extended deterrence problem is usually understood as how to use threats
to prevent an antagonist from attacking a protege or client. The underlying game, at its sim8
plest, has one player deciding whether to attack another and if an attack takes place the third
party decides whether to intervene on behalf of its client or not (Signorino & Tarar 2006).
The client state is typically treated as a non-strategic actor. The central problem to be
solved is one of making the threats credible, given that carrying them out would entail costs
for the threatener as well, particularly in the nuclear arena (Powell 1990).
Deterrence theory has found a natural application to third party intervention. Harvey
analyzes the Bosnia conflict and finds that early threats lacked credibility (Harvey 1998).
Timothy Crawford develops a theory of “pivotal deterrence” in which the third party acts as
a pivot between the two antagonists, threatening to intervene against either one if it starts
a war (Crawford 2003). To the extent that a third party could make such threats credible
to both sides of a civil conflict, it could presumably prevent war and hence atrocities.
In line with this perspective, supporters of intervention argue that what is needed to
prevent atrocities is clear and credible threats by the international community to intervene
forcefully to prevent them. This will have the effect of deterring would be human rights
violators, and ensure that wars, if they are fought at all, will not be accompanied by atrocities.
1.2
The Moral Hazard Perspective
While this logic seems intuitive and compelling, some argue that intervention may actually make atrocities more likely by encouraging rebellion by organizations representing the
potential victims. Timothy Crawford and Alan Kuperman have applied the logic of moral
hazard to the problem (Crawford & Kuperman 2006). Most incidents of mass killing take
place in the context of a war in which an organization from the victim group challenges
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state authority. The prospect of intervention from the international community may encourage such rebellion from groups too weak to succeed on their own. Kuperman argues this
dynamic was at work in the Kosovo conflict in 1999, in that Kosovo rebels realized they
were too weak to successfully confront Serbia by themselves but hoped to provoke massacres
which would bring in the international community (Kuperman 2008b). The logic of moral
hazard holds that the prospect of international intervention on behalf of weak victim groups
encourages risky rebellions, much as insurance is said to encourage greater risk acceptance
and the prospect of public bailouts may encourage people to live in flood plains. The usual
remedies for this kind of problem in economic contexts are difficult to apply in the intervention context, but Kuperman recommends very close attention to whether rebel groups
provoke state genocides or are genuinely responding to them, and only intervening in the
latter case (Kuperman 2008a). The ability of states to monitor rebel group behavior, in fact,
raises questions as to whether the problem is really one of moral hazard, or the alternative
adverse selection in which information, rather than actions, is hidden (Rauchhaus 2009).
The idea that the possibility of intervention can be provocative is also found elsewhere in
the intervention literature. Jenne (2004) argues that third party support radicalizes minority
groups and makes war more likely. In response to Chaim Kaufmann’s argument that third
parties should support partition as a solution to ethnic civil wars, James Fearon argued that
this would create incentives for aspiring ethnic entrepreneurs to cause trouble in the hope
that the international community would eventually hand them a state (Fearon 2004).
The moral hazard argument, that intervention causes war rather than peace, is certainly
provocative. The analytical framework is problematic, however, because it treats the state
actor in the conflict as non-strategic. The state is compared, by analogy, to fires, floods, and
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other acts of nature against which insurance is purchased. But the state actor should also be
making calculations about the likelihood of intervention, and should scale back its demands
the more likely intervention is to take place against it (Grigoryan 2006, Rauchhaus 2006).
Thus a full explanation of how the prospect of intervention encourages genocide would have
to explain why rebel group demands escalate faster than state concessions in the face of an
increase in the likelihood of intervention. Some scholars also challenge the moral hazard
argument empirically, showing that a rise in multidimensional peacekeeping has not seen a
similar rise of atrocities and that in past mass atrocities there is little evidence that promises
of intervention spurred rebels to take actions they would not have otherwise taken (Bellamy
and Williams 2011).
1.3
Game Theoretic Approaches
While there is a small related game theoretic literature on third party intervention, few
authors tackle the debate between deterrence and moral hazard head on. Two papers by
Carment and Rowlands examine the impact of intervention on the likelihood of war and
the fighting effort of the parties. In the first, they focus on the interaction between the
third party and the stronger of the two warring parties, with the weaker side assumed to be
willing to accept whatever the third party can secure for it. They find that the greater the
salience of the conflict to the third party, the more likely the warring party is to concede and
therefore the more likely the intervention is to be successful (Carment & Rowlands 1998).
In the second paper, Rowlands and Carment examine a model influenced by Hirshleifer
(1995) in which two antagonists allocate their resources between fighting and productive
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activity (Rowlands & Carment 2006). They find that third party intervention can increase
or decrease the fighting effort of the two parties. Both models lack any explicit bargaining,
so cannot illuminate how intervention affects the bargaining between the two antagonists.
Rupen Cetinyan argues, in contrast to both the deterrence perspective and the moral
hazard perspective, that the prospect of third party intervention should have no impact on
the likelihood of conflict, only on the terms of the agreement (Cetinyan 2002).1 However,
his model differs from the usual setup in that the outcome of war is a deterministic result
of the balance of power and effort between the third party and the state actor. If the third
party stays out, the state imposes its ideal point with certainty. The more effort the third
party expends, the more the outcome shifts in its preferred direction, but the outcome is
always deterministic. This leaves open the question of whether the result holds when war is
considered a risky outcome, as it usually is.
The closest analysis to ours is Grigoryan (2010). Grigoryan examines escalation within
a civil conflict to higher levels of violence such as mass killing. The model assumes that the
third party is biased in favor of the weaker side and posits uncertainty about the resolve of
the third party to intervene in the conflict. A low likelihood of intervention generates an
equilibrium in which a deal is reached based on the bilateral strength of the parties. Raising
the likelihood of intervention can cause war because of uncertainty about whether the third
party will intervene and the temptation to demand more in the face of such uncertainty. A
high likelihood of intervention leads to a deal on terms preferred by the third party.2
1
See Wittman (1979), Fearon (1993) and Powell (1996) for related work on the effect of the balance of
power on stability.
2
For a somewhat similar result in the context of mediation, see Favretto (2009).
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Grigoryan’s analysis is very helpful, but he makes certain assumptions that renders it
not perfectly appropriate for our purposes. First, he assumes that the demand made by the
minority group is fixed, rather than subject to adjustment. Given the well known result that
issue indivisibilities can cause conflict as well as uncertainty, it leaves unclear what is driving
the conflict in the model, the indivisibility or the uncertainty. We assume instead that the
parties can make any demand along a continuum, and so can smoothly adjust the demand
in response to changes in relative power, uncertainty, or other factors. Second, by assuming
that the third party’s payoff is a function of one of the two bargainers, Grigoryan cannot
consider the case where a third party is relatively unbiased and intervenes with the aim of
reducing atrocities and achieving some compromise solution. In fact, in his discussion of
the Kosovo case he agues that third parties do not try to restrain provocative rebel groups
because they share their antipathy to the state and are using the rebellion as a convenient
pretext to weaken their shared opponent. While this may be true in some cases, it is not a
fair characterization of what advocates of humanitarian intervention are proposing, namely
a more or less unbiased intervention capability designed to limit atrocities in war. Finally,
the way Grigoryan structures the model, escalation to high levels of atrocities can only
happen after an initial intervention by the third party. While this closely corresponds to the
Kosovo case, it ignores the fact that many cases escalate to high levels of atrocities without
any international intervention. A model that fairly evaluates the utility of an unbiased
intervention capability must at least have a possibility for high levels of atrocities without
international intervention.
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2
A Model of Intervention
There are three actors, the government side, player 1 and the rebel side, player 2, and
the third party and potential intervenor, player 3. The players confront a set of possible
issue resolutions, represented by the unit interval X = [0, 1], illustrated in Figure 1. Player
1 has increasing preferences, player 2 has decreasing preferences, and player 3 has single
peaked preferences and an ideal point, I3 ∈ [0, 1], that can be anywhere in the interval. The
bargaining parties utility functions are normalized so that they value their own ideal point at
1 and their adversary’s at 0, ui (Ii ) = 1, ui (Ij ) = 0. The third party also values its own ideal
point at 1 and values the government and rebels’ ideal points equally at zero, u3 (I3 ) = 1,
u3 (0) = u3 (1) = 0. This last assumption implies that the third party will be motivated to
intervene primarily by a desire to reduce the costs of the conflict rather than to affect the
bilateral probabilities that the parties achieve their most desired outcome.
The three players play a game illustrated in Figure 2. Player 1 starts the game by making
an offer to player 2 of some issue resolution x ∈ X. If Player 2 accepts the offer the game ends
with payoffs u1 (x), u2 (x), u3 (x). If player 2 rejects the offer, a war breaks out. Player 1 then
has the choice of how to fight the war. Specifically, it chooses a level of atrocities to commit,
a ∈ [0, 1] where 0 indicates a “clean” counterinsurgency campaign that scrupulously avoids
targeting non-combattants, and 1 indicates an all-out genocidal campaign against civilians
associated with the rebels. Player 3 then has a choice to impose sanctions on the party
committing atrocities, or to intervene in the war. We assume that sanctions remain in place
even if there is an intervention, so the choice is to impose sanctions alone or in combination
with intervention. Sanctions impose a cost s1 on player 1.
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Figure 1: The Player’s Utility Functions
15
Figure 2: The Intervention Game
16
We model war, following the usual convention, as a lottery in which the victor imposes
its ideal point. Departing somewhat from convention, we assume that this holds true in a
trilateral war as well as a bilateral one. That is, we assume that the third party fights to
impose its own ideal point, rather than aligning with one of the two parties and helping them
impose their ideal point. This assumption is motivated by the fact that there is no reason
for a third party to fight to impose a solution more extreme than the one it prefers. If a
third party intervenes on behalf of the weaker of the two sides, say, and prevents its defeat
why should it then go on to destroy the other side and impose it’s ally’s preferred outcome?
It would make much more sense to stop fighting once the outcome approximates its ideal
point or even switch sides if its ally becomes too powerful and threatens to achieve a total
victory. Of course, if the third party’s ideal point is near 1 or 0, it will effectively fight for
its ally’s ideal point, so this can be considered a special case of the model. But by assuming
that third parties fight to impose their own ideal points, we can consider a range of more
realistic scenarios in which third parties have interior ideal points and so prefer, and fight to
achieve, compromise solutions.
We assume that the government’s chance of victory against the rebels depends on the
level of atrocities. Specifically, we assume that player 1’s chance of winning a bilateral war,
denoted pb1 (a), is an increasing function of a, so the government side increases its chances of
winning by engaging in more atrocities. We fully realize that this may not be the case in all
civil wars, but in such cases the government would not be tempted to engage in atrocities,
so the international community would not face a question of whether to intervene to prevent
them. Since we are concerned with the effects of intervention motivated by atrocities, we
focus on the case in which the war participants at least believe that they have incentives to
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commit them.3 We define the rebel’s chance of winning a bilateral war as pb2 (a) = 1 − pb1 (a)
so the rebels are less likely to win the higher the level of atrocities. We assume that the third
party’s chance of winning if it decides to intervene, denoted p3 is unaffected by the level of
atrocities. The chance of winning a trilateral war after an intervention for the government
and rebels are defined as pti (a) = (1 − p3 )pbi (a). The trilateral chances of winning therefore
also sum to 1 as they should, (1 − p3 )pb1 (a) + (1 − p3 )pb2 (a) + p3 = 1.4
The parties pay costs if there is a conflict. The direct cost for player i of fighting is denoted
ci . The third party only incurs direct costs if it decides to intervene. The rebel group and the
third party also suffer costs as a function of the level of atrocities, denoted k2 a and k3 a, where
ki > 0. These costs from atrocities are incurred by the third party regardless of whether
it intervenes. Finally, if the third party does intervene, it punishes player 1 for committing
atrocities by imposing an additional cost k1 . This represents the additional sanctions and
other punishments that accompany interventions targeted at coercing a state into refraining
from atrocities, such as the punishment of leaders involved in atrocities before international
tribunals.
Finally, we assume that intervention prevents some atrocities from occurring. That is, we
assume that intervention reduces the level of atrocities by a factor of δ ∈ [0, 1] so that if the
government selects a level a and the third party intervenes, the resulting level of atrocities
3
We assume that the government side has a positive chance of winning even if it commits no atrocities,
pb1 (0) > 0, and that it may still lose even if it engages in all out genocide, pb1 (1) < 1.
4
The familiar assumption that the probability of winning equals the ratio of military power exhibits this
feature. If we assume each side has military power, mi , player 1’s chance of winning a bilateral war with
player 2 is pb1 =
to pt1 =
m1
m1 +m2
but if player 3 joins the war, making it trilateral, player 1’s chance of winning falls
m1
m1 +m2 +m3 .
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Table 1: The War Payoffs
Without Intervention
With Intervention
Player 1 pb1 (a) − c1 − s1
pt1 (δa) + p3 u1 (I3 ) − c1 − s1 − k1
Player 2 pb2 (a) − c2 − k2 a
pt2 (δa) + p3 u2 (I3 ) − c2 − k2 δa
Player 3 −k3 a
p3 − c3 − k3 δa
will be δa where δa < a. Note, it may be that in some cases intervention increases the level of
atrocities, in such cases the third party should not intervene for humanitarian reasons.5 Here
we are focusing on the potential effects of a humanitarian regime motivated by preventing
atrocities, so we will assume that the intervention, if it occurs, actually does so.
Putting all of this together, the war payoffs are shown in Table 1. If the third party
stands aside, the two parties fight a bilateral war and the third party pays the indirect cost
of fighting, k3 a, associated with refugees, humanitarian aid, etc. If the third party intervenes,
the war becomes trilateral. The third party has a p3 chance of imposing its ideal solution,
pays the direct costs of fighting, c3 , and its intervention reduces the level of atrocities to δa.
2.1
The Complete Information Case
We first solve the game assuming complete information between the two bargaining parties,
using subgame perfection as the solution concept. Starting at the end of the game, the third
5
For instance, Grigoryan (2006) makes the point that the high level of Serbian ethnic cleansing in Kosovo
was a response to rather than cause of NATO intervention in 1999.
19
party will intervene if
−k3 a < p3 − c3 − k3 δa.
or if the level of atrocities exceeds a certain threshold
a > a† ≡
c3 − p3
.
k3 (1 − δ)
(1)
Note, if the third party’s power exceeds the cost of intervention, p3 > c3 , then the third
party will intervene even in the absence of atrocities, when a = 0. Given the low probability
of this holding true in the context of humanitarian intervention, we assume that c3 > p3 , so
that the intervention threshold is positive, a† > 0.
Turning to player 1’s choice of the level of atrocities to commit, any level a < a† is
dominated by a† since the latter results in no intervention and a greater chance of winning.
Any level greater than a† but less than 1 is dominated by 1 because intervention is assured
in any case, so player 1 might as well maximize atrocities. Player 1 therefore compares the
utility of a† with no intervention and a = 1, with intervention. Player 1 will choose to abide
by the threshold if
pb1 (a† ) − c1 − s1 > pt1 (δ) + p3 u1 (I3 ) − c1 − k1 − s1
or rearranging slightly
pb1 (a† ) − pb1 (δ) + p3 (pb1 (δ) − u1 (I3 )) + k1 > 0.
(2)
The greater the threshold, a† , the the more likely equation 2 will hold and player 1 will
observe the threshold. The lower the threshold, the lower the left hand side is and the more
danger there is of player 1 escalating beyond the threshold.
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Turning now to player 2’s choice, there are two cases to consider. If player 1 will choose
a† , the war will be bilateral and player 2 will reject the offer if
u2 (x) < pb2 (a† ) − c2 − k2 a†
and accept it otherwise. Let r2b be player 2’s reservation value, or the level of x that solves
this equation with equality. If player 1 opts for a = 1, there will be intervention and player
2 will reject the offer if
u2 (x) < pt2 (δ) + p3 u2 (I3 ) − c2 − k2 δ
Let r2t be the level of x which solves this with equality.
Finally, consider player 1’s offer. If the war will be bilateral, player 1 compares player
2’s bilateral reservation value with its war payoff and will make an offer that satisfies player
2 if it is better for player 1 than war, or if
u1 (r2b ) ≥ pb1 (a† ) − c1 − s1 .
(3)
If player 1 will violate the threshold and intervention will take place, player 1 will make the
peaceful offer if
u1 (r2t ) ≥ pt1 (δ) + p3 u1 (I3 ) − c1 − s1 − k1
(4)
What is the relationship between intervention and war in the complete information version of the game? We show in the Appendix that with risk neutral preferences, there will be
no war in the complete information version of the game, regardless of whether intervention
takes place or not. However, with risk acceptant preferences, there can be war in complete
information bargaining games (Fearon 1995). We therefore consider the following questions.
If the parties have risk acceptant preferences that cause war, can intervention reduce the
21
level of atrocities in these wars? Does the prospect of intervention ever cause war when it
would not have taken place otherwise? If it does, what can be done to reduce the likelihood
of this occurring?
A few numerical examples, presented in Table 2, can help answer these questions. In
the example, we assume that player 1 and player 2 are both risk acceptant, u1 (x) = x2 and
u2 (x) = (1 − x)2 . Some parameters are the same in all the cases considered, namely, δ = 0.9,
k1 = .01, and c1 = s1 = c2 = k2 = 0.1. Parameters that vary are listed in the table.
The first two cases, 1a and 1b, illustrate the ability of the shadow of intervention to lower
the level of atrocities that occur in wars that are brought on by risk acceptant preferences.
In these cases, the two sides are relatively evenly matched. Shifting from a clean counterinsurgency to maximal atrocities increases player 1’s chance of winning from 40% to 60%.6
Because the two sides are evenly matched and risk acceptant, war is likely since balanced
compromises are undervalued by both sides. The third party is quite powerful in comparison
to the parties, p3 = 0.8, and heavily biased in favor of player 2, I3 = .1. In case 1a, the third
party is uninterested in atrocities, with a relatively low k3 of 0.5. This produces an a† of 1,
which means that the third party will not intervene for any level of atrocities that player 1
selects. As a result, player 1 maximizes the level of atrocities, but the war occurs anyway
because of the even matching of the two parties.
In case 1b, the third party cares more about atrocities, k3 has increased to 2. This means
player 3 will be willing to intervene if the level of atrocities goes over a† = .5. The fact
that player 3 is so powerful and so biased in favor of player 2 convinces player 1 to observe
the threshold, so intervention does not take place. War still occurs however, but the level
6
The function is assumed to be linear, pb1 (a) = 0.4 + 0.2a.
22
Table 2: The Complete Information Case: Numerical Example
Case 1a
Case 1b
Case 2a
Case 2b
Case 2c
p3
0.80
0.80
0.25
0.25
0.25
c3
0.90
0.90
0.30
0.30
0.30
k3
0.50
2.00
0.50
2.00
2.00
a†
1.00
0.50
1.00
0.25
0.25
I3
0.10
0.10
0.10
0.10
0.50
u1 (I3 )
0.01
0.01
0.01
0.01
0.25
u2 (I3 )
0.81
0.81
0.81
0.81
0.25
pb1 (a† )
0.60
0.50
0.85
0.59
0.59
pb2 (a† )
0.40
0.50
0.15
0.41
0.41
pt1 (δ)
0.12
0.12
0.61
0.61
0.61
pt2 (δ)
0.08
0.08
0.14
0.14
0.14
Player 3
Stays Out Stays Out Stays Out Intervenes
Intervenes
r2
0.55
0.41
1.00
0.61
0.89
r1
0.63
0.55
0.81
0.64
0.68
Outcome
War
War
Peace
War
Peace
23
of atrocities is lower because player 1 restrains its conduct in order to avoid intervention.
Thus the contrast between case 1a and 1b illustrates the potentially beneficial effect of the
shadow of intervention, it can cause states that fight to moderate their conduct, even when
intervention does not take place.
In the next three cases we consider the potential unintended consequences of intervention
and how they can be mitigated. In these cases, the third party is weaker, with p3 only equal
to 0.25. We also assume that the balance of power between the two sides is more lopsided
in favor of player 1, so with no atrocities player 1’s chance of winning is pb1 (0) = 0.5 and
with maximal atrocities it is pb1 (1) = .85. In case 2a we again assume that the third party is
uninterested in stopping atrocities so k3 = .5 and a† = 1. In this case, player 1 will maximize
the level of atrocities if war occurs, and this will produce a very lopsided balance of power
in its favor. This imbalance of power is conducive to peace, however, for it convinces player
2 to accept any deal in preference to war. The result is a peaceful bargain, favoring player
1, backed up by the threat of a very brutal war.
In case 2b, the third party has become more concerned about atrocities, with k3 = 2.
The threshold for intervention falls to a† = 0.25, so the third party is attempting to enforce
a fairly low threshold. However, its weakness, in combination with the great military utility
of atrocities, convinces player 1 to violate the threshold and escalate its level of atrocities
to a = 1. The third party therefore intervenes if war occurs. Unfortunately, the prospect
of friendly intervention encourages player 2 to hold out for more in the negotiations, since
although the third party is weak, at least it is on their side, which boosts their overall
chances of “winning” into the middling range where compromise becomes difficult with risk
acceptant preferences. Case 2b, therefore, illustrates the moral hazard argument. A lopsided
24
peace, case 2a, is disrupted by a weak threat of intervention which encourages intransigence
on the part of the weaker side, which ends up causing war and atrocities, the very outcome
intervention was supposed to prevent.
Can this unintended consequence be avoided? In case 2c we alter only one variable by
making player 3 more neutral between the players, by setting I3 = 0.5. Because of player 3’s
weakness and low threshold, player 1 would still violate the threshold, and player 3 would
intervene in a war. However, the neutral ideal point of the third party depresses player 2’s
appetite for war, because a victory for the third party is no longer nearly equivalent to a
victory for player 2. Since player 3 would impose an undesirable compromise settlement, it
does not raise player 2’s way payoff as much as in the case when player 2 is more heavily
biased in favor of player 2. The result is that player 2 becomes less intransigent in the
negotiations and there is now a bargaining range that both sides prefer to war. A peaceful
settlement is reached, just as in case 2a. The only difference is that player 2’s bargaining
position has been somewhat strengthened by the intervention regime, so it does better in
the negotiations.
We can sum up the results from the complete information case as follows. If the parties
have risk acceptant preferences, war is possible with complete information, especially when
power is relatively balanced between the two sides. The threat of intervention if a side
commits atrocities above a certain threshold can reduce the level of atrocities suffered in
these wars. However, the moral hazard perspective is correct in arguing that intervention
can provoke war as well. When power is imbalanced, and the third party is biased in favor
of the weaker side it may help move the balance of power into the middling range which
makes compromise impossible. However, this problem is less severe when the third party
25
has a more neutral ideal point, and does not overly favor one side or the other.
The complete information case sheds some light on the debate over intervention. However,
the assumption of risk acceptant preferences may not hold in many cases. An alternative
mechanism that can produce war even with risk neutral preferences is private information
about the costs of conflict. We turn next to an exploration of this case.
2.2
The Incomplete Information Case
We introduce uncertainty over player 2’s costs for fighting. Assume that player 2’s direct
costs for fighting are uniformly distributed over the interval [0, 1]. This assumption ensures
a full spectrum of behavior for player 2, in that the lowest cost type will fight if player 1
demands anything more than its relative power would justify, that is anything over p1 , while
the highest cost type will accept any deal at all rather than fight. The likelihood that player
2 has costs below c2 is F2 (c2 ) = c2 . Player 2 learns its own cost when the game begins, the
other players are uncertain.
The intervention decision by the third party is the same as in the complete information
case, as is the decision by player 1 on the level of atrocities to select. When we turn to
player 2’s decision, however, there are now a continuum of types and a resulting probability
of acceptance and rejection.
If player 1 will choose a† , the war will be bilateral and player 2 will reject the offer if
c2 < pb2 (a† ) − k2 a† − u2 (x)
The probability of bilateral war, denoted P (W b ), is just the the likelihood that the offer is
26
rejected, or
P (W b ) = F2 (pb2 (a† ) − k2 a† − u2 (x))
= pb2 (a† ) − k2 a† − u2 (x)
If player 1 opts for a = 1, there will be intervention and player 2 will reject the offer if
c2 < pt2 (δ) + p3 u2 (I3 ) − k2 δ − u2 (x)δ
The likelihood of trilateral war in this case is
P (W t ) = F2 (pt2 (δ) + p3 u2 (I3 ) − k2 δ − u2 (x))
= pt2 (δ) + p3 u2 (I3 ) − k2 δ − u2 (x)
Finally, consider player 1’s offer. Any offer less than p1 will be dominated by offering
x = p1 since the result will be certain acceptance for any such offer. If it demands more than
p1 , then there will be some chance of war. Once again we consider two cases, one in which
player 1 will opt for a† and one in which it will choose a = 1.
When player 1 will choose a† , the payoff for offering x = pb1 (a† ) is u1 (pb1 (a† )). Demanding
more than this will result in some chance of war and a payoff of
P (W b )(pb1 (a† ) − c1 − s1 ) + (1 − P (W b ))u1 (x)
(5)
When player 1 will choose a = 1, then the payoff for offering x = pt1 (δ) is u1 (pt1 (δ)). Demanding more will result in a chance of war and a payoff of
P (W t )(pt1 (δ) + p3 u1 (I3 ) − c1 − s1 − k1 ) + (1 − P (W t ))u1 (x)
(6)
Player 1 will choose an offer, denoted x∗ , that maximizes its payoff, depending on its future
behavior in war.
27
Table 3: Comparative Statics: Incomplete Information Version
Equilibrium Quantities
a†
p3
-
c3
+
k3
-
x∗b
P (W b ) P (W T ) E(a|W b ) E(a|W t )
-
I3
δ
x∗t
+
+
+
-
+/-
a†
+
pb1
+
+
c1
-
-
-
-
-
-
s1
-
-
-
-
-
-
k1
k2
-
+
+
+/-
-
-
-
-
There are four main variables the values of which are determined in equilibrium: the
intervention threshold, player 1’s offer, or demand, the likelihood of war, and the expected
level of atrocities. We discuss each in turn. All results assume risk neutral preferences, and
proofs are in the appendix. A table summarizing the comparative statics results is given in
Table 3.
28
2.2.1
The Intervention Threshold
The influence of the parameters on the intervention threshold, a† , are straightforward. Increasing the cost of intervention, c3 , raises the threshold, so player 1 can get away with more
atrocities. Increasing the power of the third party, p3 , decreases the threshold, reducing
the level of atrocities that will be possible without intervention. Increasing the sensitivity
to atrocities, k3 , and lowering the level of post-intervention atrocities, δ, will decrease the
threshold, further constraining player 1.
2.2.2
The Equilibrium Offer
If player 1 will observe the threshold and set a = a† , the equilibrium offer that player 1
chooses is
x∗b = pb1 (a† ) +
1 + k 2 a† − c 1 − s 1
2
(7)
If player 1 will not observe the threshold and set a = 1, the equilibrium offer in the case of
intervention is as follows.
x∗t = (1 − p3 )pb1 (δ) + p3 u1 (I3 ) +
1 + k2 δ − c 1 − s1 − k 1
2
(8)
The equilibrium demand is increasing in player 1’s power, pb1 , and decreasing in player
1’s costs for fighting, c1 and the costs of the economic sanctions, s1 . Sanctions, by punishing
player 1 for fighting, convey some bargaining leverage to player 2. Conversely, the demand is
increasing in player 2’s sensitivity to atrocities, k2 . The more costly player 2 finds atrocities,
the better player 1 does in the bargaining.
If the war will remain bilateral, then the offer is increasing in the threshold of atrocities,
a† . The higher the threshold, the more atrocities player 1 can get a way with, so the worse
29
the bargain for player 2. Lowering the threshold will therefore favor player 2 by lowering
player 1’s demand.
If the war will involve intervention, then the more powerful the third party is, p3 and the
more costly the intervention is to player 1, k1 , the lower the demand and the better player 2
does in the bargaining. The higher player 3’s ideal point, I3 , that is the closer it is to player
1’s, the better player 1 does since this improves the war payoff for player 1. Finally, the
higher the post-intervention level of atrocities, δ, the better the deal for player 1, since this
will increase player 1’s war payoff.
2.2.3
The Probability of War
If player 1 will obey the threshold and the war will remain bilateral, then the equilibrium
likelihood of war is
P (W b ) =
1 − k 2 a† − c 1 − s 1
2
(9)
If player 1 will escalate to a = 1 and the third party intervenes, the probability of war is
P (W t ) =
1 − k2 δ − c 1 − s1 − k1
2
(10)
Note, these are identical except for two factors. First, player 1’s costs for intervention, k1 ,
enters negatively in the trilateral case, lowering it in comparison with the bilateral case.
Second, δ replaces a† , and since δ > a† , this also lowers the trilateral probability. Therefore
war is more likely in the bilateral than in the trilateral case.
The comparative statics are straightforward. Anything that increases the cost of war
makes war less likely. Increasing player 1’s costs for combat and sanctions, c1 and s1 , both
decrease probability of war. Increasing player 2’s sensitivity to atrocities, k2 , decreases the
30
likelihood of war. Raising the threshold of intervention, a† , lowers the probability of bilateral
war by increasing player 2’s costs for war. Lowering the threshold, conversely, makes war
more likely by lowering its costs for player 2.
In the trilateral case, δ plays a similar role. Increasing the post intervention level of
atrocities, δ, makes war less likely and lowering it makes war more likely, by lowering its
costs for player 2. Increasing player 1’s costs for intervention, k1 , decreases the probability
of trilateral war by making it more costly.
An important point to note is that the impact of the level of atrocities, a† and δ, on the
probability of war depends on how much player 2 cares about atrocities, k2 . If player 2 cares
a great deal about atrocities, this impact will be large, since lowering the level of atrocities
will affect player 2’s decision calculus greatly. On the other hand, if player 2 is relatively
“brutal” and does not care much about atrocities, so k2 is low, then reducing the level of
atrocities will have little impact on the likelihood of war.
2.2.4
The Equilibrium Level of Atrocities
The expected level of atrocities is the probability of war times the level of atrocities. In the
bilateral case this is
1 − k 2 a† − c 1 − s 1 †
a
2
(11)
1 − k2 δ − c 1 − s1 − k1
δ
2
(12)
E(a|W b ) =
and in the trilateral case, it is
E(a|W t ) =
Increasing the costs of war decreases the expected level of atrocities. If player 1’s costs for
combat, sanctions and intervention go up, c1 , s1 and k1 , then the expected level of atrocities
31
goes down. If player 2’s sensitivity to atrocities goes up, then the expected level of atrocities
goes down. These variables reduce the likelihood of war without having any countervailing
impact on the level of atrocities per war, so their impact is unambiguous.
Changing the threshold level of atrocities, a† , and the level of post intervention atrocities,
δ, has a more complicated effect. Lowering the level of atrocities makes each war that occurs
less costly, but makes the occurrence of war more likely. These two effects work at cross
purposes in terms of the overall impact on the expected level of atrocities.
The derivative of the expected costs of war in the bilateral case with respect to a† is
∂E(a|W b )
1 − c 1 − s1
=
− k 2 a†
†
∂a
2
(13)
The corresponding term in the trilateral case is
∂E(a|W t )
1 − c 1 − s1 − k1
=
− k2 δ
∂δ
2
(14)
If these expressions are positive then the expected level of atrocities will go up as the
level of atrocities increases, and decline if the level of atrocities is lowered. The expression
will be positive if the costs of war, c1 , s1 and k1 , are relatively low.
Once again the role of player 2’s concern for the level of atrocities, k2 is crucial. If player
2 is very concerned with atrocities, k2 will be high and these expressions could be negative,
because lowering the level of atrocities makes war more likely and this effect dominates. On
the other hand, if the rebel group is brutal, with low k2 , then this expression will be positive,
and reducing the level of atrocities per war will reduce the overall expected level of atrocities.
32
2.2.5
The Marginal Player 1
Finally, we consider the effect of converting a marginal player 1 from pursuing all out genocide
to observing the threshold on the level of atrocities. If a marginal state 1 switches from a = 1
to a = a† , then the likelihood of war will increase, the atrocities per war will decrease and
the expected level of atrocities may rise or fall. Converting the marginal threshold observer
to a threshold violator will have the opposite of these effects.
In comparing the probability of war in the trilateral case to the bilateral case, it is lower
in the trilateral case because k1 is subtracted in the numerator and we assume that δ > a† .
These additional costs for war make it less likely in the trilateral case. Shifting player 1 to
observing the threshold will therefore increase the probability of war.
In looking at the effect of switching from a = 1 to a = a† on the expected level of
atrocities, we see that k1 is no longer subtracted from the numerator in the bilateral case,
which raises the expected level of atrocities. However, δ is also replaced by a† , which is a
lower level of atrocities. As before, the result of this depends on the costs of war. If war is
less costly, that is if c1 , s1 , and k2 are low, then switching to the bilateral war may decrease
the expected level of atrocities. The more costly war is, the more likely switching to the
bilateral case will increase the expected level of atrocities.
3
Implications and Analysis
To more clearly spell out the implications of the model we consider five topics. First we
compare a world in which there is effectively no intervention policy with one in which there
is a threshold at which intervention will take place. Second, we assess the effect of lowering
33
an existing threshold, to reduce the level of atrocities per war. Third, we consider multidimensional policy changes, designed to mutually reinforce each other and lead to a better
outcome than each one individually. Fourth, we consider what has been thought to be the
problem of the brutal rebel group. Finally, we address the topic of whether the threshold
for intervention does or should vary from country to country.
3.1
From No Threshold to Some Threshold
Many would argue that there is effectively no policy in place for humanitarian intervention to prevent atrocities today. Some interventions are justified by humanitarian concerns,
but there is no widely accepted policy in place to establish a mechanism for humanitarian
intervention that could operate in a transparent fashion to achieve that goal.
We can represent the no-intervention world by considering the model when c3 is prohibitively high, so that a† > 1 and therefore the third party never intervenes. In this case,
all wars are bilateral, and the level of atrocities is a = 1.
If we then consider a policy change that has the effect of lowering c3 , say establishing
an international organization to prepare the logistics for humanitarian interventions and for
clarifying the conditions and rules under which intervention takes places, this will lower a†
to some level below δ. This will divide the population of cases into two, because some will
obey the new threshold and some will not. Those who obey the new threshold will continue
to fight bilateral wars at the new threshold level of atrocities, a† , so the level of atrocities for
these wars will decline. The probability of war will therefore go up in these cases. The net
effect on the expected level of atrocities will depend, as discussed above, on the cost of war.
34
If c1 , s1 , and k2 are low, then the effect will be to reduce the expected level of atrocities. If
they are high, it may increase the expected level of atrocities.
Those cases that refuse to obey the new threshold will now incur intervention, and the
atrocity level will be δ. The atrocity level per war will therefore decline. The likelihood of war
may or may not increase. Shifting from the bilateral to the trilateral war increases player 1’s
costs for fighting by k1 , which makes war less likely. However, changing the level of atrocities
from 1 to δ reduces player 2’s costs for fighting, which increases the likelihood of war. The
net effect could go either way, or cancel out. Consequently, the effect on the expected level
of atrocities could also go either way. If the probability of war declines, because increasing
player 1’s costs dominates decreasing player 2’s, then the result will be a decrease in the
expected level of atrocities. Otherwise the expected level of atrocities may increase if the
probability of war increases enough. Note, if k2 is low, then the effect of increasing player
1’s costs will dominate, and the expected level of atrocities will fall.
3.2
From One Threshold to a Lower Threshold
Next, consider the effects of lowering an existing threshold, to further reduce the level of
atrocities per war. If a† is lowered, there are three types of state to consider, those who obey
the new threshold, those who were not obeying the old threshold, and those who switch from
obeying the threshold to violating it.
Those who continue to obey the threshold are still fighting bilateral wars. Their level of
atrocities goes down, and the likelihood of war goes up. Once again, the net effect depends
on the costs. If war is less costly, the expected level of atrocities will decline, if war is more
35
costly, then it will increase.
Those who were not obeying the original threshold will still fight trilateral wars. Nothing
will change for this population, so there will be no impact on the expected level of atrocities
in this case.
Finally, some will switch from obeying the threshold to not obeying it, in accordance
with equation 2. For these types, war that was once bilateral is now trilateral. The level of
atrocities per war goes up from the old threshold to the post intervention level of atrocities,
δ. The likelihood of war goes down, as a result, since player 1 suffers the additional cost
of intervention, k1 , and player 2 suffers the cost of the increased level of atrocities. The
effect on the expected level of atrocities is therefore mixed, but in the opposite way from the
previous comparisons. If the costs of war are low, then raising the level of atrocities is likely
to raise the expected level of atrocities in this case, if the costs of war are high, then raising
the level of atrocities per war will lower the expected level of atrocities.
3.3
Multidimensional Policy Changes
The mixed effects of policy changes that solely target the intervention threshold, a† , is
clear from the previous discussion. Most importantly, lowering the threshold of intervention
often has the undesired consequence of raising the probability of war and convincing some
belligerents to escalate their level of atrocities beyond the threshold. This suggests the need
to consider a broader set of policy tools that could potentially be manipulated together to
negate these unwanted effects.
First, consider the fact that lowering the threshold of intervention can cause some actors
36
that previously abided by the threshold to ignore the new threshold and escalate to a = 1.
Can this be compensated for by manipulating other variables? If we examine equation 2
we can see that there are three variables that can be manipulated to keep the expression
constant, despite lowering a† . First, if the post intervention level of atrocities, δ is lowered,
this will raise the left hand side of equation 2. Second, since player 1 dislikes intervention,
(pb1 (δ) > u1 (I3 )), increasing the strength of the intervention, p3 will also raise the expression.
Finally, increasing the cost imposed on player 1 for committing atrocities, k1 , will also raise
the expression, making player 1 more likely to observe the threshold.
Note, δ and p3 enter into both the expression for a† and equation 2. Making the intervention stronger by increasing p3 , and better able to prevent atrocities by lowering δ will both
lower the threshold of intervention and increase the expression in equation 2, counterbalancing the effect of lowering a† and making player 1 more likely to obey the new threshold.
However, these effects might not balance out exactly, which could lead a marginal player 1
to change their decision. To deal with this problem we note that player 1’s costs for intervention, k1 appears in 2 but does not appear in the expression for a† , so it can be used to
adjust 2 at will to compensate for changes in a† . That is, one can always find an increased
level of punishment for states that commit atrocities sufficient to convince them, if they
were willing to abide by the threshold limit on atrocities before, to continue to do so even
if that threshold is lowered. This is particularly true if the threshold reduction has been
accomplished by making the potential intervention stronger and more capable of reducing
atrocities.
Now consider the probability of war. The crux of the moral hazard objection to lowering
the level of intervention is that it raises the probability of war. Can an alternative variable
37
be found to negate this unfortunate side effect? The sanctions variable, s1 , is the obvious
candidate. By increasing the level of sanctions, the international community can make war
more costly for player 1. If we examine equations 9 and 10, it is easy to see that the positive
effect on the probability of war of reducing a† , can be easily compensated for by increasing
s1 , so that the probability of war remains the same. In fact, one could argue that this kind
of change is itself normatively desirable, particularly if the sanctions are “smart” and target
the leaders with travel restrictions, financial barriers and the like. Transferring the costs of
civil war from the civilian victims of atrocities to the bank accounts of the leaders is all to
the good, and all the more practical since leaders may often care more about their own well
being than that of their followers.
3.4
The Brutal Rebel Group
This leads naturally to a consideration of the supposed problem of the brutal rebel group.
Moral hazard proponents have often pointed to the existence of brutal rebel groups as a
problem for any intervention regime designed to reduce atrocities. The argument goes that
if rebel groups are brutal, that is, they do not care that much about the victims of atrocities
even when those victims are the people they claim to represent, then they will be especially
likely to attempt to try to provoke atrocities in order to trigger international intervention that
will result in a political win for them. Therefore, having an international regime to prevent
atrocities plays into the hands of brutal rebel groups and will cause wars and atrocities that
would have otherwise not occurred.
The model shows the flaw in this line of reasoning. If the rebel group is brutal, it will
38
have low k2 . The model shows that the lower k2 , the less impact lowering the threshold of
atrocities has on the likelihood of war. This is because brutal rebel groups are willing to
rebel even when they face high levels of atrocities, so lowering the level of atrocities has little
impact on their decision calculus. The more brutal the rebel groups, the greater the need for
an intervention regime to lower the level of atrocities in the wars that they will provoke in
any event. The danger, in fact, is that some rebel groups might not be brutal, so that they
would be moved to rebel if the level of atrocities were lowered. But as we discussed above,
if the costs of the conflict can be transferred from the civilian victims of atrocities to the
leaders through increased smart sanctions, then the likelihood of war can be held constant
so that the expected level of atrocities declines.
3.5
Country Specific Thresholds
Finally, we consider the issue of whether the threshold is or ought to vary from country to
country. Some of the variables in the model would vary significantly from place to place.
Most obviously, the more powerful the target of intervention, the less powerful (relatively)
the intervention must be, lowering p3 , which raises the threshold for intervention, a† . This
accords with the common complaint that more powerful countries can get away with levels
of atrocities that other countries might not. For instance, the Russian wars in Chechnya
and Georgia have aroused international criticism, to be sure, but no talk of intervention.
More subtly, the other exogenous parameters might vary from country to country, producing
variations in the ability or willingness of an international regime to intervene.
Another important source of variation would be whether the international community is
39
able to adequately compensate for lowering the threshold of intervention by increasing k1
and s1 . If there were some cases where for some reason it was difficult to impose sanctions
or increased intervention costs on player 1, then the possibility that lowering the threshold
of atrocities increases the likelihood of war becomes greater. Therefore, we find that the
international community might hesitate before imposing a low threshold on conflicts where
it cannot also impose compensating costs to keep the likelihood of war from increasing.
4
Conclusion
As the uprising in Libya began to degenerate into widespread conflict and civilians were
increasingly targeted, UN Secretary General Ban Ki Moon was asked about the relatively
hard line he had taken against the Libyan regime. He answered as follows.
First of all, we have seen intolerable tragedies, genocide [and mass atrocities],
which happened in Rwanda, Srebrenica, and in Darfur. We have learned great
and very painful lessons in the past. We have reaffirmed that this should never
happen and this kind of crime against humanity and genocide should be punished. And the United Nations since then has taken strong action. We have all
these frameworks and I have appointed a Special Adviser on [the prevention of]
genocide [and] a Special Adviser for the Responsibility to Protect. As you will
remember in 2005, during the World Summit, all the leaders of the world got
together and they reaffirmed that this should never happen. That is why the Security Council and the Human Rights Council, they reacted swiftly and with one
voice. The Security Council has taken a unanimous decision to impose sanctions
40
- imposing asset freeze, travel ban and referring this case to the International
Criminal Court. And this is quite important and unprecedented, and I’ll make
sure that these measures will be implemented swiftly.
As Ban noted, the existing anti-atrocities regime is ad-hoc. A United Nations Genocide
Convention exists, with widespread ratification; the Convention includes language on how
signatories to the Convention are obligated to prevent genocide. However, the mechanisms
for how such prevention would take place are vague. Darfur is a case in point. Darfur was
considered a landmark case in which national authorities publicly declared genocide to occur,
but Darfur also revealed the limits of the Genocide Convention in the sense that calling the
violence “genocide” did not trigger specific intervention action (Straus 2005). Outside the
Convention, no agreed-upon policy framework exists to prevent or stop atrocities where
they occur in either a multilateral (United Nations or NATO) or foreign policy framework.
Given that deficit, a series of policy initiatives exist to put in place a firmer and clearer
anti-atrocities regime, in particular the Responsibility to Protect (R2P) doctrine (Evans
2008, Weiss 2006), which has been endorsed in the U.N. system and the Cohen-Albright
Commission report, which recommends a suite of policy proposals to identify, prepare, and
prevent genocide as part of U.S. foreign policy7 Examples such as Libya make this an all the
more urgent question for the international community.
In this paper, we do not evaluate the politics of whether a stronger anti-atrocities policy
will likely be implemented at the international or domestic levels. We recognize significant
obstacles to reaching international consensus. However, in a number of countries, including
the United States, and within the United Nations system there exists a strong current of
7
See also the symposium in Genocide Studies and Prevention, 4:2, 2009.
41
momentum to create an anti-atrocities regime. The moral hazard position holds that, perversely, strengthening such a regime would increase the risk of war and provoke atrocities. In
the model we build to evaluate the claim, we find some truth to it, but overall we find that
if compensating measures are taken the net impact of an anti-atrocities regime conforms to
the wishes of advocates. Imposing a cap on the level of atrocities in civil conflicts, if done
impartially and with compensating costs for the parties who commit atrocities, can lower
the expected level of atrocities and achieve the goals of the policy without undue negative
unintended consequences.
42
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45
Table 4: Notation in the Game
x
A possible issue resolution
ui (x) Utility functions over x
I3
Player 3’s ideal point
a
The level of atrocities
a†
The threshold level of atrocities that triggers intervention
δ
Reduction in atrocities resulting from intervention
pi
Probability of victory
ci
Cost of conflict
ki
Player i’s costs for atrocities
s1
Cost of sanctions on player 1
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5
Appendix
Notation in the model is summarized in Table 4.
46
With complete information and risk neutral preferences, player 1 will offer player 2 its
reservation value, player 2 will accept, and peace will obtain. To see this, note that risk
neutrality implies that u1 (x) + u2 (x) = 1. First consider the case in which intervention is
not anticipated, so player 1 will choose a† . We start with the implication of risk aversion,
u1 (r2b ) = 1 − u2 (r2b )
u1 (r2b ) = 1 − (pb2 (a† ) − c2 − k2 a† )
u1 (r2b ) = pb1 (a† ) + c2 + k2 a†
u1 (r2b ) > pb1 (a† ) − c1 − s1
and end with the condition that player 1 prefers to offer player 2’s reservation value rather
than fight. Now consider the case in which intervention is anticipated. We perform a similar
calculation
u1 (r2t ) = 1 − u2 (r2t )
u1 (r2t ) = 1 − (pt2 (δ) + p3 u2 (I3 ) − c2 − k2 δ)
u1 (r2t ) = 1 − ((1 − p3 − pt1 (δ)) + p3 u2 (I3 ) − c2 − k2 δ)
u1 (r2t ) = 1 − 1 + p3 + pt1 (δ) − p3 u2 (I3 ) + c2 + k2 δ
u1 (r2t ) > pt1 (δ) + p3 − p3 u2 (I3 ) − c1 − k1
u1 (r2t ) > pt1 (δ) + p3 (1 − u2 (I3 )) − c1 − k1
u1 (r2t ) > pt1 (δ) + p3 u1 (I3 ) − c1 − k1
and end with the same conclusion, player 1 prefers to offer player 2’s reservation value rather
than fight.
47
In the incomplete information case, to find the equilibrium offer, we maximize player 1’s
payoff with respect to its offer.
P (W b )(pb1 (a† ) − c1 − s1 ) + (1 − P (W b ))u1 (x)
With risk neutral preferences, we have u1 (x) = x and u2 (x) = 1 − x. We can therefore
re-express the above as follows
(pb2 (a† ) − k2 a† − (1 − x))(pb1 (a† ) − c1 − s1 ) + (1 − (pb2 (a† ) − k2 a† − (1 − x))x
or
(pb2 (a† ) − k2 a† − (1 − x))(pb1 (a† ) − c1 − s1 − x) + x
Taking the derivative with respect to x we get
(pb2 (a† ) − k2 a† − (1 − x))(−1) + (pb1 (a† ) − c1 − s1 − x) + 1
Setting equal to zero and solving for x we get
0 = (pb2 (a† ) − k2 a† − (1 − x))(−1) + (pb1 (a† ) − c1 − s1 − x) + 1
0 = −pb2 (a† ) + k2 a† + (1 − x) + pb1 (a† ) − c1 − s1 − x + 1
2x = −pb2 (a† ) + k2 a† + 1 + pb1 (a† ) − c1 − s1 + 1
2x = pb1 (a† ) + k2 a† + pb1 (a† ) − c1 − s1 + 1
x∗ ≡ pb1 (a† ) +
1 + k 2 a† − c 1 − s 1
2
Therefore the demand is increasing in k2 and a† , which increase the costs for player 2,
and decreasing in c1 and s1 , player 1’s costs for conflict and international sanctions.
48
Now we substitute back into the equation for the likelihood of war. The likelihood of war
in the bilateral case is pb2 (a† ) − k2 a† − u2 (x), so the equilibrium likelihood of war is
P (W b ) = pb2 (a† ) − k2 a† − u2 (x∗ )
P (W b ) = pb2 (a† ) − k2 a† − (1 − x∗ )
P (W b ) = pb2 (a† ) − k2 a† − 1 + x∗
P (W b ) = pb2 (a† ) − k2 a† − 1 + pb1 (a† ) +
1 + k 2 a† − c 1 − s 1
2
1 + k 2 a† − c 1 − s 1
2
†
1 − k2 a − c 1 − s1
P (W b ) =
2
P (W b ) = −k2 a† +
We turn to the expected level of atrocities. This is the product of the likelihood of war
with the expected level of atrocities
E(a) =
1 − k 2 a† − c 1 − s 1 †
a
2
The derivative of E(a) with respect to a† is
∂E(a)
1 − k 2 a† − c 1 − s 1
k2
=
− a†
†
∂a
2
2
∂E(a)
1 − c 1 − s1
=
− k 2 a†
†
∂a
2
Now consider the case where the threshold will be ignored, player 1 will choose a = 1,
and the third party will intervene. In this case, player 1’s payoff for an offer x is
P (W t )(pt1 (δ) + p3 u1 (I3 ) − c1 − s1 − k1 ) + (1 − P (W t ))u1 (x)
This can be rewritten as
(pt2 (δ)+p3 u2 (I3 )−k2 δ−(1−x))(pt1 (δ)+p3 u1 (I3 )−c1 −s1 −k1 )+(1−(pt2 (δ)+p3 u2 (I3 )−k2 δ−(1−x)))x
49
or
(pt2 (δ) + p3 u2 (I3 ) − k2 δ − (1 − x))(pt1 (δ) + p3 u1 (I3 ) − c1 − s1 − k1 − x) + x
The derivative with respect to x is
(pt2 (δ) + p3 u2 (I3 ) − k2 δ − (1 − x))(−1) + (pt1 (δ) + p3 u1 (I3 ) − c1 − s1 − k1 − x) + 1
Setting this equal to zero and solving for x we get
0 = (pt2 (δ) + p3 u2 (I3 ) − k2 δ − (1 − x))(−1) + (pt1 (δ) + p3 u1 (I3 ) − c1 − s1 − k1 − x) + 1
0 = −pt2 (δ) − p3 u2 (I3 ) + k2 δ + 1 − x + pt1 (δ) + p3 u1 (I3 ) − c1 − s1 − k1 − x + 1
2x = 1 − pt2 (δ) + 1 − p3 u2 (I3 ) + k2 δ + pt1 (δ) + p3 u1 (I3 ) − c1 − s1 − k1
2x = p3 + pt1 (δ) + 1 − p3 u2 (I3 ) + k2 δ + pt1 (δ) + p3 u1 (I3 ) − c1 − s1 − k1
2x = pt1 (δ) + 1 + p3 (1 − u2 (I3 )) + k2 δ + pt1 (δ) + p3 u1 (I3 ) − c1 − s1 − k1
2x = pt1 (δ) + 1 + p3 u1 (I3 ) + k2 δ + pt1 (δ) + p3 u1 (I3 ) − c1 − s1 − k1
2x = 2pt1 (δ) + 1 + 2p3 u1 (I3 ) + k2 δ − c1 − s1 − k1
x∗ ≡ (1 − p3 )pb1 (δ) + p3 u1 (I3 ) +
1 + k2 δ − c 1 − s1 − k 1
2
Now we substitute back into the expression for the likelihood of war to find the equilibrium
likelihood of war in the trilateral case.
P (W t ) = pt2 (δ) + p3 u2 (I3 ) − k2 δ − u2 (x∗ )
P (W t ) = pt2 (δ) + p3 u2 (I3 ) − k2 δ − (1 − x∗ )
P (W t ) = pt2 (δ) + p3 u2 (I3 ) − k2 δ − 1 + x∗
P (W t ) = pt2 (δ) + p3 u2 (I3 ) − k2 δ − 1 + (1 − p3 )pb1 (δ) + p3 u1 (I3 ) +
50
1 + k2 δ − c 1 − s1 − k1
2
P (W t ) = (1 − p3 )pb2 (δ) + p3 u2 (I3 ) − k2 δ − 1 + (1 − p3 )pb1 (δ) + p3 u1 (I3 ) +
1 + k2 δ − c 1 − s1 − k1
2
1 + k 2 δ − c 1 − s1 − k1
2
1 + k2 δ − c 1 − s1 − k1
P (W t ) = −k2 δ +
2
1
−
k
δ
−
c
−
s
−
k1
2
1
1
P (W t ) =
2
P (W t ) = 1 − p3 + p3 − k2 δ − 1 +
Finally, we turn to the expected value of atrocities.
E(a) = P (W t )δ
E(a) =
1 − k2 δ − c 1 − s1 − k 1
δ
2
The partial derivatives with respect to k1 , k2 , and c1 are all negative. The derivative with
respect to δ is
∂E(a)
1 − k2 δ − c 1 − s1 − k1
k2
=
−δ
∂δ
2
2
∂E(a)
1 − c 1 − s1 − k1
=
− k2 δ
∂δ
2
51