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 and½.21 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()/(21), 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. 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