journal of peace research - new york · pdf filejournal of peace research doi:...

http://jpr.sagepub.com

Journal of Peace Research

DOI: 10.1177/0022343307087175 2008; 45; 163 Journal of Peace Research

Joan Esteban and Debraj Ray Polarization, Fractionalization and Conflict

http://jpr.sagepub.com/cgi/content/abstract/45/2/163 The online version of this article can be found at:

Published by:

http://www.sagepublications.com

On behalf of:

International Peace Research Institute, Oslo

can be found at:Journal of Peace Research Additional services and information for

http://jpr.sagepub.com/cgi/alerts Email Alerts:

http://jpr.sagepub.com/subscriptions Subscriptions:

http://www.sagepub.com/journalsReprints.navReprints:

http://www.sagepub.com/journalsPermissions.navPermissions:

http://jpr.sagepub.com/cgi/content/refs/45/2/163SAGE Journals Online and HighWire Press platforms):

(this article cites 45 articles hosted on the Citations

© 2008 International Peace Research Institute, Oslo. All rights reserved. Not for commercial use or unauthorized distribution. at Bobst Library, New York University on March 17, 2008 http://jpr.sagepub.comDownloaded from

http://www.prio.no/

http://jpr.sagepub.com/cgi/alerts

http://jpr.sagepub.com/subscriptions

http://www.sagepub.com/journalsReprints.nav

http://www.sagepub.com/journalsPermissions.nav

http://jpr.sagepub.com/cgi/content/refs/45/2/163


163

Introduction

A recent upsurge in empirical studies on thecauses of conflict attempts to connect variousfeatures of the distribution of relevant char-acteristics (typically ethnicity or religion) toconflict. There are several distributional

indices (polarization, fractionalization orLorenz-domination) as well as various speci-fications of conflict (onset, incidence orintensity). Overall, the results are far fromclear, and, as they are combined with themixture of alternative indices and notions ofconflict, it is not surprising that the readermay come away thoroughly perplexed.

© 2008 Journal of Peace Research,vol. 45, no. 2, 2008, pp. 163–182Sage Publications (Los Angeles, London, New Delhiand Singapore) http://jpr.sagepub.comDOI 10.1177/0022343307087175

Polarization, Fractionalization and Conflict*

JOAN ESTEBAN

Institut d´Anàlisi Económica, CSIC, Barcelona

DEBRAJ RAY

Department of Economics, New York University & Institut d´AnàlisiEconómica, CSIC, Barcelona

This article provides a theoretical framework that distinguishes between the occurrence of conflict andits severity, and clarifies the role of polarization and fractionalization in each of these cases. The analysishelps in ordering the various definitions, and in providing explanations for the empirical observations onthe relationship between conflict, on the one hand, and polarization or fractionalization, on the other.The behaviour of players in conflict is described as a game, and equilibrium payoffs to all players arecomputed. The status quo is characterized by a set of political institutions that channel the differentopposing interests and turn them into a collective decision, with a second set of payoffs. Groups rebelagainst the status quo political institution whenever the latter set of payoffs is dominated by the former.When society is highly polarized, the potential cost of rebellion is extremely high, and this cost may serveas the guarantor of peace. So, in highly polarized societies, the occurrence of open conflict should be rare but its intensity very severe, whenever it happens. On the other hand, highly fractionalized societiesare prone to the occurrence of conflict, but its intensity will be moderate. It matters, therefore, whetherone studies the intensity of conflict, conditional on conflict breaking out, or the likelihood that conflictactually occurs. Specifically, it is shown that: (i) measures of fractionalization and polarization tend torun in opposite directions, (ii) the onset of conflict critically depends on the political system in place,(iii) the occurrence of conflict and the intensity of conflict also tend to move in opposite directions, (iv) the relationship between polarization or fractionalization and conflict is non-monotonic and (v) theintensity of conflict depends positively on the degree of polarization.

* We are thankful to Han Dorussen, Glenn Martin, Gerald Schneider, Marta Reynal-Querol and three anonym-ous referees. Esteban gratefully acknowledges support fromthe Polarization and Conflict project CIT-2-CT-2004-506084 funded by the European Commission-DG ResearchSixth Framework Programme, Barcelona Economics (XREA),

Generalitat de Catalunya, Ministerio de Educación y Cienciagrant no. SEJ2006-00369 and the Instituto de EstudiosFiscales. Ray is grateful for support from the National ScienceFoundation under grants 0421852 and 0241070. Contact:[email protected] and [email protected].

087175_JPR_163-182.qxd 2/17/2008 6:36 PM Page 163



The aim of this article is to provide atheoretical framework that permits us todistinguish between the occurrence of conflictand its severity and that clarifies the role ofpolarization and fractionalization in each ofthese cases. Our analysis brings togetherstrands from three of our previous contribu-tions: on polarization (Esteban & Ray, 1994;and Duclos, Esteban & Ray, 2004), on conflictand distribution (Esteban & Ray, 1999) andon the viability of political systems (Esteban &Ray, 2001).

Interest in the connections between in-equality and conflict is not new. Political sci-entists have been much concerned with theseissues; see, for instance, the prominent contri-butions by Brockett (1992), Midlarsky (1988),Muller & Seligson (1987) and Muller, Seligson& Fu (1989). Midlarsky (1988) and Muller,Seligson & Fu (1989) had already voiced theirreservations with respect to the standardnotion of inequality as an appropriate tool forconflict analysis. To go even further back,Nagel (1974) had argued that the relationshipbetween inequality and conflict should benon-linear. Indeed, as Lichbach’s (1989) surveyconcludes, the empirical studies on the rela-tionship between inequality and conflict – andthese typically posit a linear relationship – havecome up with only ambiguous results.

In the area of economics, the analysis of thelink between distribution and conflict waslargely inspired by a desire to study pathwaysbetween inequality and growth.1 Certainly, thepossibility that inequality is a determinant ofsocial conflict and – via this route – impedesgrowth is a contender for one of the moreimportant pathways. The most recent round ofinterest in this connection was triggered by thecontribution of Easterly & Levine (1997), whoshifted the emphasis to ethnic fractionalizationrather than economic inequality, but continuedto emphasize the ‘reduced-form’ connectionswith growth. Among the more relevant

contributions to the literature on inequalityand conflict are Alesina, Baqir & Easterly(1999), Collier (1998, 2001), Collier &Hoeffler (2004), Fearon & Laitin (2003),Hegre et al., (2001), La Porta et al., (1999),Montalvo & Reynal-Querol (2005), Østby(2008), Reynal-Querol (2002a) andSchneider & Wiesehomeier (2006).

But the empirical results are ambiguous, ifnot controversial. By and large, it is fair to saythat most of the literature fails to find any sig-nificant evidence of ethnic fractionalization asa determinant of conflict. Fearon & Laitin(2003), and more recently Hegre & Sambanis(2006), could not identify a link betweenfractionalization and conflict. This negativefinding is underlined by Montalvo & Reynal-Querol (2005), who obtain, instead, a signifi-cant relationship between ethnic polarizationand the incidence of conflict. Collier &Hoeffler (2004) also argue that the contesteddominance of one large group rather than frac-tionalization increases the probability of civilconflict. However, Schneider & Wiesehomeier(2006), using a different dataset and focusingon onset, rather than incidence, of conflict,obtain that fractionalization is a better predic-tor of low-level conflict than polarization.

Our purpose is to provide a simple theor-etical framework that might help in orderingthe various definitions and in providingsome explanations for the variety of em-pirical observations. To do this, we followEsteban & Ray (2001).2 We first model thebehaviour of players in case of conflict as agame and compute the equilibrium payoffsto all players. The status quo against whichgroups might rebel is characterized by a setof political institutions that channel the dif-ferent opposing societal interests and turnthem into a collective decision. Examples ofsuch institutions range from democracies withproportional representation to autocratic oli-garchies and to single-ruler dictatorships.

journal o f PE AC E RE S E A RC H volume 45 / number 2 / march 2008164

1 See Bénabou (1996) for a deep and comprehensive survey. 2 This line is also adopted in Reynal-Querol (2002b).

087175_JPR_163-182.qxd 2/17/2008 6:36 PM Page 164



It is a caricature, but not an extreme one, torepresent these institutions as alternativefunctions mapping the share of the popula-tion supporting each interest group into par-ticular collective decisions.

In this article, we take political institutionsas given and disregard any potential en-dogeneity. As Lipset & Rokkan (1967) stressed,political systems might be endogenous, influ-enced by the particular social structure of thecountry. But if this is the case, why do soci-eties fail to adapt their institutions so as toalways prevent domestic conflict? A numberof arguments have been put forward explain-ing why society might be unable to reachinstitutional arrangements that prevent con-flict. The most notable contributions havebeen made by Powell (2004, 2006), Fearon(1995) and Leventoglu & Slantchev (2007).We shall not pursue this line of inquiry hereand will take the political system as given.

Concerning the onset of conflict, weassume that groups rebel against the incum-bent political institution whenever the out-come is worse than what they can obtainthrough conflict. What the groups fight forwe also consider to be exogenous. In con-trast, Powell (2004) and Wagner (2000) con-sider conflict as an integral part of thebargaining process that will ultimately estab-lish new sharing rules.

We distinguish between the intensity ofconflict, conditional on conflict breaking out,and the likelihood that conflict actuallyoccurs. The point that we make is simple.When society is highly polarized, there mayactually be a wider range of status quo allo-cations that groups are willing to accept. Thisis because the potential cost of rebellion is sohigh that it serves as the guarantor of peace.If conflict is very costly, as it will be in highlypolarized societies, it is easier to find anagreement that is Pareto superior to the con-flict regime. But, if conflict were to occur forsome reason, its intensity would be higher in polarized societies. It follows that the

intensity of conflict (conditional on its oc-currence) and the likelihood of conflict maymove in opposite directions with respect tochanging polarization.

When the cost of conflict is low, the partieswill more easily reject proposals that slightlydepart from what they can get through con-flict.3 In the spirit of the fractionalization vs.polarization controversy, this argument can besummarized as follows. Highly fractionalizedsocieties might be more prone to the onset ofconflict, but the intensity of such conflict willbe moderate. In highly polarized societies, theoccurrence of conflict should be rare but itsintensity very severe. We develop this argu-ment and show that: (i) measures of fraction-alization and polarization tend to run inopposite directions, (ii) the onset of conflictcritically depends on the political system inplace, (iii) the occurrence of conflict and theintensity of conflict also tend to move inopposite directions, (iv) the relationship be-tween polarization or fractionalization andconflict is non-monotonic and (v) the inten-sity of conflict depends positively on thedegree of polarization.4

Our article is organized as follows. Webegin by comparing the indices of fraction-alization and polarization. Next, we developa simple model of conflict based on the generalclass studied in Esteban & Ray (1999). Inorder to present the ideas in their starkestform, we then study the occurrence andintensity of conflict, focusing on the case ofjust two opposing groups. This case permits aneat understanding of the causes of intensity

Joan Es teban & Debraj Ray FR AC T I O N A L I Z AT I O N A N D CO N F L I C T 165

3 This point is also made by Mann (2005). In his ‘thesis’4.b, he posits that, when an ethnic group is large and per-ceives that it can eliminate the small one at a low cost, itwill do so.4 This discussion can shed light on the controversy on thestabilizing or destabilizing effects of ‘polarity’ – a classic inthe international relations literature; see, for example,Waltz (1964) and Deutsch & Singer (1964). Powell(1999), although using an approach different from ours,also finds that the probability of conflict is minimal in thetwo extreme cases of a very uneven or an equal distributionof power and benefits.

087175_JPR_163-182.qxd 2/17/2008 6:36 PM Page 165



of conflict and the causes of its occurrence.However, in the case of two groups, thenotions of fractionalization and polarizationare indistinguishable from each other. We gen-eralize the results to the case of an arbitrarynumber of groups. Now polarization and frac-tionalization perform differently. We end thearticle with some concluding remarks.

Polarization and Fractionalization

The index of fractionalization F is intendedto capture the degree to which a society issplit into distinct groups. The measure hasbeen widely used in studies that attempt tolink ethnolinguistic diversity to conflict,public goods provision, or growth (see e.g.Collier & Hoeffler, 1998; Fearon & Laitin,2003; Easterly & Levine, 1997; Alesina,Baqir & Easterly, 1999; and Alesina et al.,2003).

Let ni be the share of the populationbelonging to group i, i �1,…,G. The frac-tionalization index is defined as the proba-bility that two randomly chosen individualsbelong to different groups. The probabilitythat an individual of group i is chosen is ni.Hence, the probability that, if chosen, she ismatched with someone from another groupis ni(1–ni). It follows that the probability thatany two individuals belong to differentgroups is

(1)

F is a strictly quasiconcave function of thepopulation share vector. From this strict quasi-concavity, we can derive the following prop-erties of F:

(a) Any transfer of population from a groupto a smaller one increases F.

(b) For a given number of groups, G, F ismaximized at the uniform populationdistribution over these groups.

(c) Over the set of uniform distributions, Fincreases with the number of groups.

(d) The split of any group with populationn into two new groups with populationsn� and n�, n��n��n, increases F.

Esteban & Ray (1994) conceptualize polar-ization as the sum of interpersonal ‘antag-onisms’. Antagonism results from the interplayof the sense of group identification (groupsize) and the sense of alienation with respectto other groups (intergroup distance, bij).Alternative notions of polarization not basedon the identity/alienation framework havebeen proposed by Wolfson (1994), Wang &Tsui (2000), Reynal-Querol (2002c) andZhang & Kanbur (2001). An alternative andconsiderably cruder specification of polariza-tion, which also does not account for in-tragroup homogeneity, is the concept ofdominance that Collier (2001) introduced. Itqualifies societies as ‘dominated’ if the largestgroup contains between 45% and 90% of thepopulation.

Esteban & Ray’s polarization measure,5 P,can be written as

(2)

where b is the matrix of intergroup distancesand � is a positive parameter that capturesthe extent of group identification. Esteban &Ray (see also Duclos, Esteban & Ray, 2004)derive restrictions that bound � above (by1.6 to be exact).

A situation of particular relevance is thecase in which individuals in each group feelequally alien towards all groups other thantheir own. That is, bij�bi for all j � i. In thiscase, P reduces to

(3)

Observe that if we set ��1 and bi�1 for alli, we obtain the measure of polarization

P n n bi i ii

( , )� � ��b 1 (1 ) .∑

P n n bi j ijj ii

( ) 1� � ��

�

, b ∑∑

F n n ni i iii

� � � �1 1 2( ) ∑∑ .


5 Esteban & Ray (1994) examine the main properties ofthis measure. The interested reader can also see Duclos,Esteban & Ray (2004) for a measure of polarization forcontinuous distributions.

087175_JPR_163-182.qxd 2/17/2008 6:36 PM Page 166



introduced by Reynal-Querol (2002c),P(1,1), a special case of (2). It is also true thatwe can formally set ��0 in (3), as well asbi�1 for all i, to arrive at the measure offractionalization (1). We emphasize that thisis a formal and not a conceptual connection:for (3) to be a measure of polarization, it isnecessary that � be strictly positive.Nevertheless, it is useful to record that

P(0, 1) �F (4)

where the entry 1 stands for the matrix of all 1’s.

In order to simplify the computations, inthis article we shall work with the specialclass of polarization indices, P(1,1), that is

(5)

In order to examine the properties ofP(1,1), we start by observing that it is the sumof the function p(n) �n2(1 � n) evaluated atthe different ni. But now p(.) is convex orconcave as n () 1/3. Therefore, we have thefollowing properties for P(1,1).

Properties of P(1,1)

(a) A transfer of population from a group to asmaller one increases P(1,1) if both groupsare larger than 1/3. If the two groups aresmaller than 1/3, the equalization of popu-lations will bring P(1,1) down.

(b) For any given number of groups, P(1,1)is maximized when the population is con-centrated on two equally sized groupsonly.

(c) Over the set of uniform distributions,P(1,1) decreases with the number ofgroups, provided that there are at leasttwo groups to begin with.

(d) The split of a group with population n intotwo groups with n� and n�, n��n��n,increases P(1,1) if and only if n �2/3.

The contrast between the properties of frac-tionalization and of the family of polarization

measures clearly shows that the two behavequite differently from each other, except whenthere are just two groups. The essential differ-ence is clear: fractionalization is maximal wheneach individual is different from the rest, whilepolarization is maximal when there are onlytwo types of individuals.

A Model of War and Peace

ConflictIn modeling conflict, we follow Esteban &Ray (1999). Related models of conflict maybe found in Hirschleifer (2001), Grossmann(1991, 1994) and Skaperdas (1992, 1996).

We concentrate on a special case studiedin Esteban & Ray (1999): the class of con-flict games called contests. Assume that thereare G alternatives, i �1,…, G. Individualsdiffer in the alternative they like the mostand are indifferent to the other availablealternatives. Individuals in a specific group i are all alike, in that they like alternative i thebest, and the difference in valuation betweentheir most preferred alternative and any otheris the common value bi.6 Let ni denote therelative size of group i. Note that the alter-natives here are public goods because their valuation by the individuals is independentof the number of beneficiaries.

By a political system, we shall refer to a par-ticular way of choosing among the differentalternatives. By conflict, we mean a challengeto such a system, which is costly. Specifically,we take the following view. Conflict entailsresource contributions ri (to be determinedpresently) from every member of group i, sothat the overall contribution of group i is niri.In the absence of a political rule, the particu-lar alternative that will eventually comeabout is seen by the players as probabilistic.The probability that alternative i will be

P n ni ii

( , )1 21 � �(1 ).∑


6 Notice that b appears in (2), and the same notation is usedagain here. This is deliberate, as the ‘distance’ between twogroups may be viewed as one group’s utility distance betweenits preferred outcome and that of the other group.

087175_JPR_163-182.qxd 2/17/2008 6:36 PM Page 167



established is assumed to be equal to theresources niri expended by the group relativeto the total resources R expended. In short,the probability of success pi is just

(6)

where R is the sum of all the group contri-butions. In the sequel, we shall take this veryR to be a measure of the overall intensity ofconflict (or wastage) in the society.

To understand how contributions aredetermined, suppose that there is a utilitycost of spending ri; call it c(ri).7 Take thisfunction to be of the constant-elasticity form

(7)

Given the resources expended by theothers, the expected utility of an individualof group i when spending ri is

(8)

Expected utility is clearly concave in ri, andhence the utility maximizing level of expend-iture can be characterized by the first ordercondition:

(9)

An equilibrium of the conflict game is avector r such that (9) is satisfied for alli �1, …, G.

There is always an equilibrium of the con-flict game. Esteban & Ray (1999) demonstrate,

furthermore, that if ��1, then such an equi-librium is unique.8

In order to simplify the computations, weshall focus on the case of symmetric valu-ations, with bi�1 for all i, and ��1.Multiplying both sides of (9) by , we see that

(10)

and transposing terms, we conclude that

(11)

The equilibrium value of R has to be suchthat the sum of the probabilities adds up tounity. In view of (11), this condition impliesthat

(12)

There exists a value of R that solves (12), andit is unique. The left-hand side of (12) is strictlydecreasing in R. Using (10), it is immediatethat when R goes to zero, the left-hand sidetends to G 1 and that when R tends to infin-ity, the left-hand side tends to zero. This estab-lishes the claims of existence and uniqueness.

nn R

i

ii

2

2 ��

21∑

pn

n Rii

i

��

2

2 2.

nR

p pii i

⎛⎝⎜

⎞⎠⎟

2

(1 )� �

nR

i

c rr

ii( )

10.

1

��

� ��

, with

pn rn r

n rRi

i i

j jj

i i�∑

�


7 One could also have taken the line of measuring the costin terms of the utility loss incurred. We have opted to usethe resources expended, R.

8 This model is admittedly simple. However, we wish tomake two points here. One is that our model has been con-ceived as a benchmark case, so that in some cases the con-sequence of deviating from our assumptions can be inferred.The second point is that some of the assumptions are lessrestrictive than they look. To illustrate the first point, startby taking the case of identical payoffs. If we drop thisassumption, the player with the higher payoffs will put moreresources into conflict and will have higher win probabilityand a higher equilibrium expected utility. The opposite willhappen with the players with lower payoff. It follows thatthe high payoff player will be more inclined to challenge theexisting political system. Similarly, we can easily figure outwhat would happen if the marginal cost of conflict werehigher for one player over the other. Let us now turn to oursecond point. In the model, we allow for asymmetric groupsizes. But notice that n simply is a parameter that turns agiven effort cost (measured in utiles) into effective influenceon the win probabilities. Therefore, n can be interpreted ascapturing all the factors that may influence the effectivenessof a given effort. This can include differential wealth, poweror group motivation, as well as sheer population size.

087175_JPR_163-182.qxd 2/17/2008 6:36 PM Page 168

u p b c r

n rR

br

i i i i

i ii

i

( )

.

r � �

� ��

��

( )1

1

nR

n rR

bnR

p b ri i ii

ii i i1 (1 )� � � � �⎛

⎝⎜⎞⎠⎟ .



Substituting the equilibrium R into (11)yields the equilibrium probabilities for eachgroup’s preferred alternative to be imple-mented. In order to obtain a useful expres-sion for equilibrium payoffs, we multiplyboth sides of (9) by to see that

(13)

Using (13) in (8) yields

(14)

For the case of two groups, G �2, settingn1�n and p1� p, the equilibrium values areeasy to compute:

(15)

(16)

and

(17)

Using (11), (12) and (14), one obtains theequilibrium conflict payoffs for any G groups.For two groups, one can use the simpler ex-pression (17). These conflict payoffs will bethe benchmarks against which individuals willcompare the peace payoff that the politicalsystem gives to them. In this way, they willdecide whether to trigger conflict or not. Inwhat follows, the equilibrium payoffs to con-flict for player i will be simply denoted by ui.

PeaceIn a situation of peace, individuals accept thepayoff that the political system allocates tothem. We define a policy to be a vector ofshares, with i denoting the share (and also,therefore, the payoff ) of group i. Hence, wecan interpret as a ‘compromise policy’ com-

posed of a convex linear combination over theavailable alternative types of public goods.

Formally, we shall have peace whenever

ui� i for all i �1,…, G. (18)

It is trivial but nevertheless useful to observethat whether we have conflict or peace criticallydepends on what the ruling political systemdelivers to the different contending groups.

We shall examine here various sharingrules and check for their ability to guaranteepeace. Specifically, we shall study dictatorialrules, fixed shares, majoritarian rules and pro-portional rules.

We hasten to add that regimes such as dic-tatorship cannot be fully described by some-thing as simple as a mere sharing rule. Theseare just names we use to brand particularsharing rules that are precisely described below,and capture some but not all of the features ofthe regimes they are meant to approximate. Wefocus on these four rules because they aresimple and can be taken as benchmarks. But,obviously, they do not exhaust the set of pos-sible sharing rules covered by this model.

Our first example of a political system isthe dictatorial rule. This will be the case whenthe alternative preferred by some group i isbrought into effect, irrespective of the numberof individuals for whom this is the bestchoice. If group i is the dictator, then i�1and j�0 for all j � i.

The second case is fixed shares, which gen-eralizes the dictatorial rule. The policy consistsof a vector assigning a share to each groupindependent of its population size. There aremany instances of such a political system.Various political bodies have fixed propor-tional representations of the different opposinginterests (often rural vs. urban). There are alsocases where the chairs of the two chambershave to alternate between the different ethnicor religious groups in the country.9

The majoritarian rule generates the pol-icies that earn the support of a majority of

un n and

un n

1

( 1)

2(1 )(2 )

2

( )

( ) .

r

r

��

��

2

R n n� �(1 )

p n� ,

up p

ii i(

1r )

( ).�

�

2

1

21

1

22p p r c ri i i i( )� � � ( ).

ri

2


087175_JPR_163-182.qxd 2/17/2008 6:36 PM Page 169




citizens. For the case of G �2, this is veryeasy to define: i�1 if and only if ni½.For G 2, the characterization of the policiesresulting from a majoritarian rule is moreintricate, as it involves the formation of amajoritarian coalition. In some special envir-onments, there is a well-defined pivotal group(the median voter) who can impose its pre-ferred policy on the rest of the majoritariancoalition. This is not the case here, and,hence, most of what we can say will berestricted to the two-group case.

This is an extremely stylized representa-tion of the majoritarian rule. Real-worldmajoritarian democracies do not work likethis. A number of written and/or unwrittenrules protect minorities from the tyranny ofthe majority.10

Finally, the proportional rule produces the policy that assigns to each group a shareequal to its population size: i�ni. Parlia-mentary representations satisfy this rule formost countries (but not in the UK, where each seat corresponds to one constituency).Although most decisions simply require a majority vote in the chamber, the resultingpolicies tend to give some weight to theminoritarian opposition. Decentralization ofgovernment also contributes to giving the dif-ferent groups an overall weight that bringsthem closer to their population share.

In the next section, we study the relation-ship between polarization, fractionalizationand conflict under the different politicalsystems for the case of two groups. We latergeneralize to the case of more than two groups.

Polarization, Fractionalization,Conflict and the Political System (G �2)

We are interested here in two quite differ-ent aspects of conflict. First, we want tocharacterize the relationship between theintensity of conflict and polarization whenconflict actually takes place. This relationship isindependent of the political system. Second,we wish to identify the relationship betweenpolarization and the occurrence of conflict.

Intensity of ConflictWe start by noting that, for G �2, the meas-ures F and P are proportional to each other.Furthermore, they all attain their maximum atn �½. It follows that any comparative test ofthe performance of P relative to F as a predic-tor of conflict should focus on cases with G �3.

Using (5), we can obtain that, for G �2,P �n(1�n). Hence, in view of (16), the levelof conflict R is just the square root of P andconflict intensity is an increasing function ofpolarization and fractionalization.11

Figure 1, left panel, plots the intensityof conflict as a function of the population shares n. The right panel does the same as afunction of the level of polarization. Conflictintensity is maximal for n �½. Polarization isalso maximal at that value of n, with P �¼.

It will also be useful to keep track of theequilibrium utility payoffs as given by (17). Wedo so in Figure 2. These payoffs depend on thepopulation distribution parameter n. Theequilibrium utility for each player is the winprobability p �n minus the cost of

9 This was the first constitutional arrangement for theLebanon after independence. The constitution establishedthat the president had to be a Christian. The faster popu-lation growth rate among the Muslim population made thisprovision untenable and possibly contributed to the out-break of the civil war. Another example is the EU ‘rotatingpresidency’ that passes between the member countries witha frequency that is independent of their population.10 Cox (1997) represents a careful attempt at categorizingthe different existing democratic systems.

11 If we drop the restriction that ��1 but retain b �1,P(�,1) ceases to be proportional to F, but continues tobehave like it. Indeed, P(�,1) is concave and attains itsmaximum at n �½. Therefore, it will still be the case thatincreases in P(�,1) go with increases in the level of conflict R.Things are different when we allow for asymmetric inter-group distances. It can be readily verified that if b () 1both polarization and conflict are maximized at (two dif-ferent) values nP,nR()½. Therefore, except for values ofn within this interval, the level of conflict will be strictlyincreasing with polarization. The non-monotonicity withrespect to F and P will be for n in the interval (½, nR).

087175_JPR_163-182.qxd 2/17/2008 6:36 PM Page 170




the resources expended in conflict, which is thesame for all types of players when G �2. Thewin probabilities are points on the straight line between (0,1) and (1,0), the utility possi-bility frontier. Given n, from the correspond-ing point on the frontier, we move inwardsalong a 45� line for a length equivalent to theutility loss caused by the expended resources.This gives us a utility equilibrium pair. As wevary n, we generate all the points of the equi-librium payoff curve. The maximum distancebetween the payoff curve and the frontier is atn �½, where the conflict loss is maximal.

We now turn to the occurrence of con-flict. This depends on the payoffs obtained inpeace. The latter depend, in turn, on thepolitical system.

Dictatorial RuleThe first rule we examine is the dictatorial one.Will there ever be peace? The answer is no. Inequilibrium conflict, all players receive a strictlypositive payoff because they could have optedfor contributing nothing to conflict, thus guar-anteeing for themselves a payoff of zero. Hence,for a non-dictator, a peace payoff of zero isalways dominated by the conflict payoff. Ofcourse, this is a trivial case, and a more com-plete analysis is provided in what follows.

Fixed SharesWe next examine the case of fixed shares .The necessary and sufficient condition forconflict is that either

(19)

The situation is captured in Figure 3.Consider the peace share and the corre-sponding utility payoff. For a population para-meter like n�, the payoffs to conflict aredominated by the peace payoff for the twoplayers. However, if we decrease sufficientlythe population share of the first group – all theway down to n” – the second group would have

a strong advantage over the first in conflict andwould, therefore, prefer conflict to the peacepayoff.

To be more specific, let us rewrite the in-equalities in (19) as

(20)

The left-hand side of the two inequalitiesis strictly increasing in n (one convex and theother concave). Therefore, there exist n � andn� such that if n �[n�, n�] there is peace, whileif n falls outside this interval, there is conflict.

In Figure 4, we depict the values of n forwhich we have peace (given a fixed vector ofshares). These are the values of n bounded bythe points on the equilibrium utility curve atwhich one of the two players is indifferent tothe peace payoff.

Clearly, the interval of values of n for which there will be peace depends on the biasexhibited by the fixed-shares policy . Let ustake as a benchmark the case of equal treat-ment of the two groups of players with �½. From our previous analysis, it followsthat for very low polarization (i.e. for verylow or very large n) there will be conflict, butits intensity will be low. As polarizationincreases, the intensity of conflict will increasetoo. But, further increases in polarization willproduce peace and bring the level of conflictdown to zero. The overall relationship betweenpolarization or fractionalization and conflict istherefore non-monotonic.

We can address the complementary ques-tion of the range of policies that would guar-antee peace for given n. This range is given bythe gap between the two bounds: n(1�n).Hence, the widest range for peaceful policiescorresponds to n �½. High polarization allowsfor a wider choice of peaceful fixed-share policies.The intuition for this result is straightforward.If there is conflict, higher polarization pro-duces larger losses. Hence, it is only when thepolicy is very biased against one group that

nn

��

��

( )

2

1

2

1or

( )nn

n n .

n n n n(1 )

2or

(1 )(2 )

2

�

� � � 1 .

087175_JPR_163-182.qxd 2/17/2008 6:36 PM Page 171




that group will decide to incur the heavy costof conflict. With low polarization, the costs aresmaller, and hence a lower bias in might beenough to trigger conflict.

Majority RuleThe case of majority rule is equivalent toletting the largest group be a dictator. By thesame argument as before, we shall never have

1/20 1 n

R

1/40 P

R

u2

1

1�n’

1�n’’

u11n’ n’’

Figure 1. Intensity of Conflict, Group Size and Polarization

Figure 2. Equilibrium Conflict Payoffs and Group Size

087175_JPR_163-182.qxd 2/17/2008 6:36 PM Page 172




peace as the minoritarian group will alwaysobtain a higher payoff under conflict thanunder peace. Hence, with majority rule we shallalways have conflict, and the level of conflict, willpositively depend on the degree of polarization.

We remind the reader that this statementhas to be interpreted with due caution, andwill apply only to the extent that an existingmajoritarian democracy actually permits thetyranny of the majority.

Proportional RuleWe start by noting that in the previous caseof fixed shares, in view of (20), when is suf-ficiently close to the win probability of agroup, peace will not be challenged by thatgroup. Under our assumptions, p �n andhence making �n would guarantee peace.This precisely is the proportional rule thatgives each group a share equal to its popula-tion size, that is, i�ni

Therefore, for symmetric valuations weshould never observe conflict under the pro-portionality rule.12

The intuition for this result is that the pro-portionality rule gives to each group a weightthat is close to their win probability under con-flict. Hence, it never pays to challenge thepeace allocation. As we will see, this result isspecific to the two-group case and does notextend to the case of a larger number of groups.

Diagrammatically, we can see in Figure 2that the point (n,1�n) always dominates theconflict equilibrium payoffs.

Summing UpIn this section, we have obtained two mainresults. The first one is that it does matter forconflict which political system is in place.

u2

1

1-�

u11n’ n’’

1�n’’

1�n’

�

Figure 3. Conflict vs. Peace Payoffs Under Fixed Shares

12 This is no longer true for asymmetric valuations. Theequilibrium p can be made arbitrarily close to unity bychoosing b for one group sufficiently close to zero.

087175_JPR_163-182.qxd 2/17/2008 6:36 PM Page 173




Dictatorial and majoritarian systems neveryield peace. Fixed shares may give peacefuloutcomes for some parameter values. Theproportional system always yields peace, atleast whenever there are just two groups.

The second result is that while the inten-sity of conflict is positively related to thedegree of polarization, the incidence of con-flict is not. Only in the fixed shares systemdoes the incidence of conflict depend on thedistribution of the population across the twogroups. For the other three political systems,the incidence of conflict is independent ofthe distribution (and hence of the degree ofpolarization). For the fixed shares system,conflict is more likely at low levels of polar-ization and peace more likely at high levels.Therefore, if there is any relation between con-flict and polarization, this is non-monotonic.

Polarization, Conflict and PoliticalRules with Several Groups

We shall examine now whether our previousconclusions can be extended to the generalcase of several groups. As we shall see, thereare some important differences.

Intensity of ConflictThe relationship between the intensity ofconflict and polarization has been extensivelystudied in Esteban & Ray (1999, section 6).Adding up (10) over all i and multiplyingboth sides by R2,we have

(21)

Comparing (21) with the measure ofpolarization P in (4), we can observe that, if

Rpn

n n bi

ii i i

i

2 21

1(1 )�

�

�� .∑

u2

1

1-�

1-n’

1-n’’

u11n’ n’’

Peace

�

Figure 4. Range of Peaceful Group Sizes with Fixed Shares

087175_JPR_163-182.qxd 2/17/2008 6:36 PM Page 174




pi�ni, the level of conflict R would be equalto the index of polarization P(1,b).

The n/p ratio is determined in equilib-rium and will generally be different fromunity. Therefore, how closely related P is toR critically depends on how much n/p variesacross the different groups in equilibrium. Itcan be shown that the case in which ni/pi�1for all i is specific to the symmetric case forG �2 or for uniform distributions overG 2 groups. Therefore, on these groundsalone, we should a priori expect a positive butincomplete association between polarizationP(1,b) and the level of conflict R.

Drawing on the results in Esteban & Ray(1999), we can restate the following propertiesof R, implicitly determined in (12), to be con-trasted with the properties of F and P pres-ented in the previous section:

(i) A transfer of population from a group toa smaller one increases R if both groupsare larger than 1/3. If the two groups aresmall enough, the equalization of popu-lations will bring R down.

(ii) For any given G, R is maximized whenthe population is split into two equallysized groups only.

(iii) Over the set of uniform distributions, Rdecreases with the number of groups G.

(iv) The split of a group with population ninto two groups with n� and n�,n��n��n, increases R if and only if thegroup size is sufficiently large. If n issmall, the split will decrease R.

Do the properties of our theoreticalmodel align with our intuition on the inten-sity of conflict? Consider conflict amongthree groups of varying size. Property (i) saysthat equalizing the size of the two largestgroups will increase conflict, while reducingthe size of the second largest group at thebenefit of the smallest will reduce conflict.Property (ii) appears to conform to the

common intuition that conflict is worstwhen society is split into two equally sizedgroups. In the case considered by Property(iii), each group becomes progressivelysmaller, while its collective opponent (therest of the groups) becomes larger. In thiscase, the smaller groups will commit fewerresources to conflict. As for Property (iv),consider first the case of a monolithic societythat gets split into two distinct groups. Thismust increase the intensity of conflict. Thesame has to be true even if the initial societywas not monolithic, but had a small ‘dissi-dent’ group. But suppose now that after thefirst split, the second-sized group splits intotwo smaller groups. Then we would expectthat conflict would come down, because nowthe untouched group has become relativelylarger than the others. The smaller groupsmay not be willing to contribute much toconflict. In sum, the properties displayed byour conflict model do not seem to contradictour intuitions about conflict intensity.

Let us now compare the properties of Rand P. It is immediate that the two sets ofproperties describe movements in the samedirection for the type of population changesconsidered. Hence, we should expect astrong positive relation between polarizationand conflict intensity (see below for a para-metric illustration).

How does the index of fractionalization F behave relative to R? Property (i) of R is notsatisfied by F. Property (a) of F says that anyequalization of sizes will increase F. Incontrast, R may go either up or down de-pending on the size of the groups involved.Properties (ii) and (b) are aligned as long asthere are two groups in conflict to start with.With more groups, F is maximized at theuniform distribution, while R continues to bemaximal when the population is concentratedon two equally sized groups. Properties (iii)and (c) are exactly the opposite of each other.

087175_JPR_163-182.qxd 2/17/2008 6:36 PM Page 175




Finally, when we compare Properties (iv) and(d), we observe that any split always increasesF, while R may either decrease or increase,depending on the size of the broken group.

We can thus conclude that we can expect astrong positive relationship between polariza-tion and conflict, and a weak and (if anything)negative relationship between fractionaliza-tion and conflict, at least insofar as intensity isconcerned.

We now turn to an analysis of the inci-dence of conflict when there are more thantwo groups.

Dictatorial and Majoritarian RuleNotice that our arguments on the impossi-bility of peace under dictatorial or majoritar-ian rule did not depend on the number ofgroups. In both cases, the excluded groupsobtain a lower payoff than what they getunder conflict.

Fixed SharesFrom (14), we have that there will be conflictwhenever

(22)

Using (11) in (22), we obtain that the con-dition for conflict is

(23)

Consider G �3 groups, any given vector ofshares and a particular group of size nj.Observe that the conflict payoff ui can takevalues in (0,1), depending on R. Therefore,the condition for conflict is most likely to besatisfied when R is small and, hence, polar-ization is small too. To be precise, supposethat all the remaining groups have the samesize, . It can be readily verified from (12) that R is strictly decreasing in G. Tosee this, start by noting that (12) now becomes

that is

Totally differentiating with respect to G and R,we can see that if and only if ,where D is the denominator of the second frac-tion. Performing the differentiation, we obtain

Notice now that

.

Using this inequality, we obtain that

So, R is strictly decreasing in G. Therefore, itfollows that there is a G sufficiently large so thata uniform distribution over the G �1 remain-ing groups would induce group i to prefer con-flict. Note that, as G becomes large, polarizationcomes down and fractionalization goes up.Therefore, we shall see conflict with low levelsof polarization and high levels of fractionaliza-tion, but the intensity of conflict will be low.

In the discussion above, observe that theuntouched group, the group that has becomelarger relative to the others, is the one thatprefers conflict to peace. Hence, even in thiscase, one might argue that it is not high frac-tionalization as such that precipitates conflictbut the coexistence of one large group withnumerous small groups. In fact, if we nowequalize the size of all the groups, thus in-creasing F and decreasing P, no group wouldhave an incentive to challenge the peace share,

dDdG G

n ��

� 12

11 0.

2⎛

⎝⎜

⎞

⎠⎟( )

1

1

1( 1)

12

2

�

�

��

n

n

GG R

2

( )( )

dDdG G

nG

G R��

��

��

11

(1 )1

( 1) .2

2⎛

⎝⎜

⎞

⎠⎟

dDdG

�0dRdG

0

nn R

n

n

GG R

2

2 2

2

2

2

1

1

1( 1)

1.�

��

�

��

�( )

( )

nn R

G

nG

nG

R

2

2 2

2

2

2

( 1)

11

11

1,�

� �

�

�

�

��

�

⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟

nn

G, j ij

i��

��

1

1

un

n Rn

n Rii

i

i

ii�

��

�

1

21 .

2

2 2

2

2 2

⎛

⎝⎜

⎞

⎠⎟ �

p pi Gi i

i

(1 )

2for some 1, ..., .

� �

087175_JPR_163-182.qxd 2/17/2008 6:36 PM Page 176




and we would have peace with higherfractionalization.

To sum up, for the egalitarian fixed sharespolicy, conflict will not occur in societies withhigh polarization/low fractionalization. Fordistributions displaying low polarization/high fractionalization, the relation betweenconflict and F or P will be non-linear. Con-flict will be most likely for distributions withone large group and many small ones (andhence with relatively high fractionalizationand low polarization).

As the rule of fixed shares departs fromegalitarianism, the occurrence of conflict willcritically depend upon the bias introduced bythe rule.

Proportional RuleEquation (14) tells us that under the pro-portional rule there will be conflict whenever

(24)

In the previous section, we have seen that forG �2 the proportional rule always guaranteespeace. Does this property extend to G 2?

A first observation is that, for the distribu-tions under which the equilibrium win prob-abilities are very close to the population shares,Condition (24) will not be satisfied and weshall observe peace. We shall only have conflictwhen pi is sufficiently larger than ni for somegroup i.

Using (10) in (14), we can rewriteCondition (24) as

(25)

The left-hand side of (25) can take values in ,depending on R. We have already seen

that there is a distribution of the population(for G sufficiently large) so that R can bebrought very close to zero. Esteban & Ray(2001) demonstrate that, under these assump-tions, there always are distributions for which

(25) is satisfied for one group. Here are twonumerical examples: G �5 with one groupbeing of the population and the other fourof size ; and G �4 with one group of size ½and the other three of size .13

As in the case of fixed coefficients, conflictoccurs in very skewed distributions by size. Onelarge group together with a number of smallsized groups is the type of distribution thatwould be more likely to generate open conflict.Because of the returns to scale in conflict, thewin probability of the large group may amplyexceed its population share. Furthermore, pre-cisely because of the returns to scale, the smallgroups will be deterred from expending manyresources in such an uneven conflict, and,hence, we shall observe a low conflict loss R.

Therefore, we conclude that, with G 2,under the proportional rule we may haveconflict. This will be associated with dis-tributions with low polarization and high frac-tionalization. However, the relationship willbe non-monotonic: additional increases infractionalization may bring peace rather thanfurther conflict.

In order to illustrate this relationship, con-sider the following parametric example. Thereare three groups with n1�½, n2��½ andn3�(1��) ½, 0 ��½. When ��0, wehave two groups with the same populationand, thus, maximal polarization. When ��½,we shall have the same first group facing twogroups of half the size. F and P can be com-puted to be

(26)

and(27)P

F( )

3

8

1

2 4

2

� ��

� � .

F ( )1

2

2

� ��

1

21 1.

2 2

2

2 2

n

n R

n

n Ri

i

i

i��

�

⎛⎝⎜

⎞⎠⎟

p np

i 1, ... , Gi i

i

� �

1

2for some .

13 The case of India has been taken as a critical test forLijphart’s claim that ‘consociational’ systems – hence pro-portional – are guarantors of ethnic peace. Most of thedebate (Lijphart, 1996; Wilkinson, 2000) has focused onwhether India was more ‘consociational’ under Nehru ormore recently. Our analysis suggests that the change in popu-lation sizes of Hindus, Muslims and others that has actuallytaken place in India in 1961–2001 might also have a role inexplaining the evolution of ethnic conflict.

087175_JPR_163-182.qxd 2/17/2008 6:36 PM Page 177

( , 1

)0ni




From (27), it is plain that when � changes,fractionalization and polarization move inopposite directions: as we move away fromthe perfect bipolar distribution, P comesdown but F goes up.

Using this parameterization for the distrib-ution of the population in Expression (12), weimplicitly obtain the equilibrium intensity ofconflict R as a function of �. Totally differenti-ating, we obtain that R decreases as � increases,that is, as P decreases and as F increases.Conflict intensity goes from R(0) �0.5 toR(½) �0.211. This is depicted in Figure 5.

Whether there will be conflict or peaceunder the proportional rule depends on whether the untouched group – always withpopulation ½ – obtains a conflict equilibriumutility higher or lower than ½. In Figure 5, wealso depict u1 as a function of �. Not surpris-ingly, as � increases, group 1 is facing smallerand smaller enemies. Hence, u1 increases with �. The large group obtains a higher utilityfrom conflict the less polarized the distribu-tion is. The equilibrium utility goes fromu1(0) �0.375 to u1(½) �0.837. It follows thatfor low �, the equilibrium utility of group 1will be below the peace payoff, and there willbe peace. This corresponds to the highestlevels of polarization and lowest of fractional-ization. For �� (see Figure 5), there willbe conflict. Therefore, open conflict will beassociated with low polarization and highfractionalization.

We finally combine the intensity with theoccurrence of conflict and derive the relation-ships between observable intensity of conflictand both fractionalization and polarization.This is depicted in Figure 6. As we can see, inboth cases the relation is non-monotonic. Forthe case of fractionalization, there is peaceuntil the threshold level F � is reached. At thispoint, there is conflict, and it attains itsmaximum intensity. For higher values of F, wecontinue to have conflict, but its intensitymonotonically comes down. The relationship

between P and the observable intensity of con-flict is the other side of the coin. Open con-flict occurs at low levels of polarization. Aspolarization goes up, the intensity of conflictrises until the threshold P � is attained. Forhigher levels of polarization, the costs of con-flict are so high that we will observe peace. Thetwo functions are depicted in Figure 6.

Summing UpWhen we consider distributions with morethan two groups, it is still true that the occur-rence of conflict critically depends on the par-ticular political system in place. The dictatorialand the majoritarian rule can never bringpeace, as we already observed for G �2. Butin general, both fixed shares and proportionalrule fail to universally guarantee peaceful out-comes. We shall not see conflict either forvery low or for very high levels of fractional-ization.14 A mirror-image, inverted patternwould be followed by the conflict–polarizationrelationship.

Concerning the general relationship bet-ween polarization, fractionalization and con-flict, our results suggest that they will besignificantly non-linear.15 Under some politi-cal systems, the occurrence of conflict is inde-pendent of the shape of the distribution, whilein other systems, it does depend on the shape.Under the first class of political systems, theintensity of conflict will be positively related tothe degree of polarization (and negatively tofractionalization). Under the second class(fixed and proportional shares), we shallobserve zero intensity at high and very lowlevels of polarization (and fractionalization).For the range of levels of polarization for which

14 This seems to contradict the result obtained by our para-metric example above. This is due to the very special changein the distribution that our parameterization allows for.Consider, for instance, our limit case with ��½ (n1�½,n2�¼, n3�¼) Fractionalization is maximal and we still haveconflict. However, if we now move to n1�n2�n3�1/3 – notallowed by our parameterization – fractionalization wouldbe even higher, but there would be no conflict.15 These results are in line with the empirical findings ofSchneider & Wiesehomeier (2008).

087175_JPR_163-182.qxd 2/17/2008 6:36 PM 8




we shall have conflict, higher polarization willbe positively related to higher intensity of con-flict. As far as fractionalization is concerned,there seems to be no regular relationshipbetween its level and the intensity of conflict.

All these results suggest that there may bemore to be learned from empirical exercisesthat put all the evidence together and alsoattempt to control for the political system ofeach country. Political scientists have long beenaware of the critical role played by the

political institutions in preventing domestic conflict. The work of Lijphart (1977) is fun-damental here, as well as the recent contro-versy between Horowitz (2006) and Fraenkel& Grofman (2006) on the effectiveness ofconstitutional engineering. Our point is that,in spite of this important line of literature,empirical tests on the determinants of con-flict have very seldom controlled for thedifferent specific forms of democracy. Recentexceptions are Reynal-Querol (2002b, 2005)

12

12

38

~ 56

λλ0

u1

Figure 5. Conflict Intensity, Individual Payoff and Group Size

R

PF

R

F 0P0

Figure 6. Conflict Intensity, Fractionalization and Polarization

087175_JPR_163-182.qxd 2/17/2008 6:36 PM Page 179



and Schneider & Wiesehomeier (2008), whodo study the relationship between politicalsystems and domestic conflict.

Conclusions

We provide an analytical framework thatpermits an interpretation of recent empiricalexercises that study the relationship bet-ween population distributions over opposinggroups, and the emergence or intensity of con-flict. We argue that conflict typically breaksout when the payoffs delivered by the politi-cal system fall short of what one group canobtain by precipitating non-cooperation.While the intensity of conflict clearly dependson the shape of the distribution, the occur-rence of conflict also depends on the respon-siveness of each political system to the popularsupport for each of the competing alterna-tives. When we combine occurrence withintensity, the relationship between conflictand polarization/fractionalization becomessignificantly non-linear and contingent on theruling political system.

The rationale behind our result is straight-forward. Conflict is costly and hence payoffs areless than what are achievable under peace. Thecostlier such conflict is, the easier it becomes toassign payoffs to groups that Pareto dominateconflict payoffs. Therefore, the political systemswith highly unequal outcomes (such as dicta-torial or majoritarian rule) will always be chal-lenged, even when the cost is high. Under‘fairer’ systems, no group would be willing topay too high a cost to obtain a different payoff.Therefore, it is only when conflict is nearly cost-less to one group (such as the case of one large

group and a number of small opponents) thatthe outcome of the political system will be chal-lenged, by precisely that large group.16

Highly polarized situations may be fairlypeaceful. This is what happened during theCold War period. The cost of challenging theinternational status quo was so immense that,even if one of the two sides considered the divi-sion of international power disproportionate,it could not – or would not – trigger a worldconflict. At the same time, when polarizationis extremely low, there is little to fight about.Consequently, we would expect the overalldegree of conflict to be maximal in societieswith intermediate levels of polarization.

Two recommendations appear to emergefor future empirical exercises. First, thereshould be a serious attempt to account forthe non-linearity between polarization andconflict.17 The broader prescription is simplythis: the empirical specification needs to bemore firmly grounded in theory, even if thattheory is simple.

Second, the incidence of conflict dependsnot only on the shape of the distribution butalso, critically, on the ruling political system.Alternative political systems perform quite dif-ferently in guaranteeing peace. For countrieswith political systems that always yield conflict,we shall observe that the intensity of conflict is(roughly) positively related to polarization andnegatively to fractionalization. However, incountries with political systems that may yieldpeace, the occurrence and intensity of conflictwill typically have a highly non-linear relation-ship with polarization and/or fractionalization.It follows that the exercise critically demandsthat political systems be controlled for.


16 Note the similarity of this point with the findings ofCollier (2001) on the dominant ethnicity provoking civilwar. One should qualify these points, however, by observ-ing that small groups can provoke conflict when privategoods are at stake. For more on this issue, see Esteban &Ray (2006).

17 On a similar issue arising in the empirical debate oninequality and growth (though for very different reasons),see Banerjee & Duflo (2003).

087175_JPR_163-182.qxd 2/17/2008 6:36 PM Page 180



References

Alesina, Alberto; Rez Baqir & William Easterly, 1999.‘Public Goods and Ethnic Divisions’, QuarterlyJournal of Economics 114(4): 1243–1284.

Alesina, Alberto; Arnaud Devleeschauwer,William Easterly, Sergio Kurlat & RomainWacziarg, 2003. ‘Fractionalization’, Journal ofEconomic Growth 8(2): 155–194.

Banerjee, Abhijit & Esther Duflo, 2003. ‘Inequalityand Growth: What Can the Data Say?’, Journalof Economic Growth 8(3): 267–299.

Bénabou, Ronald, 1996. ‘Inequality and Growth’,in Ben Bernanke & Julio Rotemberg, eds,NBER Macroeconomics Annual. Cambridge,MA: MIT Press (11–74).

Brockett, Charles, 1992. ‘Measuring PoliticalViolence and Land Inequality in CentralAmerica’, American Political Science Review86(1): 169–176.

Collier, Paul, 1998. ‘The Political Economy ofEthnicity’, paper presented at the AnnualWorld Bank Conference on DevelopmentEconomics, Washington, DC, 20–21 April.

Collier, Paul, 2001. ‘Implications of EthnicDiversity’, Economic Policy 32(16): 127–166.

Collier, Paul & Anke Hoeffler, 1998. ‘OnEconomic Causes of Civil War’, OxfordEconomic Papers 50(4): 563–573.

Collier, Paul & Anke Hoeffler, 2004. ‘Greed andGrievance in Civil War’, Oxford EconomicPapers 56(4): 563–595.

Cox, Gary W., 1997. Making Votes Count: StrategicCoordination in the World’s Electoral Systems.Cambridge: Cambridge University Press.

Deutsch, Karl Wolfgang & J. David Singer, 1964.‘Multipolar Power Systems and InternationalStability’, World Politics 16(3): 390–406.

Duclos, Jean-Yves; Joan Esteban & Debraj Ray,2004. ‘Polarization: Concepts, Measurement,Estimation’, Econometrica 72(5): 1737–1772.

Easterly, William & Ross Levine, 1997. ‘Africa’sGrowth Tragedy: Policies and Ethnic Divisions’,Quarterly Journal of Economics112(3): 1203–1250.

Esteban, Joan & Debraj Ray, 1994. ‘On theMeasurement of Polarization’, Econometrica62(4): 819–851.

Esteban, Joan & Debraj Ray, 1999. ‘Conflict andDistribution’, Journal of Economic Theory87(2): 379–415.

Esteban, Joan & Debraj Ray, 2001. ‘SocialDecision Rules Are Not Immune to Conflict’,Economics of Governance 2(1): 59–67.

Esteban, Joan & Debraj Ray, 2006. ‘On theSalience of Ethnic Conflict’, unpublishedmanuscript.

Fearon, James D., 1995. ‘Rationalist Explanationsof War’, International Organization 49(3):379–414.

Fearon, James D. & David D. Laitin, 2003.‘Ethnicity, Insurgency, and Civil War’,American Political Science Review 97(1): 75–90.

Fraenkel, Jon & Bernard Grofman, 2006. ‘Does theAlternative Vote Foster Moderation in EthnicallyDivided Societies? The Case of Fiji’, ComparativePolitical Studies 39(5): 623–651.

Grossman, Herschell I., 1991. ‘A General EquilibriumModel of Insurrections’, American Economic Re-view 81(4): 912–921.

Grossman, Herschell I., 1994. ‘Production,Appropriation and Land Reform’, AmericanEconomic Review 84(3): 705–712.

Hegre, Håvard & Nicholas Sambanis, 2006.‘Sensitivity Analysis of Empirical Results onCivil War Onset’, Journal of Conflict Resolution50(94): 508–535.

Hegre, Håvard; Tanja Ellingson, Scott Gates &Nils Petter Gleditsch, 2001. ‘Towards aDemocratic Civil Peace? Democracy, PoliticalChange, and Civil War, 1816–1992’, AmericanPolitical Science Review 95(1): 33–48.

Hirschleifer, Jack, 2001. The Dark Side of Force:Economic Foundations of Conflict Theory.Cambridge: Cambridge University Press.

Horowitz, Donald L., 2006. ‘Strategy Takes aHoliday: Fraenkel and Grofman on theAlternative Vote’, Comparative Political Studies39(5): 652–662.

La Porta, Rafael; Florencio Lopez de Silanes,Andrei Shleifer & Robert Vishiny, 1999. ‘TheQuality of Government’, Journal of LawEconomics and Organization 15(1): 222–279.

Leventoglu, Bahar & Branislav L. Slantchev,2007. ‘The Armed Peace: A PunctuatedEquilibrium Theory of War’, American Journalof Political Science 51(4): 755–771.

Lichbach, Mark Irving, 1989. ‘An Evaluation of“Does Economic Inequality Breed PoliticalConflict?” Studies’, World Politics 41(4):431–470.


087175_JPR_163-182.qxd 2/17/2008 6:36 PM Page 181



Lijphart, Arend, 1977. Democracy in PluralSocieties. New Haven, CT & London: YaleUniversity Press.

Lijphart, Arend, 1996. ‘The Puzzle of Indian Demo-cracy: A Consociational Interpretation’, AmericanPolitical Science Review 90(2): 258–268.

Lipset, Seymour & Stein Rokkan, 1967. PartySystems and Voter Alignments: Cross-NationalPerspectives. New York: Free Press.

Mann, Michael, 2005. The Dark Side ofDemocracy: Explaining Ethnic Cleansing.Cambridge: Cambridge University Press.

Midlarsky, Manus I., 1988. ‘Rulers and theRuled: Patterned Inequality and the Onset ofMass Political Violence’, American PoliticalScience Review 82(2): 491–509.

Montalvo, José G. & Marta Reynal-Querol,2005. ‘Ethnic Polarization, Potential Conflict,and Civil Wars’, American Economic Review95(3): 796–816.

Muller, Edward & Mitchell Seligson, 1987.‘Inequality and Insurgency’, American PoliticalScience Review 81(2): 425–452.

Muller, Edward; Mitchell Seligson & Hung-derFu, 1989. ‘Land Inequality and PoliticalViolence’, American Political Science Review83(2): 577–596.

Nagel, Jack, 1974. ‘Inequality and Discontent: A Non-Linear Hypothesis’, World Politics26(4): 453–472.

Østby, Gudrun, 2008. ‘Polarization, HorizontalInequalities and Violent Civil Conflict’,Journal of Peace Research 45(2): 143–162.

Powell, Robert, 1999. In the Shadow of Power:States and Strategies in International Politics.Princeton, NJ: Princeton University Press.

Powell, Robert, 2004. ‘Bargaining and LearningWhile Fighting’, American Journal of PoliticalScience 48(2): 344–361.

Powell, Robert, 2006. ‘War as a CommitmentProblem’, International Organization 60(1):169–203.

Reynal-Querol, Marta, 2002a. ‘Ethnicity, PoliticalSystems, and Civil Wars’, Journal of ConflictResolution 46(1): 29–54.

Reynal-Querol, Marta, 2002b. ‘Political Systems,Stability and Civil Wars’, Defense and PeaceEconomics 13(6): 465–483.

Reynal-Querol, Marta, 2002c. ‘A Contribution onthe Measurement of Religious Diversity’, PRPES

Working Paper No. 4, Weatherhead Center forInternational Affairs, Harvard University.

Reynal-Querol, Marta, 2005. ‘Does DemocracyPreempt Civil Wars?’, European Journal ofPolitical Economy 21(2): 445–465.

Schneider, Gerald & Nina Wiesehomeier, 2006.‘Ethnic Polarization, Potential Conflict, andCivil Wars: Comment’, unpublished manu-script, University of Konstanz.

Schneider, Gerald & Nina Wiesehomeier, 2008.‘Rules That Matter: Political Institutions andthe Diversity–Conflict Nexus’, Journal of PeaceResearch 45(2): 183–203.

Skaperdas, Stergios, 1992. ‘Cooperation, Conflict,and Power in the Absence of Property Rights’,American Economic Review 82(4): 720–739.

Skaperdas, Stergios, 1996. ‘Contest SuccessFunctions’, Economic Theory 7(2): 283–290.

Wagner, R. Harrison, 2000. ‘Bargaining andWar’, American Journal of Political Science44(3): 469–484.

Waltz, Kenneth N., 1964. ‘The Stability of aBipolar World’, Daedalus 93: 881–909.

Wang, You-Qiang & Kai-Yuen Tsui, 2000.‘Polarization Orderings and New Classes ofPolarization Indices’, Journal of PublicEconomic Theory 2(3): 349–363.

Wilkinson, Steven Ian, 2000. ‘India, ConsociationalTheory, and Ethnic Violence’, Asian Survey40(5): 767–791.

Wolfson, Michael C., 1994. ‘When InequalitiesDiverge’, American Economic Review Papersand Proceedings 84(2): 353–358.

Zhang, Xiaobo & Ravi Kanbur, 2001. ‘WhatDifference Do Polarisation Measures Make?An Application to China’, Journal ofDevelopment Studies 37(3): 85–98.

JOAN ESTEBAN, b. 1945, D.Phil. Oxon1988, Research Professor, Instituto de AnálisisEconómico-CSIC, Bellaterra-Barcelona, andPresident of the Society for the Study ofEconomic Inequality (2007–09).

DEBRAJ RAY, b. 1957, PhD in Economics(Cornell University, 1983); Julius Silver Professorof Economics and Director of Graduate Studies,New York University (1999– ).


087175_JPR_163-182.qxd 2/17/2008 6:36 PM Page 182



journal of peace research - new york · pdf filejournal of peace research doi:...

Documents