ELECTIONS, GOVERNMENTS, AND PARLIAMENTS IN PROPORTIONAL REPRESENTATION SYSTEMS*

Transcription

1 ELECTIONS, GOVERNMENTS, AND PARLIAMENTS IN PROPORTIONAL REPRESENTATION SYSTEMS* DAVID P. BARON AND DANIEL DIERMEIER This paper presents a theory of parliamentary systems with a proportional representation electoral system, a formateur selected based on party representation in parliament, and parties that cannot commit to the policies they will implement once in government. Government formation involves efficient protocoalition bargaining, and elections yield unique strong Nash equilibrium outcomes. Depending on the status quo, minimal-majority, surplus, or consensus governments can form. If parties and voters are myopic and the status quo is subject to shocks, consensus governments and centrist policies occur only in a crisis. Otherwise, governments are minimal winning, and policies reflect only the preferences of the government parties. I. INTRODUCTION The game-theoretic analysis of multicandidate elections has made important advances in recent years [Cox 1997; Myerson 1999], but developing a strategic theory of parliamentary systems with proportional representation has remained a challenge. Not only do parties strategically choose policies and bargain over government formation, but because government policies are a consequence of coalition bargaining, voters have incentives to vote strategically as well. The paucity of strategic theories not only represents a gap in our understanding of parliamentary systems but also hinders a systematic comparison of political systems. A theory of parliamentary systems should be based on a model of coalition government formation and policy choice and a model of elections. In parliamentary systems governments with the support of a parliamentary majority control the legislative process, and elections determine representation but not which government forms. Voters thus must anticipate which policies the possible governments would choose and may not cast their ballot for their most preferred candidate or party if voting for another party leads to a coalition government that would choose a more preferred policy. 1 A political equilibrium encompasses all these * This research has been supported by National Science Foundation Grant No. SBR The authors would like to thank three anonymous referees, the editor, and Timothy Groseclose for their very helpful comments. 1. Similar issues arise in the study of U. S. elections. See, for instance, the literature on divided government and split ballots (e.g., Alesina and Rosenthal 2001 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology. The Quarterly Journal of Economics, August

2 934 QUARTERLY JOURNAL OF ECONOMICS considerations and consists of a legislative equilibrium, a government formation equilibrium, and an electoral equilibrium. As an example of strategic behavior consider the 1998 election for the German Bundestag with a moderate supporter of the Christian Democrats (CDU) who prefers a coalition government of the CDU with the Liberals (F.D.P) to a single-party government by the CDU. If the CDU is very close to gaining an absolute majority of seats, the voter is better off voting for the F.D.P. In German elections this phenomenon frequently occurs because small parties are at risk of failing to win enough votes to cross the 5 percent minimum representation threshold. Strategic voting of this kind is a common theme in electoral campaigns and is known as lending votes (Leihstimmen). 2 Austen-Smith and Banks [1988] present a full equilibrium model of a parliamentary system with proportional representation, three parties, and a unidimensional policy space. They characterize an equilibrium in which parties adopt distinct policy positions and a substantial fraction of the electorate votes for its second preferred party to ensure a coalition government rather than a single-party government. Their model, however, is difficult to analyze and has an abundance of qualitatively different equilibria, none of which can be eliminated by iterated weak dominance, the standard refinement in electoral models. We provide a full equilibrium model in a two-dimensional policy space with three parties that generates results on government formation, policy choice, election outcomes, and representation. The electorate is policy-motivated, and elections are conducted under proportional representation, the most common electoral rule in parliamentary systems. Parties have preferences over both policy and office-holding, so bargaining over government formation and policy choice depends on the status quo. Since voters cast their ballots based on their expectations about government policy choice, their voting strategies are status quo dependent. 3 [1996] and Fiorina [1996]). Most models of U. S. electoral competition, however, focus on competition within districts [Cox 1997]. 2. See Riker [1982] for an early reference and Cox [1997] for empirical evidence on strategic voting in a variety of political systems. 3. If the choice space is unidimensional and the formateur is chosen probabilistically each period, status quo dependence is mitigated, and the policy moves toward the core, the median legislator s ideal point [Baron 1996]. In multidimensional policy spaces, however, the core in general does not exist, and thus policies would not be expected to converge. Multidimensional models of government for-

3 ELECTIONS, GOVERNMENTS, AND PARLIAMENTS 935 There are two key assumptions that distinguish our model from the previous literature. First, we rely on efficient protocoalition bargaining. Second, we assume that government formateurs are selected in proportion to their seat shares. The first assumption allows us to deal with the status quo dependence. Adding the second assumption permits us to generate a unique strong Nash electoral equilibrium outcome for every status quo. To implement efficient bargaining, we allow the parties to exchange office-holding benefits to which they have some entitlement. For example, Strom [1990, p. 108] refers to a variety of office and policy inducements used to obtain support from the least expensive coalition partner. Earlier research usually interprets these office-holding inducements as cabinet portfolios [Browne and Fendreis 1980; Laver and Schofield 1990]. 4 But in many parliamentary democracies parties receive a variety of other benefits about which voters may be indifferent as to their allocation. These benefits include jobs for party stalwarts, board seats on public companies or the national television system, and transfers to interest groups and party foundations. Again consider Germany. All the major parties (as well as interest groups like churches and labor unions) occupy seats on the supervisory boards of the national television system and major corporations (such as Volkswagen). Moreover, each major party receives substantial amounts of public money for its research and education foundations. Similar arrangements are common in many other parliamentary democracies, especially Austria and Italy. Entitlements to such benefits can be interpreted as longestablished norms. 5 For example, cabinet portfolios are on average allocated proportionally to the seats a party contributes to a governing coalition [Browne and Fendreis 1980; Laver and Schofield 1990], but the allocation of portfolios frequently differs substantially from this proportionality norm. These deviations can be interpreted as implicit transfers of office-holding benefits that allow parties to bargain efficiently. 6 mation without elections are studied by Baron and Ferejohn [1989] and Baron [1991, [1993], and Banks and Duggan [2000] provide a more general theory of bargaining in multidimensional policy spaces. 4. Note that any interpretation of the office-holding benefits as ministries is strained in a model with a unidimensional policy space. 5. See Diermeier [1995] for a theory of such norms in a legislative setting. 6. We thus use a model of cabinet bargaining rather than a model of ministerial delegation as in Austen-Smith and Banks [1990] and Laver and Shepsle [1990, 1996] where ministers choose policies in a decentralized manner.

4 936 QUARTERLY JOURNAL OF ECONOMICS We also use a stochastic selection rule under which the formateur is selected with a probability proportional to its seat share, a procedure that is empirically well supported [Diermeier and Merlo 1999]. Since, as we demonstrate below, each formateur chooses a unique proto-coalition, each potential formateur is associated with a unique government policy. From the point of view of voters, each distribution of seat shares thus corresponds to a probability distribution over government policies. It follows that if no party obtains a majority of seats, each voter is pivotal for the selection probabilities. This feature of the model yields unique voting equilibrium outcomes. The model yields a host of refutable predictions about government formation, policy choice, elections, and parliamentary dynamics. With respect to government formation the following results obtain. First, a formateur forms a government with the party that is the more disadvantaged by the status quo, provided that that party s ideal point is not too distant from that of the formateur. For any government the policy maximizes the aggregate utility of the government parties, and the formateur makes policy concessions to its government partner(s) in exchange for office-holding benefits. For example, the German Greens may be willing to give up an extra portfolio for the SPD s promise to close nuclear power plants. Government partners thus have influence over the policy. Second, if no party has a majority of seats, minimal winning governments result when the status quo is not extreme. Third, consensus governments can result, and they choose centrist policies. Consensus governments are more likely the more extreme is the status quo relative to their ideal policies and thus are more likely after a crisis that causes the status quo to be outlying. Fourth, unless the status quo is very favorable to the other parties, a party that obtains a majority in an election forms a consensus or a surplus government rather than a singleparty government. With respect to the electoral equilibrium, the results include the following. First, for each status quo there exists a unique strong Nash equilibrium outcome. This outcome may be a lottery over at most three different policy positions. Second, all three parties are represented in parliament in any strong Nash equilibrium. Third, some voters do not vote for the party closest to their ideal point, so representation in parliament need not closely reflect voter preferences. Fourth, when the parties form minimal winning governments, there is an implicit pre-election coalition

5 ELECTIONS, GOVERNMENTS, AND PARLIAMENTS 937 in which if selected as the formateur each of two parties in the coalition forms a government with the other. Fifth, when the parties form minimal winning governments, the electoral equilibrium has one large and two small parties where the large party is the one with an ideal policy closest to the status quo. Sixth, if the status quo is extreme, each party if selected as the formateur forms a consensus government, and hence they split the vote. Seventh, depending on the status quo, a party can receive a majority of the votes in an election. These results identify two features of parliamentary systems with proportional representation that differ from the customary normative understanding of these systems. First, government policy does not reflect the preferences of all the parties represented in parliament. Instead, it reflects only the preferences of those parties in government. Second, in an election some voters vote strategically; i.e., they do not vote for the party closest to them. Representation in parliament thus need not closely reflect the distribution of voter preferences. 7 We also investigate the consequences of our model for the dynamics of government formation and policy choice. Since each status quo policy is uniquely associated with a (possibly degenerate) lottery over policy outcomes, the dynamics of policy choice can be easily characterized by a Markov chain. In particular, we show that incumbent governments are replaced precisely when they implement their most preferred policies. Further, after the first period no party represented in parliament receives a majority of seats, and only minimal winning governments form, unless there are large shocks to the status quo which can lead to supermajority governments. This approach to the study of the dynamics of parliamentary systems is based on the assumption that parties (or their leaders) have short-term political horizons and care only about the current period. II. THE MODEL We consider a two-dimensional spatial model of elections, government formation, and policy choice with three parties. 8 Voters have quadratic utility functions over government policies, 7. Austen-Smith and Banks [1988] reach similar conclusions. 8. Increasing the number of parties increases the number of possible coalitions and hence the complexity of the characterization of electoral equilibria.

6 938 QUARTERLY JOURNAL OF ECONOMICS so for a policy x R 2 the preferences of a voter with ideal point z are represented by a utility function u( x; z), u x; z x 1 z 1 2 x 2 z 2 2, where z Z R 2, the space of voters ideal points. We assume a large but finite (and even) number N of voters. The voters are also assumed to be symmetrically and uniformly distributed about the centroid of the Pareto set of the parties, so no party has a natural electoral advantage. To simplify the analysis, we assume that there are no voters who are exactly indifferent between any two parties ideal policies. Each party i has preferences for both policies and officeholding benefits y i R, where i 1 y i Y and y i 0 if party i 3 is not in government. The preferences of party i are represented by a quasi-linear utility function U i ( x,y) given by U i x,y u i x y i, i 1,2,3, where u i ( x) represents party i s policy preferences and y ( y 1,y 2,y 3 ). For the sake of tractability the policy preferences are assumed to be quadratic: 9 (1) u i x x 1 z i 1 2 x 2 z i 2 2, where z i R 2 denotes party i s ideal point. In the basic model the parties ideal points are assumed to be symmetrically located so that the governments that form are based on institutional characteristics and strategies rather than on preference alignments. In Appendix 1 we show how this and other assumptions can be relaxed. Policies are continuing, so when a government is formed, the status quo q R 2 is the policy in place under the previous government. The policy chosen by the new government becomes the status quo for the following period. This provides a natural interperiod link to investigate parliamentary dynamics. If a new policy is not enacted, the status quo remains in place. Although parliament chooses policy, the government in effect controls policy as long as it is supported by a parliamentary majority. This is the consequence of two features of parliamentary systems, one institutional and the other operational. The 9. Quadratic preferences are not needed for many of the results, but they allow a simple characterization of which governments form (e.g., in (11)) and allow a convenient graphical representation of certain properties of the equilibrium (e.g., in Figures II V).

7 ELECTIONS, GOVERNMENTS, AND PARLIAMENTS 939 institutional feature is that the parliament selects the government, so the executive and a parliamentary majority are closely aligned. The operational feature is that the government controls the legislative agenda, in part through control of the ministries. 10 We focus on governments as majoritarian coalitions. That is, a government is a coalition C of represented parties with support of a majority of the members of parliament. Given a parliamentary government s control over the legislative agenda, this implies that the policy is chosen by the governing coalition. 11 Parties thus are unable to commit credibly to the policies they will subsequently choose if they are in government. 12 A period is the length of an interelection period and consists of three stages, as illustrated in Figure I. The first stage involves an election that determines the seat shares of the parties in parliament. The second stage involves government formation, and the third stage is legislative and involves the choice of a policy in the parliament. After an election one party is selected as the formateur. Selection is governed by a proportionality rule with the probability of selection equal to the party s seat share in parliament, unless one party has a majority of seats in which case it is selected as the formateur. In a study of parliamentary governments in twelve countries for the postwar period, Diermeier and Merlo [1999] found strong support for a proportionality rule with a sizable premium for selecting the incumbent (the formateur of the previous government). Their data do not support a rule under which the party with the most seats in parliament is selected with certainty. Proportional selection implies that the formation process and hence legislative outcomes are responsive to seat 10. Silk and Walters [1995, p. 109] note that in the United Kingdom almost all government bills are enacted, and in all were passed. Baron [1998], Diermeier and Feddersen [1998], and Huber [1996] consider institutional features that allow governments to control the agenda. 11. In some countries minority governments are common [Strom 1990]. In these cases our model should be interpreted as focusing on the supporting coalition that commands a majority of seats and maintains the minority government. 12. Models of electoral competition with policy-motivated candidates have been provided by Wittman [1977, 1983] and Calvert [1985]. As pointed out by Alesina [1988], these models crucially rely on the fact that parties are able to commit to electoral platforms. Otherwise, a party could strategically announce a platform intended to increase its seat share in parliament but once in office revert to its policy preferences rather than its announced platform. Rational voters would recognize this incentive and base their votes on the party s policy preferences rather than its announced platform. In a repeated voting game credible platform announcements can be sustained endogenously as subgame-perfect equilibria [Alesina].

8 940 QUARTERLY JOURNAL OF ECONOMICS FIGURE I The Model shares. This establishes a direct link between a vote in the election and policy outcomes. The formateur selects a proto-coalition, i.e., a nonempty subset of parties represented in parliament that bargains over the government policy and the allocation of office-holding benefits. These office-holding benefits allow parties with preferences over both policy and benefits to bargain efficiently. The resulting coalition, policy, and distribution of office-holding benefits must obtain the confidence of a chamber majority. If it fails to win a majority or if the members of the proto-coalition cannot agree on a proposal, a caretaker government assumes offices. The status quo then remains in place, and no office-holding benefits are transferred among the parties. As we demonstrate, with efficient coalition bargaining the government policy depends on the coalition members ideal points and not on the status quo or the details of the bargaining procedure. The distribution of office-holding benefits, however, de-

9 ELECTIONS, GOVERNMENTS, AND PARLIAMENTS 941 pends on the status quo and the bargaining protocol. If the formateur could make a take-it-or-leave-it offer, his party would capture most of the rents. With counteroffers, however, more equal distributions of benefits would result, as in the models of legislative bargaining [Baron and Ferejohn 1989]. Consequently, although the nature of the bargaining process does not affect the policy chosen by the government, it can affect the formateur s preferences over proto-coalitions. We focus on the case where the formateur can make a take-it-or-leave-it offer, and we consider another bargaining model in Appendix 1. The electoral system is proportional representation with a minimum vote share m required for representation, where m M/N, m (0, 1 4], and M is the minimum vote threshold for representation. 13 If the vote shares i of all parties are at least m, their seat shares are i. 14 If party i s vote share is less than m, it is not represented in parliament and the other parties have seat shares l l /(1 i ), l j, k, l i. Since voters have preferences over policies and policies are the result of parliamentary action led by the government, voters choose prospectively based on their expectations about which governments form and the policies each would enact in parliament. Information is complete, so voters understand which governments may be formed given an election outcome and which policies the possible governments would choose. Since the government formation process involves the choice of the formateur with probabilities proportional to the seat shares of the parties, voters cast their ballots taking into account the effect of their votes on the probability distribution of policies. III. GOVERNMENT FORMATION AND LEGISLATION This section characterizes the governments that form and the policies they choose as a function of the status quo and the vote shares. Proto-coalition bargaining is considered first, and then the formateur s choice of prospective coalition partners is characterized. 13. The upper bound on m allows all three parties to be represented in parliament when one party has half the votes, as in the results in the electoral equilibria characterized in Proposition The German 5 percent-hurdle is probably the most well-known example of a representation threshold. But many other electoral systems with proportional representation rely on seat-quotas, e.g., the Droop quota, that in the context of our model are equivalent to representation thresholds. See Cox [1997] for details.

10 942 QUARTERLY JOURNAL OF ECONOMICS A. Proto-Coalition Bargaining Let C be a proto-coalition with a majority of seats. A party j votes for a proposal ( x C, y C ) if and only if (2) u j x C y j C u j q. An efficient government policy x C for C is given by (3) x C,y C arg max u i x y i x,y i C subject to u j x y j u j q, 3 y j Y. j 1 j C For any formateur i in the proto-coalition C, the optimal policy x C is the efficient policy: (4) x C 1 z C k, k C which is independent of the aggregate office-holding benefits and the seat shares of the parties. For two-party coalitions C {i, j} the optimal policy x ij is (5) x ij 1 2 z i 1 2 z j, i j, which is the midpoint of the contract curve for the government members. If C {1,2,3}, the policy x C of the consensus government is the centroid z of the Pareto set. The policy z is centrist and reflects the preferences of all members of C. IfC {i}, i.e., if party i commands a majority of seats, the policy is x C z i. When the formateur i makes a take-it-or-leave-it offer to obtain j s support, the office-holding benefits y C j necessary to implement x C satisfy the equality in (2) or (6) y C j u j q u j x C, j C, j i, and y C k 0, k / C. The utility W j ( x C ) for each member j of the proto-coalition other than the formateur is thus (7) W j x C U j x C,y C u j q. The utility of the formateur i is (8) W i x C U i x C,y C u j x C u j q Y. j C j i C

11 ELECTIONS, GOVERNMENTS, AND PARLIAMENTS 943 Finally, if C {i, j}, the utility of the out party k is while if C {i}, W k x ij U k x C,y C u k x ij, W k z i u k z i. In equilibrium the formateur makes a policy compromise to its government partner(s) in exchange for office-holding benefits, so y j C can be negative. Given the formateur s strong bargaining position, it captures all the rents associated with adopting x C. With counteroffers by the other parties, office-holding benefits may be transferred in either direction depending on the bargaining process and the status quo. Examples are considered in Appendix 1. B. Proto-Coalition Selection: Government Formation in Minority Parliaments Equation (8) identifies the formateur s utility for each protocoalition, so the choice of a proto-coalition is a straightforward maximization problem. The formateur s choice depends on the number of parties represented in parliament and whether some party commands a majority of seats. If no party commands a majority, we say the parliament is minority. This case is analyzed first. In a minority parliament the formateur may either select one of the other parties to form a minimal winning government or may form a consensus government that includes all three parties. We first show which of the minimal winning coalitions a formateur would select and then characterize the conditions under which it would choose a minimal winning government. PROPOSITION 1. In a minority parliament with three parties with ideal points located at the vertices of an equilateral triangle, if the formateur i forms a minimal winning government, it is with the party whose ideal point is farther from the status quo q; i.e., with party j if and only if u j (q) u k (q), j,k i, and is indifferent between the two other parties if u j (q) u k (q). Proof of Proposition 1. From (8) the difference in the utilities W i ( x il ) of the formateur i for governments C {i, l} with parties l j,k is

12 944 QUARTERLY JOURNAL OF ECONOMICS FIGURE II Symmetric Configuration of Party Preferences and Government Policies N.B. z 1 (0,0); z 2 (1,0); z 3 ( 1 2, 3 2). W i x ij W i x ik u i x ij u j x ij u j q u i x ik u k x ik u k q. By symmetry, u i ( x ij ) u i ( x ik ) and u j ( x ij ) u k ( x ik ), which implies that W i x ij W i x ik u k q u j q. QED Proposition 1 has a simple graphical interpretation. Consider without loss of generality the case in which the parties ideal points are normalized at z 1 (0,0), z 2 (1,0), and z 3 ( 1 2, 3 2), as illustrated in Figure II. Let the policy space be divided into six regions Q j, j I,...,VI, given by the intersections of the half spaces defined by the lines through the ideal points and the centroid z of the triangle. For example, Q I {(q 1,q 2 ) R 2 q ( z 1 1 z 1 2 ), q 2 z (q 1 z 1 1 )}. As illustrated in Figure II, the policies x ij are on the side opposite the status quo

13 ELECTIONS, GOVERNMENTS, AND PARLIAMENTS 945 of the lines through the out party k s ideal policy and the centroid z. As an example consider a status quo in Q VI, as illustrated in Figure II. If party 1 is the formateur, it forms a coalition with party 2, since party 2 is farther from the status quo and thus has the stronger incentive to forgo office-holding benefits in exchange for policy concessions by the formateur. Similarly, party 2 would select party 3, while party 3 would select party 2. The formateur thus prefers to form a government with a policy that is on the opposite side of the Pareto set from the status quo. This results because the formateur seeks the best bargain, and that bargain is obtained with the party that is in the weaker bargaining position, i.e., the party that is disadvantaged by the status quo. Intuitively, the formateur prefers to form a government with the party that would be worst off if no new government formed and the status quo persisted. For example, if an incumbent party were selected as formateur, it would prefer to form a government with the party that was previously in the opposition. As another example, Strom [1990, p. 218] indicates that in 1935 the Labor party in Norway assumed power for the first time by forming a government with the Agrarians, who were in a weak position because the agricultural sector had been hit hard by the depression. If the status quo is on one of the bisecting lines, the formateur is indifferent between the two minimal winning coalitions. For example, if party 3 is the formateur and q Q I Q II,itmay form a government with party 1 at policy x 13 or with party 2 at policy x 23. Note that for a status quo not on a line through the centroid and an ideal point only two government policies are possible. In the example depicted in Figure II, these are x 12 and x 23. Note also that the party closest to the status quo (here party 1) is disadvantaged with respect to proto-coalition selection, since it is only included in a government if it is the formateur. But conditional on being selected as the formateur, party 1 is advantaged, since its possible coalition partners have stronger preferences for a policy change from the status quo and hence are willing to exchange more office-holding benefits with the formateur. Since we consider an even number of voters under proportional representation, it is possible that only two parties are represented in parliament, neither of which has a majority of seats. This is the case if one of the parties fails to win at least M votes and the remaining two parties split the available seats. In

14 946 QUARTERLY JOURNAL OF ECONOMICS this case the formateur party i forms a government with the other represented party j with government policy x ij. A consensus government includes all three parties, and hence from (4) the government policy is centrist; i.e., the centroid z of the Pareto set. A consensus government is attractive when both government partners seek substantial policy changes from the status quo and make office-holding concessions to the formateur to obtain those changes. If party 1 is the formateur and forms a consensus government, its utility W 1 ( z ) is (9) W 1 z u 1 z u 2 z u 3 z Y u 2 q u 3 q 3u 1 z Y u 2 q u 3 q, where the second equality follows from symmetry. If party 1 forms a minimal winning government and q Q I Q II Q III, by Proposition 1, it is with party 3; and its utility W 1 ( x 13 ) is, using symmetry, W 1 x 13 u 1 x 13 u 3 x 13 Y u 3 q 2u 1 x 13 Y u 3 q. Party 1 prefers to form a consensus government rather than a minimal winning government with 3 if and only if (10) W 1 z W 1 x 13 3u 1 z 2u 1 x 13 u 2 q 0. Consequently, if the out party 2 is quite disadvantaged by the status quo (i.e., u 2 (q) is very negative), party 1 prefers to form a consensus government to obtain office-holding concessions from party 2 as well as from party 3. To be more explicit, consider the case in which the parties ideal points are normalized as above. The condition in (10) then is (11) W 1 z W 1 x u 2 q 0, which defines a disk D 2 {q 1 2 u 2 (q)} with center at z 2 and radius 1 2 such that for q D 2 (Q I Q II Q III ) party 1 prefers to form a minimal winning government with party 3, and for q (D 2 ) c (Q I Q II Q III ), where c denotes complement, party 1 prefers to form a consensus government. That is, if the status quo q is sufficiently distant from party 3 (i.e., q Q I Q II Q III ) and from party 2 (q D 2 ), i.e., q D 2 D 3, both of the other two parties are in weak bargaining positions. Both seek substantial changes in the status quo and are willing to make office-holding concessions to obtain the more favorable

15 ELECTIONS, GOVERNMENTS, AND PARLIAMENTS 947 FIGURE III Minimal Winning and Consensus Governments D 1 D 2 D 3 f consensus government by each formateur q / q D 1 and q / D 2 D 3 f consensus government by party 1 policy z. 15 Analogous conditions identify status quos such that parties 2 and 3 form consensus governments if selected as the formateur. Finally, if the status quo is equidistant from parties 1 and2(q Q I Q II ), party 3 is indifferent between forming minimal winning governments with party 1 or 2. Then, for q (D 12 ) c (Q I Q II ), where D 12 is a disk with radius 1 2 and center at ( 1 2,0), party 3 forms a consensus government. As illustrated in Figure III, consensus governments result only when the status quo is extreme. For q / D 1 D 2 D 3, each party forms a consensus government if selected as the formateur. To illustrate this, consider a status quo q on the line from z 3 through the centroid z as illustrated in Figure III. If q is more than a distance of 1 2 from the Pareto set, each of the three parties forms a consensus govern- 15. Similarly, if q Q IV Q V Q VI and q / D 3 {q 1 2 u 3 (q)}, party 1 as formateur prefers to form a consensus government.

16 948 QUARTERLY JOURNAL OF ECONOMICS ment if selected as the formateur. The results for minority parliaments are summarized in the following proposition. PROPOSITION 2. In a three-party minority parliament, the formateur i forms a consensus government rather than a minimal winning government with party j only if both the other parties are substantially disadvantaged by the status quo. If q / D 1 D 2 D 3, all three parties form consensus governments. Consensus governments choose centrist policies. Figure III summarizes the types of governments that form in three-party minority parliaments. Intuitively, consensus governments are most likely to form if the status quo is bad for many parties, as when the country faces an economic or security crisis. This is consistent with the literature indicating that national unity governments are most likely to form in these circumstances [Laver and Schofield 1990]. For example, several national unity governments were formed in Europe in the immediate postwar period. C. Proto-Coalition Selection: Government Formation in Majority Parliaments In a three-party parliament a majority party may form one of three types of governments surplus (with one other party), consensus (with both of the other parties), or single-party, in which case the policy is at its ideal point. If party 1 has a majority and forms a single-party government, its utility is W 1 ( z 1 ) Y. Ifit forms a consensus government with policy z, its utility is W 1 ( z ) 1 Y u 2 (q) u 3 (q). If q / D 2 D 3, then u j (q) 1 2, j 2,3, so W 1 ( z ) W 1 ( z 1 ). When q / D 2 D 3, majority party 1 thus forms a consensus government with policy z. The intuition is the same as above. Both of the other parties are disadvantaged by the status quo and thus in weak bargaining positions, so they provide office-holding benefits to obtain policy concessions from the formateur. If q D 2 D 3, the majority party 1 forms a surplus or a single-party government. By the same arguments as in Proposition 1, a surplus government would be formed with the party that is the more disadvantaged by the status quo. Let that be party 3; i.e., q Q I Q II Q III. Then, using (8), W 1 z 1 W 1 x u 3 q.

17 ELECTIONS, GOVERNMENTS, AND PARLIAMENTS 949 FIGURE IV Government Formation if Party 1 has a Majority of Seats Consequently, if q / D 3, the majority party 1 forms a surplus government rather than a single-party government. 16 The analysis is analogous for the case of two-party and single-party parliaments. Proposition 3 summarizes the results, and Figure IV illustrates the results. PROPOSITION 3. Suppose that party 1 has a majority of seats in parliament. (A) In a three-party parliament, party 1 forms (1) a consensus government with centrist policy z if and only if q / D 2 D 3, (2) for q D 2 D 3 and q / D 2 D 3 a surplus government with policy x 1 j with the party j that is the more disadvantaged by the status quo provided that q / D j, and (3) for q D 2 D 3 a single-party government with policy at its ideal point. (B) In a two-party ({1,2}) parliament, majority party 1 (a) forms a single-party government with policy z 1 if 16. If potential government partners cannot make office-holding concessions to the formateur in exchange for policy concessions, surplus governments do not form.

18 950 QUARTERLY JOURNAL OF ECONOMICS q D 2, and (b) forms a surplus government with policy x 12 if q / D 2. (C) If party i is the only party in parliament, the policy is z i. D. Robustness This subsection addresses the robustness of the results for minimal winning governments with regard to asymmetric preference configurations, different intensities of policy preferences, and an alternative government formation process. The supporting analysis is presented in Appendix 1. Only three-party minority parliaments are considered. If ideal points are not symmetrically located as in Figure II, both the status quo and the degree of preference alignment among the parties affect which governments form and the policies they choose. In a three-party parliament if two parties are equally distant from the status quo, the other party as formateur forms a government with the party with which its preferences are better aligned. This is reminiscent of the concept of connected parties in a unidimensional policy space [Axelrod 1970]. The theory presented here modifies this intuition by taking into account the bargaining positions of the parties as determined by the status quo. Governments thus are formed by parties with aligned preferences unless a party with more extreme policy preferences is particularly disadvantaged by the status quo. An extreme party thus is not an attractive government partner unless it is in a weak bargaining position and hence is willing to provide substantial office-holding benefits in exchange for policy concessions. The specification of policy preferences in (1) implies that parties have the same intensity of preferences for each policy dimension. If policy intensities differed among parties and between policy dimensions, the policies chosen by a government would differ from those in (4) and the sets of status quos that give rise to particular governments would change. The basic intuition remains unchanged, however. Suppose that party 2 had a greater preference intensity for the policy represented by dimension 1 than by dimension 2. Then, if party 1 were to form a government with party 2, the policy on dimension 1 would be closer to the ideal point of party 2 than to the ideal point of party 1. Also, party 2 would be a less attractive government partner if it had a greater policy intensity than party 3, as indicated in Appendix 1. The basic model incorporates one round of bargaining over government formation. Government formation, however, could

19 ELECTIONS, GOVERNMENTS, AND PARLIAMENTS 951 involve multiple rounds of formation attempts or sequential proto-coalition bargaining where, for example, each party in a proto-coalition is selected to make a bargaining proposal with probability equal to its seat share. As noted above, this does not affect the policies the resulting government would choose, but it does affect the allocation of office-holding benefits and which governments form. Thus, the regions identified in Figures III and IV would have different shapes. The basic intuition about which governments form remains unchanged, however. The government is formed with the other party that is the more disadvantaged by continuing to a subsequent round of government formation attempts. Moreover, multiple rounds of government formation increase the reservation values of the potential government partners, and hence the formateur may make office-holding concessions to the government partner. IV. ELECTORAL EQUILIBRIA Since parties are unable to commit credibly to the policies they will implement, voters electoral preferences are derived from the policies governments would choose and which governments would form as a function of the selection of the formateur. Parties are thus instrumental, and from the point of view of voters represent different bargaining positions in parliament. Voters can influence the policy outcome in three ways. First, they may be representation pivotal. That is, their votes determine which parties are represented in the legislature. Second, they may be coalition pivotal; i.e., their votes determine the set of decisive coalitions in parliament. For instance, an additional vote for party j may give it a majority of seats. Finally, voters may be selection pivotal. If no party commands a majority of seats, an additional vote for party j increases the likelihood that j is selected as the formateur. Electoral games commonly have many Nash equilibria. In our model for a given q, there can be a continuum of Nash equilibria, but these equilibria always yield a unique strong Nash equilibrium outcome. That is, there is a unique policy, or a lottery over policies, that is robust to deviations by groups of voters. Moreover, the set of Nash equilibria that support an outcome can be characterized. The outcome of the electoral stage is summarized in the following proposition, which is proved in Appendix 2.

20 952 QUARTERLY JOURNAL OF ECONOMICS PROPOSITION 4. (A) Given q, if there is exactly one party j that as formateur would form a consensus government, every strong electoral equilibrium leads to a majority parliament with three parties represented, where the majority party j forms a consensus government with policy z. (B) Given q, if no party as formateur would form a consensus government, all strong electoral equilibria result in a minority parliament and an even lottery over some pair ( x ik, x ij ), (j k i), of policies in (5) as the unique equilibrium outcome. (C) Given q, if all parties would form a consensus government, election of any three-party parliament is a strong electoral equilibrium with policy z. (D) (1) If party i as formateur would randomize between x ij and x ik and the other two parties would form governments with party i; e.g., i 3 and q Q I Q II D 1 D 2, a minority parliament results and the unique strong electoral equilibrium yields i m, equal vote shares for the other two parties, and policy outcomes x ij and x ik with probability one-half. (2) If party i as formateur would randomize between x ij and x ik and the other two parties would form governments with each other; e.g., i 3 and q Q V Q VI D 1 D 2, a minority parliament results with a strong electoral equilibrium with vote shares i 4 9 and m l 1 2, l j, k, and j k 5 9, resulting in unique equilibrium policy outcomes x ij and x ik with probability 2 9 and x kj with probability 5 9. The electoral equilibria have the following properties and interpretations. First, some voters do not vote sincerely, i.e., for the party with the closest ideal point. Figure V illustrates the voting equilibrium for Proposition 4 (B) and indicates that some voters near the ideal point of party 3 vote for party 1. This results because voters care about policy and not about parties per se. Representation in parliament thus does not reflect the distribution of preferences in the electorate. 17 Second, in minority parliaments all voters are selection pivotal, but they are not necessarily representation pivotal. Third, the equilibrium vote shares of the parties depend on the status quo because the subsequent government coalitions, and hence policies, depend on the status quo. Since voters have 17. Austen-Smith and Banks [1988] reach the same conclusion for the equilibrium they study.

21 ELECTIONS, GOVERNMENTS, AND PARLIAMENTS 953 FIGURE V Example of Electoral Equilibrium with Representation Threshold m preferences over policies, their voting strategies depend on the status quo as well. There is thus a mapping from the status quo to election outcomes and to governments and their policies. Fourth, depending on the status quo either minority or majority parliaments may result. Fifth, the only policies implemented by a government are { z, x 12, x 13, x 23 }. Sixth, all three parties are represented in parliament. Seventh, the party closest to the status quo is overrepresented in parliament unless all parties would form a consensus government policy z. Depending on the location of the status quo, it will either be a majority party or in minority parliaments have the largest seat share. But this does not mean that policy outcomes are biased toward the largest party. A majority party, for instance, forms a consensus government with a policy at the centroid of voters preferences. Indeed, voters overrepresent the party closest to the status quo precisely because it has no incentive to exploit its seat share advantage in the government formation process. To illustrate the strategies that constitute a strong Nash equilibrium, consider a status quo such that in a minority parliament each party would form a minimal winning government,

22 954 QUARTERLY JOURNAL OF ECONOMICS TABLE I EQUILIBRIA FOR A THREE-PARTY MINORITY PARLIAMENT AND MINIMAL WINNING GOVERNMENTS Status Quo Vote shares Party 1 Party 2 Party 3 q Q I 1 2 o 1 2 o q Q II o o q Q III 1 2 o 1 2 o q Q IV 1 2 o o 1 2 q Q V o 1 2 o 1 2 q Q VI o o N.B. 1 2 m o m. with party 1 choosing x 12 and parties 2 and 3 choosing x 23. Then, as indicated in Figure V, N/ 2 voters with z vote for party 1 with probability one, M voters with z vote for parties 2 and 3 with probability one, and the remaining voters with z randomize among parties 2 and 3. That is, if party 1 has half the votes, the other two parties have vote shares o and 1 2 o, where 1 2 m o m. The seat (and vote) shares are summarized in Table I. As indicated in Table I, the parties disadvantaged by the status quo are also disadvantaged in the election and receive the lowest vote shares. Comparing Figure IV and Table I indicates that one of the parties disadvantaged by the status quo is in the government. That is, a party that is in a weak bargaining position is an attractive government partner, as established in Proposition Similarly, comparing Table I with Figure II, the party nearest the status quo receives half the vote. Voters overrepresent the party advantaged by the status quo because as shown in Proposition 1 it is not an attractive government partner for either of the other two parties. The only way voters can obtain a policy on that party s contract curve is if it is selected as formateur. Voters thus balance the possible government policies by increasing that party s vote share. For example, if q Q I, parties 2 and 3 form 18. Austen-Smith and Banks [1988] also obtain this result. In this model, it is due to the bargaining position determined by the status quo, whereas in their model it is because the smallest party can be the formateur only if the other two parties fail to form a government.

23 ELECTIONS, GOVERNMENTS, AND PARLIAMENTS 955 governments with each other with policy x 23, and party 1 forms a government with party 2 with policy x 12. To balance these two possible policy outcomes, voters give party 1 half the vote. Electoral equilibria are thus both balancing and centering. The electoral equilibria also generate what may be interpreted as implicit pre-election coalitions. That is, for status quos that lead to minimal winning governments, two parties form a government with each other when one is selected as formateur. This pre-election coalition, however, is due to government formation incentives rather than to a pre-election commitment. In our model, voters anticipate the formation of this implicit pre-election coalition and balance the election outcome to give it only half the votes. Laver and Schofield [1990, pp. 25, 28] give examples of pre-election coalitions in Ireland, The Netherlands, Portugal, and the United Kingdom. The coalition between the CDS and the PSD in Portugal developed into both a government and a policy coalition. V. EXOGENOUS DYNAMICS The distribution of government policies in electoral equilibria is fully determined by the status quo. For extreme status quos this distribution is degenerate: the centroid of voter preferences is chosen with probability one. For less extreme status quos there is an even lottery over two policies. This defines a natural dynamic of policy change, where the current government s policy determines next period s status quo. Table I can then be used to determine the next electoral equilibrium and vote shares. Proposition 4 thus implies the following corollary. COROLLARY. If parties and voters only care about the current period s payoff, then for all periods after the first: (A) There are only minority parliaments with all parties represented. (B) Only minimal winning governments form. (C) All realized government policies are of the form given in (5). (D) Government policy changes every period. To see this, recall from Proposition 4 that regardless of where the status quo is located at the beginning of the first period, the government implements a policy x ij or z. For whichever is the status quo for the next period a minority parliament results in all future periods, and the governments are minimal winning with policies x ij given in (5). This follows directly from Table I. Note

24 956 QUARTERLY JOURNAL OF ECONOMICS that implication (D) should not be interpreted too literally. It follows from the fact in our frictionless model any government can (without delay or distortion) implement the most efficient policy. A more realistic model would incorporate exogenous shocks to the status quo, for instance due to fluctuations in the economic environment. Consider the case in which the shocks follow a distribution that is unimodal around the chosen government policy. The random draws of realized status quos then generate a stochastic process and a distribution over electoral outcomes and government policies. For example, if in Figure IV the status quo q is drawn such that q / D 2 D 3 and q D 1, parties 2 and 3 would form a minimal winning government with policy x 23 and party 1 would form a government with policy z. Then, from Proposition 4 party 1 receives a majority in the electoral equilibrium. Majority parliaments thus can result from shocks to the status quo. However, the Corollary implies that they occur only after a large shock, such as an economic or security crisis. Similarly, a large shock can result in a consensus government. The modal case is a minority parliament with a minimal winning government and policy that reflects the preferences only of the government parties. These results are derived under the assumption that parties and voters do not take into account the future consequences of their current actions. Strategic dynamics, as in Alesina and Tabellini [1990], is the subject of future research. VI. CONCLUSIONS Models of parliamentary systems that incorporate proportional representation elections, government formation, and policy choices are necessarily complex. We provide a relatively tractable model based on efficient coalition bargaining and formateurs selected in proportion to seat share. This allows a simple characterization of government formation and policy choice in a twodimensional spatial model. Moreover, we find unique strong equilibrium outcomes in the electoral stage. The tractability of the model allows it to be used as a component of a theory of the dynamics of parliamentary systems. In this paper we investigate the dynamics of policy choice and government formation in a multielection setting where parties and voters care only about the current period payoffs. In this case, the equilibria characterized for the single-period model identify the