The political economy of power–sharing
George Tridimas*
University of Ulster, School of Economics
Newtownabbey, Co. Antrim, BT37 0QB, UK
Abstract
The paper analyses why office-motivated political rivals may agree to cease conflict to
control the government and share power on the basis of an election outcome under
proportional representation. As the outcomes of conflict and elections are uncertain, for
each rational player the choice depends on which setting secures the highest expected net
payoff. Adopting the methodology of the economics of conflict, I show that the factors of
crucial importance are attitudes to risk, the comparative effectiveness of the adversaries
in contesting election relative to a war, the size of the benefits from office, how the
benefits are shared in a power-sharing agreement, and the proportion of the benefits
destroyed by fighting.
JEL Classification: D72, D74, H56
Key words:
Power-sharing, consociational theory, post-civil-war democratisation, nonmajoritarian institutions, proportional representation, risk aversion, splitthe-surplus formula
*Tel: +44 (0) 28 90368273, fax: + 44(0) 28 0366847, e-mail: G.Tridimas@ulster.ac.uk
1.
Introduction
Power-sharing is an arrangement whereby warring political factions jointly exercise the
power of office rather than fight. Examples of power-sharing of varying success are
contemporary Iraq, Kenya, Lebanon, Northern Ireland and Zimbabwe. Power-sharing and
consociational government can be a mechanism for managing conflict in societies
divided along ethnic, racial, religious, linguistic and cultural lines. However, agreement is
required of all rival factions, including those who may feel that they stand a better chance
to win a war than an election. Why would an office-seeking, utility-maximising leader
decide to lay down his weapons and abide by the rules of democratic politics?
Recognising that victory after a war is uncertain and so is the election outcome, the
present study examines the circumstances under which two opposing political groups
choose to end conflict and share power when the gains from office are divided according
to the outcome of an election under proportional representation.
In a homogeneous society under a democratic polity, where each political party has a fair
chance of winning an election, it may be accepted that the winning majority earns the
right to pursue its preferred policy in a “winner-takes-all” division of the spoils of
electoral victory.1 However, in a deeply divided society, where one community enjoys an
inbuilt majority by virtue of its greater number of members and individuals vote
according to identity rather than policies and political competence2, collective decisions
based on simple majority rule systematically privilege the larger community and
permanently exclude the minority from office. In such a setting, simple majority rule
outcomes can be expected to be viewed as illegitimate by the losing minority. A sense of
injustice combined with related grievances may then lead the minority community to take
up arms and seek to take over the state or to secede. Violent conflict and civil war cost
1
The policy making authority of the majority in a democracy is not unfettered but subject
to various non-majoritarian constitutional restrictions including constitutional judicial review.
Legislative acts and policy measures that violate the constitution can be annulled by the judiciary;
for a survey see Tridimas (2010).
2
Voting according to identity is a manifestation of expressive voting, that is, one where a
citizen derives utility from casting a vote that expresses his preferences, rather than deriving
instrumental benefits from influencing the election outcome, see Brennan and Hamlin (1998) and
(1999).
1
lives and property to both rival communities while the outcome is uncertain. Under
power-sharing, the electoral majority shares power with the minority and the agreement
required to reach decisions generates more moderate outcomes in comparison to a rule
that allows decision making to be concentrated in the hands of the winning larger
community.
The present study leaves the question of the consequences of power-sharing on policy
outcomes for future investigation. Power-sharing is a form of insurance against the losses
that a minority will incur when the majority rules. Whether or not rational political
players respect the power-sharing agreement and abide by its rules depends on whether it
is credible and its provisions are enforced, and whether it secures a higher expected
payoff for all players than the alternative of war. Credibility depends, amongst other
things, on implementation mechanisms, including the presence of a “higher authority”,
for example, a foreign power trusted by both parties that has the resources and the will to
enforce the terms of the agreement; or a self-enforcement mechanism, as for example
when the two adversaries give up their weapons, integrate their military into a united
defence force, and set up a single police service and an independent judiciary.
My focus is on the determinants of the payoffs from power-sharing given enforceability,
and on whether power sharing is preferable to war and to majoritarian rule. In the
tradition of political economy, the issue is not approached as a question of avoiding war
and adopting democracy for normative reasons but as one of self-interest. A large
literature analysing the benefits of settlement over conflict compares the uncertain
outcome of conflict over an asset to the deterministic outcome of dividing that asset.
Contrary to this work, the present study compares the uncertain outcome of conflict to the
uncertain outcome of an election, which determines how resources are shared between
disputants.
The paper is structured as follows. The next section discusses the relation of the present
study to various strands of research on civil war, power-sharing in democratic
government, and electoral rules and coalition formation. Given the voluminous literature,
2
the discussion can only be selective. By way of an example of the workings of a powersharing arrangement, I provide a brief description of the 1998 peace agreement in
Northern Ireland between Unionist-Protestants and Nationalist-Catholics. Section 3
introduces the conceptual framework and studies the circumstances under which two
opposing groups lay down their weapons and share power according to their electoral
shares. Modelling power-sharing on the basis of proportional representation is sensitive
to assumptions about attitudes to risk. Assuming first risk neutrality, I analyse the choices
between war and a power-sharing formula based on dividing the gains from peace
equally. I then extend the analysis to the case of risk aversion and study when the
opponents give up violent conflict and adopt democratic politics under proportional
representation. Section 4 concludes.
2.
A selective review of civil war and power-sharing
Wars are ex post inefficient because of costs of arming, injury and loss of life, and
destruction of property. The present study is related to strands of a large political science
and economics literature on conflict and civil war, post-civil-war resolution and the
debate between consociation and centripetal form of government, and policy making
under proportional representation. The following is a selective description of some of the
themes in this literature.
2.1.
Civil War
The first branch of studies relates to a growing economic literature on war based on game
theory. The economic analysis of war uses the insights of the theory of incomplete
contracting and conflict (Hirshleifer, 1995): When it is in their interests, the participants
are not able to make commitments that they will not engage in war against each other.
After scrutinising a number of arguments, Fearon (1995) concludes that there are three
rational explanations of war. (1) Incomplete information and strategic misrepresentation:
That is, leaders who go to war may have private but incomplete information about
relative ability and willingness to fight and strategic incentives to misrepresent such
information in order to gain a better deal. In addition, waging war may act as a signal
3
about willingness to fight and military strength.3 (2) Inability to commit: Rival powers
may be unable to commit credibly to peace because of strong incentives to renege on a
bargain (even though there are no problems of information asymmetry or strategic
misrepresentation). This is likely under three circumstances, namely, when a pre-emptive
war increases the chances that a country wins decisively; when a preventive war
increases the chances that a country will not be strong enough to mount an attack in the
future; and when a country cannot be trusted that if it is offered a concession it will not
demand more later (a case of failure of appeasement). (3) Indivisibility of the issue in
dispute: Some issues may be indivisible; for example, who sits on the throne, or who has
authority over a territory. In this case, the disputants consider the issue at hand as a binary
variable, all-or-nothing, and will be unable to negotiate a mutually beneficial division,
that would result in a peaceful resolution. Powell (2006) argues that indivisibilities
should be seen as a commitment problem, and observes that despite the insights gained
by models based on incomplete information, “war comes when a state becomes
convinced that it is facing an adversary it would rather fight than accommodate” (p.194).
Looking more specifically at civil wars, Grossman (1991) presented an economic model
of insurrection, where labour time is divided between production, soldiering for the
lawful government and insurrection and depends on the technology of conflict.
Gershenson and Grossman (2000) examined civil wars in a setting in which adversaries
attach different values to being politically dominant and study whether civil conflict ends
when the challenger becomes dominant or it never ends.4 Collier and Hoeffler (2007)
survey the causes, duration, consequences and costs of civil war. The most common
causes seem to be ethnic and religious divisions and social and income inequality. Civil
wars seem to last ten times longer than international wars; their direct cost of destruction
is compounded by capital flight and economic decline, higher mortality, adverse effects
3
Bester and Warneryd (2006) analyse settings where one side underestimates the strength
the other as a result of which war erupts.
4
See also Sambanis (2004) for a critical review and synthesis of the many interesting
questions regarding what constitutes and what causes civil war, “greed” or “grievance” and
misperception of opportunities.
4
on human health, deterioration of political institutions and human rights, and a high risk
of renewed hostilities. Garfinkel and Skaperdas (2007) survey the theoretical work on the
economics of conflict. They explain that conflict arises when property rights are neither
perfectly nor costlessly enforced, and analyse how conflict may impact on the
distribution of output and the conditions conducive to settlement.
Summarising earlier contributions on civil war, Skaperdas (2008) starts from the premise
that divisions arise as a result of geography (where the central government finds it
difficult to control remote and inhospitable territories), ethnic differences, sharp
economic and social changes, the dissolution of existing states and the creation of new
ones, intervention by external powers that break the existing order (geopolitics) and a
power vacuum that can be filled by rival groups fighting against each other rather than
negotiating. Fighting may break out because the groups are imperfectly informed about
their fighting capabilities and opportunities, but perhaps more interestingly, even when
they are fully informed, because the long-run expected payoffs from fighting exceed the
short-term incentives to compromise, since by fighting and vanquishing his opponent the
victor will no longer need to arm and fight a future war.
Conflict occurs when one side has supreme value objectives that it attempts to impose on
others: see Bernholz (2004) and the literature cited therein. Supreme values refer to
ideological or religious aims that override all other aims. In seeking to satisfy their
supreme ideological objectives, acts of terror may be committed in which “true believers”
take the lives of others while forgoing their own lives. Bernholz models this type of
behaviour by a preference function in which the supreme-value aims lexicographically
preferred to all others. With a lexicographic preference ordering, resources are spent on
other aims only insofar as they are not needed to satisfy the goals designated by the
supreme values. He then derives demand functions for terrorist instruments displaying the
standard properties (decreasing in prices and increasing in income), but with the
additional property that a zero amount of consumption goods may be demanded, which is
interpreted as believers’ willingness to die in terrorist acts.
5
The ferocity of identity conflicts may be explained by expressive behaviour, defined by
Hillman (2010) as the self-interested quest for utility through acts that confirm a person’s
identity rather than providing material gain. Contrary to instrumental behaviour, which
focuses on the expected material benefit from the outcome of an action, material gain is
willingly sacrificed in expressive behaviour when offsetting expressive utility is higher.
Behaviour may be explained that in material terms alone would be considered as
irrational. However, when both sides expressively engage in such acts, they may end up
fighting a costly war for which material loss exceeds expressive utility.
A number of studies have also inquired into the role of third party intervention to a
conflict. Chang et al. (2007) find that it is more costly for a third party to support an ally
to maintain peace than to gain a disputed territory by attacking. Amegashi and Kutsoati
(2007) show that the optimal policy for a third party acting as a benevolent planner is not
to offer financial help to the weaker side of a conflict when success in the war depends on
effort, because it would increase the aggregate cost of conflict. However, the nonintervention result does not hold when either the conflict is infinitely repeated, or the
third party decides to intervene militarily to care for non combatants. Asnik and Weikard
(2009) illustrate the change of incentives that may be triggered by a third party, namely,
intervention may be counterproductive since it may lead a contestant not to compromise
through bargaining but to fight on the hope that the third party will provide him with a
outcome than he can secure in bilateral negotiations.
Looking specifically at power-sharing, Wantchekon (2000) uses a game theoretic model
to show that credible power-sharing institutions are necessary for stopping a civil war and
adopting democratic institutions, and that arrangements such as integration of the military
of the warring factions and guaranteed positions in civil service enhance the credibility of
the peace deal. Wantchekon and Neeman (2002) and Wantchekon (2004) distinguish
between civil wars that end with and without establishing a democratic polity. They show
that a negotiated settlement is more likely when government revenue depends on private
investment rather than natural resources or foreign aid; no decisive winner emerges from
the war and the warring factions demilitarise. Brams and Kilgour (2008) examine the
6
stability of power-sharing agreements. In their model the division of the rents from office
is exogenous rather than being determined by the election outcome. Using both one-shot
and repeated game settings, they examine the circumstances under which each player will
attack first, where (contrary to the present work) the probability of defeating the opponent
is exogenous, and they show that the loss from conflict mitigates the incentive to start a
war but does not eliminate it completely.
A distinct line of statistical research on civil wars relates to the use of power-sharing
institutions to end a civil war and secure democracy in a divided society. In a much
quoted study, Licklider (1995) observes that a civil war is more intense and more difficult
to resolve than a war between two sovereign states because the stakes are higher (after
the violence ends the combatants still have to live in the same country), and because there
is no institution to enforce agreements between the combatants. Using an international
sample of 91 post-1945 civil wars, he finds that a negotiated settlement is more likely to
break down than a settlement based on military victory because it creates a structure of
decision making power that prevents the government from functioning effectively. In
addition, civil wars regarding identity issues (such as ethnic, religious, racial and
linguistic differences) are more difficult to resolve by peace agreements than conflicts
regarding politico-economic issues. Doyle and Sambanis (2000) using 124 post WWII
civil wars present evidence that peace-keeping operations supported by substantial UN
financial assistance help sustain peace and support democracy, especially after long, not
very costly, non-identity civil wars in relatively developed countries. Hartzell and Hoddie
(2003) find that, of the civil wars that are resolved peacefully, those that end with
extensive power-sharing arrangements and those enforced by a third-party are more
likely to result in an enduring peace. Gurses and Mason (2008) find support for the
hypotheses that civil wars that end in negotiated settlements rather than clear military
victories by government or insurgents are more likely to lead to democratic politics,
while civil wars triggered by the wish of a group to preserve its ethnic or religious
identity are less likely to do so. However, contrary to Doyle and Sambanis (2000), they
7
do not find any significant support for the argument that peace keeping operations lead to
higher levels of democracy.5
2.2.
Power-sharing mechanisms
The second strand of literature relates to the organisation of government in post-conflict
societies. The theory of consociational government, developed by Lijphart (1984, 1999),
investigates how peace and democracy can be established in a society afflicted by deep
divisions and violent conflict.6 Forming a government and formulating policies that
command support from the opposing communities rules out the use of majoritarian
electoral systems; instead it requires the adoption of institutions that will achieve crosscommunity consensus. Consociational government includes mechanisms to share
political and military power, divide economic resources, guarantees of the security of
participants by third parties, retributive justice (in the form of an amnesty), restorative
justice (in the form of repatriation of displaced civilians), and guarantees that basic rights
will be protected. Sharing political power consists of a number of components, namely,
executive power-sharing, where each of the main communities participates in an
executive formed on the basis of representative government; proportionality, where each
community is represented in key public institutions and receives public expenditure
benefits in proportion to its numbers; veto-rights, where each community has the power
to veto policy measures that may harm its interests; and self-government, where each
community enjoys some distinct measure of autonomy, particularly in cultural matters.
However, power-sharing is not without problems. The inclusion of opposing sides in the
executive may decrease competition, reduce political accountability; slow down decision
making and implementation; and discourage the search for new ideas and policies.
Moreover, a power-sharing arrangement, which requires parties to declare themselves on
5
Gurses and Mason (2008) attribute the divergence of these results to their use of a
continuous rather than a binary measure of democracy for controlling for the pre civil war level of
democracy and for taking into account whether the civil war ended with a government or rebel
victory.
6
The list of countries which at some point in time or still operate some form or other of
consociational arrangements comprises cases of both developed and developing nations across
the world; examples include Austria, Canada, Colombia, Cyprus, the European Union, Fiji, India,
Malaysia, the Netherlands, South Africa and Switzerland; see Lijphart (2004).
8
the basis of the political / ethnic group they represent, may aggravate rather than mitigate
divisions. In contrast to consociation, the centripetal (or incentive, or integration) view of
Horowitz (2000, 2008) argues for institutions that encourage politicians to reach out
across identity boundaries and policies to promote social integration and increase public
expenditure to redress sectarian differences. It envisages a system of electoral incentives
where parties will moderate their ethnic stance and appeal to voters from both sides of the
inter-community divide, like in a presidential system.
2.3.
Proportional representation and coalition government
As already indicated, an important component of power-sharing is the application of a
proportional representation electoral rule as opposed to a majoritarian one. It is well
established that the two systems yield different equilibrium policies. Majoritarian
electoral systems offer voters clear choices among competing political parties, but may
fail to represent fully the entire spectrum of voter preferences, and typically lead to single
party government. On the other hand, proportional representation produces a multi-party
system reflecting different interests and ideological objectives. Thus, it accommodates
different policy preferences, but with no single party obtaining a parliamentary majority
it leads to power-sharing that makes difficult to identify who is responsible for policy
choices.7 Mueller (2003) offers an introduction to the voluminous literature examining
different formulas of proportional representation for allocating parliamentary seats, the
related questions of the effective number of parties, the factors affecting the composition
of the winning coalition of parties, the equilibrium set of policies in multi-dimensional
space, the stability of the government and the incentives of voters to vote strategically for
parties that have a better chance to be elected to parliament, rather than those that best
reflect their preferences.
In multi-party parliamentary democracies, the parties that form the government, the
allocation of portfolios, and the policies to be implemented are decided by bargaining
7
There is an extensive political economics literature on the effects of majoritarian and
proportional representation rules on the size and composition of public expenditures; see for
example Persson and Tabellini (1999), Austen-Smith (2000), Lizzeri and Persico (2001) and MilesiFerreti, Perotti and Rostagno (2002).
9
among parties whose electoral strength is determined by their vote shares, which in turn
depend on how voters vote. Formally, voting in elections, government formation and
policy decisions is analysed as a multi-stage game.8 In explaining coalition government
formation, two sets of factors are deemed important (see Martin and Stevenson, 2001, for
a review and empirical tests). First is the size of a party in terms of number of
parliamentary seats won, and its ideology; and second, institutional structures, that is,
rules and procedures that define the formateur (the party and political leader with the
power to propose a coalition government); the power (or lack thereof) of the incumbent
to call an election; the reversion point that will prevail if the negotiation to form a
coalition fails; the investiture rule (the formal requirement to obtain a majority vote in
parliament instead of forming a minority government that seeks ad hoc parliamentary
votes for proposed policies); and norms of behaviour, like pre-electoral commitments to
form coalition government only with parties of related ideologies.9
A further question of interest is whether power-sharing arrangements moderate party
politics. Parties face a trade-off between advocating their policy preferences at the risk of
obtaining little support from uncommitted voters and moderating policy proposals to
increase support and hence policy influence in a post-election coalition government.
Merrill and Adams (2007) show that when voters support the party whose policy
programme best reflects their policy preferences, power-sharing does not make parties
more extreme in comparison to arrangements in which a single party dominates. In
accordance with the theoretical argument that power-sharing fosters political
compromise, empirical studies drawing on western democracies conclude that power8
Extensive treatments are found in the works of amongst others Cox (1990) and Lijphart
(1994), while Myerson (1999) and (2004) offers surveys. More recently, Bandyopadhyay and
Oak (2008) study how diverse coalitions in a parliamentary democracy may emerge as a result of
changes in the importance of rents relative to ideology as well as seat shares.
9
The literature has studied two procedures by which a political party is selected to try and
form a coalition government. First, selection is based on the share of parliamentary seats, that is,
first the party with the highest number of parliamentary seats, then the one with the second
highest and so on, see Austen-Smith and Banks (1988). Second, selection is probabilistic with the
probability of being called to form a government being higher the larger the number of
parliamentary seats occupied, see Baron and Ferejohn (1988) and Baron and Diermeier (2001).
Using data from 11 parliamentary democracies applying PR rules Diermeier and Merlo (2004)
find stronger statistical support for the former, but they also find that a combination of these two
bargaining procedures explains the data even better.
10
sharing leads to more moderate policies than arrangements that allow a single party to
exercise power, and that such policies reflect closer the preferences of the median voter
(see for example McDonald et al. 2004; Budge and McDonald, 2006). However, when
voters take into account that under power-sharing arrangements parties can only partly
influence government policy, they and the parties they support will adopt more extreme
positions in order to shift policy towards their preferences. It follows that power-sharing
under proportional representation may change the incentives of parties and voters, as it
creates new opportunities to challenge the existing dominant parties and even replace
them.
2.4
An example: Power-sharing in Northern Ireland
By way of illustration of consociation and power-sharing, I briefly describe the Northern
Ireland power-sharing institutions established by the Peace Agreement, also known as the
“Good Friday Agreement”, of 10 April 1998 aiming to end 30 years of “low intensity
civil war” between Unionist-Protestants and Nationalist-Catholics. Amongst other
institutions, the Agreement established the ‘New Northern Ireland Assembly’, the
members of which are elected under the Single Transferable Vote system. The Assembly
has full legislative and executive authority for the following matters: The office of the
first minister and deputy first minister, who must stand for election jointly, and have
cross-community support by the parallel consent formula, (that is, a majority of
Assembly Members who have designated themselves as Nationalists and a majority of
those who have designated themselves as Unionists, as well as a majority of the whole
Assembly); agriculture; culture; education; employment; enterprise; environment;
finance; health; and regional and social development. It excludes matters that remain the
responsibility of the Westminster Parliament. Parties with links to paramilitary
organisations were allowed a place on the executive only after they decommissioned their
weapons. The parties elected to the Assembly choose ministerial portfolios in proportion
to their party strength using the d’Hondte procedure. In addition, the agreement set up
two external institutions, a North–South Ministerial Council and a British–Irish Council.
Jennings (2007) argues that they have primarily symbolic value, the former for the
nationalist community and the latter for the unionist. He concludes that the Agreement set
11
up institutions that provide a focus for expressive choice that is more likely to achieve
peace.
Looking at the circumstances conducive to power-sharing, Evans and O’Leary (2000, p.
82) wrote: “Consociation ... works best where communities wish to maintain their
differences without having strong integrationist or assimilationist ambitions towards the
respective others; where there is an existing (or emerging) balance of power between
communities; where no community can successfully control or conquer the others
through war; and where external parties to the region promote accommodation rather than
antagonism. Arguably these conditions are emerging in Northern Ireland.” Coakley
(2008) charts the competition between two ethnically based dominant parties from the
1880s to the 1970s under a plurality electoral system, and since then the intra-communal
fragmentation of this system following the introduction of major institutional reforms,
including proportional representation. The latter allowed successful “ethnic outbidding”
from inside the ethnic base of each party and worked against parties that sought to
mobilise the uncommitted centre as well as against the parties that sought to redefine
political competition in terms of non-ethnic issues. Tilley et al. (2008) document how the
emergence of a consociational form of government has changed party competition and
resulted in the more extreme parties on both sides of the division, the Democratic
Unionist Party and the Sinn Fein, claiming the largest electorate support after both the
2003 and 2007 elections, a polarising trend in the post-agreement environment.10
Jennings (2010) examines how these trends can be explained by different game-theoretic
approaches to the selection of leaders in groups whose members have different
preferences and where different groups compete for office, and whether this move
towards the extremes has adverse welfare consequences.
3.
Equilibrium outcomes under conflict and power-sharing
10
Extended analysis of the nature of the 1998 Peace Agreement can be found in among
others McGarry and O’Leary (2006a and 2006b), who are critical supporters of the consociation
view, Horowitz (2001) and (2002) and Tilley et al. (2008) and the literature cited therein.
12
3.1
Preliminaries: Modelling power-sharing and proportional representation under
risk neutrality and risk aversion
The focus of this study is on the circumstances under which two opposing political
groups choose to end violence and share power according to the outcome of elections. In
discussing the benefits of peace, the economics of conflict literature models war as a
costly lottery and peaceful settlement as a division of a disputed asset that makes one
combatant ex ante better off compared to the probabilistic outcome of the war, and the
other at least ex ante indifferent. In this setting the division equilibrium is a deterministic
outcome in which each side receives a share of the disputed asset. It may be an
appropriate modelling framework in conflicts over a resource. However, it does not
capture the essence of the resolution of a civil war by power-sharing. Under the latter, the
combatants agree to disarm, hold elections and set up political arrangements to share
power in the post election government, so that the election loser is assured of receiving a
number of seats in the cabinet, budgetary resources, and various guarantees that rights
and freedoms will be respected. It is this kind of arrangement that I investigate. Like the
war outcome, the election outcome is probabilistic, but depends on factors that differ
from those required to win a war while it avoids its destructive effect.
I consider a setting with two rival players, A and B, based on two rival groups of a
divided population that compete for office and for the rents that are gained from holding
power. I abstract from intra-group collective choice issues and each player is treated as a
unitary actor, so that A and B can be thought as the leaders of two rival groups. The
winner of the contest for office receives a rent R that is assumed to be exogenous.
Following civil war modelling, I confine attention to economic rents only and leave other
objectives for future study.11 Office rents can be gained either by winning a violent
conflict like a civil war, or by winning an election contest.
11
Since R represents a monetary value it is also reasonable to assume that both A and B
value it equally. Further, the assumption of exogenous rent implies that the rent from office is
independent of the economic output as per standard practice in the literature.
13
However, war is ex post inefficient. A violent conflict results in severe destruction that is
modelled as reducing the rent available by a proportion 1<12, so that the victor’s gain
from war is (1–)R, while the defeated has nothing. Let Q be the probability that A
defeats B in a civil war; the probability then that B defeats A is 1–Q. If as in the standard
treatment of the economics of conflict the two players are assumed to be risk neutral, then
A’s and B’s expected benefits from winning the war are respectively Q(1–)R and (1–
Q)(1–)R. On the other hand, if the two players are risk averse, as for example when the
utility with respect to rents is logarithmic Ui=lnR, i=A,B, the expected benefits are
UA=Qln[(1–)R] and UB=(1–Q)ln[(1–)R].13
No rent destruction occurs when office is contested in an election, that is,  =0. Let P and
(1–P) denote the probabilities that A and B respectively win the election, which are
typically taken to be equal to their expected vote shares. Under a majoritarian electoral
rule, the winner takes all the rent with a probability equal to the probability of winning
the election. Under a proportional representation rule, each party takes a share of the rent
equal to its probability of winning the election. If the sides are risk neutral, the expected
benefits of A and B from the election are respectively PR and (1–P)R irrespective of
whether the electoral rule is majoritarian or proportional representation (assuming that
the shares of the votes are the same under the two rules). The equality of the expected
benefits from the majoritarian and proportional representation rule under risk neutrality
creates a serious analytical problem: It does not allow for differentiation between the
different voting rules. Yet, proportional representation is an integral part of powersharing agreements. I overcome this problem by modelling a power-sharing arrangement
as a post-election settlement in which the election winner is rewarded with a fraction of
office rents (1–k), and the loser is given the remaining fraction k. Typically, as the
election winner occupies the top office of president, or prime minister, and is allocated
12
A similar form of losses from conflict has been employed for example by Grossman
and Kim (1995) in studying offensive and defensive expenditures and by Hausken (2004) in a
model of choice between exchange and raiding.
13
Note that the logarithmic utility function effectively implies that the defeated party
whose payoff is zero still gets a rent of 1 unit, since ln(1)=0. In the analysis which follows the
logarithmic specification is used because of its ability to yield closed form solutions for the
expected payoffs from civil war and power-sharing.
14
the largest share of cabinet posts and budgetary sums, it is assumed that 0  k < ½. The
expected benefits of A and B therefore are respectively UA=P(1–k)R+(1–P)kR and
UB=(1–P)(1–k)R+PkR. Subsection 3.2 studies power-sharing under risk neutrality by
employing the latter formulation. However, when the two sides are risk averse, the two
electoral rules produce different expected benefits.14 Using the logarithmic utility
function, under proportional representation the expected benefits are UA=ln[PR] and
UB=ln[(1–P)R]. The implications of the latter are investigated in sub-section 3.3.
Adopting Fearon’s (1995) template, both specifications show that power-sharing
transforms the indivisible variable over which inefficient fighting takes place into a
divisible variable over which compromise is possible.
3.2
Conflict and power-sharing under risk neutrality
Let the expenditures to finance the effort, weapons and other activities associated with
fighting a civil war by the two factions be ZA and ZB respectively. Following standard
practice, the probability Q of civil war victory is modelled as depending positively on A’s
expenditure on war effort and negatively on that of B according to the contest success
function (see Tullock, 1980; Hirshleifer, 1989; and Garfinkel and Skaperdas, 2007)
𝑄 = 𝛾𝑍
𝛾𝑍𝐴
𝐴 +(1−𝛾)𝑍𝐵
.
(1)
Parameters 0  and 0  1– measure the effectiveness of A and B respectively in
fighting the civil war. This formulation captures the possibility that the two sides may
differ in their fighting ability, with one having access to better hardware, technology and
organization (the government), while the other relying on its knowledge of terrain and
commitment of its members (the anti-government rebels).15 In the case where A is a more
effective fighter than B, ½ 1–. When the two sides are equally effective fighters,
=1–=½; if in addition they spend equal sums of resources to fight the civil war,
14
Skaperdas (1991) also examines the effects of risk attitude. He assumes that the two
participants have different attitudes towards risk, while the present inquiry assumes that both
participants have identical risk attitudes, either neutrality or aversion.
15
For a similar formulation of the contest success function see Chang et al. (2007).
15
ZA=ZB, they stand an equal probability of success, Q=1–Q=½. Under risk neutrality the
expected net payoffs of the two rival factions from fighting civil war are16
UAW
=
Q(1–)R–ZA
UBW
=
(1–Q)(1–)R–ZB
(2.A)
.
(2.B)
Let XA and XB be the election campaign expenditures of the two groups. In common with
Q, the probability P that A wins the election is modelled as increasing in the resources
spent by A campaigning and decreasing in those of B, as described by the equation
𝑃 = 𝜀𝑋
𝜀𝑋𝐴
𝐴 +(1−𝜀)𝑋𝐵
.
(3)
Parameters   and 0  1– 1 measure the effectiveness of A and B respectively,
in their election campaigns; may depend on how good campaigner A is in attracting
votes, how well he can translate financial resources to voter support and the like.17 It
bears noting that neither nor P are equal to the number of people who broadly identify
with A, although the latter may affect them. Winning the election depends on the number
of those who actually vote for A. The difference between those who may be counted as
members of A and those who vote for A is explained by franchise restrictions, voter
apathy or alienation, distribution of voters across constituencies, campaign issues and
personal appeal of the leader. Similarly, one may presume that and are positively
correlated, if for example they depend on the relative size of group A, but as explained
above it does not have to be the case. Unlike the usual assumption of spatial decision
models where electoral competition depends on the policy positions of the competing
parties, in the present model the probability of electoral victory depends only on
campaign expenditure. This treatment is justified not because policy positions are not
important, but because, in the present setting, parties are only interested in rents from
office.18
16
Throughout the analysis it is assumed that both A and B have enough resources to
finance the required sums for fighting the conflict.
17
In Tridimas (2007) I apply a similar formula in analysing electoral campaigns.
18
For a more general treatment see Baron (1994), who explores a model of electoral
contest where the voting outcome depends on both campaign expenditures (financed by policyoriented interest groups) and policy positions. In his framework, informed voters vote on the basis
of proposed policies, while uninformed voters are influenced by campaign expenditures.
Competing parties face a fundamental trade off: Pursuing the policies preferred by interest groups
increases the financial contributions received from them and hence the ability to influence
16
Using the formula by which the loser of the election is guaranteed a k percentage of rents,
and the winner receives (1–k), the expected net payoffs of the two adversaries from
contesting the election are
UAG
=
P(1–k)R + (1–P)kR – XA
(4.A)
UBG
=
(1–P)(1–k)R + PkR – XB
(4.B)
The case of majoritarian politics, where the winner takes all the rents from office, can be
derived as a special case of the above by setting k =0.
In the Nash-equilibrium solutions of the civil war and election-power-sharing games,
each faction chooses the form of contest that brings the highest expected payoff.19 The
Nash equilibrium of the civil war game is obtained when A maximizes (2.A) with respect
to ZA subject to (1) treating ZB as given and B maximizes (2.B) with respect to ZB subject
to (1) treating ZA as given. Solving we obtain the following equilibrium values of
expenditures for fighting and probability that A wins the civil war (it can easily be
checked that the second order conditions for maximization are satisfied)
ZA* = ZB* = (1–)(1–)R;
Q* = 




That is, both factions choose to spend identical sums on the effort to fight the war, and
this sum rises with the size of office rents. On the other hand, the probabilities of victory
of A and B differ and are simply equal to their respective fighting effectiveness.
Substituting the above expressions into (2.A) and (2.B) we obtain the corresponding
equilibrium net expected payoffs as
VAW
=
(1–)R
(5.A)
VBW
=
(1–(1–)R
(5.B)
In a similar manner for the election contest, we find
XA* = XB* = (1–)(1–2k)R;
P* = 




uninformed voters, but may reduce the proportion of votes from uncommitted informed voters. In
the present setting, where only rents matter, the policy positions of the competing parties do not
affect the electoral outcome.
19
A Nash equilibrium of the civil war sub-game (ZA*, ZB*) requires that for all ZA,
UA(ZA*,ZB*)  UA(ZA, ZB*) and for all ZB, UB(ZA*, ZB*)  UB(ZA*, ZB), and analogously for the
election game. Given the assumptions of the model a unique Nash equilibrium of the civil war
(and election) games always exist.
17
As before, the two groups incur equal levels of campaign expenses but are characterised
by different probabilities of success equal to their respective election campaign
effectiveness. Comparison of (5) and (6) shows that we cannot say a priori whether
fighting a violent conflict is more expensive than fighting an election, for this depends on
the relative effectiveness parameters  and  and the destructive effect of the conflict ,
which tends to decrease the size of resources committed to winning the conflict.
Substituting into (4.A) and (4.B), we obtain corresponding equilibrium net expected
payoffs as
VAG
=
[+k(1–2)]R
(6.A)
VBG
=
{(1–+k[2(2–)–1]}R
(6.B)
A peaceful political arrangement will prevail if both rivals are better off under that
arrangement, that is, when AGW  VAG–VAW >0 and simultaneously BGW  VBG–VBW >0.
Conflict arises if at least one of the two adversaries expects a higher payoff by engaging
in a violent fight, that is, if (AGW<0, BGW>0), or (AGW>0, BGW<0), or (AGW<0,
BGW<0). Upon substitution, we find
AGW = [+k(1–2) – (1–)]R
(7.A)
BGW = {(1–) + k[2(2–)–1] – (1–)(1–)}R
(7.B)
With the coefficients ,  and  exogenously given, the size of the power-sharing
parameter k emerges as a crucial variable in the decision to accept a peace settlement.
Following Garfinkel and Skaperdas (2007), it is assumed that the rival groups agree to
divide the gains that are realised when a settlement is agreed according to the “split-thesurplus” formula, which postulates that each side obtains the same gain by avoiding war.
Formally, this division rule implies that AGW= BGW.20
Substituting from the sets of equations (7), and solving with respect to k, we obtain the
equilibrium size of k
𝑘∗=
1
2
2𝛾−1
[1 − (1 − 𝜃) 2𝜀−1] .
(8)
“Under risk neutrality, this rule coincides with the prescription of any symmetric
bargaining solution, including the Nash bargaining solution, and is implementable noncooperatively by a number of alternating-offers games...” Garfinkel and Skaperdas (2007), p.24.
20
18
The latter is defined for values such that  ½. Equation (8) shows that the powersharing parameter depends on the fighting and electoral campaigning effectiveness of the
rival groups and the destructive effect of war. More specifically, two components are
identified: (1) The quantity ½, which may be called the “equality component”, that is,
other things being equal the two sides split the rents equally; and (2) the expression ½(1–
)(2–1)/(2–1). The quantity (1–) indicates the marginal income surviving the civil
war. Noting first that 2–1 = –(1–) is the difference in the war fighting effectiveness of
A and B, and similarly, 2–1 = –(1–) is the difference in the election campaign
effectiveness of A and B, the ratio of the two differences (2–1)/(2–1) is the relative
effectiveness of A fighting a civil war rather than an election to win office. Obviously,
this ratio can be greater, equal or smaller than zero. Thence, the expression ½(1–)(2–
1)/(2–1) can be thought of as half the value of income that survives the civil war
weighted by A’s war-election relative effectiveness. It reflects how the destructive effect
of war, in conjunction with the balance of war and electoral victory, may affect power
sharing.
Regarding the equilibrium size of k*, after the relevant manipulations, we find that for 0
< k*<½ it must be either >½ and >½, or ½ and½.21 That is, awarding the
election winner a larger share of power than the election loser requires that one of the two
opponents is more effective in both fighting the war and campaigning in elections.
Intuitively, power-sharing of the type outlined is possible in a situation where one of the
two groups is more likely to prevail in both the civil and the election contest. Using the
above, we find that when >½ and >½, it will be k* > 0 if <2()/(21), while
when <½ and <½, it will be k* > 0 if >2()/(2). When =½ the two sides are
equally matched in an election contest, so the side that is more likely to win the war will
not settle for peace. With =½, we have from (7.A) and (7.B) that AGW=[¼+(k/2)–(1–
)]R and BGW=[¼+(k/2)–(1–)(1–)]R. The equation AGW=BGW is now independent
of the value of k and can only be satisfied if =½=, that is, the two adversaries are
These follow from (8) upon observing that for 0 < k*, it must be either 2–1> 0 and
2–1>0, or 2–1< 0 and 2–1<0.
21
19
equally matched in both the war and the election front. If this is the case, we make the
presumption that the peace settlement is preferred and k can take any value 0 ≤ k ≤ ½.
Table 1: Comparative static properties of k*
k* = power awarded to the election loser
Sign when
½ & ½
½ & ½
Derivative
(A=likelier winner of election & war)
𝑑𝑘∗
𝑑𝛾
𝑑𝑘∗
𝑑𝜀
𝑑𝑘∗
𝑑𝜃
1−𝜃
= − 2𝜀−1
=
(1−𝜃)(2𝛾−1)
(2𝜀−1)2
1 2𝛾−1
= 2 2𝜀−1
(B= likelier winner of election & war)
–
+
+
–
+
+
Table 1 reports the comparative static properties of k. The first row shows that, when A
is more likely to win the election and the war as his fighting effectiveness rises, more
power is allocated to the election winner (that is, A). On the other hand, if A is less likely
to win the election but his fighting effectiveness rises, less power is allocated to the
election winner (likely to be B) in order to give A the incentive to participate in the
power-sharing arrangement, a result that accords well with intuition. The signs of the
derivative in the second row indicate when A is the likely election winner, an increase in
his electoral effectiveness, which reduces the probability that B may win the election
even further, is followed by an increase in the rents given to the election loser, to co-opt
B to the power sharing arrangement. On the other hand, if B is the likely election winner,
an increase in the electoral effectiveness of A is accompanied by more powers for the
election winner, as both groups now see the election offering them a way to gain the rents
of office. The third row presents the effect of an increase in the destructive effect of war
and shows that, irrespective of whoever is more likely to win the civil war and the
election, an increase in the destructiveness of war induces both parties to award more
office rents to the election loser to avoid war.
Substituting k* from (8) into (7.A) we find the corresponding value of  as
∆=
𝑅
[1 − (1 − 𝜃)
2
(1−2𝜀 2 )(2𝛾−1)+2𝛾2 (2𝜀−1)
(2𝜀−1)
]
(9)
20
Power-sharing is established for  > 0. However, the sign of the quadratic expression
cannot be determined unambiguously at this level of generality, a feature that also implies
that an increase in the size of rents has an ambiguous effect on the division of such rents
between the two contestants. After manipulating we have
Sign  = Sign (2–1)[–2(2 –1)(1)2 –2(1–2 2)(1–)+2–1+(1)(1–2 2)].
Denoting the roots of the quadratic expression above by  and , with  < , we obtain
for
< ½, > 0 when 0 ≤  <  < ≤ ½
for
> ½, > 0 when ½ ≤  <≤ 1
or
(9.1)
½ ≤  <  ≤ 1
(9.2)
In order to gain a better understanding of what is involved, figure 1 shows the range of
values of  (upper and lower limit) that yield  > 0 for parameter values of = 0.1, 02,
0.3, 0.4, 0.6, 0.7, 0.8 and 0.9, and = 0.1, 0.3, 0.5 and 0.9. The pattern that emerges is
widely diverse. For = 0.1 the interval of values of  (= war effectiveness of A) that lead
to power-sharing shrinks as  (= election effectiveness of A) rises for values of <½, but
it increases as >½, while the opposite is true for =0.3 and =0.5; it is nevertheless
widest (0, ½) as the destructive effect of war increases, =0.9, and <½.
Finally, equation (8) can also be used to identify when the two rivals will agree to lay
down their weapons and adopt majoritarian politics. Setting k* = 0 and solving we obtain
1– = (2–1)/(2–1)
.
(9.3)
That is, the two rivals will choose to establish a majoritarian democracy in the case where
A’s election-war relative effectiveness equals the marginal income surviving the war.
Since it is only by chance that this special condition is satisfied in practice, adoption of
majoritarian democracy by the mutual agreement is unlikely.
21
Figure 1: Values of over which A and B choose power-sharing given ,  and R
(a)  = 0.1
0.424
=0.9
0.338
0.420
=0.8
0.287
0.895
•
½
0.304
0.721
0.813
0.783
0.263
0.737
=0.5
0.187
0.842
0.810
0.692
=0.6
0.217
0.912
0.941
0.848 0.873
0.827
•
½
0.353
=0.7
0.249
0.542
•
½
0.226
0.751
0.696
=0.4
0.158
0.190
0.127
=0.2
=0.1
0.059
0.647
0.308
=0.3
•
½
0.152
0.173
0.713
0.662
0.58
0.88
0.105
0.458
•
½
0.576

•
½
0
1
(b)  = 0.3
0.526
0.407
0.927
0.938
=0.9
0.319
0.879 0.899
0.400
=0.8
0.266
0.867
0.331
=0.7
0.227
0.835
0.280
0.194
0.163
0.199
=0.2
=0.1
0.721
0.320
0.133
0.162 0.165
=0.3
0.670
0
1
0.773
0.734
0.681
0.101
0.035 0.122
0.062
0.074
1
0.806
0.763
0.199
=0.4
0.839
0.837
0.802
0.680
=0.6
=0.5
0.965 1
0.600
0.474
0.593

1
22
Figure 1 – continued
(c)  = 0.5
0.502
0.382
0.973
0.978
=0.9
0.290
0.428
0.837
0.937
=0.8
0.236
0.903
0.881
0.296
=0.7
0.195
0.243
0.78
=0.6
0.160
0.199
=0.5
0.128
0.158
=0.4
0.012
=0.3
0.842
1
0.840
0.801
0.805
0.757
0.22
0.097
0.119
0.764
0.704
0.710
0.063
0.078
0.63
0
=0.2
=0.1
0.988 1
0.872
0.022
0.027
0.498
0.618

0
1
(d)  = 0.9
0.195
1
0.296
1
=0.9
0.075
0.109
1
0.837
=0.8
1
1
0.004
0.005
=0.7
1
1
=0.6
1
1
=0.5
=0.4
•
½
=0.3
•
½
=0.2
•
½
=0.1
•
½
0.966
0.996
0.995
0.891
0
1
0.704
0.925
0.805

1
Notes on Figure 1:
Intervals (•,•) show the range of values of  which lead to power-sharing under risk neutrality, see
(9),  >0
Intervals (|, |) show the range of values of  which lead to power-sharing under risk aversion, see
(15.A) & (15.B), with R=100
Intervals ( , ) show the range of values of  which lead to power-sharing under risk aversion, see
(15.A) & (15.B), with R= 50
23
3.3
Conflict and power-sharing under risk aversion
As already shown, under risk aversion the expected benefits from a majoritarian and a
proportional representation rule differ. I proceed to analyse power-sharing without
employing the formula for division of rents used in the previous sub-section. When A and
B seek office by fighting a civil war, the expected net payoffs of the two rival factions are
expressed as (where by assumption ln[(1–)R]>0)
UAC
=
Qln[(1–)R]–ZA
(10.A)
UBC
=
(1–Q)ln[(1–)R]–ZB .
(10.B)
Proceeding as before, that is, A maximizes (10.A) subject to (1) treating ZB as given and
B maximizes (10.B) subject to (1) treating ZA as given and solving, we obtain the
following equilibrium values of expenditures for fighting, probability that A wins, and
corresponding net expected payoffs
ZA* = ZB* = (1–)ln[(1–)R];
Q* = 



VAC
=
ln[(1–)R]
(11.A)
VBC
=
(1–ln[(1–)R].
(11.B)
Clearly, the properties of the equilibrium mirror those found above – see the sets of
equations (5) and so on.
Under power-sharing where elections take place using a proportional representation rule
and rents are allocated according to the share of votes polled by each party, the expected
net payoffs are
UAS
=
ln[PR]–XA
(12.A)
UBS
=
ln[(1–P)R]–XB
(12.B)
The expected utility from power-sharing is the benefit from a proportion of the rents from
office, where the proportion equals the vote share. At the Nash equilibrium
𝑋𝐴 ∗ =
√1−𝜀
√𝜀+√1−𝜀
𝑋𝐵 ∗ =
√𝜀
√𝜀+√1−𝜀
√𝜀
)
𝜀+√1−𝜀
√
𝑉𝐴 𝑆 = 𝑙𝑛𝑅 + 𝑙𝑛 (
𝑉𝐵 𝑆 = 𝑙𝑛𝑅 + 𝑙𝑛 (
√1−𝜀
√𝜀+√1−𝜀
−
)−
𝑃∗=
√𝜀
√𝜀+√1−𝜀
√1−𝜀
𝜀+√1−𝜀
√
√𝜀
√𝜀+√1−𝜀
(13)
(13.A)
.
(13.B)
24
In contrast to the previous case, the equilibrium levels of expenditure for fighting the
election differ between the two parties and, in addition, they only depend on the
campaign effectiveness of A and B (that is, they are independent of the size of rent from
office). Both VAS and VBS are assumed to be positive.
Comparing power-sharing to violent conflict we have
√𝜀
ASC  VAS – VAC = (1 − 2 )𝑙𝑛𝑅 + 𝑙𝑛 (
√𝜀+√1−𝜀
BSC VBS
–
)−
= (2 − )𝑙𝑛𝑅 + 𝑙𝑛 (
VBC
√1−𝜀
√𝜀+√1−𝜀
√1−𝜀
√𝜀+√1−𝜀
)−
− 2 ln(1 − )
√𝜀
√𝜀+√1−𝜀
(14.A)
− (1 − )2 ln(1 − ).
(14.B)
For parameter values such that both ASC and BSC are positive simultaneously, both A
and B choose a peaceful settlement. After the relevant manipulations and denoting
√𝜀
)
√𝜀+√1−𝜀
−𝐸  𝑙𝑛 (
−
√1−𝜀
√𝜀+√1−𝜀
√1−𝜀
)
√𝜀+√1−𝜀
̂ 𝑙𝑛 (
< 0 and −𝐸
−
√𝜀
√𝜀+√1−𝜀
< 0, we derive the
following critical values
𝑙𝑛𝑅−𝐸
ASC > 0 when  < A  √𝑙𝑛𝑅(1−𝜃) > 0
(15.A)
𝑙𝑛𝑅−𝐸̂
BSC > 0 when  > B  1 − 𝛾̂, where 𝛾̂ ≡ √𝑙𝑛𝑅(1−𝜃) >0
.
(15.B)
The positive signs of A and 𝛾̂ follow from the positive signs of (13.A) and (13.B); I also
assume that A<1and B>0. Thus, power-sharing is adopted for values of  that satisfy
(15.A) and (15.B) simultaneously. This requires that B < A, which in turn requires that
the following inequality is satisfied: 3(lnR)2–2[E+𝐸̂ –ln(1–)]lnR–[E+𝐸̂ +ln(1–)] 2+4E𝐸̂
> 0, which depends on the parameter values and cannot be solved analytically at this
level of generality. Contrary to risk neutrality, in the present setting there is no powersharing variable to solve for; we can only find the range of values B <  < A over which
a power-sharing settlement may be adopted. A is the upper limit of A’s war effectiveness
at which A compromises and shares power; analogously, B is the lower limit of A’s war
effectiveness at which B settles for power-sharing – see figure 2. To put it another way, if
 exceeds A, A expects a higher payoff from not compromising and pursuing the rewards
of office through fighting, while, if  is below B, B’s fighting effectiveness is so high that
25
he expects a higher payoff from fighting. If for some reason A rises or B falls, powersharing becomes more likely.
Figure 2: Power-sharing settlement under proportional representation
B
0
|
A
1
|
Power-Sharing
For B <  B chooses power-sharing
For  < A A chooses power-sharing
Power-Sharing arrangements are established for B < < A
Table 2: Comparative static properties of the boundaries of power-sharing, A and B
𝑑𝛾𝐴
𝑑𝑅
𝐸+ln(1−𝜃)
2
𝐴 𝑅 [𝑙𝑛𝑅(1−𝜃)]
1
= 2𝛾
as
𝑑𝛾𝐴
𝑑𝜃
𝑑𝛾𝐴
𝑑𝜀
√1−𝜀
√𝜀+√1−𝜀
− 𝑙𝑛
𝑑𝛾𝐵
> (<) 0
√𝜀
√𝜀+√1−𝜀
𝑑𝑅
+ 𝑙 𝑛(1 − 𝜃) > (<) 0
𝛾
= 4𝛾
1
2√𝜀+√1−𝜀
𝐴 𝑙𝑛𝑅(1−𝜃) (√𝜀+√1−𝜀)
as
𝑑𝛾𝐵
𝑑𝜃
𝐴
= 2(1−𝜃)𝑙𝑛𝑅(1−𝜃)
>0
2
𝜀√1−𝜀
>0
−1 𝐸̂ +𝑙𝑛(1−𝜃)
= 2𝛾̂𝑅 [𝑙𝑛𝑅(1−𝜃)]2 > (<) 0
𝑑𝛾𝐵
𝑑𝜀
√𝜀
√𝜀+√1−𝜀
− 𝑙𝑛
√1−𝜀
√𝜀+√1−𝜀
+ 𝑙 𝑛(1 − 𝜃) < (>) 0
−𝛾̂
= 2(1−𝜃)𝑙𝑛𝑅(1−𝜃) < 0
−1
= 4𝛾̂𝑙𝑛𝑅(1−𝜃)
2√1−𝜀+√𝜀
2
(√𝜀+√1−𝜀) (1−𝜀)√𝜀
>0
Table 2 reports the comparative static properties of A and B. The first row shows that the
effect of an increase in the rewards from office on A (the critical value of A’s fighting
effectiveness below which A chooses the power-sharing settlement) is ambiguous, as it
depends on the balance of the electoral effectiveness of A and the destructive effect of
war, and similarly for B. An increase in the destructive effect of war – see the second
row entries – increases A, since it increases the expected loss from civil war and
analogously it decreases B; it then makes a peaceful settlement more likely. Finally, an
26
increase in A’s electoral effectiveness increases A because it increases A’s expected
benefit from the electoral campaign; it also increases B since it reduces the chances that
B wins office rents through elections, so that its overall impact on a peaceful settlement is
ambiguous.
Similarly to the case of risk neutrality, the panels of figure 1 show the B <  < A
intervals that lead to power-sharing for values of 0.1, 0.5,…, 0.9 and  0.1, 0.3, 05
and 0.9, when R takes the values 50 and 100. In accordance with intuition, the size of the
(B, A) interval is larger for the larger value of the rent, R, and its size expands as 
becomes greater. In addition, the (B, A) interval expands as  rises from 0.1 to 0.5,
implying that power-sharing becomes more likely as the two rivals are more evenly
balanced when fighting an election, but it shrinks (symmetrically for the permitted
values) as  keeps on rising from 0.5 to 0.9, implying that power-sharing becomes less
likely. Finally, in comparison to risk neutrality, we observe that the interval of values of 
over which power-sharing is agreed is wider for risk aversion than for risk neutrality,
which implies that power-sharing is more likely under the former.
For reasons of completeness, the equilibrium payoffs under a majoritarian election rule
were also derived, that is, when A and B maximize PlnR and (1–P)lnR respectively. Two
more comparisons are then carried out, namely, between power-sharing under
proportional representation and the majoritarian electoral rule; and second, between
fighting a civil war and the majoritarian electoral rule. These are reported in the
Appendix. A similar pattern of results to the one discussed above emerges. That is, in
both cases, it is possible to identify a set of minimum and maximum values for the
relevant effectiveness parameters that define a range over which both rivals choose
power-sharing to a majoritarian system and also majoritarian elections to civil war.
4.
Conclusions
My purpose has been to analyse when two office-motivated political rivals agree to give
up violent conflict and share power on the basis of their electoral support. In studying the
benefits of peace, the existing literature has compared the uncertain outcome of conflict
27
over a resource to the deterministic outcome of sharing the resource according to a
division formula. I have extended this framework by comparing the uncertain outcome of
conflict to the uncertain outcome of an election that determines how the resource is
shared. For each rational political player, the choice between winning office by bullets or
the ballot box depends on which setting secures the highest expected net payoff.
A model of conflict was analysed using conventional optimization tools and game theory
concepts in which the probability of winning the fight is endogenous and depends on the
resources expended to fight and the fighting effectiveness of each adversary, and conflict
destroys part of the benefits from office. Similarly, when the rivals compete for office
through elections, the probability of winning the electoral contest depends on the
expenditure spent in the election campaign and the campaign effectiveness of each
adversary, but contrary to war the rent from office stays intact. Two formulations of
power-sharing were explored. In the first, the adversaries were assumed to be risk neutral
and power-sharing was modelled as dividing the benefits of office by granting a share of
benefits to the election loser. The share was determined from a division specifying that
after the election each side obtained the same gain by avoiding war. It then identified the
determinants of the power-sharing variable that would yield higher ex ante payoffs to
both the winner and the loser of the elections than fighting. A most interesting result here
was that power-sharing that awards the election winner a larger share of power than the
election loser is a workable arrangement when either of the two rivals is more effective in
both fighting the war and campaigning in elections. Otherwise, one of the rivals expects
to be better off by winning the civil war.
In the second formulation, the two sides were assumed to be risk averse and when powersharing was agreed they shared the benefits of office according to their vote shares.
Again this allowed identification of the circumstances where both sides choose powersharing to conflict. It was shown that power-sharing based on vote shares can offer the
likely winner of the civil war a higher benefit than military victory and, thus, it can be
chosen voluntarily. In addition, the numerical examples suggested that power-sharing is
more likely under risk aversion than risk neutrality.
28
My analysis is informative and can be extended in several important directions. In the
first instance, one may relax the implicit assumption that the two sides can always raise
enough funds to pay for their war and election efforts, and explore the constraints on the
availability of funds. For example, suppose that either or both combatants are unable to
cover their war expenditure but rely on foreign support. In this case, accepting or
rejecting power-sharing would depend on exogenous financial factors. A second
extension is to inquire into the issue of enforceability of peace agreements; that is once
the democratic arrangements are chosen, how are either of the groups prevented from
unilaterally arming and appropriating all the rents for themselves? An obvious answer is
the presence of a “higher” authority international or otherwise, which polices the
agreement. In its absence, peace will have to rely on voluntary, self-enforcing, credible
disarmament mechanisms. Related to this is the setting of Garfinkel and Skaperdas
(2007) and Skaperdas (2008), who introduce a dynamic framework where fighting today
permanently eliminates the rival and saves on expenditure for future armaments, while
elections have to be fought every period. Accounting for the discounted rewards may
change the incentive to compromise and share power. Thirdly, in accordance to the
comparative electoral systems literature, and contrary to standard modelling of conflicts,
the utility function of each player may be expanded to include policy objectives in
addition to the office rent motive. A fourth complication is to introduce intra-group
divisions. That is, although it is perfectly sensible to think of two opposing ethnic
communities going to war, when peaceful politics prevail, each group may be divided on
other non-ethnic issues implying that its members may vote for parties led by politicians
others than those leading the war effort, and given proportional representation all those
parties are represented in parliament. Yet another extension is to model rents as
endogenous to the decision of the office-holder and consider possible differences in the
tax and expenditure policies pursued by politicians who win office by the force of arms
or by elections.
29
Appendix
The appendix complements the analysis of Section 3.3 by summarising the conditions
under which the warring parties will choose power-sharing instead of majoritarian
elections and majoritarian elections instead of civil war under risk aversion. Table A1
presents the equilibrium solutions of the conflict, majoritarian elections and proportional
representation games, while Table A2 reports the conditions for choosing the different
arrangements.
Expected
Utility
Probability
that A wins
Table A1: Equilibrium solutions under risk aversion
Conflict – Civil War
Majoritarian
Power-Sharing
Elections
under PR
UAE = PlnR–YA
UAS = lnPR–XA
UAC = Qln(1–)R–ZA
E
UB = (1–P)lnR–YB
UBS = ln(1–P)R–XB
UBC = (1–Q)ln(1–)R–ZB
𝜀𝑋𝐴
𝛾𝑍𝐴
𝜀𝑋𝐴
𝑃 = 𝜀𝑋 +(1−𝜀)𝑋
𝑄=
𝑃=
𝐴
𝐵
𝛾𝑍𝐴 + (1 − 𝛾)𝑍𝐵
𝜀𝑋𝐴 + (1 − 𝜀)𝑋𝐵

Equilibrium
Probability
Q* = 
P* = 
Equilibrium
Expenditure
ZA* = (1–)ln(1–)R
XA* =(1–)lnR
Equilibrium
Expected
Payoff
VA = ln(1–)R
VBC = (1–ln(1–)R
C

E
𝑃∗=

VA = lnR
VBE = (1–lnR
𝑋𝐴 ∗ =
√𝜀
√𝜀 + √1 − 𝜀
√1 − 𝜀
√𝜀 + √1 − 𝜀
VA = lnR–E > 0
VBS = lnR−𝐸̂ > 0
S
Notes:
ln(1–)R > 0, by assumption; −𝐸  𝑙𝑛
√𝜀
√𝜀+√1−𝜀
−
√1−𝜀
√𝜀+√1−𝜀
< 0; −𝐸̂  𝑙𝑛
√1−𝜀
√𝜀+√1−𝜀
−
√𝜀
√𝜀+√1−𝜀
<0
Table A2 Choices under risk aversion
(a) A and B choose power-sharing instead of majoritarian elections when
Condition VAS >VAE & VBS>VBE

𝐸̂
𝐸
lnR > 1−𝜀2  rA >0 & lnR > 𝜀(2−𝜀)  rB > 0
Comment
For values lnR > max [rA, rB] both A and B choose power-sharing, while for
all other values of R, at least one of A and B prefers majoritarian politics and
will not consent to power-sharing
(b) A and B choose majoritarian elections instead of civil war when
Condition
VAE >VAC & VBE >VBC

𝑙𝑛𝑅
𝑙𝑛𝑅
cA 𝜀√𝑙𝑛𝑅(1−𝜃) > > 1 − (1 − 𝜀)√𝑙𝑛𝑅(1−𝜃)  cB >0
Comment
If in practice cA >  > cB is not very likely, the different groups of a divided
society will engage in conflict and reject majoritarian politics.
30
Acknowledgments: I am grateful to the editor, Arye Hillman, and three anonymous referees for
most useful comments and suggestions that helped to clarify various aspects of the paper and
improve its presentation. I also wish to thank Colin Ash and participants in the 24th Annual Irish
Economic Association Conference for stimulating discussions on an earlier version of the paper.
The usual disclaimer applies.
References
Amegashi, J.A, Kutsoati, E., 2007. (Non)intervention in intra-state conflicts. European Journal of
Political Economy 23, 754-767.
Ansik, E., Weikard, H-P., 2009. Contested water rights. European Journal of Political Economy
25, 247-260.
Austen-Smith, D., 2000. Redistributing income under proportional representation. Journal of
Political Economy 108, 1235-1269.
Austen-Smith, D., Banks, J.S., 1988. Elections, coalitions, and legislative outcomes. American
Political Science Review 82, 405– 422.
Bandyopadhyay, S., Oak, M.P., 2008. Coalition governments in a model of parliamentary
democracy. European Journal of Political Economy 24, 554-561
Baron, D. 1994. Electoral competition with informed and uninformed voters. American Political
Science Review 88, 33-47.
Baron, D.P., Ferejohn, J., 1989. Bargaining in legislatures. American Political Science Review
83, 1181– 1206.
Baron, D.P., Diermeier, D., 2001. Elections, governments and parliaments in proportional
representation systems. Quarterly Journal of Economics 111, 933-967.
Bernholz, P., 200. Supreme values as the basis for terror. European Journal of Political Economy
20, 317–333.
Bester H., Warneryd, K., 2006. Conflict and the social contract. Scandinavian Journal of
Economics 108, 231-249.
Brams, S. J., Kilgour, D.M., 2008. The instability of power-sharing. In: Braham, M., Steffen, F.
(Eds.), Power, Freedom and Voting. Springer, Berlin, pp. 227-244.
Brennan, G. Hamlin. A., 1998. Expressive voting and electoral equilibrium. Public Choice
95:149–175
Brennan, G. Hamlin. A., 1999. On political representation. British Journal of Political Science
29:109–127
Budge, I., McDonald, M., 2006. Choices parties define: Policy alternatives in representative
elections, 17 countries, 1945–98. Party Politics 12, 451–466.
Ghang, Y-M., Potter, J. Sanders, S., 2007. War and peace: Third-party intervention in conflict.
European Journal of Political Economy 23, 954-974
Coakley, J., 2008. Ethnic competition and the logic of party system transformation. European
Journal of Political Research 47, 766-793.
Collier, P., Hoeffler, A., 2007. Civil war. In: Sandler, T., Hartley, K. (Eds.), Handbook of
Defense Economics. North-Holland, New York, pp. 711-739.
Collier, P., Hoeffler, A., 2004. Greed and grievance in civil war. Oxford Economic Papers 56,
563-595.
Diermeier, D., Merlo, A., An empirical investigation of coalition bargaining procedures. Journal
of Public Economics 88, 783-797.
Doyle, M.,.Sambanis, M., 2000. International peacebuilding: A theoretical and quantitative
analysis. American Political Science Review 94, 779–801.
Evans, G., O’Leary, B., 2000. Northern Irish voters and the British-Irish agreement: Foundations
of a stable consociational settlement? Political Quarterly 71, 78-101.
Fearon, J.D., 1995. Rationalist explanations of war. International Organization 49, 379-414.
31
Garfinkel, M.R., Skaperdas, S., 2007. Economics of conflict: An overview. In: Sandler, T.,
Hartley K. (Eds.), Handbook of Defense Economics. North-Holland, New York, pp. 649-709.
Gershenson, D., Grossman, H.I., 2000. Civil conflict: ended or never ending? Journal of Conflict
Resolution 44, 808–822.
Grossman, H. I., 1991. A general equilibrium model of insurrections. American Economic
Review 81, 912-921.
Grossman, H.I., M. Kim, M., 1995. Swords or plowshares? A theory of the security of claims to
property. Journal of Political Economy 103, 1275-288.
Gurses, M., Mason, D.T., 2008. Democracy out of anarchy: The prospects for post-civil-war
democracy. Social Science Quarterly 89, 315-336.
Hartzell, A.C., M. Hoddie, M., 2003. Institutionalizing peace: Power sharing and post-civil war
conflict management. American Journal of Political Science 47, 318–32.
Hausken, K., 2004. Mutual raiding and the emergence of exchange. Economic Inquiry 42, 572586.
Hillman, A.L., 2010. Expressive behavior in economics and politics. European Journal of
Political Economy 26, 404 – 419.
Hirshleifer, J., 1989. Conflict and rent-seeking success functions: Ratio vs. difference models of
relative success, Public Choice 63,101-112.
Horowitz, D.L., 2008. Conciliatory institutions and constitutional processes in post-conflict
states. William and Mary Law Review 49, 1213-1248.
Horowitz, D. L., 2002. Explaining the Northern Ireland agreement: The sources of an unlikely
constitutional consensus. British Journal of Political Science 32, 193-220
Horowitz, D.L., 2001. The Agreement: Clear, Consociational and Risky. In: McGarry, J. (Ed),
Northern Ireland and the Divided World: Post-Agreement Northern Ireland in Comparative
Perspective. Oxford University Press, Oxford, pp. 89-108.
Horowitz, D. L., 2000. Ethnic groups in conflict. University of California Press, Berkeley and
Los Angeles.
Licklider, R., 1995. The consequences of negotiated settlements in civil wars, 1945–1993.
American Political Science Review 89, 681–90.
Jennings, C., 2007 Political leadership, conflict and the prospects for constitutional peace.
Economics of Governance 8, 83-94.
Jennings, C., 2010 Intra-group competition and inter-group conflict: An application to Northern
Ireland. Defence and Peace Economics (forthcoming).
Lijphart, A., 2004. Constitutional design for divided societies. Journal of Democracy15, 96-109.
Lijphart, A., 1999. Patterns of Democracy: Government Forms and Performance in Thirty-Six
Countries. Yale University Press, New Haven.
Lijphart, A., 1984. Democracies: Patterns of Majoritarian and Consensus Government in Twentyone countries. Yale University Press, New Haven and London.
Lizzeri, A., Persico, N., 2001. The provision of public goods under alternative electoral
incentives. American Economic Review 91, 225-239.
Martin, L.W., Stevenson, R.T., 2001. Government formation in parliamentary democracies.
American Journal of Political Science 45, 33–50.
McDonald, M., Mendes, S., Budge, I., 2004. What are elections for? Conferring the median
mandate. British Journal of Political Science 34, 1–26.
McGarry, J., O'Leary, B., 2006a. Consociational theory, Northern Ireland’s conflict, and its
agreement. Part 1: What consociationalists can learn from Northern Ireland. Government and
Opposition 41, 43-63.
McGarry, J., O'Leary, B., 2006b. Consociational theory, Northern Ireland’s conflict, and its
agreement 2: What critics of consociation can learn from Northern Ireland. Government and
Opposition 41, 249-277.
32
Merrill, S., Adams, J., 2007. The effects of alternative power-sharing arrangements: Do
“moderating” institutions moderate party strategies and government policy outputs? Public
Choice 131, 413-434.
Milesi-Ferretti, G.M., Perotti, R. Rostagno, M., 2002. Electoral systems and public spending.
Quarterly Journal of Economics 117, 609-657
Mueller, D.C. 2003. Public Choice III. Cambridge University Press, Cambridge UK.
Myerson, R.B., 1999. Theoretical comparison of electoral systems. European Economic Review
43, 671-697.
Myerson, R.B., 1995. Analysis of democratic institutions: Structure, conduct and performance.
Journal of Economic Perspectives 9, 77-89.
Persson, T., Tabellini, G., 1999. The size and scope of government: Comparative politics
with rational politicians. European Economic Review 43, 699-733.
Persson, T., Roland, G. Tabellini, G., 2000. Comparative politics and public finance. Journal of
Political Economy 108, 1121-1161.
Powell, R., 2006. War as a commitment problem. International Organization 60, 169-203.
Sambanis, N., 2004. Using case studies to expand economic models of civil war. Perspective on
Politics 259-279.
Skaperdas, S., 2008. An economic approach to analyzing civil wars. Economics of Governance 9,
25-44.
Skaperdas, S., 1991. Conflict and attitudes toward risk. American Economic Review 81, 116-120.
Svensson, I., 2009. Who brings which peace? Neutral versus biased mediation and institutional
peace arrangements in civil wars, Journal of Conflict Resolution 53, 446-469.
Tilley, J., Evans, G., Mitchell, C., 2008. Consociationalism and the evolution of political
cleavages in Northern Ireland, 1989-2004. British Journal of Political Science 38, 699-717.
Tridimas, G., 2010. Constitutional judicial review and political insurance. European Journal of
Law and Economics 29, 81-101.
Tridimas, G., 2007. Ratification through referendum or parliamentary vote: When to call a non
required referendum? European Journal of Political Economy 23: 674–692.
Wantchekon, L., 2000. Credible power-sharing agreements: Theory with evidence from South
Africa and Lebanon. Constitutional Political Economy 11, 339-352.
Wantchekon, L., 2004. The paradox of ‘warlord’ democracy: A theoretical investigation.
American Political Science Review 9, 17–33.
Wantchekon, L., Neeman, Z., 2002. A theory of post-civil war democratization. Journal of
Theoretical Politics 14, 439–64.
33