Ethnic Divisions and Civil War
Benjamin Bridgman
University of Minnesota and
Research Department
Federal Reserve Bank of Minneapolis
November 4, 2002∗
Abstract
The period since World War Two has been marked by a great deal of civil war.
Most of these civil wars have been ethnic civil wars. This paper presents a one shot
game of ethnic conflict. The government is endowed with goods that it distributes
among ethnic groups. The government is initially controlled by one of the groups
and other factions can expend resources to fight for control of the government. I
show that the incidence of war is higher in more ethnically fragmented countries.
I discuss external interventions to decrease the incidence of civil war. I show that
military aid to the government can decrease conflict while economic aid can increase
conflict.
∗
I thank V.V. Chari, Michele Boldrin, Larry Jones, and Ross Levine for their encouragement and
helpful suggestions. Comments by workshop participants at the 2001 SED Conference in Stockholm
and the University of Minnesota were also very useful. Igor Livshits translated Russian data. The
views expressed herein are those of the author and not necessarily those of the Federal Reserve Bank
of Minneapolis or the Federal Reserve System. email: [email protected]. Tel. (612) 204-5531.
Fax: (612) 204-5515.
1
1
Introduction
High profile civil wars in countries like Yugoslavia and Rwanda has sparked a great deal
of interest in civil war. Civil war has been a common occurrence in the post World War
Two era. From 1960 to 1990, 46 countries, fought civil wars (Sivard 1996). Given the
damage that civil war causes, understanding why civil wars occur is important research
project.
What are the fundamental causes of civil war? A large number of the civil wars
have a significant ethnic component. Of the 125 civil conflicts, Sambanis (2001) classifies
80, or 64 percent, as an ethnic war. From 1960 to 1997, the State Failure Project identifies
45 countries that had ethnically based civil unrest compared to 16 that had (exclusively)
non-ethnic civil unrest1 . In Licklider (1995), 69 percent of the 91 civil wars in his sample
are identified as being ethnically or ”identity” based. Given the prevalence of ethnic
conflict, understanding and reducing ethnic conflict has an enormous potential to reduce
overall conflict.
Beginning with Collier and Hoeffler (1998), there is a large literature analyzing
the relationship between ethnic divisions and war. Most of this work to this point has
been empirical. Elbawadi and Sambanis (2002) find that the incidence of civil war is
associated with ethnic divisions.
This paper presents a theoretical model of ethnic civil war. I argue that ethnic
groups compete to control governmental policy, a competition that can take the form
of civil war. There is a nation that is divided into ethnic groups. Each group receives
an endowment. There is a government which is controlled by one of the groups. The
government is endowed with consumption and transfers it to the ruling group. Groups
can devote resources to the military and fight to take control of the government.
The model can generate replicate the empirical relationship between ethnic divisions and civil war. As ethnic divisions increase, civil war increases. Ethnic groups wish
to control the government to gain control its revenue. Groups that are not in power can
raise an army to attempt to seize power. To retain power, the ruling group must raise an
army of its own to deter other groups from attempting a revolution. In countries with a
1
There is some overlap. Many nations fought both an ethnic war and a non-ethnic war. The nonethnic number refers to nations that fought a civil war but never fought an ethnically based civil war.
2
large majority (ethnically homogenous countries), the per capita cost of raising an army
is small for the majority. At the same time, it is costly for minorities to raise an army.
Therefore, it is relatively easy for the majority to deter minorities from fighting. In more
ethnically heterogeneous countries, groups are more evenly matched. Deterrence is more
difficult since it is more costly for the majority and less costly for potential rivals to raise
armies.
2
Data
The most common data set used to measure ethnic groups is found in the Atlas Narodov
Mira (1964). For every country in the world in 1960, the Atlas splits the population into
various ethnic groups and reports the population of each group. However, it does not
describe how ethnic groups are defined. Inspection of the data indicates that divisions
are cut primarily along linguistic lines. Racial and religious factors are also appear to be
important2 .
Once the population of a country is divided into ethnic groups, this information
must be summarized into a statistic. I concentrate on the most common variable used in
the literature: Ethnolinguistic Fractionalization (ELF ). The measure ELF (using the
Atlas’s data) is the most widely used measure of ethnic divisions in the literature. It is
calculated as follows. A country’s total population N is divided into I groups, with each
group’s population denoted by Ni . ELF is given by
I
X
Ni
ELF = 1 −
( )2 .
N
j=1
This variable increases as (1) more groups are added (I increases) and (2) when the
populations of groups become more equal.
Figure One shows that there is a strong positive relationship between ethnic
divisions and the prevalence of civil war. Table 1 reports the results of a regression with
the years of civil war during the years 1960 to 1997 and ELF .
2
Bridgman (2002) presents a model of ethnicity and shows that this data set matches the theory.
3
Dependent Variable
Variable
Constant
ELF60
Adj.-R2
3
3.1
Table 1: Ethnic Divisions and Civil War
CWYEARS
Coeff.
(t-Stat.)
1.123
(1.10)
5.880
(2.96)
0.067
Model
Households
There is a measure one of households. They are exogenously divided into two groups.
The measure of each group is given by λi . The households in each group are altruistic
toward each other and are not altruistic to households outside the group. Groups can
perfectly and costlessly coordinate their actions. Each group makes decisions as a single
agent to maximize the average utility of households in the group. The preferences of
group i are given by Cλii , where Ci is group i’s consumption. Households are endowed
with one unit of labor L and have an endowment of capital K. Throughout the paper,
upper case variables indicate aggregate quantities and lower case variables indicate per
capita quantities. (For example, ci = Cλii .)
3.2
Government
There is a government that is endowed with τ units of the consumption good in each
period and gives the revenue to the ruling group. The government is initially controlled
by group one. The government coordinates its policy with the ruling group and acts in
its interests.
4
3.3
Production
Output Y is produced by a technology that uses capital and labor as inputs. Production is given by the Cobb-Douglas function Y = AK α L1−α . There is a technology that
produces military arms M that uses labor as its input: M = L.
3.4
War
Groups can attempt to seize control of the government using military arms. They choose
whether to fight or concede. The strategy for fighting is given by φi ∈ [0, 1]. The
set of groups that are fighting is given by Φ. The probability of winning is given by
π(M1 , ..., MI ) :
κX
1 κ
Mi0
πi (M ) = + Mi −
2 2
2 i0 6=i
1 X
1 if Mi ≥ +
Mi0
(3.1)
κ
i0 6=i
0 if Mi00 ≥
1 X
+
Mi0 for some i00 6= i
κ i0 6=i00
If a group fights, it loses a portion θ ∈ [0, 1] of its output to war damage. If a group
wins, they receive the government’s revenue for that period. If no group fights the ruling
group, the incumbent group receives the revenue.
3.5
Timing
The timing is as follows:
1. The ruling group chooses (M1 , φ1 ).
2. The other groups simultaneously choose (Mi , φi ), for i 6= 1.
3. Based on the vector φ, the set of fighting groups Φ is realized. Based on the vector
M , control of the government is realized. Consumption occurs.
There is no private information in the model. Therefore, actions and outcomes previous
stages of the game are common knowledge.
5
3.6
Equilibrium
The equilibrium concept used in this paper in Subgame Perfect Equilibrium.
Definition 3.1. A Subgame Perfect Equilibrium (SPE) is feasible strategy functions for
each group σi∗ such that:
∗
∗
∗
1. For all i, given σ−i
, Ui (σi∗ , σ−i
) ≥ Ui (ai (ht ), σ−i
) for all feasible strategies ai (ht ).
2. At each node of the stage game, the strategy function maximizes payoff subject to
feasibility for all feasible prior actions.
4
Results
Peace in the model is the result of deterrence: The ruling group raises a large enough
army to prevent other groups from attempting to seize control of the government. A
deterrence strategy is strategy pair M1P , φP1 such that φi (M1P , φP1 ) = 0 for all i 6= 1. It
is obvious that φP1 = 1. The minimum military expenditure required to deter group i,
assuming no other group fights and φ1 = 1, is given by M1P (i).
For interior solutions, fighting military expenditure is given by
Ã
Mi = λi
·
2(1 − α)(1 − θ)Ak α
1−
τκ
¸ α1 !
.
Note that Mi (M1 ) = Mi for interior Mi . Assuming that the other groups are at
an interior solution, the deterring military expenditures are
Ã
M1P (i) = λi
¸1!
2(1 − α)(1 − θ)Ak α α
1
+
1−
τκ
κ
"
#
µ
¶
¸ 1−α
·
α
α
2λi
2(1
−
α)(1
−
θ)Ak
−
(4.1)
Ak α − (1 − θ)Ak α
τκ
τκ
·
I derive conditions to ensure that the solution is interior. If the value of the
government’s consumption good is too small, it will not pay to ever fight. This is
summarized in the following lemma:
6
Lemma 4.1. If (1 − α)(1 − θ)Akiα ≥
τκ
2
then M1P (i) = 0.
Proof. An interior solution for military expenditure requires
(1 − α)(1 − θ)Ak α (1 −
Mi −α κ
) = τ
λi
2
However, if the hypothesis is satisfied, the LHS is always larger than the RHS for any
Mi > 0. Therefore, Mi (M1 , 1) = 0 for all M1 .
The intuition for the lemma is simple. If the marginal cost of allocating labor
into fighting is too high relative to the benefits, the ruling group does not need an army
to pacify. The equilibrium in this case is trivial. There is no fighting, no group puts any
labor into the military and the ruling group maintains control of the government. In the
analysis that follows, we assume that (1 − α)(1 − θ)Akiα < τ2κ .
The previous lemma gives conditions under which military expenditures when
fighting are greater than zero. The following lemma helps establish that groups will
never choose the other corner: MiF = λi . First, the reaction functions will not be at a
corner.
Lemma 4.2. MiF (M1 ) < λi .
Proof. For MiF < λi ,
ViF
τ
>
λi
µ
¶
1 κ
κ
+ λi − M−i .
2 2
2
This expression simplifies to
·
(1 − θ)Ak
α
2(1 − α)(1 − θ)Ak α
τκ
¸ 1−α
α
·
¸1
τ κ 2(1 − α)(1 − θ)Ak α α
>
.
2
τκ
Further simplification gives the condition 1 > α which is always true.
The lemma establishes that the fighting military spending of other groups are
invariant to group one’s spending. That is, MiF (M1F ) = MiF for MiF < MiP . Therefore,
by the same argument as the lemma, M1F < λ1 .
7
4.1
Two Groups
Consider the case where I = 2. Define group one’s value of fighting V1F (λ1 ) as
µ
¶
τ 1 κ
κ
M1 1−α
F
α
)
+
+ M1 − M2 (M1 ) .
V1 (λ1 ) = max(1 − θ)Ak (1 −
M1
λ1
λ1 2 2
2
For interior solutions, this expression becomes
·
V1F (λ1 )
= (1−θ)Ak
α
2(1 − α)(1 − θ)Ak α
τκ
¸ 1−α
α
τκ
τ
+
+
2λ1 2
Ã
·
2(1 − α)(1 − θ)Ak α
1−
τκ
¸ α1 ! ·
Similarly, define group one’s value of deterrence by V1P (λ1 ) as
V1P (λ1 ) = Ak α (1 −
τ
M1P 1−α
)
+ .
λ1
λ1
In what following, I will compare the value of fighting with the value of deterrence for group one. To show that war is more likely in ethnically divided countries,
I show that the value of deterrence is higher than the value of fighting in ethnically
homogenous countries. Before moving to the main result, I prove a lemma. The lemma
gives conditions under which the per capita cost of deterrence is lower when group one
is larger.
Lemma 4.3. If
κτ
2
> Ak α , then
Proof. We show that
> 0.
< 1. We have
¸1!
2(1 − α)(1 − θ)Ak α α
1−
−
τκ
#
µ ¶"
·
¸ 1−α
α
α
∂λ2 2
2(1
−
α)(1
−
θ)Ak
Ak α − (1 − θ)Ak α
×
∂λ1 τ κ
τκ
# Ã
·
µ ¶"
·
¸ 1−α
¸1!
α α
α
α
2(1
−
α)(1
−
θ)Ak
2
2(1
−
α)(1
−
θ)Ak
Ak α − (1 − θ)Ak α
− 1−
τκ
τκ
τκ
∂M1P
∂λ2
=
∂λ1
∂λ1
Ã
∂M1P
∂λ1
∂y1P
∂λ1
·
8
1
2−
λ1
¸
To establish the claim, we need
¶"
·
¸ 1−α #
·
¸1
2Ak α
2(1 − α)(1 − θ)Ak α α
2(1 − α)(1 − θ)Ak α α
1>
1 − (1 − θ)
−1+
τκ
τκ
τκ
"
#
µ
¶
·
¸ 1−α
·
¸1
2Ak α
2(1 − α)(1 − θ)Ak α α
2(1 − α)(1 − θ)Ak α α
2>
1 − (1 − θ)
+
τκ
τκ
τκ
µ
h
Since both
2(1−α)(1−θ)Akα
τκ
i α1
·
¸
i 1−α
h
α
2(1−α)(1−θ)Akα
and 1 − (1 − θ)
are less than
τκ
one, the hypothesis is sufficient to ensure the above condition is satisfied. If
is obvious that the lemma is true.
∂M1P
∂λ1
< 1, it
Under the hypothesis of the lemma, once deterrence is feasible for some λ1 , it is
feasible for all λ01 > λ1 . Define λ1 by λ1 = M1P (λ1 ), the minimum λ1 where deterrence is
feasible. The lemma allows me to prove the main result:
Proposition 4.4. Let V1P (1) > V1F (1) and κτ
> Ak α . Then V1P (λ1 ) > V1F (λ1 ) for some
2
λ1 implies V1P (λ01 ) > V1F (λ01 ) for all λ01 > λ1 .
Proof. The condition for V1P (λ1 ) ≥ V1F (λ1 ) is
Ã
·
¸1!·
¸
α α
2(1
−
α)(1
−
θ)Ak
τ
τ
κ
1
τ
F
P
≥ y1 +
+
1−
2−
y1 (λ1 ) +
λ1
2λ1
2
τκ
λ1
Rearranging, we get
Ã
Ã
·
¸1!
·
¸1!
α α
α α
2(1
−
α)(1
−
θ)Ak
2(1
−
α)(1
−
θ)Ak
τ
τ
κ
y1P (λ1 )+
+
1−
≥ y1F +τ κ 1 −
2λ1 2λ1
τκ
τκ
Notice that the RHS is invariant to λ1 . We show that as λ1 declines, once the LHS drops
below the RHS it stays below. We have
"
Ã
· P
¸
·
¸ 1 !#
P
P
α α
M
M1
∂M1 1
1 τ
τκ
∂LHS
2(1 − α)(1 − θ)Ak
= (1−α)Ak α (1− 1 )−α
−
− 2
+
1−
2
∂λ1
λ1
λ1
∂λ1 λ1
λ1 2
2
τκ
9
First, we show this expression is positive near λ1 . Evaluate for λ1 = λ1 + ε, for ε
arbitrarily small.
·
¸
·
¸
M1P −α M1P
∂M1P 1
1
∂M1P 1
α
−α
α
(1 − α)Ak (1 −
)
−
≈ (1 − α)Ak (0)
−
.
λ1
λ21
∂λ1 λ1
λ1
∂λ1 λ1
i
h
∂M P
∂M P
By the lemma, ∂λ11 < 1 so 1 − ∂λ11 > 0. Therefore:
·
¸
M1P −α M1P
∂M1P 1
(1 − α)Ak (1 −
)
≈∞
−
λ1
λ21
∂λ1 λ1
α
Second, we show that the expression has a single zero greater than λ1 . Putting in the
expression for M1P :


"
Ã
·
¸ 1 !#
∂M1P
1
P
−
∂LHS
M1 −α  κ
1 τ
τκ
2(1 − α)(1 − θ)Ak α α
∂λ1 
α
= (1−α)Ak (1−
)
− 2
+
1−
∂λ1
λ1
λ21
λ1 2
2
τκ
The condition for a zero is:
Ã
·
·
¸ 1 !#
¸ "
P
α α
P
M
1
2(1
−
α)(1
−
θ)Ak
∂M
τ
κ
τ
1
(1 − α)Ak α (1 − 1 )−α
−
+
1−
=
λ1
κ
∂λ1
2
2
τκ
∂M P
MP
This has a single zero since ∂λ11 is constant and (1− λ11 )−α is decreasing in λ1 . If ∂LHS
is
∂λ1
∂LHS
increasing for all λ1 ∈ [λ1 , 1], the result is obvious. Suppose ∂λ1 is not monotone. Since
V1P (1) > V1F (1), we know the non-monotone part of the LHS lies above the RHS.
The proposition states that if once the value of deterrence becomes higher than
the value of fighting for some λ1 , deterrence is preferred for all λ1 bigger than λ1 . Since
ethnic divisions decline as λ1 increases, war in increasing in ethnic divisions.
Why is the proposition true? The difference between the value of deterrence and
fighting is a single-peaked, continuous function, increasing and then decreasing as λ1
increases. Moreover, As λ1 increases, the per capita cost of deterrence is decreasing. At
the same time, the per capita value of the government is declining. For λ1 near λ1 the
first effect dominates because F 0 (0) = ∞. For λ1 large enough, the other effect begins
to dominate. The assumption that V1P (1) > V1F (1) ensures that the declining part does
not fall so much that the ruling group wishes to fight.
The following lemma gives a sufficient condition for V1P (1) > V1F .
10
Lemma 4.5. If (1 − α)(1 − θ)Ak α <
τ (κ−1)
,
2
then V1P (1) > V1F .
Proof. By the hypothesis,
(1 − α)(1 − θ)Ak α <
τκ
1
(1 − ).
2
κ
Rearranging,
2(1 − α)(1 − θ)Ak α
1
<1− .
τκ
κ
Since α and the right hand side are less than one,
·
2(1 − α)(1 − θ)Ak α
τκ
Since θ < 1,
·
(1 − θ)
1
1−α
¸ α1
1
<1− .
κ
2(1 − α)(1 − θ)Ak α
τκ
¸ α1
1
<1− .
κ
Multiplying each side by Ak α and rearranging yields y1F (1) < y1P (1). Since π ≤ 1,
V1P (1) > V1F .
Note that this sufficient condition is much stronger than required. There exist a
set of parameters that violate the condition such that V1P (1) > V1F .
4.2
I Groups
We now consider the where I is an arbitrary integer greater than two. First, we adapt
the notation for this case. Define
Ã
!
X
M
τ
1
κ
κ
1
)1−α +
+ M1 −
Mi (M1 ) .
V1F (λ1 , I) = max(1 − θ)Ak α (1 −
M1
λ1
λ1 2 2
2 i6=1
Define V1F (λ1 , I) as above.
In what follows, the number of groups will be changed. Therefore, there needs to
be some structure on the size of groups given the number of groups. Let λi (I) = I1 for
all i. The following proposition shows that fighting increases as the population becomes
more divided (an increase in ELF .)
11
Proposition 4.6. Suppose V1P (1, I) < V1F (1, I) for some I. Then V1P (1, I 0 ) < V1F (1, I 0 )
for all I 0 > I.
Proof. The condition for V1P (1, I) < V1F (1, I) is:
Ã
Ã
·
¸1!
·
¸1!
α α
α α
τ
τ
κ
2(1
−
α)(1
−
θ)Ak
2(1
−
α)(1
−
θ)Ak
y1P (λ1 , I) +
+
1−
< y1F + τ κ 1 −
.
2λ1 2λ1
τκ
τκ
We show that
∂LHS
∂I
< 0. We have:
Ã
·
¸ 1 !#
¸ "
·
P
α α
∂LHS
∂M
τ
τ
κ
2(1
−
α)(1
−
θ)Ak
1
= (1−α)Ak α (1−M1P I)−α −M1P −
I +
+
1−
∂I
∂λ1
2
2
τκ
First, note that −M1P −
1
M1P =
I
Ã
∂M1P
∂λ1
I < 0. To see this, we have:
¸1!
2(1 − α)(1 − θ)Ak α α
1
1−
+
τκ
κ
#
µ
¶"
·
¸ 1−α
α
α
2
2(1 − α)(1 − θ)Ak
−
Ak α − (1 − θ)Ak α
τ κI
τκ
·
and
∂M1P
1
I=−
∂λ1
I
¸1!
2(1 − α)(1 − θ)Ak α α
1−
τκ
#
µ
¶"
·
¸ 1−α
α
α
2
2(1
−
α)(1
−
θ)Ak
+
Ak α − (1 − θ)Ak α
τ κI
τκ
Ã
·
∂M P
So −M1P − ∂λ11 I = − κ1 .
Second, (1 − α)Ak α (1 − M1P I)−α is increasing in I. We have:
Ã
·
¸1!
α α
I
2(1
−
α)(1
−
θ)Ak
M1P I = + 1 −
−
κ
τκ
#
¸ 1−α
µ ¶"
·
α
α
2
2(1
−
α)(1
−
θ)Ak
Ak α − (1 − θ)Ak α
(4.2)
τκ
τκ
This is increasing in I, so (1 − α)Ak α (1 − M1P I)−α is increasing in I.
12
As a group becomes smaller, the per capita value of the government’s consumption
goods increases. Therefore, the non-ruling groups are more willing to fight to control
the government. Dividing the population into more groups also diminishes the ruling
group’s ability to raise an army to deter the other groups. These forces make war more
likely when there are more groups.
Not all increases in ELF lead to increases in fighting. In particular, dividing
up the non-ruling population into more groups makes it easier for the ruling group to
deter the other groups. In this case, fighting is declining in ELF . To see this, consider
1
. This rule allocates the non-ruling population equally among non-ruling
λi (I) = 1−λ
I−1
groups. The following lemma proves results used in the main results.
Lemma 4.7.
1. For interior solutions, V1F (λ1 , I) = V1F (λ1 , I 0 ) for all I, I 0 > 1.
2. Let
κτ
2
> Ak α . Then
∂y1P
∂I
> 0.
3. Let
κτ
2
> Ak α . Then
∂y1P
∂λ1
> 0.
4. Let
κτ
2
Proof.
P
> Ak α . If V1P (1, 2) ≥ V1F (1, 2), then V1P (1, I) ≥ V1F (1, I) for all I > 2.
µ
i1¶
h
2(1−α)(1−θ)Akα α
. Therefore, y1P and
1. For interior solutions, Mi = λi 1 −
τκ
i6=1
Mi are invariant to I.
2. We have
∂λi
∂I
1−λ1
= − (I−1)
2 for i 6= 1. Note that
apply the proof for
∂y1P
∂λ1
1−λ1
(I−1)2
< 1 for all I ≥ 2. We can then
> 0 in the two groups case.
∂λi
3. We have ∂λ
= −1 for i 6= 1. We can then apply the proof for
1
groups case unchanged.
∂y1P
∂λ1
> 0 in the two
4. For V1P (1, I) ≥ V1F (1, I), the condition is
Ã
·
¸
¸1!·
α α
τ
τ
κ
2(1
−
α)(1
−
θ)Ak
τ
1
F
P
≥ y1 +
+
1−
.
y1 (λ1 , I) +
2−
λ1
2λ1
2
τκ
λ1
Given part 2, the result follows.
13
A single crossing result similar to the main result of the two groups case can now
be proven.
Proposition 4.8. Fix I. Let V1P (1, I) > V1F (1, I) and
most one λ1 such that V1P (λ1 , I) = V1F (λ1 , I).
κτ
2
> Ak α . Then there exist at
Proof. The proof is similar to that of the two groups case.
With the unique crossing point, we can define λ∗1 (I) by the λ1 such that V1P (λ1 , I) =
V1F (λ1 , I).
Proposition 4.9. Let V1P (1, 2) ≥ V1F (1, 2) and
I.
κτ
2
> Ak α . Then λ∗1 (I) is decreasing in
κτ
2
> Ak α , λ∗1 (I) is well defined. Fix I. λ∗ (I) is given by
Ã
Ã
·
¸1!
¸1!
·
α α
α α
2(1
−
α)(1
−
θ)Ak
τ
κ
2(1
−
α)(1
−
θ)Ak
τ
+
1−
y1P (λ1 , I)+
= y1F +τ κ 1 −
2λ1 2λ1
τκ
τκ
Proof. Since
∂y P
Increase I to I 0 . By the lemma, ∂I1 > 0, so the LHS for λ∗1 (I) and I 0 is greater than the
∂y P
> 0 at λ∗1 (I) so λ∗1 (I 0 ) < λ∗1 (I).
RHS. By the lemma, ∂λ11 > 0. ∂LHS
∂λ1
Since conflict maybe increasing or decreasing in ELF depending on the way ELF
increases, there is a question as to whether the theory is consistent with the data. The
above analysis indicates that ELF is not the measure of ethnic divisions that matches
the model best. A better measure would be the difference in group size. We use the data
from Atlas Narodov Mira (1964) to construct a new measure of ethnic diversity: DIF F .
This variable is defined by:
N1 − N2
DIF F = 1 −
N
where N1 and N2 are the populations of the first and second largest groups respectively.
The correlation between DIF F and ELF is very high. The correlation coefficient is
0.96. In the data, the two variables are essentially indistinguishable: Countries with
high ELF also have high DIF F . Therefore, most of the increases in ELF seem to be
a result of the population being divided into many similarly sized groups. The theory
indicates that these increases in ELF should increase war.
14
5
Conclusion
Civil war has been common for the last fifty years, most of which has been ethnic civil
war. This paper presented a model that can account for the relationship between the
distribution of ethnic groups and civil war.
15
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