Comparative Politics with Endogenous Intra-Party Discipline 1

Transcription

1 Comparative Politics with Endogenous Intra-Party Discipline 1 July 2009 Comments welcome. Micael Castanheira ECARES, Université Libre de Bruxelles and Benoit S Y Crutzen Erasmus Universiteit Rotterdam Abstract: Party discipline is known to be quite di erent in Parliamentary and in Presidential democracies. Yet, the theoretical literature is silent about why parties should adopt such di erent structures. We propose a setup where parties are brands. In our model, parties strategically and publicly choose their internal discipline and their ideological position. In doing so, they trade o revealing information about their candidates preferences against reducing their legislative freedom. In contrast, independent candidates have no party ties and full legislative freedom. Our results show that parties never choose intermediate levels of discipline. In a system where some legislative discipline is valuable in parliamentary regimes parties prefer maximal discipline. By contrast, minimal discipline is optimal in presidential regimes, provided that voters preferences are su ciently heterogeneous. The model s ndings rationalize the historical evidence that suggest that intraparty discipline increased and remained high after the introduction of major reforms in parliamentary regimes and the American dance between polarization and inequality observed in at least the last hundred years. Keywords: intra-party discipline, parties as a brand, political regime, polarization 1 We are grateful to Enriqueta Aragonés, Laurent Bouton, Steve Callander, Catherine Dehon, John Ferejohn, Norman Scho eld, Simon Hix, Andrea Mattozzi, Antonio Merlo, Abdul Noury, Gérard Roland, Otto Swank and Barry Weingast for insightful discussions. The comments from the audiences in Barcelona (Autonoma), Brussels (ECARES), Milan (DEFAP and ESEM2008), Namur (FUNDP-PAI), New Orleans (Public Choice Society), Paris (Conference on Changing institutions), Rotterdam (ERASMUS Universiteit), Stanford, UPenn and WZB Berlin were also particularly helpful. The usual disclaimer applies. 1

2 1 Introduction In Parliamentary democracies, political parties have gradually increased and then maintained high levels of internal discipline, with legislators sticking closely to their party leader s proposals. Cox (1987) documents this evolution for Victorian England and Wilson and Wiste (1976) and Huber (1996a) document it for France in the years between the Third and the Fifth Republic. To the contrary, in the US, intraparty discipline has always been loose and reforms typically reinforced candidate freedom. For example, the introduction of direct primaries in basically all US States between 1899 and 1915 did away with the parties hold on the selection of Congressional candidates. 2 More recent reforms have not reduced these di erences. Thus, it is not surprising that dissent between legislators and their leader is the exception rather the rule within the main British parties (Kam 2009, p. 10) whereas discipline is so low in the main two US parties, which are typically described as empty vessels (Katz and Kolodny (1994, p1). More importantly, the above facts suggest that party discipline is endogenous to the political regime. Why and how does intraparty discipline adapt to the political regime? Does it matter for policy, for example through the choice of party platforms? This paper puts forward a model to give a rst answer to these questions. We propose an electoral game in which parties are organizations that compete for seats in the legislature. They rely on district-speci c candidates, each running for a seat. 4 We focus on a universal function of political parties: they provide informational shortcuts to voters about the preferred policy of their candidates, through the strategic and publicly observed choice of both their ideologic platform (Downs 1957) and their level of internal discipline (Cox and McCubbins 199, Snyder and Ting 2002). Full intraparty discipline perfectly informs voters about the preferences of party candidates: these can no longer deviate from the party platform. Otherwise, the set of preferred policy choices of the candidates of a party is a cloud around the party platform, which leaves voters uncertain about future policy decisions. Intraparty discipline thus introduces a certainty-versus- exibility trade-o : if party discipline is high, the message sent to voters is very precise but party candidates cannot pander to the local electorate. If discipline is low, voters know that individual candidates can cater to the 2 Direct primaries are actually run for all public o ces but that of the President. An outstanding account of their introduction is Ware (2002). The view that dissent in British parties is the exception rather than the rule has not been dented by the episodes of backbench rebellion that received a lot of attention in the media in the last three decades. For example, Kam (2009, p10) con rms that [t]he vast majority of the time, parliamentary parties are highly cohesive [...]. 4 We thus concentrate on elections that are run under plurality rule in single-member districts. 2

3 preferences of their local constituencies, but the informational content of the party label is relatively limited. Voters can also vote for a local independent who is not bound to any national platform but whose preferred policy is highly uncertain. The institutions of Parliamentarism and Presidentialism are introduced in the model as a constraint on the feasible levels of party discipline. That is, we simply incorporate the ndings of Huber (1996b) and Diermeier and Feddersen (1998) in assuming that the minimal level of intraparty discipline needed to operate in a parliamentary system is high, whereas the one needed in a presidential regime is low. Turning to our results, we nd that districts close to the party platform value discipline because it makes the party platform more certain. Instead, distant districts dislike discipline because it ensures that implemented policies will be distant from their bliss point. A remarkable consequence is that intermediate levels of discipline are never chosen: it is always optimal for the party to choose either maximum or minimum discipline. Which level of intraparty discipline do parties choose in equilibrium? In a parliamentary system, parties are induced to target close districts. Hence, maximum discipline is a dominant strategy. By contrast, in a presidential regime, the party s optimal strategy is typically to target distant districts. Maximal candidate freedom is then preferred. Our analysis thus identi es a multiplier e ect of institutions: party leaders have an incentive to switch from low to high discipline when institutional changes are such that the minimal level of discipline associated with these institutions increases beyond a certain threshold. Thus, if discipline adapts to the political regime, it is through the decisions of parties, and not simply because of the constraint political institutions introduce. In Sections and 7.1., we show that this party channel is fully consistent with the historical reports of Cox (1987), Wilson and Wiste (1976) and Huber (1996a) on the evolution of intraparty discipline in England and France. How does party discipline a ect policy? We show that the parties incentive to locate close or far from the median district depends on the heterogeneity of voter preferences. To win centrist districts, parties need to abandon non-centrist districts to independent candidates. With high heterogeneity, non-centrist districts are relatively numerous and parties thus polarize. Conversely, with low heterogeneity, parties locate at the national median, because most districts are centrist. These results provide a rationale for the empirical ndings of McCarty, Poole and Rosenthal (2006) that we review in Section 7.2: polarization between the two major US parties correlates strongly with income inequality. The rest of the paper is organized as follows. Section 2 reviews some of the existing literature.

4 Section lays out the model. Sections 4 identi es the e ects of party discipline on electoral success, while Sections 5 and 6 solve for the equilibrium of the game in terms of intraparty discipline and platform positions. Section 7 discusses how our ndings shed light on a number of stylized observations. Section 8 discusses some extensions of the model and, nally, the last section concludes. Most proofs are relegated to the Appendix. 2 Related Literature Two key ingredients in our model are the screening technology of parties and the constraints on legislators freedom of action imposed by institutions. We borrow the screening technology of parties from Snyder and Ting (2002). They show how candidate selection allows party labels to become brand names that are valued by voters. In their model, candidates are not districtspeci c and platforms will typically be median unless the party brand signal is very weak. We go beyond Snyder and Ting (2002) in endogenizing the level of intraparty discipline, in letting candidates be district-speci c and in comparing party organizations across political regimes. Close to both Snyder and Ting (2002) and this paper, Eyster and Kittsteiner (2007) show that parties may adopt extreme positions to reduce interparty competition. Yet, party structures are still exogenous in their setup. Conversely, Ashworth and Bueno de Mesquita (2008) focus on how incumbent party members decide about the breadth of admissible party policies, that is, intraparty discipline. In their model, party platforms are exogenous and there are no independents. Thus, they abstract from the link between party structures and polarization. Turning to the role of institutions, we build on Huber (1996b) and Diermeier and Feddersen (1998). Huber (1996b) proposes a model rationalizing how institutions such as the vote of con dence procedure lead to high intraparty discipline in parliamentary democracies. Yet, the focus of his analysis is on the bargaining game between the Prime Minister and the exogenously given supporting majority in Parliament. He does not analyze how the characteristics of the electorate shape the supporting majority in parliament, intraparty discipline or polarization. Diermeier and Feddersen (1998) propose a model that rationalizes di erences in cohesion between individual legislators across parliamentary and presidential regimes. Yet, while the authors analyze how di erent political regimes impact on legislative cohesion, their model abstracts from the role of parties: these are simply absent from the analysis. We introduce parties explicitly and study the incentives for party leaders to impose discipline and to polarize national party platforms, both as a function of the political regime and of the socioeconomic characteristics of the electorate. 4

5 Building on Palfrey s (1989) sincere voting setup, Callander (2005) introduces multiple districts and rationalizes the positive correlation between the polarization of national party platforms and inter-district heterogeneity. Yet, parties are represented as a point on the real line. Thus, we cannot use his model to rationalize the evidence put forth by McCarty et al. (2006), given that the measures McCarty et al. use build on the heterogeneous behavior of individual legislators within and between parties. Finally, our paper contributes to the growing literature on comparative politics. One common element in this eld is the marginalization of the role of parties and their internal organization. 5 For example, in Persson, Roland and Tabellini (2000), all players are unitary actors no clear distinction is made between parties and their candidates even though, through the assumptions made on the alignment of preferences between the executive and the legislative under a parliamentary and a presidential regime, they recognize that intraparty discipline is high in the former but low in the latter regime. To drive home our point on the importance of di erences in intraparty discipline under di erent political regimes, imagine what would happen in a parliamentary democracy if the executive could not rely on a disciplined (enough) majority in the legislature. Similarly, in a US-type presidential system, the checks and balances between the executive and the legislature would lose their e ectiveness if the President could impose his will on Congress because of intraparty discipline. Katz and Mair (1992 and 1994) do focus on parties. They compare party organization in 12 Western democracies and show that it correlates with the political regime. Our model rationalizes their ndings and extends them to show how the polity s socioeconomic characteristics correlate with party structures. The Model We propose a model to investigate how political parties jointly select their ideology and their internal discipline, given the economic and social environment. The policy space is unidimensional and represented by the real line. Following Snyder and Ting (2002), we model parties as brand names: the policy of a given candidate is uncertain, and party discipline can reduce that uncertainty. Our focus is thus on an electoral game with three types of players: voters, candidates and parties, where parties are the main character of interest. 5 See for example Persson, Roland and Tabellini (1997 and 2000), Persson and Tabellini (1999, 2000, 200, 2004a and 2004b), Lizzeri and Persico (2001), Milesi-Feretti, Perotti and Rostagno (2002), Persson, Tabellini and Trebbi (200), and Acemoglu and Robinson (2006). 5

6 The Legislature. The economy is divided into a continuum of districts, each electing one legislator under plurality rule. Once elected, each legislator controls a fraction of the decisions that are taken during the legislature, and implements her preferred policy. 6 This fraction is the same for party members and independents. 7 Voters. The median voter of district i is always pivotal and has bliss policy y i 2 R. Her preferences are single-peaked and quadratic. 8 She votes for the candidate that o ers her the highest expected utility, given her beliefs about the preferred policy of the candidates running in her district. That is, she votes for the candidate that maximizes: h E [u (y i ; x c )] = E (y i x c ) 2i ; where E is the expectation operator on x c 2 R, the preferred policy of candidate c. Candidates. Each candidate s preferred policy position x c is private information. It is common knowledge that x c is a realization from the uniform distribution on Y i [y i 1; y i + 1], which is district-speci c. 9 This is meant to capture the fact that in many democracies candidates must reside in the district in which they run. 10 information about his preferred policy. Parties. Alone, a candidate cannot reveal additional By being the only agent that can produce additional information about candidate preferences, parties intermediate between the voters demand for and the candidates supply of policies. The standard Downsian approach assumes that a party policy can be represented by a point on the real line. We extend that approach by letting parties de ne a range of admissible policies: they admit candidates with preferences distant up to P from the party platform. 6 One should read this assumption di erently when thinking about parliamentary systems: the random component is then about who, out of the elected representatives, will be selected as a cabinet member, with powers to set his preferred policy on the issues that fall within in his portfolio. 7 Giving more decision powers to party members would not alter the main insights of the model, as long as independents retain some decision making powers. 8 This parametric form of the utility function is only useful to obtain tractable closed-form solutions. See Section 8 for a generalization. 9 Again, we use the uniform distribution only to obtain tractable closed-form solutions. See Section 8 for a generalization. 10 There are two di erences with citizen candidate models: rst, candidate entry is not strategic as in Besley and Coate (1997) and Osborne and Slivinski (1996). Second, there is information asymmetry between voters and candidates. In the framework of citizen candidate models, the impact of information asymmetries is studied among others by Casamata and Sand-Zantman (2008) and Großer and Palfrey (2008). These papers however abstract from the role of political parties. 6

7 Thus, the platform of party P 2 fl; Rg is de ned by two variables: an ideological position x P and the party candidates freedom of action, P. These two dimensions of party policy are chosen strategically and they are publicly observed by the voters. Thus, any voter knows that a candidate running under the banner of party P must have preferences x c in the range: x c 2 X P [x P P ; x P + P ] : (1) Timing. We consider the following timing: 11 At time 1, party leaders L and R select their national platforms: x L and x R. At time 2, party leaders select intraparty discipline: L and R, and candidates are assigned to parties. At time, each district median elects his preferred candidate, and payo s realize. Institutional and economic environment. We introduce two parameters that de ne the country s institutional and socioeconomic environment. The country s institutional environment is summarized by its level of legislative cohesion and the socioeconomic environment by the heterogeneity of voter preferences, ; which represents ideologic preferences and economic inequality in the country. Legislative cohesion is known to vary substantially across political regimes; it is typically higher when government survival depends on legislative support; see for example Huber (1996b) and Diermeier and Feddersen (1998). Given that these two contributions focus on how institutions shape cohesion among individual legislators independently of party discipline, 12 we can use in our model to identify how a group of legislators would behave in the absence of party discipline. Formally: Assumption 1 Institutional constraints determine the discipline feasibility set of the parties, identi ed by the parameter 2 (0; 1). This parameter represents the minimal level of legislative cohesion: candidate freedom can be further restricted by party discipline: P 2 [0; ]. 11 Reversing the timing between periods 1 and 2 produces the same results. 12 Diermeier and Feddersen (1998, p611), for instance, look for an institutional explanation for voting cohesion that relies on the incentives created by the characteristic features of parliamentary constitutions. Our focus is instead on why parties organize the way they do in di erent environments. Huber (1996b) deals with parliamentary systems only and in his model the size and characteristics of the coalition supporting the executive is exogenously given. In contrast, our model is centred on the endogeneity of the characteristics of this supporting majority. 7

8 From Huber (1996b) and Diermeier and Feddersen (1998) among others, we know that is smaller in UK-type of parliamentary regimes than in US-type of presidential regimes. We will thus associate low values of to parliamentary regimes and high values to presidential regimes. 1 Finally, party discipline constrains candidate selection in all districts only if P is smaller than 1. It is thus natural to focus on values of below 1. Turning to the economic environment, McCarty, Poole and Rosenthal (2006, chp) show that economic inequality typically maps into more polarized voter preferences. 14 Castanheira et al (2010) also illustrate that inequality in the US is associated with increased income dispersion across States, probably because inequality favors the clustering into rich and poor districts. We capture these stylized facts with the following assumption: Assumption 2 The distribution of district medians y i is a centered Normal with variance 2 : f (y i ) = exp yi 2 p = 22 ; 2 2 where represents preference heterogeneity across districts. In the next three sections, we solve for the perfect Bayesian equilibrium of the game in terms of intraparty discipline and party platforms. 4 How Does Discipline Impact on Voting? (time ) Three sets of candidates can run in each district: (1) independent candidates, who are not a liated with any party; (2) candidates a liated with party L and () candidates a liated with party R: Since voters cannot observe candidate preferences directly, all candidates within one of these sets are identical in the eyes of the voters. The district median s expected utility from electing any local independent is: Eu (y i ; x c jx c 2 Y i ) = E xc2y i h (y i x c ) 2i = (y i y i ) 2 1= = 1=: Voters have more information about party candidates: rst, given that he runs in district i, the party candidate must have preferences somewhere in Y i 2 [y i 1; y i + 1]. Second, being a party candidate, he must also have preferences somewhere in X P [x P P ; x P + P ] (see (1)). 1 For convenience, we normalized the lowest value of P to 0 across both political regimes. We discuss in Section 8 how this restriction impacts on our ndings. 14 The relationship between economic inequality and polarization is reinforced by the clustering of individuals into subgroups that are internally homogeneous. See e.g. Esteban and Ray (1994) for a conceptualization of this argument. 8

9 Thus, voters know that a candidate of party P who runs in district i has preferences uniformly distributed on the set: 15 P i (x P ; P ) Y i \ X P : It follows that the median voter s expected utility from electing a candidate of party P is: E i u (y i ; x c jx c 2 P i (x P ; P )) = (y i i [x P ; P ]) 2 2 i [x P ; P ] ; (2) where, by the properties of uniform distributions: 8 >< >: i [x P ; P ] = max [y i 1; x P P ] + min [y i + 1; x P + P ] ; 2 2 i [x P ; P ] = (max [y i 1; x P P ] min [y i + 1; x P + P ]) 2 ; 12 () The district median s decision to vote for either candidate depends on the distance between the median s bliss point y i and the platforms of the two parties. For each party, we can separate the districts into those that are close and those that are distant from the platform x P. De ne close districts as the set of districts i such that y i is within distance 1 P of x P : jy i x P j 1 P. In these districts, the party set X P is within the district set Y i. Distant districts are the set of districts further than 1 P from x P. In these districts, the set of party candidates is both a function of the district and of the party set. This is illustrated in Figure 1: x P y y y Close districts y y y Distant districts x { φ P P x + P φ P Figure 1: Set of possible platforms for party candidates. The important di erence between close and distant districts is how candidate freedom P in uences the expected position of the party candidate in the district. In close districts, this 15 If the set is empty, no candidate from party P is expected to enter. In the out-of-equilibrium case one such candidate runs, beliefs are such that the candidate s platform is the relevant boundary of Y i. 9

10 expected position is x P, independently of P. By contrast, candidate freedom does in uence the party candidates expected position in distant districts. A consequence is that close and distant district have opposite preferences regarding a (marginal) change in candidate freedom: close districts prefer more disciplined parties, whereas the opposite is true in distant districts (see Lemma 2 in the Appendix for a formal proof). When choosing how much freedom of action to grant its candidates, the party thus has to weigh the preferences of these two sets of districts against one another. Our rst proposition shows how the choice of a party structure maps into a given party catchment area, which is de ned as the set of districts that prefer the party candidate to an independent candidate (omitted proofs are in the appendix): Proposition 1 All districts y i within distance ( P ) of the party platform x P prefer the party candidate to the local independent. The catchment area of a party is therefore a compact set: E i u (y i ; x P ) E i u (y i ; x I ), jy i x P j ( P ) ; q 1 where ( P ) max 2 P ; P, has a global minimum at P min = 1=2; a local maximum at P = 0; and a global maximum at P = 1. The catchment area of a party is displayed in Figure 2. φ P x P κ(φ P ) x P + κ(φ P ) Catchment area φ P = 1/2 x P y i Figure 2: Party P s catchment area depends on its internal structure Proposition 1 and Figure 2 show how party discipline maps into electoral success. The size of the catchment area is minimal for intermediate degrees of candidate freedom and party discipline: the size of the party s catchment area, ( P ), reaches a minimum in P = 1=2. The 10

11 reason is that a party structure that generates intermediate levels of party discipline satis es neither close nor distant districts. Parties thus prefer extreme forms of organization. The intricacy is that the identity of the marginal district changes with the level of discipline. Indeed, for relatively low levels of candidate freedom, marginal districts are close. Thus, to expand its catchment area, the party bene ts from further disciplining its candidates. A local maximum is found when candidate freedom is actually reduced to 0, that is, when there is maximal party discipline. This is the bottom part of the gure. By contrast, the marginal districts are distant when party discipline is su ciently weak ( P > 1=2). These districts prefer more candidate freedom, because it allows candidates to propose policies that are closer to the district, and further from the party. The global maximum is found when there is full candidate freedom ( P = 1) we return to this point in the next section, where we examine the e ect of institutions. We wish to emphasize the fact that the party catchment area is a compact set. This contrasts with the standard assumption in two-party models of electoral competition, where there is no party alienation. In these models, the party catchment area of the left-wing party is an open set stretching from the left-most voters up to some cuto, and from this cuto to the right-most voter for the right-wing party. The reason is that traditional Downsian analyses abstract from independent candidates. By assumption any candidate belongs to one of the two parties (see also Section 7 where we introduce the possibility of entry). Proposition 1 shows that when parties must provide more valuable policies than local independents to command voter support, their catchment areas are actually bounded. This is key to the other ndings below. On a more technical note, the shape of the function is only partly in uenced by the parametric choices we made so far. The fact that is a square root for P < 1=2 results from the combination of a quadratic utility function and a uniform distribution of preferences. Yet, the fact that = P for P > 1=2 extends to generalized utility functions and (symmetric) distribution of preferences see Section 8. Indeed, for any distribution of candidate preferences symmmetric around y i, the median voter is indi erent between the party candidate and the independent when the party party candidate has his bliss policy in exactly half the support of the independent s bliss points, i.e. the set P i (x P ; P ) = [y i 1; y i ] or [y i ; y i + 1]. Thus, for any P > 1=2, the district at distance P from the party platform x P is indi erent between the party candidate and the independent, while further districts strictly prefer the independent. 11

12 5 Equilibrium discipline (time 2) At time t = 2, parties need to set their optimal level of intraparty discipline, taking as given the optimal ideological positions chosen in the previous stage. We distinguish between two cases: the rst in which institutional constraints are tight, the second in which they are loose. 5.1 Case 1: tight institutions: < 1= p We have: Proposition 2 When institutional constraints are tight ( < 1= p ), maximal party discipline is a dominant strategy for any distribution of districts and any degree of polarization. The intuition for this result is a direct consequence of the ndings of section. Suppose rst that the two party platforms are polarized to such an extend that their respective catchments areas cannot overlap. Then proposition 1 applies directly and full discipline is the optimal choice for both parties. Suppose now that the two platforms are close enough that the two catchment areas (may) overlap. Then parties compete both against each other and against independents for the centrist districts but against independents only for the districts on their respective outer sides. From Proposition 1, the level of discipline that maximizes the number of districts on the sides of the distribution is still = 0. What about the optimal strategy to attract the districts that are between the two ideologic platforms? Given that, for the two catchment areas to overlap, the party platforms cannot be further away from each other than 2 < 2= p, districts in which both parties compete are such that their medians are at most at distance 1= p from the closest party platform. Then, as is clear from gure 2, all the districts that each party can attempt to attract are close in the terminology of the previous section and value discipline. It is therefore a dominant strategy for both parties to choose full discipline. 5.2 Case 2: loose institutions: > 1= p We have: Proposition When > 1= p, If the two catchment areas do not overlap for any level of discipline, the optimal choice is maximal freedom: ( P = ) If the two catchment areas overlap for some values of P, equilibrium structures depend on the heterogeneity of voter preferences across districts,. Set = 1. Then, there exists a cuto (x) 12

13 such that parties choose full discipline ( P = 0) for < (x) and maximal freedom ( P = 1) for > (x). Propositions 2 and show how institutional constraints, ideologic polarization and the socioeconomic environment interact to determine intra-party discipline. They reveal a hierarchy of incentives: if institutional constraints are tight, parties necessarily choose full intraparty discipline, irrespective of any other consideration. If institutional constraints are lax and platforms happen to be highly polarized, parties choose to give maximal freedom to their candidates. Socioeconomic factors enter into play when institutional constraints are lax and parties are ideologically close. If voters are ideologically heterogeneous across districts, then maximal freedom dominates; loosely speaking, the mass of non-centrist districts is such that maximizing the size of the catchment area by granting candidates as much freedom as possible is the best strategy. If voters are ideologically homogeneous across districts, most districts are centrist and maximal discipline dominates. 6 Equilibrium platforms (time 1) We distinguish again between tight and loose institutional constraints. 6.1 Case 1: tight institutional constraints: < 1= p If < 1= p, we know from proposition 2 that parties necessarily enforce maximal discipline: P = 0. Therefore, at time 1, parties anticipate that their ideological location cannot in uence neither their own nor the other party s structure. The parties vote shares are (remark that x L +x R 2 = 0): We then have: V L ( L = 0; x L ; x R ) = R min[x L+ 1 p ; 0] x L 1 p df (y i ) ; V R ( R = 0; x R ; x L ) = R x R+ 1 p max[x R 1 p ; 0] df (y i) ; (4) Proposition 4 For 1= p ; parties always adopt full discipline ( P = 0) and the equilibrium pair of manifestos is: ( x L = x R =) x = 0; for 2 < 1= (6 log 2) ; = p 2 log 2 p 1=; for 2 2 [1= (6 log 2) ; 2=( log 2)] ; = 1= p ; for 2 > 2=( log 2): Hence, the median voter theorem holds only for a su ciently homogeneous polity. 1

14 Thus, the two parties choose the median voter s preferred platform only when preferences are su ciently homogeneous across districts. Otherwise, polarization increases in preference heterogeneity. Yet, there is an absolute ceiling to polarization. This stems from an endogenous alienation e ect: since voters prefer the independent candidate when the party platform becomes too distant, polarizing parties can only win seats in non-centrist districts at the expense of losing districts at the center. Conversely, moving to the center means that districts on the sides of the distribution are lost to independents. Consider the out-of-equilibrium case in which the two parties are so polarized that their catchment areas do not overlap. In that case, both lose the center to independents. Since there are more centrist than extremist districts, each could increase its seat share by moderating its platform. Thus, parties never polarize beyond the point in which they lose the center. Given that the maximal size of a party s catchment area cannot exceed 2= p ; 2= p is also the ceiling to polarization. x 1/ 0 σ 2ln 2 1/ 1/ 2 σ Figure : Polarization as function of preference heterogeneity Up to which point will the two parties converge to the center? Because centrist districts are more numerous compared to non-centrist ones, they will certainly continue to converge until their catchment areas are tangent to each other. Will they move further towards the center? If yes, then their catchment areas overlap. With an overlap, each party wins only half as many centrist districts as in the absence of an overlap: from (4), party L only wins the districts between x L 1 p and (x L + x R ) =2. Thus, for (x L + x R ) = 0, a marginal move dx L to the center costs f x L 1= p dx L seats from districts on the left side of the distribution and brings [f (0) =2] dx L (instead of f (0) dx L ) districts from the center. Thus it is only when is small enough, that is, when the density of districts around the national median is su ciently big that parties will converge and catchment areas will overlap. This convergence will continue as long as 14

15 the bene t from moving towards the center, the attraction of half the centrist districts entering the catchment area, is larger than the cost of convergence, the loss of all districts at the side of the distribution that exit the catchment area. 6.2 Case 2: lax institutional constraints: > 1= p If institutional constraints are lax, parties anticipate that their platform choice can induce the other party to change intraparty discipline at stage 2. Equilibrium platform positions are thus the result of more elaborate strategic considerations. We have: Proposition 5 For > 1= p ; there exist B () and T (6 log 2) 1=2 such that: i) > B () is a su cient condition for parties to choose maximal candidate freedom ( P = ) and polarized platforms (x L ; x R ) = ( ; ) in equilibrium. In particular, B ( = 1) = p 2= log 2. ii) Conversely, T is a su cient condition for parties to choose maximum discipline ( P = 0) and centrist platforms (x L ; x R ) = (0; 0) in equilibrium. Proof. See Appendix. As in the previous proposition, the median voter theorem thus holds when nationwide preferences are su ciently homogeneous. The reason is the same as before: when centrist districts are su ciently many, parties prefer to adopt centrist manifestos. The di erence with tight institutional constraint is that this choice of platform positions also impacts on party structures. Since parties are centrist and preference heterogeneity is small, both parties end up ghting for the same, moderate, districts. Proposition tells us that in this case parties choose full discipline. The picture is di erent for large voter preference heterogeneity. In this case, parties prefer to adopt polarized positions up to the point where their catchment areas are tangent to each other, which implies that they no longer compete directly for the same districts. Then, in any district, e ective competition is only between a party candidate and an independent. The reason is that both parties want to earn the support of the tails of the distribution of districts. Parties thus grant their politicians maximal freedom ( P = ) and they locate as far as possible from the center as they can while avoiding losing seats there: (x L ; x R ) = ( ; ) : 6. Wrap Up The following gure summarizes our ndings: 15

16 λ large High internal discipline No or low polarization Low internal discipline High polarization σ small σ large High internal discipline No or low polarization High internal discipline Moderate polarization λ small Figure 4: Summary of the results From the gure it is clear that the celebrated Downsian Median Voter Theorem holds only in a world in which preferences are very homogeneous ( small, left-hand side of the Figure). Note as well that our model suggests that even in US-type presidential systems, if the polity s heterogeneity of preferences were to shrink su ciently (right to left movement in upper part of the gure), parties would switch from their current, low-discipline organization, to one that would mirror much more closely the organization of parties in Westminster-type parliamentary democracies. Further, our model also predicts that in such an event parties would be characterized by a similar level of polarization. In a nutshell, our model predicts that, in a world were voters are very homogeneous, the political regime has little, if any, bite on the way parties organize. It is only when preferences are more heterogeneous ( large, right-hand side of the Figure) that both institutional characteristics and the degree of heterogeneity of voter preferences determine party polarization and party structure. We thus have: Proposition 6 When voter preferences are very homogeneous across districts, a move from a parliamentary to a presidential regime does not a ect how parties organize and how they position themselves on the ideologic spectrum. Conversely, when preference are heterogeneous, political institutions in uence how parties organize and, in turn, how polarized their positions are. Proof. Direct consequence of Propositions 2-5. To the best of our knowledge, this prediction that the socioeconomic characteristics of the polity are as important as if not more important than political institutions to explain how 16

17 parties organize and where they locate on the ideologic spectrum has not been pointed out so far in the literature. 7 Applications The rst application relates to the comparison of party structures across political regimes and to the determinants of the evolution of intraparty discipline in France and England. The second application focuses on party polarization in the U.S. and provides a theoretical rationale for the dance between polarization and inequality uncovered by McCarty et al (2006). 7.1 Comparative Politics of Intra-Party Discipline Parliamentary versus Presidential Regimes The contributions by Huber (1996b) and Diermeier and Feddersen (1998) identify a potent e ect of the vote of con dence procedure on legislative cohesion, even in the absence of parties. Our analysis identi es a multiplier e ect that operates through party structures: a marginal tightening of the institutional constraints on legislative freedom can trigger a discrete switch in party structure, whereby legislators are deprived of their freedom of action and forced to stick to the party line. Formally, the model identi es a critical value for, 1= p, where the trigger operates. We believe that this party channel provides a complementary rationale to the one advanced by Huber and Diermeier and Feddersen for the observed correlation between institutions and legislative cohesion. UK-style parliamentary regimes are associated with signi cantly stronger intraparty discipline than US-style Presidential regimes. Surprisingly, our model predicts that parties will not free-ride on institutional constraints but, instead, adopt measures that amplify initial di erences in institutional constraints. Thus, even minor di erences in institutions can trigger widely di erent cohesion patterns, both inside a given party and between parties of a coalition. How do parties achieve discipline? First, they produce legislation that constrain the candidates freedom, for example through restrictions on the freedom to levy personal nance. In many parliamentary countries, the bulk of campaign nance must go by law through the party endowment, and is often public money (see e.g. Katz and Mair 1995 and 2002). By contrast, in the U.S. most of campaign nance is levied by the candidates themselves. This makes them much more independent from their party and more prone to pander to their constituencies. Second, which candidate personalizes the party in each district can either be controlled by the 17

18 party (as in the U.K., where parties can easily expel a candidate from the party if he or she does not follow the party line) or by local primaries that fall outside the parties span of control (as in the US, since the inception of the American Direct Primary in the early 20th century see Ware 2002). Third, parties can develop means to expel candidates who do not follow the party line su ciently closely. In the UK, even prominent gures such as Ken Livingstone can be expelled. In the US instead, there are virtually no sanctions for breaking party ranks (Katz and Mair, 1994, p40). All these evolutions are endogenous to the party dynamics and t the model s predictions The Evolution on Intraparty Discipline in Victorian England Of course, many other dimensions di erentiate US and UK politics. To isolate the e ects of legislative constraints, we should thus identify a single country where institutional constraints changed, and check how intraparty discipline evolved. The UK is a case in point, analyzed by Cox (1987). 16 Consistently with the key nding of our model, he argues that the gradual increase in the level of intraparty discipline in the second half of nineteenth century Victorian England materialized after a few important changes to the rules of the political game, two of which are key. First, the passing of the three Reform Acts increased greatly the competitiveness and transparency of electoral races. This raised in turn the incentives of member of parliament (MPs) to adopt a legislative behavior that was both more visible and more in line with the interests of their constituency (the increase in the number and circulation of newspapers and the invention of the telegraph played a major role in this development too; see Cox 1987, pp.1-15). Second, the materialization of what Walter Bagehot (1865) coined the e cient secret of the English Constitution namely the close union, the nearly complete fusion, of the executive and legislative powers (Cox 1987, p. 51) with the cabinet as the key connection made it accepted practice to link the survival of executives or even of Parliament to the passing of crucial government bills. In short, institutional constraints such as the vote of con dence procedure, that are typical of modern parliamentary systems, materialized around the middle of the nineteenth century (Cox 1987, pp.80-87). These two developments thus put the government and the MPs on a collision course, with the government needing the support of a majority of legislators to operate and individual MPs wanting the legislature to devote more time to issues linked to their individual constituencies. The solution to this dilemma was quickly found by the 16 On top of analyzing how the introduction of institutions such as the vote of con dence procedure impacted on intraparty discipline, Cox (1987) analyzes the importance of changes in the behavior of the electorate and the extention of the franchise. For reasons of tractability, we abstract from these dimensions in our model. 18

19 government: increase intraparty discipline. Indeed, the data on intraparty discipline reported by Cox (1987,pp.21-1) suggest forcefully that parties increased internal discipline after, as a reaction to the developments we described above: the data show a marked increase in discipline from the late 1860s onwards, that is, after the reforms had modi ed the rules of the political game. The data thus suggest that, instead of freeriding on the vote of con dence procedure, party leaders exploited the threat of dissolution of Parliament after a defeat on any important vote to discipline their troops. This strategy proved highly e ective because individual politicians knew that the dissolution of parliament brought with it a substantial risk of non re-election: electoral competition had become much sti er after the Reform Acts and parties started using their power not to grant dissidents the right to use the party label at the election. On top of this, because party leaders controlled rmly the cabinet, they could also increase discipline through the strategic allocation of future ministerial positions (Cox 1987, pp ) The Evolution on Intraparty Discipline in France after World War II Another interesting case is France. 17 Under the Third Republic (i.e. until 1940), French deputies had the reputation of being extremely undisciplined and individualistic. After World War II, the reforms of the Fourth and Fifth Republic (in 1946 and 1958 respectively) went in the direction of a tightening of legislative constraints. In particular, these reforms increased the powers of the Prime minister. Yet, this alone did not create su cient discipline (see Wilson and Wiste 1976). The second reform game increased powers to the President, and gave political parties and groups a new, more prominent, role. All parties did not react at the same time nor in the same way to these institutional changes. The Gaullist UDR is the most interesting case for our purpose: this was the party with initially the lowest internal cohesion because it had the most diverse set of legislator preferences in With the Fifth republic, thanks to the enhanced powers of party groups, this party could eventually develop ways to improve candidate discipline: UDR leaders [took] steps to enforce e ective discipline: deputies who failed to observe party discipline were subject to immediate exclusion. [...] Even a single refusal of discipline on a key vote could bring expulsion (Wilson and Wiste 1976, p482). Other parties such as the Communists were instead uni ed against the Gaullists. This made them cohesive even in the absence of party whips. The French case thus provides a second example where, rst, self-imposed party constraints 17 We thank Howard Rosenthal for drawing our attention to the French case. 19

20 on discipline were undoubtedly introduced as a direct reaction to a change in institutional constraints. What is more, we see that a hybrid constitution (the Fourth Republic) produced a highly unstable situation, because the Parliament had enlarged powers but parties could not su ciently discipline their candidates. According to our analysis, parties are indeed weakest under intermediate levels of discipline. In turn, this provides another rationale for the reform of the Fifth Republic: improved legislative cohesion was needed. 7.2 The American Polarization Dance A second prediction of our model is that equilibrium party polarization is commensurate to voter preference heterogeneity. We believe that this result provides a theoretical foundation for the ndings of McCarty, Poole and Rosenthal (2006) who identify a strong statistical correlation between party polarization and economic inequality in the U.S. Their initial nding can be summarized by Figure 5, which is borrowed from their internet site, Figure 5: Income Inequality and Political Polarization This gure illustrates what they call the dance between inequality and ideological polarization over the course of that century. We wish to emphasize that previous contributions, such as Callander (2005) do provide a rationale for the positive correlation between income inequality and the distance between party platforms 2x in our model but cannot rationalize the evidence put forth by McCarty et al. (2006), for the following reason. The measure of polarization that McCarty et al. o er is based on the fraction of individual legislators who vote with legislators 20

21 of their own party as opposed to legislators of the other party. That is, in the terminology of our model, their measure of polarization increases when the overlap between the two party catchment areas decreases. We thus need a model that captures both the equilibrium distance between party platforms and the equilibrium degree of intraparty discipline to understand such ndings. This is precisely what our model achieves: from propositions 4 and 5, under weak institutional constraints and strong preference heterogeneity, parties bene t from low intra-party discipline, and the overlap between their catchment areas shrinks when voter preference heterogeneity,, increases. Using the results of the previous section, the mechanism that lies behind the positive correlation between preference heterogeneity and polarization is thus the incentive of parties to give more prominence to districts that are in the tails of the distribution when preference heterogeneity increases and, as a consequence, the centrality of moderate districts is reduced. The following gure on polarization in the US House of representatives provides indirect evidence of this The evidence is indirect for the following two reasons. First, this picture captures probably two effects: changes in polarization and changes in the width of the ideologic spectrum. Secondly, what is measured actually is not the polity s but, rather, the individual legislators ideology. The gures are available at 21

22 Figure 6: Democrat-Republican polarization dance and overlaps 8 Discussion and Extensions 8.1 Preferences of Candidates and Voters In this section, we show that the two assumptions that (a) candidate preferences are uniformly distributed and (b) voters have quadratic preferences are not necessary for our results to carry through. As will become clear below, they are nonetheless useful to obtain closed form solutions. Generalizing our setup, suppose that voter preferences are de ned by some function f: u i (x c ) = u (y i ; x c ) = f (jx c y i j) ; such that f 0 < 0 and f To maintain comparability with the quadratic case, we normalize f (0) to zero. Turning to the bliss point of a candidate, x c is distributed according to some density function g i (x c ), with mean y i. This district-speci c distribution g i () is the translate of a distribution g (): g i (x c ) = g (x c y i ) ; such that, for any pair of districts i and j, and any x 2 R we have g i (x y i ) = g j (x y j ). g is symmetric: g ( x) = g (x) and quasi-concave: g 0 (x) 0 8x > 0, with a support [ 1; 1]. Thus, the support in district i is Y i [y i 1; y i + 1], and the CDF of candidate preferences is G i (x c ) with G i (y i 1) = 0 and G i (y i 1) = 1. In this generalized setup, voter i s expected utility of electing a local independent is: U I Eu (y i ; x c jx c 2 Y i ) = Z yi +1 y i 1 u i (x) g i (x) dx: The bliss point of a party candidate must be in the subset P i (x P ; P ) Y i \ X P ; where X P [x P P ; x P + P ]. Focusing here on values of x P y i (the analysis is symmetric for x P < y i ), through Bayesian updating, voters determine that a the bliss point of party candidate is distributed according to the density function g ip (x c ), given by: g ip (x c ) g i (x c ) G i (min fy i + 1; x P + P g) G i (x P P ) ; where the function G i () is the CDF associated with g i (). As before, two subsets must be considered: (i) districts that are close to party P, such that x P + P y i + 1: (ii) districts that are distant from party P, such that x P + P > y i + 1: It follows that the expected utility 22