One Tick and You re Out: The Effects of the. Master Lever on Senator Positions

One Tick and You re Out: The Effects of the Master Lever on Senator Positions Olga Gorelkina University of Liverpool, Liverpool Ioanna Grypari Max Planck Institute, Bonn This Version: October 2016 Abstract This paper accounts for the effects of the master lever (ML), aka the straight-ticket voting option, on elected US senators from 1960 till 2012. The ML, still present in some states, allows voters to select a specific party for all elections listed on a ballot, as opposed to filling out each office individually. Introducing it leads to an increase in the number of partisan votes, and thus changes the groups of voters targeted by parties and shifts the positions of senatorial candidates. Theoretically, we examine this change in tradeoffs by building a model of multidimensional pre-election competition. Empirically, we identify the effect of the ML by using a triple difference estimator to account for selection into treatment. Controlling for party trends, we find that it leads to a right-wing shift of senatorial positions, an effect that is larger for the Republican party. We use the theory to explain how the political climate, as observed by the data, implies the specific result. Keywords: Ballot Design, Elections, Political Positions, U.S. Senate - JEL: D72, K16, N42 The authors thank Ying Chen, Paola Conconi, Mira Frick, Martin Hellwig, Johannes Hörner, Anna Kochanova, Rida Laraki, Derek Stemple, Stan Veuger, Maurizio Zanardi and participants of the CRETE and EEA conferences and the MPI workshop; as well as Darya Babushkina and Georg Treuter for excellent research assistance, and the Cowles Foundation at Yale University for hosting Gorelkina in 2015-2016. University of Liverpool Management School, Chatham Street, Liverpool L69 7ZH, UK, olga@liv.ac.uk. Max Planck Institute for Research on Collective Goods, Bonn 53113, Germany, grypari@coll.mpg.de. 1

1 Introduction The Senate is one of the two chambers of the legislative branch in the US. Each state is represented by two senators, regardless of population, who serve staggered six-year terms. In other words, in every midterm or general (Presidential) election, at most one seat is up for election. The master lever, also known as the straight ticket voting option is a box at the top of a ballot that offers voters the possibility to vote for one party for all offices listed. The existence of a master level has been heavily debated and the number of states that offer the option has been decreasing over time. The main argument used against the master lever is that since in its presence voters are more likely to vote by the partisanship of the candidate as opposed to by her positions this leads to less informed voters and a lack of accountability for the politicians. However, another side to this issue is that the presence of the master lever shifts the groups of voters targeted by politicians. If introducing the master lever leads to more voters voting according to their partisanship, the parties will now have less incentive to target these partisan and put forth candidates with positions that will satisfy other groups of voters. In this paper, we provide a theory of multi-dimensional pre-election competition that models the incentives described above and which we estimate using data from the US Senate from 1960 till 2010. We find that the effects of the master lever on how moderate or extreme politicians are in their positions depends on the partisanship of the state (which party voters prefer), the average preferred voter position in each issue and the covariance between the two, the likelihood that a socially conservative voter is a republican partisan for example. This paper contributes to the literature on pre-election competition by studying the way a change in the ballot affects the game politicians play and thus offering a novel insight on the interaction of partisanship, policy positions and voting technology. 2

It also contributes to the growing empirical literature that studies the polarization of congressional positions, by introducing a so-far overlooked aspect, namely an important difference in ballots across US states. 1 Understanding these incentives is also a first step towards making policy recommendations with respect to the presence of the master lever by considering its effect on senator positions and thus congressional gridlock. We build a static model of parties and voters in a multi-dimensional issue space. Parties select which senatorial candidate to put forth by effectively picking their positions in each issue and voters vote for the candidate that they prefer. 2 Parties maximize their vote share in the election which they discount by the distance of their candidate s position from the party bliss point. The latter represents the party s willingness to be united in order to be able to pass more policies, or one can think of this as an incentive to maintain ideological purity and consistency over time. We find that equilibrium politician positions in each issue depend on the average partisanship of voters in the state, the average bliss point of voters and the covariance between the two. 3 In particular, introducing the master lever shifts the parties targeted group of voters away from weak partisans, i.e. those who could still vote by position but with the introduction of the master lever are more likely to vote by party. 4 If a party is the strong majority in the state, then the master lever will allow that party to put forth politicians closer to the party bliss point (since they will win the state anyway). If, however, we are in a weak partisan or non-partisan state by shifting the focus away from weak partisans both parties will have to target non-partisan voters or partisans of the other party. The positions they use to do this 1 We do not however claim that the master lever is enough to account for the evolution of senatorial positions over time. 2 For a discussion of primary elections and the senator already in power please see the theory section 3 Note that we separate between partisanship and positions and allow for liberals to be Republican for example. 4 The strong partisans will vote by party anyway. 3

depends on the covariance between voter partisanship and their bliss points. If for example we are in a non-partisan state where swing voters are more likely conservative, relative to the state s average, the introduction of the master lever will lead to both parties putting forth more conservative candidates (to try to appeal to swing voters). We use data from 1960 to 2010 to estimate the model. Voter-level data from Enns and Koch (2013) which use opinion polls to create state-level voter opinion data in two dimensions. For senatorial positions, we use the Poole and Rosenthal (2015) dataset which is estimated using the history of a senators roll call votes. 5 We build our own data set on the history of the master lever in each state as well as on senator characteristics, including their political history. In order to identify the treatment effect we employ the methodology of Ravallion et al. (2005) to account for the selection bias into having a master lever in the state. We separate the states into three groups 1. participant stayers (ML always), 2. participant leavers (ML, then no ML) and 3. non-participants. We construct a difference-in-difference (DD) estimator for stayers over non-participants and another one for leavers over non-participants and then take the difference between the two. This way we account for the effect of the ML as long as three things are satisfied: the selection is time-invariant, there is not selection into abolishing the ML and no lasting effects on winning senatorial positions after it is removed. We verify all three in section 4.6. We find that the master lever is a significant determinant of senator positions and our results fit the predictions of the model. We observe an asymmetry between the effects depending on whether the senator is a Democrat or a Republican, which we are able to explain using the empirical relationship between partisanship and preferred positions in the electorate. Overall, due to the parameter constellations, 5 The Yay or Nay when a bill is up for a vote. 4

the gradual removal of the master lever has in fact worked against the increasing political polarization of the Senate. The purpose of this paper is to account for the tradeoffs senators, and the parties behind them, face in the presence of a straight ticket voting option on the ballots. Theoretically, we model the way both the positions and share of votes of senatorial candidates are affected by a ML introduction and empirically we document the significance and direction of these changes for elected senators in the US. We observe that progressively more states are removing their option from their ballots and find that this change has negatively affected the number of Republican senators elected. Moreover, the parameter constellation in the data is such that postremoval Republican senators became more moderate and Democratic senators more extreme. This has direct implications for the composition of positions and parties in the Congress. This paper is organized as follows: section 2 presents the model and theoretical results, section 3 the data set, estimation and results, section 4 concludes. 2 Related Literature In this paper we account for the tradeoffs that senators, and the parties behind them, face in the presence of a straight ticket voting option, and document empirically the effects of the gradual removal of the ML across the US on the party and positions of elected senators. As this has direct implications on the composition of Congress, our paper relates to the literature on political polarization. 6 Political polarization is defined as the gap between Democratic and Republican parties at the mass and/or elite-level in some issue or ideological space. There is general agreement that political elites in the US are polarized. McCarty et al. (2006) 6 To be clear, we do not aim to explain the increasing Congress polarization. Instead, we examine the importance of a common ballot characteristic on the type of senators that get elected. 5

show that the difference in mean positions between the two parties has continued to grow since the 1940s in both the House of Representatives and the Senate and that this increase is driven more by the Republican Party. 7 There is an extensive literature on the causes of this phenomenon, 8 with a strong focus on the role of the voters. At the national level, there is no evidence of mass polarization and changes in the Congress composition have not been following changes in voter ideology, overall and across issues. 9 At the district-level, there is conflicting evidence on the importance of the electorate s preferences in predicting legislative behavior. Krasa and Polborn (2014) find that there is a stronger effect from politicians to voters, as opposed to the other way around, whereas Kirkland (2014) and McCarty et al. (2015) show that within state or district heterogeneity does lead to more extreme politicians. Harden and Carsey (2012) show that voter preferences can predict senatorial positions only in homogeneous states and that the voters party affiliation is a much more important determinant of political polarization. In fact, there is a growing literature on the importance of party sorting (the increased correlation between voter positions and their party affiliation) and within-state party strength in determining Congress members positions, with the direction of causality debated. 10 McCarty et al. (2006) and Garand (2010), among others, have examined the importance of income inequality in determining political polarization. In general periods of higher income inequality are associated with more extreme legislatures, that are also more right-leaning (Voorheis et al. (2015)). A lot of attention has also been given to the interaction of mass media with the electorate. 11 Campante and Hojman (2013) show that broadcast TV has led to more extreme Congress members, but Prior 7 Note that we use their dataset on senatorial positions. 8 See Barber and McCarty (2015) for a review. 9 E.g. Abramowitz (2010), Ansolabehere et al. (2006), Bafumi and Herron (2010), Fiorina et al. (2005), Fiorina and Abrams (2008), Tausanovitch and Warshaw (2013). 10 See Krasa and Polborn (2014), Layman and Carsey (2002) and Levendusky (2009), among others. 11 See Strömberg (2015) for a review of the literature. 6

(2013) finds no significant evidence of partisan media, in particular, influencing voter preferences. On the other hand, Snyder and Strömberg (2010) point to the importance of media coverage, with higher coverage leading to less ideologically extreme Congress members. Other factors that have been considered as a source of the increasing political polarization have been gerrymandering (redistricting), midterm vs Presidential elections, characteristics of the primaries and different elements of campaign financing. Engstrom (2013) accounts for the importance of redistricting on a variety of political outcomes (competitiveness of elections, partisan control, etc), but McCarty et al. (2009) find little evidence of a causal relationship between gerrymandering an ideological extremism, specifically. Different types of elections have been studied as well, with Halberstam and Montagnes (2015) finding that midterm elections are in fact associated with more extreme senators, whereas there is growing evidence that primary elections are weak in explaining polarization. 12 Lastly, in terms of campaign contributions, Barber (2016) finds that higher donation limits on PACs 13 lead to moderate legislators, and a larger number of donations from individuals to more extreme. The effect ballot design on polarization has not been considered, however there has been extensive research on the way it can affect voting behavior. Different ballot characteristics that have been examined are ballot secrecy (e.g. Heckelman (1995)), the ordering of names (e.g. Chen et al. (2014)), and the office bloc vs. party column ballot form (e.g. Walker (1966)). In terms of the ML in particular, as expected, its presence reduces the number of split tickets (voting for different parties for different offices), with varying effects depending on the party and office up for election. 14 Note also that when selecting 12 See Hirano et al. (2010), McGhee et al. (2014) and Barber and McCarty (2015). 13 Political Action Committees 14 See Kimball et al. (2002), McAllister and Darcy (1992) and Rusk (1970), among others. 7

the ML, all partisan elections on the ballot 15 are automatically voted on, and all non-partisan elections are counted as non-votes, unless a voter specifically chooses a candidate for these offices as well. In fact, Feig (2007), Feig (2009) and Kimball et al. (2002) do find that the ML decreases voter roll-off 16 and Bonneau and Loepp (2014) show that it decreases participation in non-partisan elections. In terms of voter errors, on the one hand Herrnson et al. (2012) demonstrate that a straight ticket voting option increases the occurrences of people not voting for the candidate they intend to, and on the other hand, Kimball and Kropf (2005) find that it reduces over-votes, i.e. cases when voters mark too many candidates. For our purposes, the most important take-away from this literature is that the ML is in fact used by voters, and it matters even for offices further up the ballot. 17 This paper brings together these two strands of literature. We do not examine directly the effects of the ML on electoral behavior, but we go one step further and account for the importance of this characteristic of ballot design on the positions and parties of elected senators. We contribute to the political polarization literature, by offering one more significant determinant, one that has direct policy implications. 3 Theory 3.1 Setup Fix a state and an election period, the offices listed on the ballot are indexed by k, k K {1, 2..K}. Let µ {0, 1} indicate the availability of the master lever (ML), or straight-ticket option, in the given state period. µ = 1 implies that ML is present 15 Those were candidates have party affiliations. 16 Lack of votes for offices further down the ballot. 17 In terms of which voters actually use the ML, Feig (2007) and Feig (2009) show that blacks are more likely to use it, and in a lab experiment Lewkowicz (2007) finds that Democrats and Republicans are equally likely to select the ML, but strong, weak and non-partisans in order have decreasing probabilities of using it. 8

and µ = 0 implies that ML is not available on ballot. We consider a multi-dimensional policy space P = [ 1 2, 1 2] N, where N is the number of policy issues, such as economics and ideology. Three types of actors are positioned within the policy space: voters, parties, and candidates for a given seat. The candidates as well as the parties they represent (one candidate per party) are indexed by j, where j {R, D}. The party has a bliss point denoted by Y j = (Y j1, Y j2,...y jn ) P. (1) Without loss of generality, we label issue positions so that the Democratic party s bliss point is to the left of the Republican bliss point in every coordinate, Y Dn < Y Rn, n {1, 2..N}. The bliss point of candidate j {R, D} is denoted y j, y j = (y j1, y j2,...y jn ) P. (2) Let y jn = y jn y jn represent the difference in candidates positions and y n = y jn +y jn 2 the average between the two, 18 and similarly let Y jn and Y n denote the difference and the average of the parties bliss points. Note that Y j is taken as exogenous in the model, but y j is endogenous and results from the party s optimization program stated below (11). by x i, There is a unit mass of voters indexed by i. Voter i s position is given exogenously 18 j = {R, D} /j. x i = (x i1, x i2,...x in ) P. (3) 9

Integrating over the mass of voters we obtain the average voter position in the state period X = x i di P. (4) [0,1] Apart from their political positions, the voters are characterized by the status of partisanship. Let p i (j) denote the probability that voter i (whose position is x i ) is a partisan of party j. 19 The realisation of the random variable is denoted Ii P ; Ii P = 1 implies that the voter is partisan, and I P i = 0 implies thaht the voter is non-partisan, or swing. Assuming that a voter can be a partisan of at most one party, we introduce the total probability of being a partisan p i = p i (j) + p i ( j). (5) Party j s partisan advantage in the state period is denoted p (j) = p (j) p ( j). The mass of voters who are partisans of party j is p (j), where p (j) = p [0,1] i (j) di. By analogy, p is the average partisanship status, p = p [0,1] idi = p (j) + p ( j). The average partisan position on issue n is given by X P n = 1 p i x in di P. (6) p [0,1] A given voter s political positions and partisanship status are generally not independent, the covariance is given by (p i p) (x in X n ) di. In our analysis, we shall use its negative, namely the covariance between the voter s position on issue n and the likelihood of being a swing (non-partisan) voter: 20 19 Alternatively, p i can be thought of as the mass of partisan voters within voter group i characterized by position x i. In contrast, p i cannot be interpreted as partisanship strength. Idiosyncratic variations in the strength of partisanship that we may observe in the data are absorbed by other model parameters such as the cost of going through the ballot and the error term in (10). 20 Here we use (1 p i ) (1 p) = (p i p). 10

σ n = (p i p) (x in X n ) di. (7) If σ n is positive then the swing voter status is associated with a more conservative (right-wing) position on issue n compared to the rest of the state. If σ n is negative, then the swing voters views on issue n tend to be more liberal (left-wing) than the state s average. Players, Actions, and Payoffs. Our model of an election with the master lever is an incomplete information game between two parties and a mass of voters. The game proceeds according to the following time-line: t = 1 Party j chooses a candidate (y jk ) to compete for seat k. The party derives utility from the share of votes it gets and incurs a loss if its candidate s positions differ from the party s bliss point (11). t = 2 Voter i decides whether to use the ML, if available. If the voter does not use the ML, she goes through the whole ballot incurring cost c i. t = 3 Voter i elects a candidate. The voter chooses the candidate to maximize her payoff (10). Conforming with the logic of backward induction, we analyze the game in reverse chronological order. t = 3 : Electing Candidates. If the voter uses ML, she solves a single maximization problem for the entire ballot: Û i = max j {R,D} k=1,..k u ik (j). (8) 11

Let ĵ i {R, D} denote the problem s solution: ĵ i is the party that gives maximum payoff to voter i in the election. If the voter goes through the ballot office by office, she solves a sequence of K distinct maximization problems: U i = k=1,..k max u ik (j k ). (9) j k {R,D} Clearly, the more refined solution (j i1, j i2,..j ik ) {R, D}K yields greater utility to the voter: U i Ûi. This is due to the restriction of the domain in (8) compared to (9). The voter s utility component in (8) and (9) is given by n u ik (j) = ω n (x in y jn ) 2 + β k + ε ij, if i is a partisan of j,, (10) n ω n (x in y jn ) 2 + ε ij, otherwise. The payoff from electing candidate j is depends on the discrepancy between the voter s and the candidates positions, the partisanship statuses and the candidate s unobserved characteristics. The first component of (10), n ω n (x in y jn ) 2, is the dis-utility experienced by i if the candidate j s positions differ from i s bliss point x i, where every issue n has weight ω n > 0. The second component is a partisanship bonus β k > 0, an extra payoff that the voter gets from electing his preferred party candidate. 21 Thirdly, ε ij is a preference shock, an advantage over the opponent j (ε ij = ε i, j ) that results from various factors such as presidential approval, differences in personality traits, perceived competence, candidate s visibility, campaign funding etc. 22 Regarding the shock, we assume that ε ij is uniform on [ 1 2, 1 2] and 21 The model predictions do not change if the utility function is modified so that electing a counterparty candidate yields a negative payoff to a partisan voter. 22 In a model focusing on the winning probability, as opposed to vote share, we would introduce 12

independent of (x i, p i ). t = 2 : Voter s Choice to Use the Master Lever. The voter decides whether to use the option by comparing the cost c i > 0 and the benefit U i Ûi of making a better choice by going through the entire ballot. Here, c i represents the cognitive effort and opportunity cost associated with solving K decision problems while she works on the ballot. 23 t = 1 : Party s Choice of Candidate. We model the party s problem as a tradeoff between attracting votes and satisfying its own policy agenda (ideological purity). The party solves the following optimization problem: 24 max y jn { V j n γ n (Y jn y jn ) 2 }, (11) where V j E i Pr (j i j) is the share of votes for candidate j, and γ n > 0. The first term of the party s maximization program reflects the natural driving force of political competition. The second term corresponds to the party s cost from being represented by a candidate with views diverging from the party. In a wider interpretation the term captures any force that deters optimal candidates from converging to the midpoint as implied by the standard Downs (1957) model. 25 Note that we have assumed that parties can freely select a candidate with the optimal position y j. In reality, the party s choice may be restricted by primary elections; we do not study this possibility here, but we do account for them in the empirical an aggregate candidate-specific shock η j. 23 If the cost of going through the ballot was negligible, we would have observed equal participation in the elections for all offices on the ballot. A recent study by Augenblick and Nicholson (2016) shows that this is not the case, therefore the cost is relevant. 24 We can think of the party s { global election problem, i.e. the problem where the party cares about all seats k K: max y k π ke i Pr (j k i j k ) k,n γ jkn (Y jn y jkn ) 2} with some weights jkn π k, γ jkn. Due to the additive separability of the said global election problem in y jkn, we can focus directly on (11). 25 See Harden and Carsey (2012) for an overview of work showing that candidates do not converge while campaigning for office, but rather tend to take divergent positions. 13

exercise. 26 Assumptions We let n ω n = n γ n = 1 and β < 1 to guarantee that the solutions are interior. We assume α n 2 γn ω n 1, for all n, implying that there is not too much disagreement between the parties and the voters on the issues relative importance. 27 To simplify the exposition, we also assume that the cost c i of going through the ballot satisfies the following double inequality: Ui IP ( ) ( ) Ûi c i U IP i =1 i Ûi. i =0 Then the voter uses ML if and only if she is a partisan. Qualitatively, our results do not depend on this assumption. In a separate appendix, we consider an alternative set-up where c i are not constrained to the above interval and distributed independently across the population of voters. 28 In this framework, the partisans are only more likely to use ML than the swing voters and the ML effects are the same as reported in Section 3.2. 3.2 Master Lever Effects The change in master lever status observed in the data provides exogenous variation in µ {0, 1}. 29 In this subsection we study the model s solutions with and without the master lever and deduce the ML effects on three outcomes: candidates platforms (Proposition 1), winning probabilities (Proposition 2), and the expected platform of the election winner (Proposition 3). 26 Hirano et al. (2010) and McGhee et al. (2014) find little evidence of primaries effect on the platforms pf the elected officials. 27 If parties and voters weight issues equivalently then α n = 2. 28 See Supplementary material included in this submission. 29 We solve the problem of selection into ML status (states either always had, never had or had and then removed the ML) using DDD. 14

3.2.1 Candidates Platform We start by characterizing the optimal platform derived as a solution of the Bayesian game of three stages. Proposition 1. The optimal position of candidate j on issue n, yjn, is a convex combination between the average voter position in the state X n and the party s bliss point Y jn with a drift proportional to the swing-position covariance σ n. The master lever increases the weight of the party s bliss point Y jn and the effect of the swingposition covariance σ n. The statement follows directly from the following expression derived in the Appendix (see Proof of Proposition 1 in appendix A.1) y jn = for all n, where α n 2γ n /ω n. 1 µp 1 µp + α n X n + α n 1 µp + α n Y jn + µσ n 1 µp + α n (12) When the ML is introduced voters are diverted from position voting. This implies, on the one hand, that the candidate s position has a smaller effect on the voters behavior and thus the party can choose a loyal candidate. On the other hand, since partisan voters use the ML, swing votes get a higher weight in position voting. Therefore, the party has to pay increased attention to swing voters preferences. We start by discussing these effects as they appear in (12). First effect: Party loyalty. To pin down the first effect, we focus on a state where the voter s partisanship status and her position on issue n do non-correlated (σ n = 0). (As an example take any 0-symmetric distribution of positions x i and let partisanship p i be an even function of the position, i.e., p i (x i ) = p i ( x i )). In this case, the optimal senator position is a convex combination of that of the average voter and the party bliss point, irrespective of the existence of the master lever. 15

However, in the presence of the ML the party can afford to choose a candidate whose views on the issue conform better with the party s views. This effect is stronger in more partisan states, supporting the conclusion from Kirkland (2014). However in an extreme conservative state, where Y Dn < Y Rn < X n, introducing the master lever leads the Republican party to choose instead a more moderate candidate. The same is true for the Democratic party in an extremely liberal state, where X n < Y Dn < Y Rn. Second effect: Following the swing voter. Now let us drop the assumption of zero covariance. In states with few partisan voters introducing the master lever will force the party to follow the direction of the swing voter. The reasoning is as follows. Suppose that holding more liberal (left-wing) views is associated with being a partisan and, therefore, associated with using the master lever. Since ML attracts left-wing voters, the average position of those who through the ballot and judge the candidates by their political positions shifts to the right. Hence, the optimal candidate s position must satisfy a more right-wing voter when ML is introduced. In other words, rightwing swing voters become decisive in voting by position. Thus, when σ n is positive the ML effect is also positive. If instead σ n is negative, the argument is symmetric: since swing voters tend to the left, then so does the average voter among those who pay attention to candidates platforms. Therefore, the party can increase the winning probability by choosing a more left-wing candidate. Note that since σ n can be viewed as a proxy for heterogeneity in an asymmetric state, the swing voter effect increases if the voters in a state hold more extreme views. Total effect. The direction of the total effect of the master lever depends on the relation between the effects of party loyalty and swing voter, which may reinforce or counteract each other. The direction of the total effect is determined by a single intuitive inequality: Introducing the master lever results in a right shift of y jn if and only if α n Y α n+1 jn + 1 X α n+1 n > Xn P. In particular, if both the party and the average 16

voter are more conservative than the partisan voter, then the ML results in a right shift. If both are more liberal than the partisan voter, then the ML results in a left shift. When neither is true, the ML effect depends on the partisan voter s position relative to a convex combination between the party and the average voter. The effects of party loyalty, swing voter and the total effects are discussed formally in appendix A.1 Lemmas 1, 2, and 3. 3.2.2 Effect on Vote Share While both parties choose their candidates position to maximize the share of votes they get, one of the parties will have an advantage due to partisanship support and the distribution of voters positions in the state. The master lever has a differential effect on relative importance of these determinants of vote share. Proposition 2. The Republican (Democratic) party gets more votes in the state where (i) the Republican (Democratic) party has more partisan support, (ii) the swing voter is more conservative (liberal) than the state s average voter, and (iii) the average voter s bliss point is to the right (left) of the average between the parties bliss points. The master lever increases the effect of (i) and (ii), and decreases the effect of (iii) in the number of votes recieved by the parties. The determinants of the parties success in the election, such as voters positions and partisanship, have the obvious effects. The party that is in one way or another closer to the electorate gets a larger number of votes. What is more surprising is that the master lever has a differential effect on these determinants. While it reinforces the role of partisanship and the covariance effect, it devalues the advantage of position proximity between the state s average voter and the party, ceters paribus, in particular given the same partisan support. What does it actually mean, to fix partisanship and covariance, while shifting the average position, say, to the right? This can be achieved by introducing a uniform right shift in all voters positions without changing their 17

partisanship status. The claim of the proposition is that the Republican party would benefit more from such a right shift if the master lever is absent. The intuition for the result is as follows. ML makes both partisanship and swing voters more decisive in the election, while the position of the average voter becomes less important, since fewer voters elect by position. Remark that our result has important implications on the parties target audiences in states with different ML status. In non-ml states the parties will try non-discriminatorily to affect the positions of voters in a states through mass media outlets that reach a wide audience. In ML states, however, the parties will target a specific group: the swing voters. In ML states the parties can thus achieve higher vote shares by using the same amount resources in a more focused way. 3.2.3 Compound Effect: Expected Position of the Elected Senator Knowing the optimal positions of candidates and vote shares we can evaluate the expected position of the election winner. y n = V j y jn + (1 V j ) y jn. (13) The expected platform of the election winner y is a convex combination of the endogenous positions of the Republican and Democratic candidates, where respective vote shares serve as weights. 30 Proposition 3. Consider two states that differ in the ML status, but are equivalent otherwise. In expectation, the winner in the ML state is more right-(left-)wing on an issue than the winner in the non-ml state if (i) the states are red (blue) (ii) the swing voter tends to be right-(left-)wing, (iii) the average voter is left-(right-)wing, and (iv) the average and the swing voter agree with the Republican (Democratic) party 30 In a model with aggregate noise, vote shares represent the winning probabilities; in this case (13) is the mathematical expectation of the election winner s position. 18

on other issues. This finding sheds light on the interplay between the results we obtained in propostions 1 and 2. The effect of the master lever on the ultimate position of the senator comes through both the determination of the winning party and and the shift in candidates positions. The party with larger partisan support is more likely to win in an ML state and therefore the elected candidate is more likely to represent this party and its platform. The same is true of the party that attracts voters on the whole set of issues. However, as we know from Proposition 2, ML makes the average voter less decisive in an election, therefore the winning candidate in a non-ml state will better represent the average voter s views. The swing voter effect works similarly on both candidates, and thus on the elected senator. 4 Empirics In this section, we identify the effect of the ML on an elected senator s position and party and use the theory to account for the mechanism behind our findings. We focus only on elected senators as this is what we can observe in the data, and throughout we discuss any issues arising from the lack of information on the losing candidate s platform. 4.1 Data We use data from the 87th (1961-62) to the 112th (2011-12) Congresses and their preceding elections. Our main dependent variable is taken from Poole and Rosenthal s DW-NOMINATE scores, which summarize a senator s position, using her (roll-call) voting history, into a two-dimensional vector for each congress. 31 The first dimension 31 See Poole and Rosenthal (2015). DW stands for dynamic weighted and allows for cross-congress comparisons. The scores are from around -1 to around 1 (some observations outside the interval), and we have converted them from 0 to 100. 19

is the one that explains most of the variation in votes and the second one, perpendicular to the first, is set to explain the rest of the variation (Carroll et al. (2009)). We use only the former and it corresponds to y j in the theory. 32 Moreover, we construct the following senator variables using information on the US Senate website and the CQ Press Guide to US Elections: their party, year(s) of election, years in Senate, whether they were an incumbent, appointed into office (i.e. not elected) or did not complete a full term. For each senator we also note the position and characteristics of the senator in power (SIP), i.e. the one was not up for election in the same year. State-level data on the average voter position, X in the theory, is taken from Enns and Koch (2013). 33 They combine select questions of all available public opinion polls into a two-dimensional dynamic state policy mood on the size and scope of government. This is in contrast with our variable for senators that sums up positions on all issues. However, as voter beliefs on the role of the government have direct implications on most Senate policies, we assume that the two policy spaces are comparable. 34 As with the DW-NOMINATE scores, the policy mood has a major and a (orthogonal) minor component, which is weak in explaining voter opinion and which we do not use. Enns and Koch (2013) also create state-level party identification variables (fractions of self-declared Democrat, Republican and non-partisan voters) that we use both as controls and as a way to classify states into red (mostly Republicans), blue (mostly Democrats), swing (mostly non-partisans) and purple (almost equal and high numbers of both Democrat and Republican partisans). Appendix A.2 gives the precise empirical definition of this partisanship classification. We also create a positional 32 Poole and Rosenthal (2007) find that after 1978 the one main dimension is sufficient in explaining Congress member behavior. If we do use the second dimension, which captures deviations from a senator s main bliss point, the effect of the ML becomes insignificant. 33 It varies from 0 (left-wing) to 100 (right-wing). 34 This assumption is not essential for the identification. 20

classification, which separates states into extreme left-wing, moderate and extreme right-wing states, depending on the position of the average voter with respect to the parties bliss points (see appendix A.2). We define the latter as the median DW- NOMINATE score of all elected members of each party for a specific Congress. 35 Note also the Democratic party used to be internally divided. In some southern states its members were representing more right-wing views, as opposed to the North. After the passage of the Civil Rights Act of 1964 and the Voting Rights Act of 1965 the party division slowly dissipated. 36 Mapping this to the theory, it suggests potentially two sub-parties with two different bliss points. To allow for this possibility, we create a dummy variable southd that takes the value 1 when considering one of these originally deviant states. 37 Lastly, we construct our own data on the existence of the ML per state and Congress, which we compare with that of Klarner (2010) for corroboration. 38 4.2 Summary Statistics In the 26 Congresses that we examine, there are 894 senators up for election, 39 a total of 2620 observations (all senators, all Congresses) and 423 unique senators (excludes incumbents), belonging to either the Democratic or the Republican party. 40 The left graph of figure 1 depicts the decrease in the number of states with a ML over time, and the right one the evolution of the average position of elected senators per party. The distance between the two parties defines the polarization in 35 We use these classifications in section 4.5 when employing the theory to understand our empirical findings. We point out that a state can move across classes from one election to another, and also that these classes are based on self-declared voter opinions and not on actual votes. 36 See McCarty et al. (1997) for an analysis. 37 a. They are Arkansas, Georgia, Kentucky, Louisiana, Mississippi, North Carolina, Oklahoma, South Carolina, Tennessee, Texas and Virginia. b. For convenience we will call non-southd states, northern. 38 In the contradicting cases we found sample ballots or other evidence to deal with the discrepancy. Note also that Washington, DC does not elect senators. 39 Before each Congress there is normally at most one seat up for election per state. 40 We have removed the very few observations of Conservative and Independent party senators. 21

the Senate, which has been increasing. 41 As it can be seen here, and consistent with previous findings, the Republican party seems to be the stronger driving force of the polarization. 42 # States 10 15 20 25 30 1960 1968 1976 1984 1992 2000 2008 Year Average Position 30 40 50 60 70 80 1960 1968 1976 1984 1992 2000 2008 Year # States w/ ML DEM REP Notes - Left: Number of States with ML over time. Right: Evolution of average party position in the Senate, from left (0) to right-wing (100). Source: Data from Poole and Rosenthal (2015) Figure 1: ML Presence & Senate Polarization On the left panel of figure 2, we show the evolution of the average senatorial position per party, separating states by whether or not they offer a ML on their ballots. 43 It is evident that for the Republican party a straight ticket option is correlated with more right-wing senators (closer to 100), whereas for the Democratic party the relationship, if any, is not clear. The right graph displays the fraction of Democratic senators, by ML presence. Keeping in mind that there is a lot of variation across periods away from both fitted lines, we still see that in states without a ML there is not much change in the fraction of representatives by party over time, which is about equally split. For ML states, however, in early periods the Democratic party seems to be benefiting from its presence, whereas over time, as the set of states with the option decreases, there is stronger representation of the Republican party. 41 There are different definitions of polarization used in the literature, we picked one for illustration. 42 See McCarty et al. (2006). 43 Note that the sets of states with and without ML changes over time (figure 1). 22

Average Position 30 40 50 60 70 80 % Elected Senators 0.2.4.6.8 1 1960 1968 1976 1984 1992 2000 2008 Year 1960 1968 1976 1984 1992 2000 2008 Year DEM ML DEM no ML REP ML REP no ML DEM ML DEM no ML Notes - Left: Evolution of average party position in the Senate separating states by ML presence; positions vary from left (0) to right-wing (100). Right: Fraction of elected senators that are Democrats by ML presence. Source: Data from Poole and Rosenthal (2015) Figure 2: Positions and Party of Elected Senators by ML Presence On the flip side of the market, we have the voters. Figure 3 shows the evolution of self-declared positions and partisanship of voters by ML presence, on the left and right graphs respectively. Voters do not seem to be systematically different across types of states, with an exception towards the end of the time period. 44 Moreover, as we discuss in section 4.1, we have created partisanship and positional classifications of states since the predictions of the theory may vary within each. 45 States can move across classes from one period to the next, and table 1 displays the number of states, in the whole time period, per class and ML. Note first that the latter is significantly present in all subcases. Second, the skewness observed across positional classes (more extreme left than extreme right-wing states) should be viewed with caution as the definitions of voter and senator positions, that determine this classification, do not perfectly align. 46 44 Note that the remaining fraction of voters missing from the right graph are self-declared swings (non-partisans). 45 Definitions in Appendix A.2. 46 See section 4.5 for a discussion. 23

Average Position 30 40 50 60 70 80 1960 1968 1976 1984 1992 2000 2008 Year % Partisans 10 20 30 40 50 60 1960 1968 1976 1984 1992 2000 2008 Year Voters ML Voters no ML % DEM ML % REP ML % DEM no ML % REP no ML Notes - Left: Evolution of self-declared average voter position by ML presence; positions vary from left (0) to rightwing (100). Right: Fractions of Republican and Democrat partisans by ML presence. Source: Data from Enns and Koch (2013) Figure 3: Positions and Party of Voters by ML Presence Lastly, figure 4 includes scatter-plots depicting the correlation between the average voter position and different fractions of partisanship types across all states. As expected, a higher fraction of Democratic voters corresponds to a more left-wing average voter position (top right graph), and vice versa for the Republican voters (top left), although in this case the relationship is not as clear. In terms of partisan and swing voters, there is no ex-ante reason to expect a specific direction, but we notice that a higher fraction of partisans is associated with leftist states (bottom left), whereas more swing voters imply a more right-wing state (bottom right). These correlations are key in explaining our empirical findings. 4.3 Identification In order to identify the effects of the ML on elected senators we will employ a triple difference estimator (DDD). The treatment is whether or not a state offers a straight ticket voting option on their ballots in a specific election. There are two kinds of 24

Table 1: Number of States by Classes & ML Type ML = 0 ML = 1 Total Red 87 46 133 Blue 311 278 589 Swing 250 146 396 Purple 99 83 182 Extreme Left 104 111 215 Moderate 619 425 1044 Extreme Right 24 17 41 Total 747 553 Notes: Number of states by ML, partisanship and positional classes; definitions in appendix A.2. Source: Data from Poole and Rosenthal (2015) and Enns and Koch (2013) states in our sample, nonparticipants, i.e. states that never had a ML (21 states), and participant states. The latter are split into stayers, that always had the ML (15 states) and leavers, those that originally offered the option and then abolished it during the sample period (14 states), so that overall we have three groups of states. 47 Selection Bias. Whether or not a state offers the ML is a state-level decision, the result of local politics, and arguably of federal-level party politics as well. 48 The same forces behind this selection bias affect also the choice of senatorial candidates and thus our dependent variables. Since we do not have pre-treatment data for participants (i.e. there are no states that introduced the ML after 1960) we cannot use simple difference-in-difference (DD from now on) to control for time-invariant group effects. However, we do have data on leaver states after they removed the ML, and they can be used as a control group. We also account for the possibility of economy-wide changes that could affect stayers and leavers differently, in the absence of the ML, by comparing both of these groups to nonparticipant states. In particular, as in Ravallion et al. (2005), the DDD estimator, is the difference 47 a. We are using the terminology of Ravallion et al. (2005). b. Michigan, Oklahoma and Texas that removed the ML only for one year are treated as stayers. 48 For example, a popular media opinion is that the party that is losing the state is the one pushing for the removal of the ML. 25

X vs % REP X vs % DEM X 0 20 40 60 80 X 0 20 40 60 80 0 20 40 60 80 % X vs % Partisans 0 20 40 60 80 % X vs % Swings X 0 20 40 60 80 0 20 40 60 80 % X 0 20 40 60 80 0 20 40 60 80 % Notes: Scatter plots of average voter positions, from left (0) to right-wing (100) vs fractions of republican (top left), democrat (top right), partisan (bottom left) and swing (bottom right) voters, in all state-congress combinations. Source: Data from Enns and Koch (2013) Figure 4: Average Voter Position and Partisanship Per State between the DD of stayers over nonparticipants and the DD of leavers over nonparticipants (left panel in figure 5). They show that this estimator isolates the treatment effect of the ML as long as the following hold. Identifying Assumptions (IA). Conditional on state and Congress characteristics, 1. there is no selection into removing the ML, and 2. there are no lasting effects of the ML after it is removed. The right panel in figure 5 shows the implications of these in the simple case where there is one date of removal for all leaver states. The assumptions guarantee that leavers are the right control group, so that the DDD estimator is not picking up 26

any leaver effects. Condition (1) implies that all participant states experience the same effects of the ML regardless of whether or not it is removed in the future, and (2) that post-ml removal leavers are behaving like non-participants states. To sum up, as the graph shows, we need leavers to have common trends with stayers before the removal of the ML and with non-participants after. We verify these conditions in section 4.6. DDD stayers (ML always) DD Identifying Assumptions y stayers nonparticipants (no ML) DDD leavers DD leavers (ML, then no ML) Figure 5: Identification remove ML nonparticipants t Specification & Clustering of Errors The corresponding regression framework is the following. Let j denote the party, s the state and t the Congress: y jst = β 0 + β 1 ML st + Controls jst + η s + η t + η p + η pj t + ε jst (14) where ML st is the treatment dummy, η s, η t, η p and p jt are state, Congress and party fixed effects and a party trend. 49 We cluster the errors at the senator-level, assuming thus that there are unobservables for each senator that may affect her position. For example her charisma may allow her further positional deviations from the voters 49 In the full specification (column (5) of table 2), we include interaction effects of the controls with the ML as we know that the parties are facing different tradeoffs and could be moving in opposite directions. We also take this into consideration when verifying the identifying assumptions. 27