Intra-Party Discipline, Rent Extraction and Electoral Rules¤

Benoit S Y Crutzeny

This Draft: March 2004

Abstract

This paper analyzes how intra-party competition a®ects rent extraction. We show that the career-concern motives that in°uence rent extraction by individual politicians are sensitive to intra-party discipline. Compared to majority rule, proportional representation o®ers parties a broader range of devices to discipline politicians, thanks to its electoral lists. The active use of these lists by the party is proven to yield outcomes that increase the electorate's welfare under proportional representation relative to majority rule. These results also o®er a new interpretation of the available empirical evidence.

Keywords: Party Discipline; Rents; Electoral rules JEL classi¯cation: D72, H41

¤I am indebted to Micael Castanheira, Catherine Dehon, Estelle Malavolti, Abdoul Noury and Nicolas Sahuguet for their insightful suggestions and their time during the preparation of this draft. Many thanks too to seminar participants at ECARES. yCorrespondence address: ECARES { C.P. 114, Universit¶e Libre de Bruxelles, 50 F D Roosevelt Ave, B-1050 Brussels, Belgium. Tel: +32-2-650.33.75; fax: +32-2-650.40.12; email: [email protected]

1 "When it comes to electoral rules, the devil is in the details". (Persson and Tabellini, 2004: 15)

1 Introduction

Elected o±cials have plenty of opportunities to abuse their positions. Once in o±ce, incumbents can easily extract rents from the budget they control. This may go against the interest of the electorate, because resource diversion decreases their welfare. And it may also go against the interests of the incumbents' own party, because its objectives may not coincide totally with those of its politicians. How to control politicians is a question that has received substantial attention in the Political Economics literature. Seminal contributions include Barro (1973) and Ferejohn (1986). Myerson (1993, 1999) and Persson, Roland and Tabellini (1997) extend this strand of the literature by examining the role of the electoral rule and regime. Yet, all these contributions maintain the classical Downsian assumption that parties are unitary actors, that is, that parties and politicians are perfect substitutes. As a consequence, the role played by parties, in addition to voters, in controlling individual politicians is out of their reach, by construction. Hence, of the three fundamental characteristics of electoral rules { district magnitude, the electoral formula and the ballot structure { these analyses can only examine how the ¯rst two impact on the control of politicians. The role of the third, the ballot structure, is left out of the analysis.1 The main contribution of this paper is to let parties be groups or organizations. Once parties and politicians are modelled as di®erent actors, parties become 'political intermediaries', to borrow from the terminology of Caillaud and Tirole (1999, 2002), and the control of politicians becomes two-dimensional: the electorate exerts some control on parties and politicians through its voting decisions, and parties exert some control on politicians through their decisions regarding their internal governance structure. This implies in turn that, if seeing parties as organizations allows us to examine the role played by the ballot structure, we can also split the e®ect of political competition along two complementary dimensions: a horizontal and well known one, where the focus is on competition between politicians belonging to di®erent parties { label it inter-party competition; and a vertical one, which has been overlooked by most until now, where competition takes place between politicians within the same party { we label this dimension intra-party yardstick competition.

1District magnitude refers to the proportion of the legislature that is elected in each district. The electoral formula governs how vote shares are translated into seat shares. Finally, the ballot structure governs how the electorate casts its votes.

2 To facilitate comparisons with the literature, our analysis builds on the textbook model of Persson and Tabellini (2000). They put forward a career-concern model where parties are viewed as groups of purely rent-seeking politicians and study how electoral rules shape the individual politicians' incentives to perform once in o±ce. They compare individual rent extraction under majority rule and closed-list proportional representation (PR). Un- der closed-list PR, voters do not have the option of voting for single politicians, but can only vote for their favorite party, which presents voters with a ¯xed and non-negotiable list of party candidates. Hence politicians are not individually accountable to voters anymore. This implies in turn that the intra-party arrangements governing the writing down of the electoral lists o®ered to the electorate become of primary importance. Yet, the authors analyze only the benchmark case in which intra-party yardstick competition is completely absent: each politician's position on the electoral list is given once and for all and cannot be modi¯ed. With this simplifying assumption at hand, their results highlight that PR may be associated with weak incentives for individual politicians to perform once in o±ce and therefore higher equilibrium rent extraction than majority rule. The authors having abstracted from the role played by the vertical dimension of political competition, one may wonder how the introduction of intra-party yardstick competition a®ects their results. Filling this gap is the core goal of the paper. In order to do this, we need to model more precisely the internal organizational details governing political parties. Roemer suggests that parties typically consist of three di®erent factions of individuals: the candidates, the rank-and-¯le and the militants (Roemer, 2001: 7). To make our life easier, we neglect the role of militants and let parties have a two-tier structure with the rank- and-¯le on the one hand and the politicians running for election on the other. This allows us to deliver most clearly the main message of the paper: the electoral lists characterizing closed-list PR are double-edged knifes. If lists may reduce the accountability of individual politicians to the electorate, thereby exacerbating the agency problem between the electorate and incumbents, as argued by Persson and Tabellini (2000), we show that these same lists can also be used by the party to increase accountability of individual politicians to the party and therefore reduce the extent of the intra-party agency problem. Main Results We start by opening the political party's black box. We let the party { that is, the rank-and-¯le { and its politicians disagree on the preferred policy.2 Indeed, individual politicians are unlikely to internalize the e®ects of their individual decisions on the re- election prospects of the party as a whole. To answer the question of how equilibrium policy is in°uenced by the intra-party agency problem, the paper suggests two di®erent

2Without disagreement on policy parties and politicians would become again perfect substitutes and there would be no scope for intra-party competition!

3 mechanisms that may allow the party to discipline its politicians. The ¯rst mechanism we focus on is present under PR but absent under majority rule: the electoral lists. Once we let parties actively use these lists to discipline individual incumbents (a case we label conditional-list PR), the political career-concern game yields outcomes that make the electorate's welfare higher under PR. Thus, one can view conditional-list PR as a means of steepening the electoral competition incumbents face: not only are they challenged by the opposition party, as usual, but they are also held accountable by their own party, indirectly, through the intra-party competition for the best positions on the party list. The second mechanism we study is more direct: we let parties commit to ¯ring incompetent incumbents and replacing them with new candidates prior to the new election. We show the threat of ¯ring incompetent politicians lowers equilibrium rent extraction under majority rule. Yet, the reduction in equilibrium rent extraction is stronger under PR, implying that, as is the case with the previous mechanism, voters are better o® under closed-list PR than under ¯rst-past-the-post. The main conclusion we can therefore draw from our analysis is that the addition of a second, vertical competitive dimension highlights that the comparative politics results are sensitive to the degree of intra-party discipline. How reasonable is it to believe that intra-party institutional arrangements have such an important impact on real world policies, as compared to, for example, reforms modifying the electoral rule or regime? Given that a switch to a new electoral rule usually requires a constitutional reform, any such change is more costly than a simple modi¯cation of a party's internal governance structure. This may explain why major electoral reforms are not as commonly observed or advocated as one might be lead to expect. In this case, less costly disciplining devices such as the ones examined in this paper may be favored by political parties. Indeed, we strongly believe that real world prima facie evidence does point out that the most prominent and best performing politicians are guaranteed the safest electoral seats, whereas younger politicians are relegated to much riskier positions, at least until they have proven their worth.3 Thus, the use of conditional-list PR may be a lot more pervasive than commonly believed.4 Related Literature This paper is not the ¯rst to study how inter-party and intra-party competition impact on the control of politicians. A branch of the political science literature adopts this strategy too. Important contributions include Cain, Ferejohn and Fiorina (1984, 1987) and Carey and Shugart (1995). They partition electoral rules according to whether they are party-

3In our setup, the safest positions are the ones at the top of the list. 4Readers may think that succesful leaders are very often allowed to go undisputedly their own way until they lose their party's 'con¯dence'. This is exactly the message we wish to push through in this paper: conditional-list is a mechanism that achieves just that.

4 centered or politician-centered. They show that the intra-party agency problem is less likely under party-centered electoral rules such as PR than under politician-centered rules such as ¯rst-past-the-post, under which the incentives to create a personal electoral base or a 'personal vote', to use the terminology of Cain et al. (1987), plays a more important role. Empirically, the importance of distinguishing between party-centered and politician- centered rules has been con¯rmed by Hix (2003): he studies the pattern of vote of members of the European Parliament between 1999 and 2000 and shows that the members that seem to have followed more closely the party line are those that where elected through more party-centered rules. Yet, these contributions stop somehow short of highlighting which mechanisms may explain why party-centered electoral rules may be more e±cient at controlling individual politicians when compared to politician-centered ones. Our contribution complements this literature by ¯lling this exact gap: we highlight that parties have an extra tool at their disposal under closed-list PR to discipline incumbents, the party lists, which implies in turn that the control of individual politicians may be looser under majority rule than closed-list PR. The rest of the paper is structured as follows. Section 2 presents the main building blocks of the model. The next section deals with the voting strategy of the electorate and the optimal electoral strategy of the parties. Section 4 examines the consequences of letting parties actively use their electoral party lists. Section 5 deals with the case in which parties commit to ¯ring politicians that are perceived as incompetent and replacing them with new recruits before new elections are held. The ¯nal section concludes and makes some proposals for further research.

2 Building Blocks

This section presents the basic structure of the model, which is borrowed from Persson and Tabellini (2000).5 Our game is a two-period one. Consider an economy subdivided into three districts, indexed with J; J = 1; 2; 3: Each district contains a continuum of voters of mass 1 and is run by a single politician. Politicians belong to one of two parties competing in elections. One of the parties is also assumed to be the incumbent in period 1. The incumbent party controls the whole economy in the ¯rst period: three of its politicians are in charge of the three available districts.6 Politicians are purely rent-seeking in the sense

5For the orginal presentation of the model by these authors, see Persson and Tabellini (2000), chapter 4, section 5 and chapter 9, section 1. 6Thus, the incumbent party is lucky enough to control the whole of the economy, at least in the ¯rst period of the game. Given that at the start of the game, as will be clear from below, the party's information about each of its members is identical, we can freely describe the process leading to the appointment of

5 that they have no preferences about ideology and the policy implemented in equilibrium. All they care about is the amount of rents they can extract from the game. Denote with J rt the rents the politician in charge of district J decides to extract in period t: Then all three incumbents maximize the following objective function:

J J J E v = r1 + pr2 (1) ¡ ¢ where p stands for the probability that the incumbeent will keep an o±ce in period 2. As we will see below, p turns out to be a function of both the electoral rule and the party's governaence structure. We assume no discounting, without any loss of generality. The policy space is kept as simple as possible. In each period, each politician provides a local public good to its district. This public good is ¯nanced through taxes. The tax rate, ¿; is exogenously ¯xed. Individual income, y, is also exogenously given and is equalized across districts. Finally, the district-speci¯c government budget must be kept in balance in each period and there are no spillovers from one district to the other. The preferences of a voter in district J and period t are linear in (net) private income and the local public good. Label with ® 1 the individual (constant) marginal utility ¸ from the local public good. Individual preferences are then given by:

wJ = y (1 ¿) + ®gJ (2) t ¡ t J where gt is the local public good. Turning to the government budget constraint in district J and period t; it is given by:

gJ = ´J ¿y rJ (3) t ¡ t where ´J is the realization of a random variab¡le a®ect¢ing the returns to taxation in district J. We restrict rJ to be smaller than the district-speci¯c tax base: 0 rJ r < ¿y: This t · t · ensures that the career-concern dynamics we wish to analyze are always meaningful (i.e. that gJ > 0 for any rJ (0; r)). We return to this point in section 3.1. The aim of the 2 2 2 J 3 paper is to characterize the equilibrium vector rt J=1 under di®erent electoral rules and di®erent intra-party institutional arrangements©. ª Borrowing from the terminology of Persson and Tabellini (2000), ´J can also be described as the competence of district J's politician in delivering the local public good: J Together with the rents, rt ; it is the key variable of the model. We follow Persson and Tabellini (2000) in assuming that the realization of ´J determines the competence of politician J in both periods 1 and, provided she is re-appointed, 2.7 ´J is distributed according the three period 1 incumbents as party selection or as random draws from the pool of the incumbent party members. 7Hence competence is not a®ected by seniority and there is no on-the-job learning.

6 1 1 to a uniform distribution with support on 1 ; 1 + . We assume that an interior ¡ 2» 2» solution to the politician's problem always·exists and, to ¸ensure that competence never takes on negative values, that » 1=2. The distributional assumption regarding ´J also ¸ implies that a politician's competence is independent of the district she is in charge of: the support does not depend on J. Thus, the district-speci¯c ´J 's are i.i.d. realizations from a common distribution.

2.1 Timing

The timing of the game is presented in ¯gure 1 below and is similar to that of standard career-concern models. There are two main periods:

1. At the beginning of the ¯rst period, parties choose their internal governance structure. Then Nature randomly selects an incumbent party. Three politicians belonging to the incumbent party are then appointed to head the three districts of our economy. They set optimally their ¯rst period rents. Then, their competences are realized without anybody observing them and voters observe the residually determined local public good.

2. At the beginning of the second period, new elections are held. Voters decide whether to back the incumbent party or not. The newly elected incumbents set optimally second period rents. Local public good provision for the second period is residually determined and the game ends.

t = 1 t = 2

Choice of internal Nature chooses Politicians set Competences are realized. New elections Period 2 politicians time governance structure. incumbent party. period 1 rents Voters only observe extract rents local public good provision

Figure 1: Timing of the game

The game we analyze is therefore one of pure moral hazard, given that none of the actors observes the vector of competences ´J . We refer readers to Snyder and Ting (2002) for the analysis of a rationale for the©roleªof parties in disciplining their politicians under adverse selection (only).

7 3 Optimal Strategies of Voters and Parties

3.1 Voting Strategy of Electorate

This section describes the optimal voting strategy the electorate will follow throughout the whole of the paper. How do voters in district J vote? Given our assumptions about individual preferences, the electorate of each district will vote to con¯rm its incumbent party provided it believes its politician is competent enough. Indeed, given that the game ends after the second period and that therefore politicians cannot be given any incentives to refrain from rent extraction in that period, period 2 rents will be set to their maximum: rJ = r; J . This 2 8 is where the assumptions that r < ¿y and that each politician keeps the same level of competence through time are crucial. They imply that the utility of the electorate in the second period is an increasing function of competence, as is obvious from (3) above, because local public good provision in period 2 is equal to:

´J ¿y rJ = ´J (¿y r) k´J ¡ 2 ¡ ´ where k is a positive constant e¡qual to (¢¿y r). ¡ Hence, the electorate will vote for their ¯rst period incumbent if and only if her perceived competence is greater or equal to that of any unknown opponent that might take her job in period 2. But the model's distributional assumptions imply that expected competence E (´) of any such opponent is equal to 1. Thus, the incumbent party receives the favorable vote of a district at the end of period 1 provided the incumbent politician's perceived competence, which is denoted by ´J ; is greater or equal to 1. J J J How is ´ de¯ned? Voters observe g1 and know both ¿ and y (but not ´ ): Given that they can solve the problem faced by their poblitician, they can compute an estimate of the b J J politician's ¯rst period rents, r1 : Plugging r1 into the district-speci¯c budget constraint (3), voters can then form an estimate of ´J as follows: b b ´J ¿y rJ ´J ¿y rJ = gbJ ´J = ¡ 1 (4) ¡ 1 1 , ¿y rJ ¡ ¡ 1 ¢ ¡ ¢ As we just explainedb, voters wbill back theibr incumbent party provided their estimate b of her competence is greater than 1, the expected competence of any unknown challenger. That is, labelling with piJ the voting strategy of individual i in district J; we have:

1 i® ´J 1 piJ = ¸ (5) ( 0 otherwise b It follows that the incumbent party's probability of winning the election in district J is given by pJ = Prob ´J 1 . Using (4) and rearranging, the event ´J 1 is equivalent ¸ ¸ h i b 8 b to: ¿y rJ ´J ¡ 1 (6) ¸ ¿y rJ ¡ 1 b

Finally, exploiting the distributional assumptions about ´J , pJ is given by:

¿y rJ pJ = 1=2 + » 1 ¡ 1 (7) ¡ ¿y rJ · ¡ 1 ¸ b We have thus derived an incumbent's probability of being perceived as competent and therefore of receiving the favorable vote of at least a majority of her district. Can we say something about the value pJ takes in equilibrium? The answer turns out to be yes. In equilibrium, all voters' conjectures must be consistent with the politicians' optimal J J J behavior. Therefore, we must have that r1 = r1 : This in turn implies that p = 1=2; and every incumbent is re-elected with probability 1/2. This is not surprising: given that the competence of both incumbents and bchallengers is unknown (to everybody) at the beginning of the game and that they are equal in expected terms, each incumbent must have probability 1/2 of being supported by (a majority of) their electorate. Nevertheless, as will become clear from the sections below, we should warn that pJ does not coincide with the actual probability that the incumbent will keep her job in the second period (this explains why in (1) above the probability that an incumbent keeps her job was labelled as pJ and not as pJ ). This latter probability is a function not only of pJ , but also of the electoral rule and the internal governance structure of the party. We therefore need to takee a stance on how vote shares are translated into seat shares under the two electoral rules. Following Snyder (1989) and Lizzeri and Persico (2001), among others, we postulate that the parties' share of the available seats is equal to:

1 as soon as the party wins the election in a majority of the districts under majority ² rule; and

its vote share under proportional representation.8 ²

3.2 The Parties' Optimal Strategy

Having fully speci¯ed the rules of our game, a ¯rst question we need to answer is: what does each party { that is, its rank-and-¯le { maximize? One obvious answer is: the party maximizes its vote share. To ensure that this is each party's goal, we assume that the sharing of monetary rents between incumbents and their party is impossible. Remark that

8Remark further that under our assumptions, a party's vote share can only take the following values: 0; 1=3; 2=3 and 1; which correspond to the party winning the election in respectively 0, 1, 2 and 3 districts.

9 our assumption about the party's objective is also consistent with previous contributions in the literature that depart from the assumption of parties as unitary actors.9 Nevertheless, even if the party were to share, at least to some extent, its incumbents' desire to extract rents from the public budget, the following argument demonstrates that the mechanism we put forth below to reduce the extent of the intra-party agency problem would still be the one selected by the party. Suppose we were to remove the random designation of the incumbent party at the beginning of period 1 and instead assume that, at t = 0; parties must commit to following one of the rules described above under PR. After the two parties have chosen their internal governance structure, the electorate is asked to choose its incumbent party. Once the incumbent party has been chosen, the game proceeds as before from period t = 1 onwards. Which rule would each party choose? That that maximizes its probability of being selected by the electorate, obviously. And that rule is the one that minimizes rent extraction in each district (because it maximizes local public good provision and therefore the electorate's welfare). Thus, in this new, extended game, both parties would follow the strategy examined in the next section.

4 Intra-Party Competition/1: The Role of Party Lists

This section assumes that parties cannot ¯re any ¯rst period incumbent that turns out to be (perceived as) incompetent. In this case, there is not much parties can do to discipline their incumbents under majority rule, as we explain below. To the contrary, under proportional representation, parties still have an obvious tool they can resort to to discipline incumbents: the electoral list.

4.1 Majority Rule

Under majority rule, the party that wins the election in two out of the three districts gets the control of all three districts. Therefore, each incumbent realizes that she is assured of retaining an o±ce in period 2 provided either of the two following events is realized: 1) she is perceived to be competent enough (and therefore her party wins the election in her district) and the same holds for at least one of her two fellow politicians; or 2) she is perceived to be incompetent (and her party looses the election in her district) but her party wins the election in the other two districts10. Both of the two above events ensure that the incumbent party wins in two out of the three districts and therefore that its three incumbents retain the control of a district in 9See e.g. Roemer (2001) and Caillaud and Tirole (2002). 10This is where the assumption that parties commit not to dismiss incompetent politicians plays a crucial role. Indeed, one may wonder why the party should keep the underperforming incumbent and not replace her with someone else. This case is analyzed in the next section.

10 period 2. Taking the perspective of the incumbent in district 1, say, the probability that the ¯rst event is realized is given by:

p1p2 1 p3 + p1p3 1 p2 + p1p2p3 ¡ ¡ ¡ ¢ ¡ ¢ whereas the probability that the second event is realized is given by:

1 p1 p2p3 ¡ ¡ ¢ where p1; p2 and p3 are de¯ned by (7) above. Overall, under majority rule, the probability that incumbent 1 retains an o±ce in the second period is given by the sum of the two above probabilities:

p = p1p2 + p1p3 + p2p3 2p1p2p3 (8) ¡ and the problem incumbent 1 solves is:

Max r1 + pr (9) 1 1 r1 © ª The ¯rst order condition associated to this problem is:

¿y r1 1 » ¡ 1 p2 + p3 2p2p3 r = 0 (10) 1 2 ¡ " ¿y r1 # ¡ ¡ b ¡ ¢ ¡ ¢ J J J But, remember that, in equilibrium, r1 = r1 and p = 1=2 for any J: Thus, given that the ¯rst order condition above characterizes the problem any of our three incumbents face, JMAJ b labelling with r1 equilibrium ¯rst period rents under majority rule, these are given by: 1 rJMAJ = ¿y »r (11) 1 ¡ 2

And aggregate ¯rst period rents are equal to: 1 rJMAJ = 3 ¿y »r (12) 1 2 J ¡ X µ ¶ Before turning to the analysis of PR, notice that the electorate of each district is treated totally equally: equilibrium rent extraction is equalized across districts. This will turn out not to be the case under closed-list PR { but only when parties do not discipline their incumbents { and will provide us with yet another rationale for seeing conditional-list PR as a feature of real world party politics.

11 4.2 Conditional-List Proportional Representation

Under closed-list PR, voters cannot pick their preferred candidate from the list but can only vote in favor or against the incumbent party and the whole of its list. If the incumbent party is unwilling to let incumbents freely set rent extraction at their preferred individual level, how can it discipline its incumbents? A very simple yet powerful mechanism is the following. It commits to ranking the three incumbents on the electoral list for the period 2 election as a function of each incumbent's performance relative to that of her two fellow politicians. The measure of performance it uses is the one that is available to the electorate at large: the vector of individual perceived competences, ´J : J =1;2;3 More precisely, the party commits to letting the best performer in the ¯rst pneriood be top of the list, the runner-up second and the worst performer last. After all, if theb electorate can form an expectation about the three incumbents' performances (the ´J 's), so can the party. Hence, if the threat of sacking incompetent politicians is beyond the party's reach, it can still discipline incumbents through intra-party yardstick competitionb, in terms of the ´J 's. Under this new intra-party arrangement, each incumbent knows that, to be top of the pbarty list, she has to choose a level of rents such that her own perceived competence is higher than that achieved by both of the other two incumbents. That is, for incumbent 1; say, to be top of the list, she needs that ´1 > max ´2; ´3 : If she manages to do better than only one of her two fellow politicians, she will h£ave to¤settle for the second position on the list. This happens if ´2 > ´1 > ´3 obr if ´3 > ´b1 >b ´2: Finally, if her performance is so dismal that she does worse than both of the other two incumbents, she is punished and ends up at the very bottbom ofbthe lbist. Thisb happbens ibf ´1 < min ´2; ´3 : This type of intra-party yardstick competition induces each incumb£ent to¤refrain from excessive rent extraction in order to avoid falling down the pbarty list anbd tbherefore facing a serious threat of non re-election. To say it another way, each incumbent is made fully responsible for her previous decision (given her level of competence). Politician 1's probability of being re-elected under conditional-list PR, which we label ; is given by the sum of three terms. Each of these terms corresponds to the probability P that two events are veri¯ed simultaneously: 1) the vote share of the party is su±cient to grant it at least X seats and 2) the incumbent ends up in a position on the party list that is higher or equal to X. That is, labelling the vote share of the party as ¼; is given by: P Pr ¼ 1=3 AND ´1 > max ´2; ´3 ¸ + Pr ¼ 2=3 AND ´2 > ´1 > ´3orif´3 > ´1 > ´2 (13) £ ¸ £ ¤¤ b1 b2 b3 + Pr £¼ = 1 AND ´ ¡< min ´ ; ´ ¢¤ b b b b b b To justify the expr£ession above, notice th£at, if ¤in¤ cumbent 1 ends up top of the list, b b b

12 all she needs to be assured of retaining an o±ce next period is that her party wins the electoral contest in at least one district, i.e. that ¼ 1=3. This yields the ¯rst of the three ¸ terms above. If the incumbents ends up in the runner up position, she needs her party to win at least two out of the three districts. This yields the second term above. Finally, if the incumbent has performed so badly that she ends up last on the list, she needs her party to win all three districts. This yields the last term above. How does conditional-list perform with respect to rent extraction? Solving the game, we have:

Proposition 1 When parties resort to intra-party yardstick competition, equilibrium rent extraction by each incumbent is equal to:

rJCOND = ¿y »r (14) 1 ¡ Furthermore, conditional-list proportional representation is associated with less equilibrium rent extraction than majority rule: 1 rJCOND = ¿y »r < rJMAJ = ¿y »r (15) 1 ¡ 1 ¡ 2 Proof. Let us focus on Pr ¼ 1=3 AND ´1 > max ´2; ´3 : Obviously, the incumbent ¸ party is assured to retain at£least one seat in period 2£ provi¤d¤ed the electorate of at least one district votes in its favor. But this can bhappen if abndbonly if at least one of its three incumbents is perceived as competent. This implies in turn that incumbent 1 realizes that if she is top of the list, that is, if ´1 > max ´2; ´3 ; she has to be perceived as competent for her party to win at least one seat. T£o be m¤ ore precise, she realizes that if ´1 < 1; being top of the list yields a pbayo® of zerbo nbext period anyway because she will not be re-appointed. Thus Pr ¼ 1=3 AND ´1 > max ´2; ´3 can be rewritten as: ¸ b 1 1 2 3 Pr ´ 1 ´ > max ´ ; ´ : Usi£ng a similar line of reaso£ning i¤m¤ plies that can be ¸ b b b P rew£ritten a¯s: £ ¤¤ b ¯ b b b Pr ´1 > 1 ´1 > max ´2; ´3 1 2 1 3 1 2 + P£r ´ >¯1 ´ > ´ £> ´ or¤¤´ > ´ > ´ b 1 ¯ b 1 b 2b 3 + Pr £ ´ > 1¯ ´ < min ´ ; ´ ¤ b ¯ b b b b b b £ ¯ £ ¤¤ 1 2 3 Finally, writing explicitly all bthe ev¯ebnts associabtedbto ´ ; ´ and ´ that are compatible with the three conditional probabilities above, simpli¯es to: P b b b Pr ´1 > 1 ! £ ¤ This immediately implies that each incumbbent faces the same problem and as a consequence will extract the same amount of rents in equilibrium. Solving each incumbent's problem with = Pr ´1 > 1 immediately yields proposition 1. P £ ¤ b 13 Proposition 1 states that the use of party lists under PR, as a disciplining device to prevent incumbents from choosing 'excessive' rent extraction, will lead the electorate's welfare to be higher under PR than under majority rule. Hence, Proposition 1 highlights how, as we said in the Introduction, party lists are double-edged knifes that may help discipline individual politicians. Whereas the intuition behind the symmetric treatment of all districts was given above and is straightforward, that behind the decrease in equilibrium rent extraction is trick- ier and relies on two forces: intra-party yardstick competition and the usual inter-party electoral competition. The role of intra-party yardstick competition is to make the position of each incumbent on the second period electoral list endogenous. It is now a function of each incumbent's relative performance in period 1: the less rents an incumbent extracts from the ¯rst period budget, the more likely it is that she will end up in a top position on the second period electoral list. And, given the number of seats the incumbent party wins at the period 2 election, the higher is an incumbent's position on the list, the more probable it is that she will keep an o±ce. Secondly, inter-party electoral competition plays the usual role: better performing parties will receive more votes. This makes incumbents realize that their party's overall performance at the election depends upon their individual choices. Hence, given their expected position on the party list, the better they perform, the more seats will their party win, and the more likely it is that the incumbents will retain an o±ce in the second period. Given the electorate's optimal voting strategy, this pushes them to realize in turn that, actually, they need to maximize the probability of being perceived as competent, conditional on their position on the list. It is the combination of these two forces that leads politicians to refrain from excessive rent extraction.11 The ¯ndings of the above proposition should be seen as another step towards a more precise bridging of theoretical and empirical research. Indeed, we have just shown that PR should lead to less rent extraction than majority rule conditionally on parties disciplining their agents. This implies in turn that as long as more precise information on parties, their structure and their degree of internal discipline does not become available { for example, information about how party lists are compiled and revised { empirical research on the causes and consequences of rent extraction in the political arena may face two serious problems. First of all, the econometric model may su®er from an omission of

11The fact that these two forces lead politicians to behave as if they were running in a purely local election is due to the speci¯cities of the game we consider, and especially to the fact that voters do not have any 'global' motive to vote for the incumbent party, that is, that their voting strategy depends on the perceived competence of their district's incumbent only.

14 relevant explanatory variable problem { given that two countries using closed-list PR may be characterized by di®erent rent extraction levels if parties di®er in their degree of party discipline. Secondly, we may also be facing an endogeneity problem, if countries where strong intra-party discipline cannot be achieved are also those where electoral reforms are enacted. What happens when parties do not actively use their electoral list, or when incumbents manage to block the active use of party lists by the party? This is the case that was examined by Persson and Tabellini (2000). We brie°y sketch it below because it will allow us to prove that having left the exogenous ego-rents out of the analysis is without loss of generality. More importantly, it will also allow us to highlight that the equilibrium they derive is characterized by a crucial yet overlooked property: voters are treated very di®erently across the three districts. Anticipating on our ¯ndings below, whereas the electorate of one of the three districts reaches the same level of welfare under majority rule and closed-list PR, that of the other two districts is strictly worse o® under closed-list PR.

4.3 Closed-List Proportional Representation

Suppose now that parties do not use their electoral lists as a disciplining device.12 Why should this be so? A ¯rst obvious explanation may be that the incumbents have enough wielding power to force their party not to use the electoral lists, that is, that politicians are the ones that set the electoral lists. After all, if the politicians are strong enough to rule unchallenged, we should also expect them to be able to set the internal governance rules without any interference from the rank-and-¯le. A second complementary reason may be that the rank-and-¯le are too numerous and too dispersed to overcome the collective action problem and discipline their incumbents.13 A third and ¯nal reason is o®ered by Persson, Tabellini and Trebbi (2003), who argue that electoral lists may be conditional on "criteria unrelated to competence in providing bene¯ts to voters, such as party loyalty or e®ort within the party (rather than e®ort in o±ce)." (Persson, Tabellini and Trebbi, 2003: 961). If the party is unwilling to use the electoral list to discipline its incumbents, when and how is the list compiled? The timing we assume is as follows: the list is compiled at the beginning of period 1 and the party commits not to modify it before the new elections in period 2. As regards its composition, we follow Persson and Tabellini (2000) yet again, and assume that an incumbent's position on her party list coincides with the number of

12For the original presentation, see Persson and Tabellini (2000): 230-234. 13A counterexample to this story is provided by Golden and Chang (2001). They cite the Italian Communist Party as a party that managed to overcome this problem. See Golden and Chang, 2001: 604.

15 her district. Hence, if an incumbent is lucky enough to 'rule' in district 1, she also knows that she is top of her party list. And being top of the list implies that, as soon as her party wins the election in one of the three districts, she will retain her own ¯rst period o±ce. It should be immediate to realize that the incentives to perform for the incumbent in district 1 are very weak. Voters realize this themselves, and understand that voting against the incumbent may not be enough to ensure that any underperforming politician is removed from o±ce. Yet, under this electoral rule and our assumptions above, it is the best the electorate can do. Thus, as observed by Persson and Tabellini (2000), the incumbent in district 1 freerides on the e®orts provided by her two fellow incumbents. Likewise, the incentives to perform for the incumbent in district 3 are very feeble, but this time because she realizes that the odds of her being reappointed are very low: to be re-appointed, she needs her party to win the election in all three districts. This bleak electoral prospect can only blunt her incentives to perform. Thus the incumbent in district 3 underperforms because of the very low career-concern incentives she faces, due to the low probability of re-election. Finally, the incentives to perform for the incumbent in district 2 are somewhat stronger than those of her two colleagues: she realizes that her con¯rmation requires that her party win the electoral contest in at least two out of the three districts. Remark that the incentives faced by the incumbent in district 2 are identical to those faced by any incumbent under majority rule: compare the reelection probability under majority rule, p; given by (8) above with that under PR, given by p2 in (16) below. Formally, label with pJ the probability that the incumbent in district J keeps an o±ce in period 2. Then, following the discussion above, bthese con¯rmation probabilities are given by: b

p1 = Pr (incumbent's party wins at least one seat) 8 = p1 1 p2 1 p3 + p2 1 p3 + p3 1 p2 + p2p3 > ¡ ¡ ¡ ¡ > b > ¡ ¢ ¡ ¢ £ ¡ ¢ ¡ ¢ ¤ > 2 > p = Pr (incumbent's party wins at least two seats) > (16) > 2 1 3 3 1 1 3 > = p p 1 p + p 1 p + p p < b ¡ ¡ £ ¡ ¢ ¡ ¢¤ > 3 > p = Pr (incumbent's party wins all three seats) > > 1 2 3 > = p p p > > b :> where pJ is given by (7) above. Thus, under closed-list PR, we can replace pJ in (1) by pJ and each incumbent's

e b

16 objective function is given by:

Max rJ + pJr (17) J 1 r1 © ª Given that the problem each incumbent facesbis di®erent { it is a function of the district she is in charge of { we need to write down explicitly the three ¯rst order conditions associated with the three district-speci¯c problems. These are given by:

1 ¿y r1 2 3 1 » ¡ 2 1 p 1 p r = 0 ¡ " ¿y r1 # ¡ ¡ 8 ¡ 1 > b ¡ ¢ ¡ ¢ > ¡ ¢ > 2 > ¿y r1 > 1 » ¡ p1 1 p3 + p3 1 p1 r = 0 (18) > ¡ 2 2 ¡ ¡ > " ¿y r1 # < ¡ b £ ¡ ¢ ¡ ¢¤ ¡ ¢ > > ¿y r3 > 1 » ¡ 1 p1p2r = 0 > ¡ 3 2 > " ¿y r1 # > ¡ > b :> ¡ ¢ J J J Solving them yields in equilibrium, remembering again that r1 = r1 and p = 1=2 and JP ROP labelling rents under this scenario as r1 : b 1 r1PROP = ¿y »r 1 ¡ 4 8 > > 2PROP 1 > r1 = ¿y »r (19) > ¡ 2 <> 1 > r3PROP = ¿y »r > 1 4 > ¡ > Looking at (22), one immedia:>tely notices that rents are lowest in district 2 and highest in districts 1 and 3. That this is so should not be surprising. Indeed, the e®ect of the performance of an incumbent and hence her incentives to refrain from rent extraction are lowest in districts 1 and 3. The incumbent in district 1 bene¯ts from a very strong free- riding e®ect: even if her performance is very disappointing, she knows she will keep her o±ce anyway provided her party wins the electoral contest in at least one district. The incumbent sitting in district 3 faces very low career-concern incentives: she knows that, in order to keep an o±ce, she needs her party to win in all three districts. Overall, ¯rst period economy-wide rents under closed-list PR are given by:

JP ROP r1 = 3¿y »r (20) J ¡ X The above ¯ndings imply that we have proved the following proposition.

17 Proposition 2 (Persson and Tabellini (2000)) If: Parties commit to let their incumbents run unconditionally in the second period election; Parties commit not to modify their ¯rst period party lists under PR; and O±ces that are awarded to the incumbent party are ¯lled by its incumbents in the order of the party list; Then Aggregate equilibrium rent extraction is lower under majority rule than under closed-list PR: 3 rJMAJ = 3¿y »r < 3¿y »r = rJP ROP 1 ¡ 2 ¡ 1 J J X X Proof. Obvious from discussion above Secondly, and more importantly perhaps, we have:

Proposition 3 The welfare of a strict majority of the population is lower under closed-list PR when parties do not discipline incumbents than under majority rule or conditional-list PR.

Proof. By inspection of (15), (11) and (19) The above equilibrium implies the economy's welfare is lower under closed-list PR not only because rents are globally higher, but also because voters are treated very di®erently across districts: if the electorate of one district is indi®erent between closed-list PR (when parties do not discipline their agents) and majority rule, that of the other two districts is strictly worse o® under closed-list PR. As a consequence, the equilibrium we derived above is suggesting that in a multi-period framework, the electorate of districts 1 and 3 may have an incentive to vote with their feet and move to district 2 or to force the political system to reform itself. Another important message propositions (2) and (3) point to is the reversal in incentives politicians face before and after lists have been compiled. Indeed, as we explained in section 3.2, if we were to add an extra stage to our game at which parties would have to choose their preferred intra-party governance structure, they would choose conditional-list PR. But the three politicians of the incumbent party, once they are in o±ce, would like the list to remain ¯xed and the intra-party yardstick competition to be removed altogether. Hence, what our results point out is that, if conditional-list PR makes voters and parties better o®, ruling politicians may be tempted to twist the rules governing the intra-party governance structure once they are in o±ce to avoid having to face the competition from their colleagues. To say it another way, the ex-ante and ex-post incentives politicians face are to be expected to di®er: as long as they are not in charge of an o±ce, politicians should have every reason to back the rank-and-¯le's desire to hold incumbents accountable, but

18 once they are given a seat, they would probably like to weaken or even severe their own accountability to the rank-and-¯le. This is yet another rationale behind our desire to augment existing empirical studies on the subject by explicitly taking into account the degree of internal discipline achieved within each party.

5 Intra-Party Competition/2: Allowing Parties to Dismiss Incompetent Incumbents

This section investigates what happens when we allow parties to behave as the electorate. That is, we allow them to remove all incompetent politicians from their o±ce and replace them before the new election takes place. We prove that this is a second very simple mechanism that leads equilibrium rent extraction to be lower under PR than under majority rule. A more rigorous de¯nition of the con¯rmation strategy of the incumbent party regarding its incumbent politicians is as follows:

De¯nition 1 (Party's con¯rmation strategy) An incumbent is allowed to stand for re-election if and only if her perceived competence ´J is bigger or equal to 1.

What this de¯nition says is simply that the incubmbent party will behave as the voters of each of district and send back home all underperforming incumbents. Having stated how the parties' con¯rmation strategy is de¯ned, we also need to take a stand on what happens once a politician is dismissed. We assume that any incompetent politician is sent home at the end of period 1 and replaced by a rookie. Under majority rule, given that the incumbents' objective function does not depend on the number of the district she is in charge of, solving the new game is relatively straightforward. Under closed-list PR, we need to be a bit more precise about what happens once an incompetent politician is ¯red. This is what we do in the following de¯nition.

De¯nition 2 (Party replacement strategy) Under closed-list proportional representation, if the incumbent ruling in district M is perceived as incompetent at the end of period 1 and is dismissed by the party, all (con¯rmed) incumbents that were ruling in any district N; with N > M; move up by one position in the electoral party list. The new candidate replacing the dismissed incumbent ends up at the bottom of the list.

As a matter of example, suppose that the incumbent in district 1 is ¯red. Then the incumbents in districts 2 and 3 become respectively ¯rst and second on the second period

19 party list, and the party member replacing the dismissed politician ends up at the bottom of the list.14 This mechanism is obviously only one of many possible rules. Yet, we believe it ¯ts reality quite well. After all, when rookies are thrown into the electoral arena, they often have to show their competence before being attributed safe positions inside the party. Why? Because the party wishes to maximize each incumbent's incentives to perform and therefore 'rewards' competent politicians by letting them move up the party list and puts new, 'untested' recruits at the bottom of the list.

5.1 Majority Rule

Let us ¯rst analyze how the game is a®ected under majority rule. Each incumbent now realizes that, in order to be both con¯rmed and retain her job in the second period, two events must be realized: 1) the incumbent's perceived competence must be bigger or equal to 1 { this happens with probability pJ; and 2) one of her two fellow politicians must be perceived as competent too. If these two events are realized, then the incumbent is in charge of a district in period 2 too. The combination of these two events implies that the probability that the incumbent in district 1, say, is con¯rmed is given by:

p1 p2 1 p3 + p3 1 p2 + p2p3 (21) ¡ ¡ where pJ is given by (7) abov£e. ¡ ¢ ¡ ¢ ¤ Incumbent 1's new problem is given by:

Max r1 + p1 p2 1 p3 + p3 1 p2 + p2p3 r 1 1 r1 ¡ ¡ © £ ¡ ¢ ¡J MAJD¢IS ¤ ª Label equilibrium rents under this scenario as r1 : The ¯rst order condition to this problem implies that equilibrium rents are given by: 3 rJMAJDIS = ¿y »r (22) 1 ¡ 4

5.2 Closed-List Proportional representation

Let us now turn to closed-list PR. We need to examine separately the problem each incumbent faces. We can prove the following lemma.

Lemma 1 All three incumbents face the same maximization problem, which is given by:

Max rJ + pJr (23) J 1 r1 © ª 14A simple rationale behind this rule is that the party wishes to maximise each incumbent's incentives to perform and therefore 'rewards' competent politicians by letting them climb up the party list.

20 where pJ is given by (7) above.

Proof. (We only prove the lemma for districts 1 and 2. The reasoning behind the proof regarding the incumbent in district 3 is identical to that of district 2's incumbent and is therefore omitted.) The incumbent in district 1 realizes that, in order to ensure that she is re-elected, she needs her perceived competence to be bigger or equal to 1. What happens in the other two districts does not matter anymore. Indeed, once she is perceived to be competent, two events are realized: 1) her party will con¯rm her; and 2) her party will win the election in her district, thus ensuring that the party is attributed at least one seat and therefore that she keeps a job in the second period (remember that district 1's incumbent always gets the ¯rst available seat under closed-list PR). Thus (23) is indeed the problem faced by the incumbent in district 1. Let us turn now to district 2's incumbent. Given our second de¯nition above, incumbent 2 knows that in order to keep a job in the last period, she needs to: 1) be perceived as competent; and 2) have her party win in enough district-wise elections to be certain to be granted an o±ce. But the second event is realized if and only if the ¯rst is. Indeed, if district 1's incumbent is perceived to be competent too, the party is certain to retain two seats and therefore incumbent 2 gets an o±ce in period 2 too. Otherwise, if incumbent 2 is perceived to be competent but district 1's incumbent is perceived to be incompetent, the latter politician is dismissed and district 2's incumbent becomes top of the party list. Then the party wins for sure the election in district 2 and incumbent 2 is attributed the job. What happens in district 3 is irrelevant. This implies that the incumbent in district 2 solves (23) too. We therefore have the remarkable result that as soon as the party commits to using all the information that is at hand to decide whether or not to con¯rm its ¯rst period incumbents, all politicians are put on an equal footing. This implies in turn that all voters are treated equally too, again allowing us to neutralizing the variance in cross-district equilibrium rent extraction characterizing closed-list PR under proposition (2) We expect that the threat of dismissal will also impact equilibrium rent extraction. Will the equilibrium be superior to that under conditional-list? Given that closed-list PR cum the threat of sacking leads each incumbent to see the electoral contests as a purely local, district-speci¯c one, the answer is that both mechanisms lead to the same equilibrium, namely:

rJPROP DIS = ¿y »r (24) 1 ¡

This in turn implies that we have established the following proposition.

21 Proposition 4 When parties commit to dismissing incumbents that are perceived as incompetent before the new election and replacing them with new politicians, equilibrium rent extraction is lower under closed-list proportional representation than under majority rule: 3 rJP ROP DIS = ¿ y »r < ¿y »r = rJMAJDIS 1 ¡ ¡ 4 1 Proof. By inspection of (22) and (24) Hence, we highlighted that a second, indirect disciplining mechanism that is within the party's reach is simply the use of the information the electorate itself has at its disposal. An intuition for this result is as follows. Given that, under proportional representation, incumbents are certain to be re-elected as soon as they are perceived as competent enough, independently of what the other two incumbents do, rent extraction in the ¯rst period will be lower than under majority rule, where incumbents are somehow 'hostage' of their party winning a strict majority of votes in the whole economy.15 Indeed, majority rule implies that incumbents face a lower probability of re-election than under proportional representation. As a consequence, their incentives to refrain from rent extraction are lower under majority rule. Nevertheless, the threat of dismissal does increase the incumbent's incentive to perform: pJ enters her probability of being re-elected with a positive sign only, whereas under majority rule without the threat of dismissal incumbent J's probability of being re-elected included a term in (1 pJ ) { compare (21) with (8). Hence, the ¡ preferences of incumbent J and her party are better aligned when the party commits to ¯ring incompetent politicians.

6 Conclusion

The main aim of the paper was to compare equilibrium rent extraction under di®erent institutional regimes. We showed that parties can exploit under proportional representation a wider set of tools than under majority rule to discipline incumbents. Yet, our results also highlight that rent extraction is more sensitive to intra-party discipline than to the electoral rule itself: equilibrium rent extraction depends on the degree of leeway incumbents enjoy once in o±ce, and may very well be lower under majority rule, provided incumbents control party lists under closed-list PR or incumbents execute mechanically the party's decisions. Hence, an urgent task for future empirical research is the gathering of information relative to the internal governance structure of parties. This should allow empirical research to reduce the omitted relevant variable problem that may be plaguing current results and o®er a new and more precise set of results on the links between rent extraction and electoral rules. 15Remark that in this case the mechanism is available under both rules, and not under PR only, as is the case when parties resort to using their electoral lists.

22 The following table summarizes all the ¯ndings of the paper, at the level of a single district16.

Rent Extraction by Individual Politician No Dismissal Dismissal Possible Full Direct Control majority rule ¿y »r=2 ¿y 3»r=4 ¿y 3»r=2 ¡ ¡ ¡ closed-list PR ¿y »r=3 ¿y »r ¿y »r ¡ ¡ ¡ cond.-list PR ¿y »r ¿y »r ¿y »r ¡ ¡ ¡

Having proposed a ¯rst analysis of the intra-party agency problem and the mechanisms that may reduce its e®ects, several key questions remain to be answered. One such question is: How and why is party discipline achieved? The importance of this question was most vivid in our discussion of the results of sections 4 and 5. Indeed, we showed the con°ict between ex-ante and ex-post interests is the key problem plaguing intra-party politicis under PR. Thus, a better understanding of the conditions and mechanisms that may reduce or, to the contrary, exacerbate the di®erence between ex-ante and ex-post objectives of individual incumbents is a pressing issue. Our feeling is that such issues require that we depart from the existing mainstream models of political economics that view parties and politicians as perfect substitutes and invest in a more detailed modelling of intra-party politics. This has already been stressed by Roemer (2001) and is the path taken by, for example, Caillaud and Tirole (1999, 2002) and Castanheira, Crutzen and Sahuguet (2004). Castanheira et al. indeed build on Caillaud and Tirole (2002) and provide a ¯rst answer to the determinants of a party's internal governance structure. They show that, in a general equilibrium framework where e®ort provision by politicians is a function of the party's internal governance structure, the choice of this structure impacts on a party's re-election prospects and therefore becomes a strategic choice variable for the party. Making further headway on this dimension would not only provide the literature with a more detailed analysis of party politics, but would also, as we highlighted repeatedly above, sketch the way towards a strengthening of available empirical ¯ndings and of the micro-political foundation of economic policy.

16In the case of closed-list PR, the level of rent extraction reported in the table is the average of that of the three districts.

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