Party Labels and Information: The Implications of Contagion in Coelection Environments

Transcription

1 Party Labels and Information: The Implications of Contagion in Coelection Environments Yosh Halberstam B. Pablo Montagnes March 13, 2009 Preliminary and Incomplete Abstract In related empirical work, we demonstrate that, relative to midterm elections, in presidential elections a more ideologically moderate electorate produces a more extreme and polarized senate. In particular, we find that senators first elected during presidential election years are relatively more extreme than their counterparts first elected during midterms; conversely, we find that incumbents who leave office in presidential elections are relatively more moderate than those who leave in midterms. In this paper we propose a model in which the presence of party labels in an environment of incomplete information produces a contagion effect across contemporaneous races for office a coattail effect. In the aggregate, this contagion generates electoral outcomes that are consistent with our empirical findings and other well-known phenomena from the literature, such as midterm attrition. Department of Economics, Northwestern University; Postal Address: 2001 Sheridan Road, Evanston, IL 60208, USA; y-halberstam@northwestern.edu Department of Managerial Economics and Decision Science, Kellogg School of Management, Northwestern University; Postal Address: 2001 Sheridan Road, Evanston, IL 60208, USA; p- montagnes@kellogg.northwestern.edu 1

2 1 Introduction The staggered terms of the presidency and congressional offices in the United States create two electoral environments: midterm elections and general elections. In midterm elections, the entire House of Representatives and one-third of the seats in the Senate are up for elections. In general elections, in addition to congressional races, the presidency is up for election. These two electoral environments generate two cohorts of senators: those who are first elected to the Senate concurrently with a president and those who are first elected in midterms between presidential election years. 1 The existence of these two electoral environments is an artifact of the variation in term lengths for senators and presidents. There was no explicit intent by the framers of the constitution to create electoral environments that would differ in any significant way; in fact, senators were originally chosen by state legislatures leaving the selection process explicitly separated from the electoral environment. Thus, the specific environment general or midterm elections in which senatorial candidates run for office is not intended to favor any one type of candidate over another. In a related paper, however, we find consistent and significance differences between these two cohorts of senators. Surprisingly, we find that the cohort of senators first elected in general elections is ideologically more extreme than the cohort of senators first elected in midterm elections. 2 Conversely, we find that senators who leave office in midterms are ideologically more moderate than those who leave in general elections. These results suggest that something beyond the coincidence of timing differentiates general election environments from midterm election environments. Such differences in these environments might include the ideological preferences of the electorate, the behavior of voters, or the types of candidates contesting in elections. In this paper we propose a model in which the presence of party labels in an environment of incomplete information produces a contagion effect across contemporaneous races 1 We exclude from analysis those senators who are only appointed. 2 In context of the United States, relative ideological extremism corresponds to more liberal positions for Democrats and more conservative positions for Republicans. As will be discussed, our left-right unidimensional ideology measure. mirrors this liberal-conservative ideology framework. 2

3 for office a coattail effect. The presence of coattails alters the range of electorally viable positions in down-ticket races, and therefore alters the expected type of winner and loser. Because coattails are only present in general elections, they constitute a significant structural difference between midterm and general elections. In the aggregate, this contagion generates electoral outcomes that are consistent with our empirical findings. In our model, candidates from the same party share a common ideology, but differ in their exact ideology due to idiosyncratic differences and local electoral conditions. 3 Citizens have prior beliefs about party platforms, but do not know the exact party position. While they may observe candidate positions in some races for office, they need not observe candidate positions in all races. For those that observe candidate positions in only a subset of races for office, citizens can update their beliefs about parties and candidates in other races. This updating introduces a rational contagion effect that alters the competitive landscape in races in which citizens do not observe candidate positions. A relatively more moderate candidate in the observed race creates a coattail effect for other members of her party running for office. This enables relatively more extreme and less electorally viable candidates to win. Alternatively, a relatively more extreme candidate reduces the range of electorally attainable positions for his ticket. Our theoretical and empirical results suggest that previous attention to the seat-voteshare relationship and the effect of coattails on down ticket performance alone may understate the impact that simultaneous elections have on each other. A broader implication of our model is that the introduction of an unbiased public signal may have perverse effects on the aggregation of private information and preferences. Before proceeding with a formal presentation of the model, we first describe the relevant institutional details and motivating empirical facts from Halberstam and Montagnes (2009). A brief discussion of the relevant literature follows. In section 2, we present our theory model in detail and derive a set of predictions and comparative statics. Following a discussion of the data, in section 4, we test intermediate and aggregate predictions of the model and find them consistent with the data. In section 5, we conclude with a discussion 3 We do not model parties or their candidate selection process directly. For examples of such models, see Snyder and Ting (2002) and Caillaud and Tirole (2002).. 3

4 of possible theoretical implications of our work on models of voting and party competition and the policy implications of our empirical findings. 1.1 Previous Empirical Findings In our previous paper, we compared the ideologies of senators first elected in midterms with those first elected in general elections. Put differently, we examined how electoral environments affect the process in which citizens preferences are aggregated and represented. Our principal finding was that the cohort of senators first elected in general elections is more ideologically extreme than the cohort first elected in midterms. This result is surprising in light of empirical evidence suggesting that the electorate s ideological composition is relatively more moderate in general elections. 4 In addition to the results on entry by electoral environments, we obtain an analogous set of results by segmenting senators according to their exit environment. Once again, counter to what empirical evidence on the electorate would suggest, senators who leave office during the time period around general elections are significantly more ideologically moderate than those who leave office in midterms. Together, these two results suggest that the relatively more moderate electorate in presidential election years generates a more extreme and polarized Senate. Looking at the relationship between electoral environments and outcomes solves some of the problems associated with testing models of electoral competition and voting behavior. Our methodology relates variation in electoral environments to outcomes, and not variation in characteristics of the electorate to outcomes. Specifically, given the exogenous oscillation between midterm and general elections, we can identify differences in electoral outcomes attributable to electoral institutional details alone; thus, we need not collect data on voter preferences or individual characteristics. This allows us to examine a long 4 Surprisingly, the literature comparing the electorates in midterm and general elections is somewhat lacking, and direct comparisons of the electorates are missing from the literature (see Leighley-Nagler (2007)); however, given the substantial and consistent variation in turnout between general elections and midterms, we can use results on the relationship between voter turnout and ideology to interpolate the differences. For example, Palfrey and Poole (1987) find that a citizen s likelihood to turn out and vote is highly correlated with ideological extremism. Leighley-Nagler (2007) find additional indirect evidence that voters are significantly more likely than non-voters to be strongly partisan. 4

5 range of electoral outcomes at the national level, instead of restricting our analysis to a particular time or locality. Since we are concerned with aggregate results, unobserved elements of electoral competition, such as the position of losers are immaterial. 5 Our focus is on establishing a relationship between types of senators and electoral environments, and not on direct tests of electoral competition models. 6 The ideology measure that we employ in both our papers is Poole and Rosenthal s DW-NOMINATE scores. These measures are based on voting records, and are the most robust and widely employed measures of ideology. Since these measures are strongly predictive of roll call voting behavior and are relatively stable over time, they can proxy for future voting behavior and policies that Congress promulgates. Therefore, consistent differences in ideologies of senators stemming from differences in electoral environments may correspond to consistent differences in policy. By looking at the types of senators produced by different electoral environments, we can connect these environments to future policy outcomes and not solely to immediate electoral concerns. Our dataset is comprised of senators who were elected to the senate from 1966 to present. For each senator we gather biographical information from the CQ Congressional Collection as well as data on the voteshares in their races and the presidential race at the state level. dataset. We combine these data with Poole and Rosenthal s DW-NOMINATE Using information about senators entry and exit environments, senate race voteshares, state-level presidential race voteshares, and party identification, we employ a non-parametric methodology to compare the DW-NOMINATE scores of senators first elected in general elections to their midterm counterparts. We perform this comparison for each congress in our 40 years of data, and run an identical analysis in which we use a senator s exit environment as the classification criterion. In order to test the predictions of the formal theory developed in this paper, we also compare the ideology of senators according to state-level presidential voteshares. We con- 5 The predictions that we test are about the expected positions of winners and incumbent losers. While any one race need not adhere to the predictions of our model, our predictions about differences in electoral environments should hold in the aggregate. 6 A discussion of how the results established in this paper relate to various models of voting and electoral competition follows in the conclusion. 5

6 firm previous researchers results linking state-level presidential voteshares to down-ticket success the coattail effect. In addition, we find that broader support for a presidential candidate is associated with more success among ideologically extreme candidates from his party, and moderate candidates from the other party. 1.2 Literature Beyond the impact of presidential coattails on down-ticket party support, literature on concurrent electoral environments is sparse. Previous research has focused on the coattail effect, or the relationship between the popularity of a presidential candidate and the prospects of other candidates from the same party (See Coate and Knight (2007) and Besley Preston (2007) for reviews of this literature). For example, Campbell (1993) has examined the difference in size and composition of the voting population in midterm and general elections, and the success of the president s party in each environment; however, previous research has overlooked whether the types of senators elected in these environments are invariant to the number of simultaneous races for office being held. Our results suggest that the effects of presidential coattails might have implications beyond success for the president s party, namely on the policy positions of senators. A more recent strand of literature has attempted to make the connection between the electorate and the ideology of elected senators; a leading example of this type of work is Aldrich et al (2007). In a forthcoming book chapter, the authors demonstrate the link between constituent demographics and the ideological position of senators as measured by DW-NOMINATE scores. They demonstrate consistent and strong relationships between the scores and state demographic characteristics. Since the data they employ include broad measures of statewide characteristics, they cannot connect the ideology of senators to the preferences of voters in particular. Moreover, this literature does not address the implications of institutional details imbedded in electoral environments. 6

7 1.3 Institutional Details Federal elections are held on the first Tuesday following the first Monday in November during even-numbered years. When two or more elections for office are held concurrently, we term them coelections. Members of the House of Representatives, senators, and presidents serve terms of two, six and four years respectively. Although all scheduled elections occur during even-numbered years, the variation in term lengths produces disparate electoral cycles. During every federal election year all 435 seats in the House of Representatives are contested; whereas, only one-third of the seats in the Senate are up for election at a time. 7 2 Model Since we are interested in the results of state-wide senatorial elections, we model elections at the state-level. 2.1 Policy Space and Parties Let the policy space be P R and let s {1, 2, 3,..., 50} denote one of the 50 states. As discussed, a major difference between general and midterm elections for senators is the presence of a concurrent presidential elections. In each race there are candidates from two parties, L and R, running for office. Depending on the election cycle, there are one or two races for office. We denote presidential and senatorial candidates with superscripts p and s respectively. Let C r q P denote the position of a candidate from party q {L, R} running for office r {p, s}. Candidates from the same party are ideologically similar, but differ due to individual idiosyncratic reasons, local state conditions, or other factors; however, in a 7 This creates three classes of senators and thus three distinct senatorial electoral cycles. At the national level, there are five electoral cycles: the two year House cycle, the four year presidential cycle, and the three classes of senatorial six year cycles. For statewide elections, there are three electoral cycles, the presidential cycle and the two senatorial cycles. Because there are three classes of six-year terms, and the two Senators from the same state belong to different classes, electoral cycles for junior and senior senators will be two or four years apart. 7

8 given race for office, the candidate from party L will always be to the left of the candidate from party R in any given race. 8 That is, C r L C r R r {p, s}. In our model, senatorial and presidential candidates are not perfectly aligned with the underlying platforms of their parties, and races for the Senate occur at the state level under different political environments. The electoral environment and citizenry attributes of states vary with some states being more conservative and others more liberal. These differences in state characteristics are also reflected in the positions of senatorial candidates across parties. Since the particulars of party strategy are in of themselves not of interest to voters. As such, we focus on the decision relevant consequences of party competition and will return to those following an initial microfoundational setup. 2.2 Citizens Citizen Preferences The main objective of our model is to explain aggregate voting behaviour and empirical regularities; thus, we are less concerned with the particular details of the microfoundations of preferences and party competition. Nonetheless, we face a trade-off when studying large elections: the tractability and clarity characteristic of modeling agents in a continuum comes at the cost of providing little motivation for strategic rational citizens to turn out and vote in any race for office since each citizen s likelihood of being pivotal is, essentially, zero. Since we focus on two-candidate races for office, however, we note that an equilibrium and its outcomes in which voters vote sincerely is equivalent to one in which they vote strategically. As we are modeling the two-party competition of the United States, our results are not compromised by focusing on underlying proximity preferences and voting. 8 Empirically, we observe that Democrat senators are almost always to the left of Republican senators; however, our assumption is made for state level races (and presidency), and in our data the assumption is always true when we observe senators from both parties in one state. 8

9 Our model of citizen microfoundations is inspired by work of Degan and Merlo (2007) in which citizens have a benefit from voting in a given race but are subjected to an ex-ante cost of voting for the wrong candidate voting for the candidate whose position is less like her own. 9 Obviously, in an environment in which there is no uncertainty about candidate positions all citizens vote for the right candidate and obtain the benefit of voting. However, in our setting these preferences have great appeal as they directly incorporate the role for different levels of information. 10 Let I s R be the set of citizens in state s. We specify for each citizen i I s a corresponding ideal point y i P, which is citizen i s most preferred policy position. At the state level, the preferences of voters are distributed symmetrically and unimodally around the state preference mean, µ s, with the corresponding cumulative distribution function, F s. We assume that citizens have proximity preferences and incur symmetric disutility from voting for candidates with policy positions equally diverging from their own. Citizens have preferences over the policy positions of winners. We model these preferences with a quadratic loss utility function to represent these preferences as follows: u i (y) = ( y i y ) 2 (1) where y is the policy position of a candidate. 11 We next follow similar model specification as in Degan and Merlo (2007) and assume that each citizen i can receive a benefit b ( 0, 1 2) for voting in a particular race for office. This can be thought of as the utility of doing one s civic duty or the right to brag of one s participation in the Democratic process. In a case in which there is no uncertainty, there 9 See Degan and Merlo (2007) for a discussion of the psychological motivations behind these preferences, as well as structural model that test the validity of the preferences with voter level data. 10 These preferences also have an interesting interpretation in light of the swing voter s curse. The cost of a voter s uncertainty as to which candidates position is closest to their own preferences can be thought of as a psychological proxy for the voter s strategic concerns. Higher uncertainty corresponds with a greater probability of making a mistake. As a voter s preferences become more extreme, the voter is less likely to make a mistake voting for one party or the other, and therefore becomes a partisan voter. 11 The actual functional form of these preferences is not essential to our model. Our result will follow exactly if we employ any form of symmetric loss preferences. More generally, our result hold for any single peaked preferences but at the expense of clarity and tractability. 9

10 is no associated cost of voting and each citizen votes for the candidate who shares a policy position that is closest to her own. Formally, citizen i votes for C r L in race for office r if and only if: u i (C r L) > u i (C r R) (2) and obtains a benefit of voting b. Given our assumption that CL r Cr R, condition (2) simplifies to: y i < Cr L + Cr R. (3) 2 Notice that the only information a citizen considers when deciding for whom to vote is the midpoint of candidate positions. Essentially, a citizen is concerned with the relative ideological position of a candidate rather than her absolute position. Given this insight, our approach henceforth will focus on candidates ideological midpoint in a race for office rather than on their particular positions Incomplete Information We now introduce an environment in which, a priory, not all citizens are perfectly informed about the policy positions of candidates. Let M r Cr L +Cr R 2 be the ideological midpoint of candidate positions running in the race for office r. Denote with r i the information set ( beliefs ) that citizen i has about the ideological midpoint of candidate positions in race r and let G r i (M r ) denote the subjective distribution that represents citizen i s beliefs in race r. Citizens are aware of the underlying party conditions and labels; thus, the subjective beliefs about candidate positions correspond with their actual distribution. If citizen i has no uncertainty about the ideological midpoint in race r then r i = M r in which case the distribution representing this information set, G r i (M r ), is degenerate; otherwise, r i = G r i (M r ). In this case, uncertainty can produce a non-zero ex-ante psychological cost of voting. Let c i (q r ; y i, r i ) denote citizen i s psychological cost associated with voting for the 10

11 candidate of party q in race r with information r i. Specifically, citizen i s cost of voting for a candidate from party L in the race for office r is: ˆ ( ) c i L r ; y i, r i = dg r i (M r ) = P ( M r < y i) (4) {M r :M r y i } This expression is a sum of all states in which voting for the candidate from party R is the better choice weighted by the subjective probability of the state. Overall, we arrive at a closed-form solution that bears some appeal: citizen i s cost of voting for the candidate of party L is the probability of making a mistake the candidate of party R shares a closer position with citizen i than the candidate of party L. Since this probability ranges from zero to one and the benefit from voting is less than half, there are now two decisions each citizen must face: whether to vote in a given race and for whom Citizen Choices and Objective Denote citizen i s turnout decision in race r by t r i {0, 1}, where if she decides to vote in race r, (t r i = 1) and if she abstains (t r i = 0), and let the ballot she casts be vi r {L r, R r }. Given these specifications, citizen i maximizes the following objective function: [ ( )] Max t r i {0,1},vr i {Lr,R r } tr i b ci v r i ; y i, r i (5) Citizen Actions Given the previous objective function, each citizen s voting and turnout decisions can be solved using backward induction. A citizen first chooses her preferred candidate, and then decides whether the benefit of voting outweighs the cost of voting for her preferred candidate. We can derive for each citizen i a conditional voting rule and a turnout rule as follows: 12 A strategic interpretation of these preference is that as the possibility of making a mistake decreases, then regardless of pivot probabilities, a voter is more likely to vote for her preferred party. 11

12 Voting Rule: Conditional on voting, vote for party L s candidate in race r if and only if: P ( M r < y i) < 1 2 (6) and for party R s candidate otherwise. Turnout Rule: Tun out to vote in race r if and only if: Min { P ( M r < y i), P ( M r > y i)} < b (7) and abstain otherwise. Notice that the voting rule is independent of whether a citizen decides to actually turn out and vote or not; it just specifies that, conditional on voting in race r, a citizen should cast her vote for the candidate from the party whose associated cost incurred by voting is less than one half. It follows that since the sum of the costs of voting for the candidates of parties L and R in race r is equal to one that if the cost associated with voting for one candidate is less than one half than the cost of voting for the other is greater than one half. Thus, conditional on voting in the race for office r, a citizen votes for the party whose candidate s position, she expects, is likeliest to be closet to her own. Since the cost of voting is less then half for only one candidate and that the benefit of voting is no greater than half, the Turnout Rule implies a cutoff position at which a citizen is indifferent between obtaining the benefit of voting and incurring the cost associated with voting for her preferred party s candidate and not turning out to vote in race r at all Citizen Classification We now segment citizens into three classes differentiated by the degree to which they are informed about races for office p and s. Although we now assume that the degree to which a citizen is informed is uncorrelated with her preferences, this assumption can be relaxed 12

13 and is not essential for generating our results. 13 Let i = { p i, s i } denote citizen i s information about the ideological midpoints in both races. Accordingly, each citizen in a given state s is classified in one of three ways: 1. Fully Informed Citizen (FIC): these citizens observe the ideological midpoints of candidate positions in both the presidential and senatorial races for office. For a citizen i in this group, i = {M p, M s } 2. Partially Informed Citizen (PIC): these citizens observe the ideological midpoint of candidate positions in the presidential race only. For a citizen i in this group, i = {M p, G s i (M s )} 3. Uniformed Citizen (UC): these citizens do not observe ideological midpoints of candidate positions in either race. For a citizen i in this group, i = {G p i (M p ), G s i (M s )} Under our reduced form model of party competition, candidates from the same party in races p and s are linked by their party labels. PICs use Bayes rule to update their priors upon observing presidential candidate positions; thus, they condition their subjective distribution over senatorial candidates using information about the positions that presidential candidates take. Consequently, in each race for office, citizens either use party labels or their observations of races to make turnout and voting decisions. Given our specification of preferences, a few results are immediate. First, FICs always observe candidate positions, turn out in both races and vote for the candidates whose positions are closest their own. Second,UCs use party labels to determine whether and for whom to vote in each race. Finally, PICs always turn out in the presidential race and use their proximity preferences to vote, they then update their beliefs about senatorial candidate positions and accordingly decide whether and for whom to vote using party labels To the degree that preferences are correlated with how well-informed a citizen is about candidate positions, empirical work indicates that ideological extremism is associated with more informed citizens, in which case our primary aggregate results would be even more profound. 14 Although, theoretically, there may exists other groups of voters, namely, those who observe senatorial candidates but not presidential ones and would employ up-ticket inference, we believe that given the 13

14 2.3 Reduced-form Party Competition As citizen s conditional voting decisions depend on proximity preferences, given our ordering of candidates by party, the essential element of party competition for citizen decision making is the distribution of the midpoint of candidate positions in races. Modeling only the midpoints of party competition has several advantages. The first is tractability; by not modeling the underlying party competition process, it is much easier to aggregate the underlying decision process of citizens. Additionally, the updating process between races that citizens employ and comparative statics on the relevant model primals will be transparent. Second, this approach highlights the robustness of our results to any model of party competition. Any spatial model of party competition will result in some distribution of candidate positions (including degenerate distributions.) These distributions of candidate positions will in turn generate a distribution of midpoints. While we employ the Normal distribution for the tractability and transparency purposes, our results are robust to any underlying midpoint generating process. Let M p be the midpoint of candidates in the presidential race, and M s be the midpoint of senatorial races. Equations (8) and (9) describe the model of midpoints for presidential and senatorial races respectively. M p }{{} Presidential Race Midpoint = }{{} Ω + }{{} ɛ p Party Midpoint Presidential Race Idiosyncratic Effect (8) M s }{{} Senatorial Race Midpoint = }{{} Θ s + }{{} Ω + }{{} ɛ s State Fixed Effect Party Midpoint Senatorial Race Idiosyncratic Effect Let the overall midpoint of party competition, Ω, be fixed but otherwise unknown to citizens. Let citizens prior beliefs over the the unknown party midpoint be represented by a Normal distribution with mean µ ω and variance σ 2 ω. Additionally, let the idiosyncratic evidence about cyclical turnout in the U.S. in conjunction with substantially more information conveyed about the presidential race than the senatorial one, for simplicity, we assume this fraction and other marginal types of voters away. (9) 14

15 race-specific effects be independently distributed Normal with mean zero and variance σ 2 ɛ,r for r {p, s}. The state fixed effect is assumed to be non-stochastic. The overall priors over midpoints in presidential and senatorial races are: M r N ( ) µ r, σr 2 r {p, s} (10) where µ s = µ ω + Θ S, µ p = µ ω, σ 2 p = σ 2 ω + σ 2 ɛ,p and σ 2 s = σ 2 ω + σ 2 ɛ,s. Since the positions of senatorial candidates and presidential candidates share a common party element, citizens can update their priors about the senatorial race using information about the presidential race; thus, it follows that the updated prior over Ω conditional upon observing the midpoint m p in the presidential race is: (Ω M p = m p ) N ( ( ) m p µ p ( ) ) µ ω + σ ω ρ ω,p, σω 2 1 ρ 2 σ ω,p (11) p where ρ ω,p is the correlation coefficient between presidential candidate midpoints and the prior distribution over Ω. Two comments about our model of midpoints and party competition are warranted, the first incidental and the second substantial. We have chosen to have the midpoints of candidate position be Normally distributed around a competition mean. While the choice of a Normally distributed idiosyncratic shock is innocuous, the choice of a Normally distributed prior over midpoints has no direct basis in theory per say. The choice is made in order to make the updating process for voters clear and tractable. Our results do not depend substantially on these assumptions and are robust to any underlying model of party competition. The second more substantial assumption in our model of parties is that the choices of candidates are not conditional on the selections in other races We implicitly assume that parties are playing a simultaneous move game. This assumption depends on the sequential nature of candidate selection, entry and primaries at the state level. In our view, this process is best viewed as a simultaneous game. 15

16 2.4 Individual Citizen Behavior Citizens decisions on turnout and, conditional on turning out, voting in Senate elections depend on their expectation and certainty about candidate positions. Citizens differ in their preference, but also importantly in their information about candidates. Electoral environments also present citizens with differing amounts of information. In midterms, citizens can only possible observe candidates in the race of interest, but in presidential races an additional signal in the position of presidential candidates is available to some citizens. In order to highlight the role of information and electoral environments, we present the behavior of citizens by information levels according to electoral environments. We describe the turnout and conditional voting behavior of citizens in the informationally poorer midterm environments, and in general elections Citizens Turnout and Voting Decisions As a baseline for the following characterization, suppose that the realized midpoints are M s = m s and M p = m p. WLOG, assume that the senatorial race midpoints in midterm and general elections are identical Uninformed Citizens The behavior of UCs is deterministic in that it depends only on priors about Senate candidate positions and not on the actual realization of candidate position. As the distribution of candidate positions does not vary by electoral environment, this implies that the conditional voting and turnout behavior of uniformed citizens will not differ between midterm and general elections. The conditional voting behavior of UCs is simply to vote for the candidate whose position is in expectation closest to their ideal position. Thus, conditional on turning out, 16

17 a UC votes for party L s senatorial candidate if and only if: 16 y i < E [M s ] = µ s This voting decision depends only on priors about candidate positions and as noted does not change in general elections. The turnout decision of UCs depends both on their ideal point and their benefit of voting. Under our maintained assumption of a constant/common benefit to voting we can define a zone of abstention where the uncertainty over which parties candidate is closer makes voting too costly for UCs. This cost of voting results in a zone of abstention centered about the expected midpoint of candidate positions. Formally, UCs find it too costly to vote and abstain when their ideal points lie in the range: 17 [ Φ 1 (b) σ s + µ s, Φ 1 (b) σ s + µ s ] (12) As the uncertainty increases or the benefit of voting decreasing, the range of abstention increases on both sides. The turnout and conditional voting behavior of uninformed voters could be described as partisan in the following sense: First, only uninformed citizens with relative extreme preferences choose to voter. Second, the citizens that do choose to vote, vote exclusively for one party. They do so, even though for some of these voters voting exclusively for one party will result in them making the wrong decision in terms of ex-post proximity. Fully Informed Citizens Like UCs, the behavior rules governing conditional voting and turnout for FICs does not vary by electoral environments. In both electoral environments, the cost of voting for FICs is zero and thus given any positive benefit to voting, FICs will turnout. Thus, like 16 Since our distribution is continuous, indifference occurs with probability zero. Nonetheless, our voting rule assigns indifferent voters to party R. For voters with incomplete information, indifference will also imply that they abstain, thus the only relevant case of indifference for senatorial races is for FICs. 17 Even if voters have a strict preference in expectation for one of the two choices they still may not turnout. 17

18 UCs, the set of FICs turning out to vote is constant. This suggests that the variation in turnout will come from the set of PICs. The voting decision of FICs is likewise simple to characterize: FICs vote for the party whose candidate s realized (actual) position is closest. Thus a FIC votes for party L s senatorial candidate if and only if: y i < m s Whereas we might classify the voting and turnout behavior of UCs as partisan, the voting and turnout behavior of FICs could be though of as swing voters. Their voting decision depends solely on the realized position of candidates and does not incorporate their prior (ex-ante) beliefs in their decision making. While FICs might exhibit an ex post bias in voting for one party or another, they will always vote for the candidate that is closest to them without regards to party label. Partially Informed Citizens Midterm Elections Like UCs, the behavior of PICs in midterms is deterministic and depends solely on prior beliefs about candidates positions. Thus, conditional on turning out, a PIC votes for party L s senatorial candidate if and only if y i < E [M s ] = µ s. Similarly, the turnout decision for PICs depends on their ideological position with citizens in the zone of abstention not turning out to vote. For midterms, the range of abstention is the same as for UCs: [ ] Φ 1 (b) σ s + µ s, Φ 1 (b) σ s + µ s 18

19 General Elections PICs differ from UCs and FICs in having different behavioral rules for turning out and voting in general elections. In general election environments, PICs observe the positions of presidential candidates and are able to update their priors about the positions of senatorial candidates. 18 The conditional rule for PICS incorporates both their prior beliefs about the positions of Senate candidates and their observation of realized presidential candidates positions, with the degree of updating depending on the the amount of correlation and the degree of variance. Formally, conditional on turning out, a PIC votes for party L if and only if the updated expected position of the L s party candidate is closer or ( ) m y i < E [M s M p = m p p µ p ] = µ s + σ ω ρ ω,p. σ p Likewise in general elections, the senatorial turnout decision of a PIC depends upon her observation of presidential candidates. The effect of observing presidential candidates is two-fold. First, the overall uncertainty about the positions of senatorial candidates is reduced, and the zone of abstention shrinks. Second, the center of the zone of abstention can move depending on the realization of presidential candidate positions. Formally, the zone of abstention is: [ ( ) m p µ ] p µ s + σ ω ρ ω,p ± Φ 1 (b) σs σ 2 σωρ 2 2 ω,p p As will be discussed later, the overall effect is that the turnout of PICs increases in general elections relative to midterms. 2.5 Aggregation of Citizen Behavior In the following sections, we discuss and present formal results about difference in aggregate behavior by electoral environments. These results form the connection between the 18 As candidates for the Presidency and the Senate share a common party element, an observation of the position of presidential candidates confers information about the overall party position. 19

20 microfoundations of voter behavior and information in our models and the comparative statics that we derive to test our model with the aggregate data that we observe. We first discuss the overall differences in the turnout by electoral environment and then turn to the question of a coattail effect generated by rational informational contagion. In this section, we focus on the differences in electoral outcomes in the senatorial race generated by midterm and general elections. Since we demonstrated earlier that the turnout and conditional voting behavior of UCs does not vary between these electoral cycles, we can simplify our analysis by renormalizing the population to preclude such citizens. Essentially, UCs who turn out are partisan voters (i.e., they vote for a given party s candidate regardless of any particular realization of the state). This allows us to focus on FICs and PICs. Let δ (0, 1) denote the proportion of PICs in the (renormalized) population Voter Turnout The turnout decisions of FICs are the same in both electoral environments. Any differences in turnout between midterm and general elections is thus generated by the behavior of PICs, and we can focus our attention on comparisons of the range of abstention between the two environments. We continue our analysis for a given realization of midpoints, such that M p = m p and M s = m s where we assume that the senatorial midpoint is identical in both electoral environments. Recall, that in midterm elections the range of PICs who choose to obtain is a connected set of length: 2Φ 1 (b) σ s centered around µ s, while in the general elections, the range of abstention is of length: 2Φ 1 (b) σs 2 σωρ 2 2 ω,p centered around µ s + σ ω ρ ω,p ( m p µ p σ p ); thus, for any non-zero correlation, the zone of abstention will be narrower in general elections than in midterms, implying higher turnout 20

21 for any given midpoint. 19 Additionally, since µ s is the median of the unimodal symmetric distribution of preferences for PICs, shifting the range of abstention (even if it is of the same size) decreases the mass of citizens abstaining. This result, combined with a strictly smaller zone of abstention implies increased turnout. The necessary condition for increased turnout is the presence of contagion across races for office. Once this condition is satisfied, the correlation and the difference between m p and µ p have a complementary effect on turnout. This result is summarized in proposition 1. Proposition 1: Turnout Citizen turnout in general elections is strictly greater than turnout in midterm elections if and only if ρ ω,p Conditional Voting Our interest is in examining the difference in voting decisions in Senate elections between electoral environments. The conditional voting decisions of UCs and FICs in the senatorial races for office are independent of the realization of the presidential candidate idiosyncratic effect.focusing on PICs, we establish a relationship between the voteshare of party L s presidential candidate and party L s senatorial candidate conditional on a realization of party midpoints. Consider a particular realization of M p = m p. We can rewrite the realized presidential effect, ɛ p = e, in terms of the fixed party effect and the realized midpoint of presidential candidates, such that e = m p Ω. The presidential voteshare among PICs for party L is now a function of the realization of the idiosyncratic presidential effect of the two candidates. Let π L,p (e) be the presidential voteshare for party L among PICs conditional the realization of m p Recall, σ 2 s = σ 2 ω + σ 2 ɛ,s, and ρ ω,p [0, 1]implies that σ 2 s σ 2 ωρ 2 ω,p σ s, with strict inequality for ρ ω,p Note, presidential voteshares at the state level are monotonically related across states. In an abuse of notation, we sometimes refer to sate level presidential voteshare as π L,p where the interpretation is clear. 21

22 π L,p (e) = F s (M p ) = F s (Ω + e) (13) Similarly let π L,s (e) be the senatorial voteshare for party L among PICs conditional the realization of party positions. Note that this it is a function of the presidential idiosyncratic realization and not the senatorial one. Let ζ e (e) be the fraction among PICs who choose to turn out and vote in race for office r as a function of the presidential idiosyncratic effect, conditional on the realization of M p = m p (in the case of the presidential race ζ p (e) = ζ p = 1), then we have: π L,s (e) = ( F s Φ 1 (b) ( )) σs 2 σωρ 2 2 ω,p + µ s + σ ω ρ Ω+e µp ω,p σ p ζ s (e) (14) Notice that since π L,s(e) e > 0 and π L,p(e) e > 0, among PICs the relationship between presidential voteshare and senatorial voteshare is positive. We term this relationship the coattail effect as it is independent of the actual realizations of the party platform and is generated solely by a good or bad (for party L) draws of the idiosyncratic characteristics of presidential candidates. Proposition 2: Contagion Among PICs, favorable idiosyncratic draws in the presidential race are associated with greater support for presidential and senatorial candidates. Formally, for any two distinct realizations of ɛ p : e and e, if e > e then π L,p (e ) > π L,p (e)and π L,s (e ) > π L,s (e) Proof: Follows directly from derivations ofπ L,p ( ) and π L,s ( ) Electoral Outcomes in the Senatorial Race for Office In this section, we focus on the differences in electoral outcomes in the senatorial race generated by midterm and general elections. Without loss of generality, we focus on party L to demonstrate the comparative statics for electoral outcomes of candidates in the senatorial race for office in state s. The following results will symmetrically hold for party R. 22

23 Midterm Elections In a midterm election, a senatorial candidate of party L in state s with senatorial race midpoint M s = m s wins office if and only if: (1 δ) F S (m s ) + δπ L,s 1 2 (15) The first term on the LHS is associated with the measure of FICs whose ideal point is to the left of the candidates positions midpoint (and, thus, will vote for the candidate for party L) weighted by their proportion in the overall (renormalized) population in state s. The second term relates to the measure of PICs in the renormalized population who vote for the senatorial candidate of party L. Since the proportion of PICs votes is split equally between the candidates of both parties independent of the realized ideological midpoint in the senatorial race, that measure is equal half. 21 Overall, this condition simplifies to: m s > F 1 s ( ) 1 = µ s, 2 which reads that party L s candidate wins if the realized senatorial race midpoint is to the right of the median citizen s ideal point in state s. Thus, the probability that a candidate of party L wins when M s = m s is: P (W in s L M s = m s ) = 1 m s µ s 0 otherwise (16) Notice that the FICs determine which candidate will be the winner in this case. Given their proximity preferences, if the senatorial race midpoint is to the right of the FIC s 21 Uniformed voters provide no advantage for any given candidate since they vote with equal proportions for both candidates 23

24 ideal point than the candidate of party L wins office. Formally, the range of midpoints that result in a victory for the senatorial candidate from party L is (µ s, ). General Elections Recall that in the previous section we derived the expressions for conditional senatorial voteshares attributed to PICs, such that when ρ = 0 these measures are equivalent to those we find in midterm elections (i.e., π L,s = π R,s = 1 ) and there is no contagion between 2 races for office in general elections. Now suppose that ɛ p = 0, as ρ ω,p increases the number of citizens induced to vote for each party increases evenly. Thus, proportion of PICs voting for each party remains the same (i.e, π L,s (0) = π R,s (0) = 1. Thus, if the realized 2 presidential idiosyncratic error is identical to its expectation then the votes of PICs in the senatorial race are split equally; however, more PICs turn out to vote relative to midterm elections. Essentially, an increase in ρ signifies that PICs have more information when facing the senatorial race for office, which in turn reduces their ex-ante cost of voting for the wrong candidate ceteris paribus. Now, suppose that ρ ω,p > 0 and that ɛ p 0 then the sign of the realized error will determine which senatorial candidate will benefit from a built-in advantage passed down from the presidential race for office. We will focus the following comparative statics on the presidential idiosyncratic error while conditioning on a fixed level of correlation, ρ ω,p > 0. In a general election with ɛ p = e, a senatorial candidate of party L in state s with senatorial race midpoint M s = m s wins office if and only if: (1 δ)f s (m s ) + δπ L,s (e) 1 2 (17) As before, the first term on the LHS of equation (1) is the measure of FICs who vote for the candidate of party L weighted by their measure in the population while the second term is the weighted measure of PICs who vote for for party L respectively. The inequality 24

25 simplifies to: 22 [ ] 1 m s F 1 S 2 + δ 2 (1 δ) (1 2π L,s (ɛ)) h s (e) (18) Thus, the probability that a candidate of party L wins when M s = m s is: 1 if m s > h s (e) P (W in s L M s = m s ) = 0 otherwise (19) Suppose there is a positive draw, such that e > 0, then µ s > h s (e). Consequently, given a positive draw of ɛ p, the range of ideological midpoints that result in a win by party L s candidate in the senatorial race contains the corresponding range derived for midterm elections. As before, the range of midpoints that result in a win for party L is (µ s, ); whereas in general elections the range is (h s (e), ).We now have the following condition: (µ s, ) (h s (e), ) e > 0 (20) The following propositions establish the relationship between the ideological positions of senators, something we observe in our data, with the electoral environment in which they were first elected. The basic result is that in general elections as the support for the 22 Notice that since π L,s (e) [0, 1], h s (e) Also, note that for ρ > 0, ( ( ) ( )) 1 F 1 S 2 δ 1, F 1 S 2 (1 δ) 2 + δ 2 (1 δ) and that h s (e) e < 0 h s (e) = µ s e = 0 in which case this result boils down to the baseline midterm election win condition, though turnout increases. 25

26 presidential candidate of party increases, the range of electorally viable positions for that party s senatorial candidate increases. This increased range of electoral viability occurs as a larger set of PICs are induced to vote for a senatorial candidate independent of the realized idiosyncratic ideology of the candidate. 2.6 Testable Comparative Statics In this section, we present propositions on the aggregate effects of our model of voting, information and party competition. We will assume a fixed underlying structure, holding constant the relative population of citizens by type, and the underlying party competition structure. Of interest, empirically, is the relationship between presidential success and the positions of entering and exiting senators; thus, instead of relating idiosyncratic realizations of presidential positions to the senatorial race, we employ presidential race voteshares. Since proposition 2 establishes the monotonic relationship between ɛ p and party L s presidential voteshare, π L,p ( ),we can instead condition on realizations of the observable presidential voteshare. Throughout we will consider three possible draws of presidential support for party L: π L,p, π L,p and π L,p where π L,p > π L,p > π L,p. 23 As results are analogous for party R, we presents proofs for party L. Proposition 3 : Entry and Coattails The expected ideological position of winning senatorial candidates for party L (R) is decreasing (increasing) in support for the presidential candidate of party L (R). Formally: 24 E [ C s L W in s L, π L,p] E [C s L W in s L, π L,p )] Proof: See Appendix 23 Each of these presidential voteshares is the result of a particular realization of the idiosyncratic realizations in the presidential race. As we will want to compare general elections to midterms we let π L,p = π L,p (ɛ ),π L,p = π L,p (ɛ)and π L,p = π L,p (0) where ɛ > 0 > ɛ. π L,p is the presidential voteshare that corresponds to a state-level split among PICS, or equivalently, the midterm voting proportions for PICs. 24 E [ CL S W ins L, ] [ π L,p = E C S L CL S [2L ( π L,p) C S R, CR S)] 26

27 Sketch of Proof: By previous result, the range of winning midpoints for a party L Senate candidate is [h s (e), ). As there is a one-to-one relationship the realization of e and realized presidential voteshare π L,p (e), we can write this range in terms of presidential voteshare: [L(π L,p ), ). If we consider a fixed party R senate candidate with position CR s = cs R, we can rewrite this range in terms of party L s Senate candidate positions: [2L(π L,p ) c s R, c s R]. A higher presidential voteshare π L,p implies a greater coattails and a increased range of viable midpoints, thus L ( π L,p) < L (πl,p ) and the overall range of winning positions for senatorial candidates from party L increases strictly on the leftward boundary and remains the same on the right boundary: [2L(π L,p ) c s R, c s R] [ ] 2L(π L,p) c s R, c s R As the positions of party L s possible senatorial candidates range over this entire support, the expected position of those that win will be strictly lower. The next proposition establish a similar result for exit. For a senator from party L, less support for party L s presidential candidate implies a greater range of losing positions. The increase in losing positions occurs at the middle of the distribution, implying that more moderate candidates are expected to lose when presidential support is low. Proposition 4: Exit and Coattails The expected ideological position of a exiting Senator for party L (R) is increasing 27

28 (decreasing) in support for the presidential candidate of party R (L). Formally, E [CL Lose s s L, π L,p ] > E [ ] CL Lose s s L, π L,p Proof: See appendix Sketch of Proof : The logic of the proof is similar to that of the previous proposition. Decreased support for party L presidential candidate implies an anti-coattail effect. This increases the range of losing positions for party L s Senate candidates on the right boundary. As the position of candidates ranges over this entire range, increasing losers on the right races the expected position of losing candidates for party L. The following proposition establishes that increased support for a party s presidential candidate is associated with a greater probability of winning in general elections for same party senatorial candidates. Proposition 5: Matched Winners A candidate in general elections is more likely to win when the presidential candidate of his party has stronger support. Formally, P ( W in s L π L,p) > P (W in s L π L,p ) Proof: See Appendix Respectively, Proposition 6 establishes that decreased support for a party s presidential candidate is associated with a greater probability of losing for candidates from the same party. Proposition 6: Unmatched Losers A candidate in general elections is more likely to lose when the presidential candidate of his party has weaker support. Formally, Proof: See Appendix P ( Lose s L π L,p) < P (Lose s L π L,p ) The final proposition compares the relative total effect of the previous propositions. 28

29 Informally, the losing effect is expected to be greater than the wining effect in the following sense. Proposition 7: Nesting In general elections, the expected positions of losers are more extreme than the expected position of winners. Formally, E [ ] [ ] CL W s in s L, π L,p > E C s L Lose s L, π L,p Proof: See Append ix 3 Data 3.1 Entry and Exit Details Our dataset consists of all senators who faced federal elections for the first time between 1966 and For each senator we gather biographical information from the CQ Congressional Collection. These data include state-level turnout rates, party identification, starting and ending dates for service in the Senate and corresponding presidential voteshares if entry or exit occurred in general elections. 25 We use these dates to construct two classification variables: the first indicates for each senator her entry environment and the second, if applicable, her exit environment. Since we focus on senators entry and exit electoral environments, we refer to cohorts of senators as follows: the general entry cohort refers to senators first elected in general elections, while the midterm entry cohort refers to senators first elected in midterms. Conversely, the general exit cohort refers to senators who leave office during the period around a general election, whereas the midterm exit cohort refers to senators who leave office during the period around a midterm election We use data on states Voter Eligible Population (VEP) to determine turnout. To proxy for the increase in turnout in general elections among PICs we divide the total turnout rate in general elections by the average turnout rates in the preceding and succeeding midterm elections. 26 Because the number of terms that senators serve varies and the electoral cycles of a junior and senior senator in a given state are two or four years apart, a state s Senate delegation may or may not display both electoral environments 29

30 We exclude senators who were appointed to fill a vacated seat, unless they are subsequently elected in regular federal elections. In our analysis of exit electoral environments, we do not distinguish between incumbent senators who lose and those who do not seek reelection; however, we exclude senators who leave office due to death or who leave office before the end of their term. Finally, we preclude from our analysis senators who were not affiliated with the Democratic or Republican parties during both their entry to and, if applicable, exit from the Senate. In table 1 below, we summarize the data by party identification with respect to our classification criteria. Table 1: Senate Electoral Composition Democrats Republicans Environment Entry Exit Entry Exit Midterm General Total Over the course of our data, 221 new senators enter and 137 incumbents exit the Senate. Of these elected senators and exiting incumbents, 45% are members of the midterm entry and exit cohorts respectively. 3.2 DW-NOMINATE As a measure of a senator s voting behavior in the Senate we use Poole and Rosenthal s DW-NOMINATE scores. The data employed for estimating these scores is (nearly) all individual roll-call votes in US congressional history. DW-NOMINATE scores are estimates derived from a dynamic weighted nominal three-step estimation procedure, which was created by Poole and Rosenthal in the 1990s. An iterative MLE is employed to recover each legislator s ideal point and roll-call midpoints of a spatial model in a random utility framework. The points are placed in a common space and constrained to lie within a unit hyperspace. The point estimates are robust to concerns about strategic voting, logrolling and time-variant ideal points. We employ the first dimension of DW-NOMINATE scores, 30

31 which captures the ideology of senators in the liberal-conservative (or left-right) space; a higher score is associated with a more conservative voting record. The dynamic weighting of roll calls in the DW-NOMINATE estimation procedure affords the scores cardinality. In other words, while information on scores alone cannot indicate the exact number of roll calls on which one senator voted differently from another, increasing disparity between their DW-NOMINATE scores suggests that the underlying voting records that generated them are increasingly different. Importantly, the use of DW-NOMINATE scores allows us to directly connect electoral environments to the spatial model framework that is central to theories of electoral competition.(for more details about these scores see Poole and Rosenthal (1995)). 4 Results In this section, we test the comparative statics of our model and the stages leading up to the empirical regularities that we establish in Halberstam and Montagnes (2009a). 4.1 The Turnout Cycle We begin our results section by asserting the empirical regularity related to turnout in federal elections. Proposition 1 of our model establishes the relationship between turnout and information. In this proposition we claim that the availability of more information in the general electoral environment alone induces all PICs to vote in the presidential race and a strictly larger proportion of them, relative to midterms, to turn out and vote in the senatorial race for office. In figure 1 we show the overall turnout rate in the United States from 1980 to The set of points in the bottom of the figure are associated with turnout in midterm elections and the ones in the top with general elections. The average turnout rate during this period is 55% and 40% in general and midterm elections respectively; thus, over 35% more citizens are induced to turn out and vote in general elections than in midterms. 31

32 Figure 1: Turnout 4.2 Senatorial Positions and Presidential Coattails Before proceeding, two caveats are necessary. First, in our model, presidential support is positively related with the latent variable that pins-down the coattail effect the realized idiosyncratic error in the presidential race. We use this relationship to derive Proposition 3, in which we prove that the expected position of a senator elected in general elections becomes more extreme as her party s presidential candidate garners more votes. While consistent with our model s prediction, an observed empirical analogue of Proposition 3 may have more to do with the ideological preferences of voters in a given state than the effect of coattails alone. For example, a Democratic presidential candidate is likely to generate more support in a liberal-leaning state, which in turn is likely to elect more liberal senators. We are in the process of moving toward an analysis that accounts for state-preferences and address this concern in the last part of this section. In the following discussion of our preliminary results, however, we employ realized (and uncontrolled) presidential voteshares as a proxy for coattails. 32

33 Figure 2: Presidential Coattails Second, we showed that a midterm election is equivalent to a general election absent of contagion between races for office. Without information contagion, PIC s make their senatorial turnout and voting decisions based on their priors, which is precisely what they do in midterms. At present, we assume that, on a national level, the average midterm electoral outcome in the senatorial race roughly approximates a general electoral outcome in the senatorial race in which presidential voteshares are split evenly between both candidates. In figure 2, we provide evidence that our predictions are consistent with the data on the United States Senate. To generate the two bar charts, we classify each senator in our dataset by her party identification and, if applicable, the voteshare decile of her party s presidential candidate who ran for office during her entry environment. Following this classification, we calculate the mean DW-NOMINATE score for all the observations in our dataset that fall into each of these decile groups. Note that not all decile groups contain observations. The notable observation is that for both parties the empirical observations are consistent with Proposition 3 : for each party the mean DW-NOMINATE scores becomes (strictly) more extreme as we move up the presidential voteshare decile group. Next, we demonstrate across time the relationship between the ideologies of senators at their time of entry to presidential voteshares. For each congress in our data set we 33

34 first segment the Senate by party identification. Next, we segment each party into three groups of senators. In the first group are those senators who are first elected in midterm elections. In the next group are senators elected in general elections in states where the presidential candidate of their party garnered the majority of the two-party (Democratic and Republican) presidential race votes. The final group contains senators elected in general elections in states where the presidential candidate of their party was defeated. For each congress of the twenty in our dataset we compute the respective average DW- NOMINATE scores for each of these groups. For expositional reasons, we then normalize these averages by using the midterm averages computed for each congress; thus, the zero horizontal reference line is associated with the midterm cohort of senators in each given congress. The ordering of these averages that is consistent with our model and our present equivalence assumption about midterms is that senators who ran with defeated presidential candidates ( Unmatched ) are, in expectation, more moderate than those who were elected in midterms. In turn, midterm senators are more moderate than senators who entered in general elections in which the presidential race in their state was won by their party s candidate ( Matched ). Figure 3 corresponds with these statements. Consistent with our predictions, we observe that the average ideology scores associated with Matched senators are consistently more extreme than those of Unmatched senators and midterm senators. Less distinct is the ranking between Unmatched and midterm senators. We realize that midterm and general elections are different in many respects other than the race for the president s office. Nonetheless, the patterns, specifically for Republicans, are suggestive that Unmatched senators tend to be at least as moderate as midterm ones if not more; thus, our working assumption that midterm electoral outcomes are comparable to general electoral outcomes in which candidates were neither Matched nor Unmatched is to some extent validated in the data. Before moving on to the last step that reproduces the empirical regularities in Halberstam and Montagnes (2009a), we will call to mind a minor yet crucial proposition. Proposition 5 establishes that in general elections, conditional on winning the senatorial 34

35 Figure 3: Matched and Unmatched Senators race, the probability of being Matched is greater than the probability of being Unmatched. Correspondingly, conditional on a incumbent losing office, the likelihood of being Matched is greater than being Unmatched. In table 2 we assert these claims empirically for entrants using our previous dataset, which extended only as far back as Out of the 76 senators who were elected, over two thirds were Matched. Table 2: Matched Entrants Variable Mean Std. Dev. Fraction Matched N 76 The empirical results for the probability of incumbents who leave office follow indirectly from those of entrants: given that in the majority of cases the candidates who receive the plurality vote in both the presidential and senatorial races for office are from the same party implies that those who receive the minority votes are also from the same party, 35