THE ART OF COMPROMISE

Transcription

1 THE ART OF COMPROMISE Maria E. Gallego 1 and David Scoones 2 January 22, 2008 Abstract A policy is the outcome of negotiations between two three-party parliamentary states. An election in jurisdiction A determines the composition of the legislature that selects a representative to negotiate an intergovernmental policy agreement with the representative from the legislature of jurisdiction B. Negotiations are modeled using Nash s (1950) bargaining framework, modified to account for a simultaneous legislative ratification vote. With heterogeneous parties, agreements and electoral outcomes depend on the negotiators willingness to compromise. Agreements between the bargainers may not follow the ordering of the parties ideal policies. An electoral outcome where support for the center party comes from extreme voters may emerge. Keywords: Vote balancing, intergovernmental bargaining, ratification, willingness to compromise. JEL Classification: D72, C72, P16 1 Author of correspondence: Maria Gallego, Department of Economics, Wilfrid Laurier University, Waterloo, ON, Canada N2L 3C5, (O) (+1) X 2635#; (Fax) (+1) ; mgallego@wlu.ca. 2 David Scoones, Department of Economics, University of Victoria, Victoria, BC, Canada V8W 2Y2; scoones@uvic.ca.

2 1. INTRODUCTION Their lack of strong political allegiances indicates that voters in many polities make decisions based on policy outcomes. 1 In addition, many policies are the outcome of negotiations between different centers of power at national and international levels 2 [Breton 1996]. Indeed, such balancing was a guiding principle in the framing of the US constitution. Even the most reform minded government member arriving newly elected in the capital finds an entrenched bureaucracy ready to skilfully channel, if not outright stymie, attempts to change the status quo. Intergovernmental negotiations between two jurisdictions may be explicitly negotiated or the link may be strategic, with policies chosen independently, but in reference to each other. Voters in different polities understand the interdependence policy formation and use this to their advantage as evidenced by voters splitting their ballot by voting for different parties at different levels of government. 3 Therefore, with heterogeneous parties and voters preferences differing across jurisdictions, voters in one jurisdiction do not expect the ruling party of the other jurisdiction to represent their interests. Voters who recognize the interdependence of policy formation understand that under delegation agreements depend on the preferences of the negotiators. Voters should then choose a government that will negotiate the best possible policy, rather than vote for 1 See e.g., Bowler et al 1994 for Australia, Canada and Germany; Lacy and Paoline 1998 for the US; Merrill III and Grofman 1999 for a wider set of countries; Blais et al for Britain, Canada, and the United States. 2 Negotiations between France first with Britain then with Germany lead to the 1986 Single European Act [Moravcsik 1991]. Negotiations between national and sub-national jurisdictions regularly occur in Canada [Simeon 1972], in the United Kingdom [Robbins 1998], and in the United States [Inman and Rubinfeld, 1997]. 3 See for example: the Americans between President and Congress [Lacy and Paoline 1998]; the British between Federal and local elections [Heath et al. 1999]; the Canadians between the Federal and provincial levels [Erikson and Filippov 2001]; the French at Presidential and legislative elections [Gschwend and Leuffen 2005]; Europeans between European Parliamentary and national elections [Kousser 2004]. Moreover, to gain more direct influence over policies, British provincial voters pressured the Federal government to create the Scottish Parliament and the National Assembly for Wales in 1999 and the revival of the Northern Ireland Assembly in

3 the party closest to their own preferences. We present a model where voters have preferences over policy outcomes and vote taking into account the elected representative in the other jurisdiction. Elections in one jurisdiction may change the governing party and thus one of the negotiators leading to policy changes. 4 The party s willingness to compromise also affects bilateral bargaining outcomes. 5 Since voters understand the interdependence of policy formation, it seems reasonable that they understand that agreements depend on the party s willingness to compromise. 6 We show that with heterogeneous parties, not only agreements but also electoral outcomes depend on the negotiators willingness to compromise as well as the party s ideal policies. More importantly, we show that even in a unidimensional policy space an electoral outcome may emerge in which support for the center party comes from extreme voters. We study voting decisions in a model where two three-party parliamentary legislatures jointly make policy decisions. With concurrent elections in two jurisdictions being rare, we focus on elections in one jurisdiction and take as given the formateur in the other and the existence of a status quo policy. We develop the simplest model that captures the point we wish to make: a single election, complete information, a unidimensional policy, the same set of parties running in the two 4 For example, Moravcsik (1991) argues that changes in the political landscape of the three major European powers, Britain, France, and Germany, lead to the sinning of the Single European Act (SEA) in 1986 that "re-launched" Europe towards greater integration. In Britain, the 1979 election changed the governing party from Labor to Conservative. During 1983, Mitterand reversed his policy on European integration. These governing party re-alignments made way for Miterrand to reach agreements first with Germany and then with Britain. 5 Moravcsik (1991) also argues that the reversal of Mitterand's policy on European integration in 1983 was the outcome of the decline in the Communist party. This decline permitted Miterrand s realignment with the moderate wing of the Socialist Party, thus allowing him to publicly increase his willingness to compromise with regards to European integration. Moravcsik and Nicolaïdis (1999) argue that parties were conscious of voters understanding of their willingness to compromise since during the negotiations of the Amsterdam Treaty of 1997 European Union officials were hesitant to publicise new policy initiatives for fear of rallying support for the Eurosceptical Tories in the UK. 6 The 2006 Canadian Federal election campaign, which most observers assumed would lead to a minority government, featured much talk from all parties about willingness to compromise. The front running Conservative leader offered assurance to voters that his government would find much common ground with the left-leaning New Democratic Party (NDP) instead of the centre Liberals party. The possibility of the Conservative-NDP balanced coalition clearly influenced some voters. 2

4 jurisdictions and formateurs selected by vote shares. Intergovernmental negotiations are carried out by the ruling parties/formateurs representing each jurisdiction with their agreement subject to a legislative ratification vote. 7 Our model applies broadly to any two jurisdictions, but we refer to Federal and sub-national State legislatures in our analysis. In the first of four stages, citizens vote in the State election. The State formateur chosen according to vote shares engages in policy negotiations with its Federal counterpart. Negotiations are carried out using Nash s [1950] bargaining model where failure to reach an agreement leaves the status quo in place. Finally, the agreement must be simultaneously ratified and the status quo remains in force if ratification fails in any legislature. 8 The resulting extensive game has a unique sequential Nash equilibrium with a simple and intuitive structure. As usual, policy depends on the State election, the legislative (majority/minority) status of the formateurs, their preferences and the location of the status quo. In addition, we show vote balancing occurs as some change their ballot if the Federal formateur or the status quo changes. Our central purpose is to show that when voters understand the role of intergovernmental negotiations, electoral outcomes are affected by a formateur s/party s willingness to compromise. When choosing among the three State parties, policy-oriented voters must rank the agreements they anticipate will be reached by each pair of potential negotiators. 9 Although the agreement will always 7 Hug and König [2002] argue that drafting a ratifiable agreement played a considerable role in the Amsterdam Treaty of In 1993, the North American Free Trade Agreement almost failed ratification in both the Canadian Parliament and the U.S. Congress. Clearly, ratification imposes constraints on negotiations regardless of the political system. 8 Failing a vote of confidence may lead to early elections. Votes of confidence are irrelevant in single-election models. In ours, ratification plays the role of a confidence vote. On votes of confidence see e.g. Diermeier and Feddersen [1998]. 9 Intergovernmental policy making has been studied in two-tier two-party systems. Alesina and Rosenthal [1995, 1996] and Fiorina [1996] among others model policy as an exogenous compromise between the policies of two governments. While this assumption is reasonable in their models, it is inappropriate when intergovernmental bargaining takes place between two three-party legislatures. Models that endogenize intergovernmental negotiations include Crémer and Palfrey [2000, 2002, 2006] on federal standards; Persson and Tabellini [1996] on risk sharing and redistribution between 3

5 lie between the ideal policies of the negotiators, the outcome also depends on the bargainers willingness to compromise [Cressman and Gallego 2007], which is associated with their intensity of preferences [Peters 1992]. This implies that the anticipated policy agreements may not follow the ranking of the party s ideal policies. A left wing and centrist party, for example, could negotiate an agreement to the right of the agreement reached between the same left party and a right wing party. Cressman and Gallego show that when the parties preferences exhibit increasing absolute risk aversion (ARA), the ordering of agreements and parties ideal policies coincide. However, when preferences exhibit decreasing ARA, the ordering of agreements can differ from the ordering of ideals. We show that voters anticipation of the ranking of policies can lead to a non-standard partition of voters among parties in a unidimensional policy space. In our model, policy-oriented voters rank parties not according to their ideal policies but by the policies they can deliver. Moreover, if parties recognize that voters understand the role of willingness to compromise in negotiations, parties take their bargaining opponent s willingness to compromise into account not only because of policy outcomes and ratification but also because of electoral outcomes. 10 Even under our strong simplifying assumptions the requirement to negotiate makes predicting the ranking of the intergovernmental agreements and the consequent electoral outcome a difficult exercise. Under Nash bargaining the rank-order of agreements depend on the entire preference profile of all parties. Our set-up brings out the crucial role in negotiations played by two fundamental characteristics of the bargainers preferences: the party s ideal policy and its willingness to compromise. The party s ideal policy represents the policy the formateur wants to implement two regions of a Federation; and Mo [1995] on international bilateral agreements. 10 Moravcsik and Nicolaïdis [1999] examine the negotiations leading to the Amsterdam Treaty of 1997 that furthered European integration and provide evidence that negotiators preference intensities affected the agreement. Member states with worse options in lieu of an agreement were forced to sacrifice on less important issues to protect more vital interests. They also demonstrate that ratification constraints played a role in constraining negotiations. 4

6 when there is no need for compromise. In collective choice environments with policy negotiation, the formateurs willingness to compromise influences agreements and thus electoral outcomes. Since voters balance the tendencies of the formateur in the other jurisdiction instead of voting for the party with ideal policy closest to their own, on the surface, voters appear to misrepresent their preferences. But this differs fundamentally from the more widely discussed strategic voting in which voters attempt an implicit coalition to rally support behind an electable party or candidate. Here, proportional representation allows voters to support the party they truly most prefer to see elected they simply recognize that the party elected will not dictate policy, and so do not focus exclusively on a party s ideal policy. Consequently, the dependence of final policy on the choice of formateur may change the voters effective left-right ordering of parties. We show that when voters rank parties and party s ideal policies differently, the supporters of one of the extreme parties are moderate rather than extreme voters. Thus, our model shows that a non-standard partition of voters among parties may emerge in a unidimensional policy space. 11 This model is related to a number of papers. At the ratification stage, the Federal and State formateurs/agenda setters [Romer and Rosenthal 1978; Denzau and Mackay 1983] make a joint proposal to their corresponding legislatures in a "bicameral" setting. 12 We introduce a ratification stage and omit the legislative bargaining stage 13 for two reasons. With final policy being the outcome 11 In fact, if given the chance the extreme parties themselves may prefer to abdicate their role as negotiator. We do not allow abdication. By assuming that parties also benefit from governing in ways additional to the power to implement a preferred policy, the incentive for abdication can be mitigated. 12 The following is well known for bicameral systems. Bicameralism introduces balancing into policy making [for an excellent review of this literature see Tsebelis and Money 1997]; diminishes the power of the agenda setter(s) as proposals acceptable to one chamber must survive alternatives in the other [Levmore 1992; Riker 1992a,b]; and prevents the tyranny of the majority [Buchanan and Tullock 1962]. In accordance with these authors, we show that for minority governments, the parties that are needed for ratification may force moderation in intergovernmental negotiations. 13 Unicameral legislative bargaining models include: Austen-Smith and Banks [1988], Austen-Smith [2000], Banks and Duggan [2000], Baron and Diermeier [2001], Baron and Ferejohn [1989], Bloch and Rottier [2002], and Diermeier and Merlo [2000]. 5

7 of intergovernmental negotiations and ratification, bargaining within the legislature only determines the range of policies over which the formateurs negotiate. With complete information and no shocks, policies acceptable to a legislative majority at the legislative bargaining and ratification stages concur. In our model, it is ratification and not legislative bargaining that matters. In consequence, we opt for the simpler model. Moreover, ratification makes formateurs accountable to the legislatures. Without ratification in a single-election model the formateurs would implement their preferred agreement, as there is no punishment for doing so. 14 In our model, each formateur has veto powers with the legislative ratification veto player depending on the identity of the formateur. This accords with Diermeier and Myerson s [1999] finding that in bicameral settings the best organizational structure has each chamber delegating bargaining to a player with veto powers followed by a free vote on the proposal for each member in the legislature. In our model, it is parties and not individual members who vote in the legislature. Once the parties have been rank ordered by their potential intergovernmental agreements, the electoral game is similar to that found in a single-level three-party legislature. 15 There are many threeparty unicameral voting models (see Footnote 13). These unidimensional models assume voters preferences satisfy a single crossing property and show that once final policy outcomes are ranked a unique voting equilibrium exists. Given the rank-order of policy outcomes, to simplify our analysis we adopt Austen-Smith s [2000] voting model and use his results to determine the electoral outcome in our model. We show how the party s willingness to compromise affects bargaining between jurisdictions, and how based on their understanding of intergovernmental bargaining outcomes voters use this information to their advantage. 14 If formateurs can ignore legislative decisions, legislatures are irrelevant, and we need not model the legislature at all. We assume that ratified policies become law and cannot be changed by the formateurs after ratification. 15 Introducing more than three parties in each legislature can be done at the expense of making the ratification vote more complex. Since this detracts from the main point of the paper, we use the simpler three-party model. 6

8 2. THE MODEL Two governments represented by a (F)ederal and a (S)tate legislature must negotiate a policy agreement that they take to the legislatures for ratification. We assume the existence of a status quo 16 policy Q that remains in force if either legislature fails to adopt a revised policy. We model this situation as a multistage game. Policy, denoted by θ, is unidimensional and assumed to lie on the interval [0,1] (as does the status quo Q). The set of players consists of the (L)eft, (C)enter, and (R)ight parties acting in each legislature, and a large number of heterogeneous voters. The voters ideal policies are distributed on the policy space according to Γ. Preferences are assumed to be unimodal over policy outcomes, θ [0,1]. For a given policy θ that is implemented, player i whose ideal policy is ˆθ i receives a payoff of u ( ) u ( ˆ i θ = i θ θi ). We assume that voter preferences satisfy Greenberg and Weber s [1985] Consecutiveness Condition (CC): for any three voters j, k and m and any two policies 0 1 θ < θ, if u ( θ j then u k 1 ) > u ( θ ( θ 1 j ) > u k 0 ) ( θ 0 and ) u m ( θ ) > u m ( θ for all k such that 1 0 ) θˆ j < θˆ k < θˆ m, (CC) that is, if voters j and k prefer 1 θ to 0 θ, so does every voter in between. We assume the same set of parties compete at the Federal and State levels 17 and make no distinction between the party and its appointed negotiator. 18 Like voters, parties are characterized by ideal policies, ˆθ for j {L, C, R }. To bring out the role and importance of the party s willingness j 16 Assuming a status quo is not restrictive since no policy can itself typically be represented as some specific point on the unit interval. The status quo may be the previous period s agreement in a repeated game (not modeled here). 17 We consider the effect of relaxing this assumption in Section V. 18 Not unreasonable as strong party discipline is exercised in parliamentary democracies [Laver and Shepsle 1996]. 7

9 to compromise on the electoral outcome we refrain from making assumptions that guarantee agreements follow the ranking of the parties ideal policies. We believe parties are long-lived institutions so that in a single election model party preferences should be taken as given. 19 We assume parties have different ideal policies in a unidimensional space and may face bargaining opponents with ideal policies on either side of their ideal. This, in conjunction with the idea that parties prefer agreements closer to their ideals, naturally leads to assuming that parties have single-peaked preferences 20 (with different ideal policies where L s is to the left of C s to the left of R s, θˆ θˆ θˆ 1). Parties may also differ in their willingness to 0 L C R compromise in negotiations (a property of their utility functions, see discussion in Section 4). For example, when parties have quadratic preferences the ordering of their ideal policies extends to all policies since in this case preferences satisfy the consecutiveness condition (CC); and ensures R is as willing as L or C to agree to a rightward shift in policy for θ < ˆθ (see the single-peaked quadratic L utility functions example in Figure 1). However, changing the willingness to compromise of two identical parties with different ideal policies, changes the voting equilibrium 21 (see Section 4). Figure 1 about here 2.1 Timing 19 We concentrate on how the party s willingness to compromise affects electoral outcomes and refrain from studying how parties chose their preferences. Snyder and Ting [2002] argue that party s preferences should be taken as given because they represent a brand name that voters can easily identify. In their model, candidates preferences may differ from the party they become affiliated with but they run under the party s brand name not their own preferences. 20 Single-peaked utility functions are commonly used in social choice and political economy models (see e.g., Austen-Smith and Banks 1999 or Persson and Tabellini 2000). 21 Parties may differ in their willingness to compromise for reasons that depend on their historical development, on the party s activists and the membership. Given our assumption that parties are long-lived institutions we do not explain here how this characteristic of their utility function is determined but show instead that electoral outcomes depend on it. 8

10 Four subgames comprise the policy revision process: the State election, the selection of the State negotiator, the intergovernmental policy negotiation, and finally the ratification vote in each legislature. All references to elections are implicitly those at the State level. Given the status quo Q and knowing the identity ( F ) and degree of legislative control of the Federal government, in the first stage citizens simultaneously vote to elect a State government. Voters must anticipate each party s behavior in the post-election negotiations and ratification vote, and these depend on a party s preferences over all outcomes. Since we assume complete information, the only credible platforms are the parties true preferences, U = (u, u, u ). The election determines the vote shares [0,1], j {L,C, R}, which, under proportional representation, represent the weight each party receives in the legislature. V j L C R After the election, the State formateur is selected according to party s vote shares. When party j wins a legislative majority, V j 1/ 2, it becomes formateur. When no party wins a majority, a formateur is randomly chosen according to vote shares. 22 Next the Federal and State formateurs engage in intergovernmental negotiations, modeled as Nash [1950] bargaining, where failure to agree leaves the status quo in place. If an agreement is reached, to become policy it must be simultaneously ratified by both legislatures; otherwise the status quo prevails. Given final policy θ *, payoffs are realized, and the game ends. 3. EQUILIBRIUM The equilibrium involves a number of cases associated with the combinations of the preset variables F = L,C,R and Q. Many of these are qualitatively similar, with one half being simple reflections 22 Diermeier and Merlo (2004) find strong empirical support for random rather than deterministic selection. 9

11 of the other, depending on the location of Q. To remove these reflections we assume Q [0, θˆ ]. We find the subgame perfect equilibrium solving backwards through the stages of the game. 3.1 The Ratification Equilibrium At the ratification stage, parties know Q, the election outcome, the formateurs and their legislative status. Let a FS represent the policy agreement subject to ratification of the Federal and State formateurs. With parties having identical preferences across jurisdictions and only two policy choices, no party can gain by voting for different policies at the Federal and State levels, 23 so we need only consider a representative legislature, h=f, S. Each party compares the payoff from ratifying and from vetoing the agreement. For any Q, let Φ Q) = { θ u ( θ) u (Q)}, j L,C, R j( j j denote the (convex) upper contour sets of formateurs F and S, the set of policies that make party j no worse off than Q. A ratification equilibrium is a triple of mutual best-response, weakly undominated legislative FS voting strategies. Let θ * = * (a,q U) be the equilibrium policy in legislature h. An agreement h θ h takes affect when ratified by both legislatures: θ * (a FS ) = θ * (a FS FS * FS a if and only if θ = a for h = F,S,Q U) = Q otherwise h. When a party holds a majority, it only ratifies policies it prefers to Q. When no party holds a majority, a legislative coalition is required. Thus, a viable policy must lie in the upper contour sets of formateur j and at least one of the other two parties. We summarize in the following proposition: C 23 To see this note that given the vote of the other parties, j s vote matters only when j is ratification pivotal, that is, if j s vote determines whether a FS is ratified in at least one legislature. Suppose that a FS passes the vote in one legislature, and that j is pivotal in the other. When a FS gives j a higher payoff than Q, j s best response is to vote for a FS in the legislature in which its vote is pivotal. Voting for a FS at the other level does not change the ratification outcome since j was not pivotal in that legislature. Casting identical votes in both legislatures does not change the ratification outcome so that j votes in identical manner in both legislatures. When j is pivotal and j gets the same payoff from both policies, we assume j breaks the tie in favor of the formateur in that legislature. 10

12 Proposition 1: Given the status quo Q [0, θˆ ], the party s preferences U and the intergovernmental policy C agreement FS * h ( FS a, the equilibrium ratification function in legislature h, θ a,q U) is as follows: (i) If party j holds a majority in legislature h, θ * h = a FS if and only if a FS Φ j (Q) (ii) If no party holds a majority in legislature h, * h FS FS θ = a if and only if a Φ (Q) Φ (Q) for i j. i j 3.2 The Intergovernmental Bargaining Equilibrium When bargaining, each formateur knows the identity of its counterpart and the composition of both legislatures. They rationally anticipate whether their agreement is ratified. Thus, they only agree to a non-ratifiable policy if at least one prefers the status quo. Two cases can be distinguished. Case 1. When the same party holds power in both jurisdictions, there is no disagreement on the best policy, so this is not a bargaining problem in the sense of Nash [1950]. However, the party must take account of the ratification round, so simply proposing its ideal policy may lead to rejection when some other compromise it prefers to the status quo would have been ratified. In such cases, the party proposes the policy it most prefers subject to that policy being ratifiable. If the party is L it can count on unanimous support for policy changes rightward from Q. If ˆ L > θ Q, it can safely propose its ideal; otherwise, C and R ensure the status quo Q remain in force. If the party is C, it can count on R supporting a move to ˆθ C. If the party is R, it must attract either C or L. Which it chooses depends on which party is willing to move the greatest distance towards R s ideal before 11

13 rejecting a policy in favor of the status quo. 24 Define the upper bound of party j s acceptable set Φ j(q) as θ j. Summarizing, Lemma 1: Given the status quo Q [0, θˆ ], the party s preferences U and the rationally anticipated ratification function, θ * if the same party j forms government in both legislatures then FS (i) when j holds a majority in each legislature, θ * (a *) = θˆ j, (ii) when j must form a coalition in either house to ratify, C θ * (a FS max {ˆ θl,q} *) = θˆ C min {max{ θ L, θ C }, θˆ R } if if if j = L j = C j = R. Case 2: When different parties become formateurs there is disagreement over which of the feasible policies is best. Since formateurs have equal "bargaining power" 25 we will use jk to denote the pair of formateurs disregarding which jurisdiction they represent. The three jk, j k, configurations are LC, LR or CR. We model negotiations using Nash s [1950] bargaining framework, where Q represents the threat point with disagreement outcome D (Q) = (u (Q), u (Q)). The situation is not completely standard since negotiators are constrained by the ratification vote. Fortunately things are somewhat less complicated than they first appear. When both formateurs hold majorities, ratification is guaranteed, and we are in the standard bargaining model. But even when one or both do not hold a majority, if they find a policy that mutually improves on Q they FS S F 24 We note that L and R may form a ratification coalition with each other rather than with C in the legislature (see Section III). 25 Unequal bargaining power, as in Roth [1979], would give the formateurs different weights in the Nash product below. 12

14 form a legislative coalition that ensures its ratification. 26 Interestingly, ratification only constrains negotiators when they do not face "true" bargaining situations (i.e. in Case 1). The bargaining set is the set of utilities pairs over which the formateurs negotiate, given by 27 B jk (Q) = {u (a),u (a) a Φ (Q) Φ (Q)}. j k j k The bargaining set B jk (Q) and the disagreement point (Q) D jk define the bargaining problem. Among the many bargaining 28 solutions, we use that proposed by Nash [1950]. For any a Φ j (Q) Φ k (Q), the Nash Solution (NS) to our bargaining problem maximizes the product of the utility gains from the disagreement point, i.e. solves max NP Using Nash [1950], we conclude: a kj (a Q) = k [u j (a) u j(q)] [u (a) u k (Q)]. Lemma 2 (Nash 1950): Given the status quo Q [0, θˆ ], the party s preferences U and the rationally anticipated ratification function, θ *, if different parties control the legislatures there is a unique solution to the intergovernmental Nash Bargaining problem. C Since the Nash solution is Pareto optimal and Pareto dominates Q, not every point on the frontier of B jk (Q) is a candidate. First assume that Q < θ ˆ j. For a [Q, θˆ j), both parties prefer rightward changes in policy (e.g., the lower upward sloping segments in Figure 2). When a [Q, θˆ ) j and θ ˆ θ, both prefer agreements to left of θ j (e.g., the top upward sloping segment in Figure k j 2(a)). In this case the set of potential agreements is [ θ ˆ, ˆ j θk ]. When a [Q, θˆ j) and θ ˆ k > θ j (e.g., 26 Again, this relies on the same set of parties compete in both jurisdictions. See Section V. 27 With concave utilities, this set is convex, closed, and bounded. 28 The results are qualitatively similar if we use instead the Kalai-Smorodinsky [1975], the Perles- Mascheler [1981] or the Egalitarian [Kalai 1977] solution. See Cressman and Gallego [2007]. For an excellent discussion on various solutions to Nash s bargaining problem see Thomson [1994]. 13

15 Figure 2(b)), this set is smaller, restricted to θ ˆ, θ ]. Thus, the set of mutually acceptable policies is A jk [ j j (Q) = [ˆ θ, min{, ˆ j θ j θk}]. When instead Q > θ ˆ j, no agreement is a Pareto improvement on the status quo, and thus 29 A jk (Q) = Q. Figure 2 about here Below we describe the nature of the agreements reached under Cases 1 and 2 to examine the effect party preferences have on voters behavior (we further illustrate our results in Section IV with examples). For now, we summarize Lemmas 1 and 2 in the following proposition. Proposition 2: Given the status quo Q [0, θˆ ], the party s preferences U and the Federal formateur F and its legislative status, intergovernmental negotiations lead to a unique ratifiable agreement. C F For a given Federal formateur F, let Θ * = { θ * (a *), θ * (a *), θ * (a *)} represent the set of ratifiable agreements. The results of Sections III.1 and III.2 are in the spirit of Romer and Rosenthal [1978] and Denzau and Mackay [1983]. In Romer and Rosenthal s seminal paper, the agenda setter s proposal must pass an electoral referendum. In Denzau and Mackay, a committee a subset of the legislature makes a proposal to its parent body. Both show, as we do, that under complete information and a closed rule, 30 some alternatives to the status quo including compromises the setter/committee accepts to gets its proposal approved are viable but the status quo may also be difficult to change. Neither paper, however, explores the consequences of this on the initial choice of agenda setter or committee members or the effect that the setter s or committee members willingness to compromise have on policy outcomes. 3.3 Selection of the State Formateur 29 This trivial case is also not a bargaining problem in the sense of Nash [1950]. 30 Under a closed rule, no legislative amendments to the proposal are allowed. FL FC FR 14

16 In multi-party systems, the formateur's ability to enact policy depends on its majority/minority status. In legislative models, formateurs are chosen by random or deterministic order using vote shares. Given stronger empirical support for random selection (Diermeier and Merlo, 2004), we assume representation in the legislature and selection of the State formateur is by vote share. When V j 1/ 2, j forms government with probability one. When no party wins a majority, j forms government with probability j V. The probability of j becoming the State formateur is μ j 1 = 0 V j if V 1/ 2 if max{v j otherwise j } 1/ The State Election At the electoral stage, voters know the preferences of each party, the identity and majority/minority status of the Federal formateur and the location of the status quo. Given complete information they can rationally anticipate the final policy resulting from any particular election outcome. Voters can then rank parties by their associated intergovernmental policy agreements (see additional discussion on policy rankings in Section IV). The fact that parties gain representation proportional to their vote shares and that voters are individually insignificant immensely simplifies the election process. Random selection eliminates strategic voting for the type of electoral coordination present in plurality rule elections where a voter s perception of how likely a party is to garner the most votes affect their choice of whom to support [see e.g., Austen-Smith and Banks 1988]. With random selection, an individual s vote increases by an equal amount the likelihood of any party forming government, so there is no benefit to coordination. Proportional representation rules out considerations that emanate from the electoral rather than the policy process. 15

17 Given the rank of intergovernmental agreements, the underlying voting model here is similar to Austen-Smith [2000], to which we refer the reader for a more formal demonstration of the following result. A voting equilibrium is a symmetric probabilistic voting strategy, π * such that for all ˆ F * Fj θ i [0,1] given Q, F, U, and the anticipated ratifiable agreements Θ *, π ( θ*(a *) Q,F,U) for j = L, C, R, is weakly undominated and maximizes i s expected payoff. i Proposition 3 (Lemma 4, Austen-Smith 2000) Given the status quo Q [0, θˆ ], the party s preferences U, the Federal formateur F and its legislative status, and the set of anticipated ratifiable equilibrium agreements F Θ *, if π * is a voting equilibrium, voter of type i votes with positive probability only for the party that offers the highest payoff conditional on that party being selected as the State formateur. C That is, voters act as Nash random dictators. They vote as if their ballot determines the outcome, supporting the party whose selection as formateur leads to the ratification most preferred outcome among those obtainable. Of course, it is possible that this choice is not unique, in which case voters are assumed to vote for the party whose ideal policy most closely resembles their own. Given the CC condition and the ranking of intergovernmental agreements, the equilibrium is characterized by the existence two unique marginal voter types ν * < ν * partitioning the space of preferences into supporters of the three parties. 1 2 We are now ready to discuss the main contribution of our paper. We show that when policy is the outcome of negotiations between multi-party legislatures, the electoral equilibrium crucially depends on the ranking of intergovernmental agreements and that depending on party preferences either a standard or a non-standard electoral equilibrium may emerge. We begin by showing that embedded in the party s preferences is their willingness to compromise. To show this we borrow from Mas-Colell et al [1995], Peters [1992] and Cressman and 16

18 Gallego [2007]. First recall that the Arrow-Pratt coefficient of absolute risk-aversion ( ARA = u"/ u' ) measures changes in concavity of a utility function and is invariant to positive linear transformations even in riskless environments such as ours (Mas-Colell et al 1995). In addition, Peters shows that the intensity of preferences of player k relative to j is associated with the concavity of k s utility function relative to j s. Together these results imply that intensity of preferences decreases as the concavity of any party s utility function increases (as the coefficient of ARA increases). Finally, Cressman and Gallego show that in bargaining games where players have single-peaked utility functions as in ours the ranking of bargaining opponents depend on the ARA coefficient of players utility functions. Thus the willingness to compromise (or intensity of preferences) of the bargaining formateurs can affect the ranking of policy outcomes and the electoral equilibrium. We make use of Cressman and Gallego s formal result on the way to proving the main point of our paper. For parties j and k whose ideal policies are such that θ ˆ j < θˆ k, in our context their result states that: Proposition 4 (Theorem 2, Cressman and Gallego 2007) Suppose u j is a unimodal utility function with arg max u ˆ j = θ j and the status quo is Q θ j < ˆ. Suppose further that u k is an increasing utility function for all a [Q, θˆ j]. Let u k, α be the horizontal translation of u k to the right by α 0 units (i.e., u k, α = u k (x α) ). If u k has increasing absolute risk aversion, the jk a associated with the NS between j and da jk ( α) k α satisfies > 0 dα. If u k is unimodal, j prefers an opponent whose ideal is closer to his own. If u k has decreasing absolute risk aversion, the a jk da jk ( α) associated with the NS between j and k α satisfies < 0, j dα prefers an opponent whose ideal is further from its own. 17

19 We rephrase the above result in the context of our paper. Let C s utility function exhibit increasing absolute risk aversion (IARA) and R s be a prefect translation of C s to the right by α units. Proposition 4 shows that the ranking of party s ideal policies and the ranking of agreements between L and C and L and R coincide. It follows from Proposition 1, 2 and 4 that the ratified equilibrium agreements between a given Federal formateur F and the three State formateurs follow the ordering of the party s ideal policies, i.e., ˆ FL FC FR θ θ*(a *) < θ*(a *) < θ*(a *) θˆ 1. 0 L R Given this ranking, from Proposition 3 we know that a unique electoral equilibrium exists. Thus, as anticipated, when C and R s utility function exhibit IARA, we obtain a voting equilibrium where 1 voters partition themselves in such a way that those to the left of the marginal voter ν * vote for L, 2 those to the right of the marginal voter ν * vote for R and those in between ( ν *, ν *) vote for C. This corresponds to the standard voting equilibrium of three-party legislative bargaining models in the literature. We call this the standard voting equilibrium. In Section 4.1 we show an example with a standard voting equilibrium. However, if C s utility function exhibits decreasing 31 ARA (DARA) we find a different electoral equilibrium. When R s utility is a prefect translation of C s to the right by α units, Proposition 4 implies that the agreement between L and R is to the left of that between L and C. In this case, from Proposition 1, 2 and 4 it follows that the ratified equilibrium agreements between a given Federal Cressman and Gallego [2007] show that Propositions 4 must be applied with care since a utility function that is always DARA must be increasing and so cannot be unimodal. They show however that the utility function must be DARA only on the interval [Q, θ *(a jk ( α))] to conclude the ratifiable equilibrium policy decreases as α increases, i.e., as the ideal policy of k gets further away from j s ideal. Consequently, k s DARA utility function can be modified so that it becomes unimodal outside [Q, θ * (a jk ( α))], i.e., for u k ( θ ) for θ > θ*(a jk ( α)). We take as given that k s unimodal utility is DARA in the interval [Q, θ * (a jk ( α))] so that the statements of Propositions 4 and 5 remain unaffected. 18

20 formateur F and the three State formateurs do not follow the standard ranking, i.e., ˆ FL FR FC θ θ*(a *) < θ*(a *) < θ*(a *) θˆ 1. 0 L R We can however apply Proposition 3 here since as shown by Austen-Smith [2000] the voting equilibrium depends only on how voters rank policy outcomes and only indirectly on the ideal policies of the party they elect as State formateur. When C s and R s utility function exhibit DARA 1 voters partition themselves in such a way that those to the left of the marginal voter ν * vote for L, 2 those to the right of the marginal voter ν * vote for C and middle-of-the-road voters, those in between ( ν 1 *, ν 2 *), vote for R. Policy-oriented voters choose the party that conditional on being chosen formateur implements the intergovernmental policy agreement they most prefer rather than for the party whose ideal is closest to their own. The repercussion of DARA on the electoral equilibrium leads to the main result of our paper: the emergence of a non-standard voting outcome in a unidimensional policy space. We show an example in Section 4.2 where this is the case. We summarize the main point of our paper in Proposition 5. Proposition 5 Suppose the conditions of Proposition 4 hold. Assume voters know the status quo Q [0, θˆ ], the party s preferences U, the Federal formateur F and its legislative status, and the set of anticipated ratifiable C F equilibrium agreements Θ *. If u k, for k = C, R has increasing absolute risk aversion, the ratifiable intergovernmental policy agreements follow the ranking of the party s ideal policies. A unique standard the electoral equilibrium emerges where voters partition themselves along the left-right scale among the three parties. If u k has decreasing absolute risk aversion the ranking of the ratifiable agreements and of party s ideal policies differ. A nonstandard electoral equilibrium emerges where some extreme voters vote for the center party and some middle-of-the-road voters vote for one of the extreme parties. We emphasize that under Nash bargaining the willingness to compromise of all parties over the 19

21 entire policy space influences negotiations and thus the ranking of agreements. Intergovernmental bargaining brings out the role of the parties willingness to compromise on negotiations and more importantly its effect on electoral outcomes. We have shown it is the party s willingness to compromise that effectively determines the voters left-right ordering of parties. The strategies of the voters, together with the ratification strategies and negotiation equilibrium constitute the unique sequential equilibrium of the entire game. 4. COMPARATIVE STATICS We now examine how changes in the status quo and in the party s willingness to compromise affect the equilibrium for a given Federal formateur. Rather than undertaking a lengthy formal comparative statics analysis considering all possible configurations of the Federal and State formateurs along with their majority/minority status, we instead demonstrate the key results using numerical simulations. We present the comparative statics results through two examples where C s and R s utility function exhibits respectively IARA and DARA. Proposition 5 shows, however, that these results apply broadly once the effect of IARA and DARA and the distribution of voters ideal points are taken into account. We first show that strategic voting vote balancing occurs in our model. After that we illustrate the importance of compromise on the voting equilibrium by changing the utility function of L s opponents. 4.1 Changes in the Status quo under IARA preferences d d u'' (u'') u''' u' When parties have quadratic utilities, since (ARA) = ( ) = > 0, utilities 2 dθ dθ u' (u') exhibiting IARA. The ranking of agreements and party s ideal policies coincide (Proposition 4) and a standard voting equilibrium emerges (Proposition 5). The following examples illustrate that vote balancing occurs under complete information. This happens as changes in the status quo affect the set of feasible intergovernmental agreements which 2 20

22 in turn affect electoral outcomes. We assume the ideal points of the voters are distributed to approximate a uniform distribution on [0,1] and that the ideal policies of the parties' preferences are θ ˆ L = 0, θ ˆ C =1/ 2, and θ ˆ R = 1. Given this, were voters to vote for the party whose ideal policy is closest to their own, the election would lead to the following partition of voters: (0,0.25) (0.25,0.75) (0.75,1) vote for party L vote for party C vote for party R. To fix ideas, assume R holds a majority in the Federal house. This means that for each example below there are five State electoral outcomes: L wins either a majority or a minority, C wins a majority, R wins either a minority or a majority. The remaining possibility that C wins a minority adds nothing, since an agreement acceptable to C will always attract the support of R. Table 1 about here Table 1 gives the equilibrium agreements for the State formateurs under majority and minority governments for Q=0 and Q=0.25 and the voting equilibrium. The agreements favor the left-most formateur 32 and follow the ordering of the parties ideals. Example 1: Q=0. Since the status quo is at L's ideal policy, if L gains control of the State legislature, L proposes the status quo. In contrast, C and R prefer changes to the status quo. Case (i) and (ii) have the same outcome since for Q=0, C is indifferent between the status quo and R's ideal policy. In case (iii) the agreement maximizes NP CR (a Q) in the Pareto set (Q). For cases PO CR (iv) and (v) L ensures that its most preferred policy, the status quo, prevails. In the Nash equilibrium, each citizen votes for the party that, conditional on being selected formateur, would negotiate the ratifiable outcome θ *(a *) the voter most prefers. A standard FP 32 Typically, the closer a party s ideal is to the status quo, the closer will be the final agreement to the party s ideal. 21

23 voting equilibrium emerges: L gets 30.5% of the vote, C 49.5%, and R 20%. Comparing this to the outcome when everyone votes for the party whose ideal policy is closest to their own, it is clear that C still receives approximately the same vote share, and a substantial chance of forming government. But those supporters are drawn from a more right-leaning segment of the electorate. L's prospects improve and R s diminishes as voters balance the influence of R's control of the Federal house. Example 2: Q=0.25. The status quo is now less extreme than in Example 1. Given quadratic preferences, not only do the ranking of agreements and party s ideal policies coincide but also the party s unimodal utility functions satisfy the CC condition. Therefore, this ranking extends to other policies, in particular to the policy that keeps C indifferent to the status quo θ C (Q). So that as the status quo shifts from Q=0 to Q=0.25, θ C (Q) shifts right. This makes the agreements reached under Section III.2 Case 1 more likely to be binding. Though this does not affect the ranking of agreements, some agreements change affecting the electoral equilibrium under Proposition 5. In the example, L again only agrees to the status quo. However, C's "power" is now increased. If C becomes the State formateur it negotiates an agreement it prefers relative to that in Example 1. Also, if R fails to form a majority, C can use its veto power to restrain R from imposing its ideal policy ˆθ R. In contrast to Example 1, ratification binds when R gets a minority. In equilibrium, a standard left-right partition of voters emerges: L gets 41% of the vote, C 25%, and R 34%. Both extreme parties benefit electorally at the expense of center party from the rightward movement of Q. Intuitively, with Q being less extreme, the influence of the ratification vote, forces State party R to credibly moderate the extreme tendencies of its colleague, Federal formateur R. C's "right-wing" vote moves to support R. Simultaneously, voters hesitant to let extreme party L negotiate, are now less worried about the result of the (inevitable) deadlock. 4.2 Changes in the willingness to compromise of L s opponents 22

24 Next we examine how making parties more willing to compromise affects intergovernmental agreements, ratification and electoral outcomes. In the next two examples, Q=0, L holds a majority in the Federal house, and parties ideal policies are θ ˆ L = 0. 25, θ ˆ C = 0. 33, and θ ˆ R = While L retains its quadratic utility function, we consider the effect of changing C and R s preference from a quadratic function (exhibiting IARA) to a logarithmic one 33 (exhibiting DARA). We note that even though there is no risk in our model we assume complete information and there are no shocks to any of the parameters of the model as C s and R s utility function changes from quadratic (IARA) to logarithmic (DARA) their strength of preference weakens [Peters ]. Thus, C and R are now more willing to compromise than under IARA preferences (Proposition 4). This time we assume L holds a majority in the Federal house. For each example below there are again five State electoral outcomes: L wins either a majority or a minority, C wins a majority, R wins either a minority or a majority; and C s minority policy receives the support of R. In both the quadratic and logarithmic utility examples, the LR-agreement lies in C s feasible set, a * Φ (Q), regardless of R s legislative status. C sees no need to constraint negotiation. Moreover, using these utility functions, Table 2 shows that all parties prefer to change the status quo and that agreements favor the left-most formateur. Table 2 about here LR C 33 Logarithmic utility functions are not unimodal. Cressman and Gallego [2007] show that logarithmic utility functions can be modified so that they become unimodal outside [Q, θ *(a jk ( α))] without affecting the statements of Propositions 4 or of Proposition Peters [1992] defines a strength of preference relation as follows. For a player facing four choices { a, b, c, d} A, let the binary relation f * be a complete transitive binary relation on A A. If (a,b) f *(c,d), then the player prefers the change from b to a to the change from d to c, i.e., for utility function u, u(a) u(b) > u(c) u(d). Peters proves that for two players the utility function of the player with the weaker strength of preference relation is a concave transformation of the other player's utility. Therefore, k s strength of preference weakens as the concavity of k s preferences increases. 23