Cross-District Variation in Split-Ticket Voting

Cross-District Variation in Split-Ticket Voting Daniel J. Lee Robert Lupton Department of Political Science Michigan State University January 10, 2014 Abstract We test hypotheses on split-ticket voting that are derived from a sincere, proximity-based theory of voting. If voters are assumed to sincerely cast votes for presidential and House candidates independently, then we expect different incentives for ticket splitting across congressional districts. Incentives vary due to predictable cross-district variation in House candidates ideological platforms, which track with district liberalism-conservatism. The effect, however, is not uniform. Increased candidate conservatism increases the likelihood of ticket splitting for some voters but decreases the likelihood for others. The proximity model, furthermore, predicts variation in the the relative likelihood of types of straight-ticket votes (i.e., straight GOP versus straight Democratic). Testing our hypotheses using 1996, 2000, and 2004 American National Elections Studies (ANES) survey data and House candidate positioning data (NOMINATE scores), we find strong support for sincere voting as an explanation for split-ticket voting. Keywords: split-ticket voting; congressional elections; voting behavior; spatial voting Assistant Professor. Corresponding author. leedan@msu.edu. 368 Farm Lane, S303, East Lansing, MI 48824 Ph.D. Candidate. luptonro@msu.edu

Introduction Divided government has become a persistent and accepted feature in American politics. Sixteen of the previous twenty-three congressional elections have resulted in the major political parties sharing the reins of power at the federal level. Given the implications of divided control of government for a host of important outcomes ranging from federal outlays (Levitt and Snyder 1995) to legislative productivity (Binder 1999) and vetoes (Cameron 2000; Rohde and Simon 1985), it is no surprise that a voluminous and contentions literature has developed on the question of its principle cause: split-ticket voting. What factors, then, give rise to citizens decision to split their tickets and endorse both parties on the same ballot? Sketching the contours of the literature on split-ticket voting provides some answers to the question, but doing so also raises quite a few more as a result of the sharp lines of disagreement that have so far prevented scholarly agreement on the determinants of ticket splitting. The two main competing theories, which we discuss in further detail in the following section, differ on whether voters are strategic or sincere. We extend the literature by considering more fully the sincere proximity voting model. A sincere split-ticket occurs because a voter prefers the Democratic presidential candidate over the Republican presidential candidate but the Republican House candidate over the Democratic House candidate (or vice versa), treating the choice for each office independently. We run two sets of analyses that each provide evidence of sincere split ticket voting. First, we simply show that vote profiles (vote for President and vote for House) are independently predicted by candidate preference for each office. Second, based on a sincere proximity model of voting, we derive hypotheses regarding a voter s propensity to vote a split-ticket, focusing on cross-district variation. This focus is beneficial for a few reasons. First, testing these additional empirical implications further buttress the overall support for the sincere model. Second, cross-district variation is one point of departure between sincere and strategic theories of ticket splitting, in which the latter does not posit such variation. Third, it highlights the incentives that drive ticket splitting by connecting voting behavior to campaigns and elections (i.e., who are the candidates). Two voters in two different districts, who are otherwise identical voters, have different incentives to split-ticket vote because the congressional districts attract (ideologically) different House candidates. These two voters, therefore, have different preferences over 1

the parties House candidates, which then contributes to different likelihoods of ticket splitting. The policy balancing model, whereby moderate voters split their ticket to moderate final policy outcomes, on the other hand, does not predict cross-district variation. Using data from the 1996, 2000, and 2004 American National Election Study (ANES), we first present general empirical support for the sincere proximity model. We then connect vote choice to district characteristics (i.e., candidate ideology) and find that ticket splitting predictably varies across congressional districts. Previous literature One prominent theory of split-ticket voting is policy balancing (Alesina and Rosenthal 1995; Fiorina 1992, 1996; Carsey and Layman 2004). In this theory, ideologically moderate voters, who are located in the middle of the two parties that exist on opposite ends of the liberal-conservative continuum, are the source of split ticket voting. These voters strategically split their tickets in order to produce divided government and thus policy moderation that balances the extremely liberal and conservative preferences of Democratic and Republican parties, respectively. In other words, ticket splitting represents a strategic decision on the part of voters to guard against the extremity of unified government. 1 Scholarship in this tradition has demonstrated that voters split their tickets as an adjustment to expectations of election outcomes and the perceived policy mix they are likely to produce (Lacy and Paolino 1998; Mebane 2000). Other work has qualified the theory by showing that policy balancing is prevalent only among sophisticated voters (Garand and Lichtl 2000) and in elections in which the result of the presidential race is certain (Saunders, Abramowitz and Williamson 2005). Still, despite the evidence in favor of policy balancing as an explanation for split-ticket voting in some quarters, the theory has received only modest empirical support in many other studies (Beck et al. 1992; Sigelman, Wahlbeck and Emmett H. Buell 1997; Mattei and Howes 2000; Born 1994,but see Carsey, 1 Other explanations for split-ticket voting have been offered. For example, some scholars argue that voters are cognitive Madisonians who explicitly prefer divided to unified government, irrespective of the anticipated policy mix that might result from various combinations of party control of government (Ladd 1990; Lewis-Beck and Nadeau 2004). We test this theory in our analysis, but note that it is not the primary theoretical alternative to sincere split-ticket voting. Jacobson (1990) argues that the previously observed pattern of divided government characterized by Republican presidents presiding over a Democratic Congress is the result of voters beliefs on the different competencies of the two parities. Namely, he argues that voters believe Democratic candidates are better at handling the redistributive function of Congress and Republicans are better at managing the economy and foreign affairs, tasks the president is most equipped to handle. We do not test this theory, but Democratic Presidents Clinton and Obama presiding over Republican majorities in the House challenge Jacobson s hypothesis. 2

2004). One significant challenge to policy balancing is voters response to elite partizan polarization. The theory predicts that voters respond to ideological extremism by splitting their ticket in order to achieve policy moderation, implying split-ticket voting increases during periods of greater inter-party ideological divergence. This expectation has not been realized empirically, however. Burden and Kimball (2002) and Brunell and Grofman (2009) instead find that split-ticket voting has decreased in the aggregate as the two major parties have polarized in recent decades, and Kimball (2004) provides individual-level evidence that declines in ticket splitting are associated with inter-party ideological divergence due to the increasing salience of party labels that drives down voter indifference. The sincere model of split-ticket voting instead assumes that some voters split their ticket between, for example, a Democratic presidential candidate and a Republican House candidate because they prefer the Democratic presidential candidate over the Republican presidential candidate but prefer the Republican House candidate over the Democratic House candidate, treating each race independently. This literature highlights voter and candidate characteristics that lead to split-ticket outcomes absent any strategic considerations on the part of voters. For example, strong partisans split their tickets less frequently than do other voters (e.g., Campbell and Miller 1957). Additional factors that serve to draw voters away from their partisan loyalties, such as opposite party incumbents (Born 2000; Mattei and Howes 2000), especially visible ones (Beck et al. 1992; Jacobson 1989) and those with superior resources relative to their challengers (Burden and Kimball 1998; Roscoe 2003), as well as candidate-centered campaigns (Wattenberg 1998), are associated with higher levels of split-ticket voting. The most recent contributions to the sincere split-ticket voting literature involve ideological motivations of vote choice. Burden and Kimball (1998, 2002), for example, show that patterns of ticket splitting are indeed associated with characteristics of the House race (see also Burden and Jones 2009; Frymer, Kim and Bimes 1997). Grofman et al. (2000) also show support for their comparative midpoints model, which makes predictions on district-level split vote outcomes (see also Brunell and Grofman 2009). In this model, split outcomes are the result of significant variation in House candidates ideology across districts. There might be a conservative district, for instance, in which the median voter prefers the Democratic House candidate to the Republican House candidate because the Democratic candidate is closer to the district median voter s ideal point (i.e., is sufficiently conservative) than the Republican 3

candidate, who is now too conservative. This district would then be expected to experience a split Republican president Democratic House outcome based on voters sincere preference for the ideological platform of the winning House candidate in each race. In this paper, we present a simple theoretical model of sincere, proximity-based voting that specifies the conditions under which various voter types split their tickets. Simulations based on the model predict that increased candidate extremity increases the likelihood of ticket splitting for some voters but decreases the likelihood for others. We also predict that one type of split may increase (say GOP president, Democratic House), while another type (say Democratic president, GOP House) may decrease with increased candidate extremity. That is, whereas Grofman et al. (2000) predict more split outcomes among extreme districts, we qualify that claim by specifying different patterns for different split types. We test our hypotheses using survey data merged with measures of candidate ideology for each House district and show that split-ticket voting is significantly influenced by House candidates ideological positioning. For example, extremely conservative House candidates will decrease the likelihood of casting a split-ticket vote for some voters in a given district, while increasing the likelihood for other voters in the same district. Our evidence is consistent with proximity-based explanations for ticket splitting (e.g., Burden and Kimball 1998, 2002; Grofman et al. 2000). Our paper extends the sincere split-ticket voting literature in a few respects. First, we test the effects of cross-district variation in House candidates ideological positioning on ticket splitting using individual-level data. Burden and Kimball (1998, 2002) rely on estimates of ticket splitting from aggregatelevel data using King s ecological inference method, and Grofman et al. (2000) and Brunell and Grofman (2009) focus on district-level split outcomes. 2 There are of course concerns regarding the use of individual-level data due to the misreporting of vote choice by survey respondents (e.g., Wright 1993). Survey data, however, remain useful as a tool for assessing previous findings by Burden and Kimball (1998, 2002), which some have questioned (Cho and Gaines 2004). Second, the sincere, proximity voting model also allows us to derive testable implications for the entire profile of ticket combinations, which stresses how an increase in one type of split-ticket voting coincides with a decrease in another. Interestingly, observing all vote profiles also shows that the mix of straight-ticket votes we expect to observe 2 Note that Cho and Gaines (2004) question the use of ecological inference methods for the analysis of split-ticket voting. 4

will vary by district (i.e., the likelihood of observing a straight Democratic versus straight Republican ticket). Support for this additional implication of the theoretical model further strengthens the case for the sincere, proximity model. Sincere Motivations for Ticket Splitting Our paper relies on a rather simple set of assumptions about voter behavior based upon the proximity model of vote choice (e.g., Hinich and Enelow 1984). That is, rather than conceptualizing voters as choosing between political parties based upon the potential balancing effects of political compromise on eventual policy outcomes, we consider voters who choose between individual candidates for elected office. We also assume that voters cast a vote for each office without concern for other offices up for election on the ballot. Proceeding from these assumptions, we present a theoretical spatial model of voting and derive hypotheses on the influence of House candidates ideological positioning on the likelihood of voters splitting their tickets. That is, we analyze why two similarly moderate voters in two different districts may have different incentives to split their ticket due to the fact that different districts attract different types of congressional candidates. Our empirical results are divided into three parts. We present initial analyses suggesting that a sincere voting model is worth considering due to its predictive power. We then test more directly the hypotheses derived from our theoretical model, providing evidence that the likelihood of split-ticket voting varies across congressional districts. Sincere proximity model of voting Let us assume vote choice is a function of an individual s ideological placement and the ideological platforms of the two major party candidates. We can also incorporate a stochastic element to vote choice using a probabilistic voting model, rather than a deterministic model. Voters then cast a vote for the ideologically closer candidate with higher probability (e.g., Burden 1997; Coughlin 1992; Hinich 1977). Let us consider basic predictions based on this familiar construction. Figure 1A illustrates a scenario in a moderate district featuring five hypothetical voter types, V 1 (extremely liberal), V 2 (moderate, liberal-leaning), V 3 (moderate), V 4 (moderate, conservative-leaning) 5

and V 5 (extremely conservative). Candidate locations are based on stylized facts about presidential and House elections. Ansolabehere, Snyder and Stewart (2001) and Burden (2004) show that the two major party House candidates competing in a given district are ideologically divergent but, importantly, that candidates track district preferences. That is, Democrats are more liberal than Republicans, and both candidates tend to be more conservative (liberal) in more conservative (liberal) districts. 3 In Figure 1A, the House candidates are drawn equidistantly around the national median. Figure 1B represents an extremely conservative district. Following the stylized facts known about candidate positioning in relation to district ideology, the Democratic and Republican candidates are more conservative in scenario B compared to scenario A (i.e., d and r shift rightward). All other actors (i.e., voters and presidential candidates) are held fixed between scenarios A and B. [Figure 1 about here.] Based on the setup in Figure 1, if voters behave sincerely, then we should observe different patterns of split-ticket voting in the two districts. That is, we should observe different propensities for ticket splitting across congressional districts due to the fact different districts attract different types of House candidates. In scenario A, for example, voters V 2, V 3 and V 4 may split their ticket, potentially from indifference. In scenario B, V 2 now much prefers House candidate d over candidate r. This preference, combined with her slight preference for presidential candidate D, implies V 2 is more likely to cast a straight-ticket vote (Dd ) under scenario B compared to scenario A. Conversely for V 4, the rightward shift of the district in scenario B makes candidate d more attractive relative to scenario A, which increases her incentive to cast a split-ticket vote given her slight preference for presidential candidate R (i.e., she is more likely to cast an Rd split-ticket than an Rr straight-ticket in scenario B). In order to add substantive intuition to this example, we can think of the V 4 voter in scenario B as being similar to a Southern white voter in the 1980s. This Southern voter supports the Republican presidential candidate but a conservative Democratic House candidate. We can further illustrate the point made in Figures 1A and 1B by simulating the probability of each voter type casting a split-ticket vote either Dr (Democratic president, Republican House) or Rd 3 This discussion also follows the stylized facts that form the base of the comparative midpoints model (Brunell and Grofman 2009; Grofman et al. 2000). 6

(Republican president, Democratic House) in a model incorporating cross-district variance in House candidate positioning. Figure 2 presents the predicted vote probabilities in a 0 to 10, liberal to conservative space, where the national median is located in the middle at 5. We consider the same five voter types as before, who are located at 0, 4, 5, 6 and 10 in the ideological space (called V 1, V 2, V 3, V 4 and V 5, respectively). The relevant candidate positioning variable, located on the x-axis, is the midpoint between the two House candidates the midpoint determines the utility for each candidate, as our proximity model assumes voters are more likely to select the ideologically closer candidate. In order to simulate the effects of House candidate positioning on split-ticket voting, we shift House candidates platforms rightward along the ideological continuum, mimicking candidates actual responses to district conservatism. The presidential candidates are assumed to be symmetric around the national median in all simulations (i.e., the presidential candidate midpoint is located at 5). [Figure 2 about here.] A first observation from Figure 2 is that the sincere voting model predicts the well-known pattern of ideological moderates splitting their tickets with a higher probability than other voters. Given this patten and our interest in cross-district variation in ticket splitting, we ignore voters V 1 and V 5, as we observe very little change in these ideologically extreme individuals vote probabilities across districts. Notice that this pattern is derived by the sincere model, absent any motives of strategic balancing by the voter. The most interesting patterns are among the moderate voters, V 2, V 3 and V 4. Looking at the top left panel in Figure 2, we see that all three voters have a high likelihood of splitting their ticket, but each responds to changes in House candidate positioning differently. Let us take as a starting point a moderate district in which the House candidate midpoint is located at 5. As the district becomes more conservative and the House candidates ideological platforms shift rightward, the probability of V 2 casting a splitticket vote decreases, but at the same time the probability of V 4 casting a split-ticket vote increases. Explicitly considering the connection between district ideology and House candidate positioning enables us to highlight the different incentives for ticket splitting facing voters across districts, a point alluded to but not explicitly made by Burden and Kimball (1998, 2002). 7

Earlier research has connected the incidence of ticket splitting to district ideology, but they do not consider how variation in district ideology simultaneously influence different types of splits in opposing directions. Burden and Kimball (1998, 2002) show that Democratic moderation (i.e., increased conservatism) increases Rd splitting, but they do not explicitly consider the effect of that moderation on Dr splitting. Grofman et al. (2000) similarly do not compare the relative propensities for each type of ticket splitting across districts in their comparative midpoints model. Comparing specific vote combinations in the full voting profile, we observe two especially strong patterns in Figure 2. As House candidates are more conservative, the probability of a Dr split relative to a straight Dd vote decreases sharply the former decreases for the moderate voter types as House candidates are more conservative (downward slope in the figure), while the latter probability increases (upward slope in the figure). The converse is true for an Rd split relative to a straight Rr vote. The probability of an Rd split relative to a straight Rr vote increases as House candidates are increasingly conservative. Changes in the location of the House candidates around fixed voter and presidential candidate locations induces changes in the entire voting profile (i.e., probabilities of Dd, Dr, Rr and Rd votes), which reveals other possible relationships worth considering. For instance, the simple proximity model also has implications on the balance of the type of straight-ticket voting we might observe in response to changes in House candidate positioning. Figure 2 shows a pronounced increase in the likelihood of a straight Dd vote relative to an straight Rr vote in increasingly conservative districts the former is increasing in House candidate conservatism, while the latter is decreasing. This prediction is somewhat counterintuitive, since one instead might expect more straight-ticket Republican voting in more conservative districts. A weaker pattern is observed for the relative likelihoods of a Dr split versus a straight Rr vote, as well as for an Rd split versus a straight Dd vote. We do not afford much attention to this type of ticket splitting in which voters defect on the presidential candidate since the proximity-based model stresses variation in preferences over the House candidates and not the presidential candidates (which are fixed). Notice that for these vote combinations, as opposed to the others discussed above, the probability of observing both split- and straight-ticket votes either both increase or decrease as can- 8

didates become more conservative. For example, the probabilities of an Rd split-ticket vote and a Dd straight-ticket vote both increase as House candidates are more conservative. The relative probabilities of observing each vote combination, however, change subtly across voter types. The increase in the likelihood of a straight Dd vote is especially large for V 2, outpacing the increase in probability of a split Rd vote. The pattern is reversed for V 4, as the probability of an Rd split-ticket vote increases more than the probability of a Dd straight-ticket vote. Thus, the likelihood of ticket splitting involving voters defecting on the presidential candidate may vary across districts, but this pattern is more ambiguous compared to the other comparisons. The simulated results in Figure 2 depict the anticipated cross-district variation in split-ticket voting for various voter types as district ideology and, consequently, candidate ideology varies. We restate our hypotheses formally here: Hypothesis 1: As House candidates are increasingly conservative, the probability of observing an Rd split-ticket vote increases relative to an Rr straight-ticket vote. Conversely, the probability of observing a Dr split-ticket vote decreases relative to a Dd straight-ticket vote. Hypothesis 2: As House candidates are increasingly conservative, the probability of observing a Dd straight-ticket vote increases relative to an Rr straight-ticket vote. We also have weaker theoretical expectations regarding voters defections from the presidential candidate. Since there is not a clear prediction, we refer to this as an additional observation: Additional observation: As House candidates are increasingly conservative, the probability of an Rd split-ticket vote relative to a Dd straight-ticket vote decreases weakly for some voters (V 2 ) but increases weakly for other voters (V 4 ). A similar pattern holds for a Dr splitticket vote relative to an Rr straight-ticket vote. Empirical analysis Our empirical analysis is presented in two parts. Using 1996, 2000, and 2004 ANES survey data, we first show that ideological (respondent s placements) preferences for candidates predictably influence vote 9

choice for presidential and House elections and, consequently, split-ticket voting. The predictive power of these variables for vote choice is taken as an initial indicator of the usefulness of our sincere voting framework. Second, we use estimates of legislator ideology (DW-NOMINATE score) as a proxy for House candidates ideological platforms to connect district characteristics to utilities for House candidates and vote choice. Sincere, proximity voting We estimate multinomial logistic regression vote models to test the sincere voting model. The dependent variable has four categories (vote profiles/pairs), coded 1 for a split Dr vote, 2 for a split Rd vote, 3 for an Rr straight-ticket vote and 4 for a Dd straight-ticket vote. 4 We measure candidate preferences using the respondent s ideological placements of herself and the candidates. The Appendix presents results that instead use feeling thermometers to measure candidate preference and gives substantively similar results. We control for both presidential candidate and House candidate preference, since the vote profile is a function of both the House race and presidential race. 5 Net House GOP Utility is calculated as ( 1) v i r i ( 1) v i d i, where v i is respondent i s ideological self-placement, r i is respondent i s perception of the Republican candidate s ideological location and d i is respondent i s perception of the Democratic candidate s ideological location. This variable is therefore an expression of the utility to the voter offered by the Republican House candidate minus that offered by the Democratic House candidate in the proximity model framework. We similarly calculate the respondent s utility with respect to the presidential candidates, labeled Net President GOP Utility. We include several control variables in both sets of models. First, in order to account for the strategic, party-balancing theory, we include the measure Party balancing, constructed by Carsey and Layman (2004, 545), which measures the respondent s relative ideological distance from the position of a particular party and the ideological midpoint between the two parties. Based on the 7-point scale of self-reported and candidate ideological placement variables, this measure ranges from 3 to +3. Respondents with low values on the measure are ideologically extreme and view the parties as polarized. 4 The percentage of each vote type for the entire sample based on respondents self-reports are as follows (and note that not all of these observations are included in the analysis due to missing data): Dd 43.2%, Rr 39.1%, Dr 10.4%, Rd 7.25%. 5 Respondents ideological placement of House candidates are not available for most ANES surveys before 1996. 10

These respondents are more likely to support unified government and, consequently, are expected to vote straight ticket. Respondents with high values on the measure are moderate and view the parties as polarized, and are thus most likely to split their tickets according to the balancing theory (see also Mulligan 2011). Party identification is the familiar 1 to 7 partisanship scale ranging from strong Democrat to strong Republican. Ideological self-identification is similarly the 1 to 7 scale ranging from extremely liberal to extremely conservative. These two measures are of course highly correlated (over 0.5 in our data), but we include both measures as a conservative estimate. We expect stronger party identifiers and more extreme respondents to be less likely to cast a split ticket and more likely to cast a straight ticket for the party with which they identify (or the more proximate party, in terms of ideological extremism). Socio-demographic variables included as controls are White, Income and Education. 6 Some states feature a ballot allowing a straight ticket vote option, which we might expect to decrease split-ticket voting (Campbell and Miller 1957; Burden and Kimball 2002). A dummy variable, Straight ballot type, equals 1 if a straight-ticket option is available, and 0 otherwise. GOP incumbent and Dem incumbent are dummy variables denoting whether a Republican or Democratic incumbent ran in the general election, respectively, meaning the omitted reference category is an open seat race. Lastly, we control for region using a South dummy variable, and for election year using dummy variables for individuals years (1996 is the omitted reference category). 7 We present two sets of models in Table 1, one with the baseline Rr and the other with the baseline Dd. The models present identical information, but we present the two baselines in order to simplify statistical inference for the comparisons of interest. 8 [Table 1 about here.] The estimated coefficients for Net House GOP utility and Net President GOP utility support the hypothesis that voters preferences for one candidate over the other contribute to vote choice, including 6 Including additional socio-demographic controls does not substantively change the results. 7 As a robustness check, we also ran a model that included the respondent s preference for divided government, which tests the cognitive Madisonian view of split-ticket voting (Lewis-Beck and Nadeau 2004). This question, however, is not included in the 1996 ANES. We chose to drop that variable because of that limitation. The substantive results of the models including the variable do not differ from those reported in the main text. 8 We use the simpler multinomial logit model over the multinomial probit because specification tests do not indicate a violation of IIA. Specification tests show that none of the categories should be combined. In particular, the tests indicate that specifying the baseline of either straight Republican or straight Democratic voting is important. 11

patterns of ticket splitting. Each coefficient suggests that a respondent is more likely to vote for the presidential and House candidate who is ideologically more proximate, treating each office independently. For instance, higher utility for the Republican presidential candidate (i.e., closer ideological proximity) increases the likelihood of casting a paired vote that includes the Republican presidential candidate over a paired vote that includes the Democratic presidential candidate (i.e., more likely to vote either Rr or Rd compared to Dd or Dr ). Sincere voting, furthermore, explains patterns of split ticket voting. For instance, the closer a voter is ideologically to the Republican House candidate relative to the Democratic House candidate, the more likely she is to split her ticket by voting Dr compared to casting a straight Dd. Cross-district variation in ticket splitting: House candidate platforms The previous section showed that individuals sincere preferences for House candidates predict voting profiles, and thus ticket splitting. We further argue that ideologically identical individuals sincere preferences for House candidates vary by congressional district due to the fact different districts attract different candidates, which should lead to cross-district variation in split-ticket voting. We in particular want to demonstrate how the propensity for ticket splitting can simultaneously increase and decrease as district ideology varies. To test the relationship between ticket splitting and district characteristics outlined in Figure 1, we utilize estimates of House member ideology, (DW-)NOMINATE scores (Poole and Rosenthal 2007), as a proxy for candidate positioning. 9 For our purposes, member ideology estimated from roll call votes is a good indicator of how congressional candidates present themselves to their districts during a campaign. 10 In the voting models in this section, rather than control for a voter s utility for House candidates using ideological placements as in the previous section, we include a candidate s estimated ideology as a proxy in order to connect voting behavior to district characteristics as posited by the dynamics outlined in Figure 1. Since NOM- INATE scores are not on the same scale as ANES survey respondents ideological self-placements, we 9 NOMINATE scores are estimated from observed roll call voting behavior in the House and range from 1 to 1 (liberal to conservative). We use the first-dimension scores, which are interpreted as capturing party conflict on issues regarding government intervention in the economy. 10 Ansolabehere, Snyder and Stewart (2001) find that revealed ideology from roll call voting in fact matches closely to the revealed ideology of candidates expressed in answers to policy questions on the National Political Awareness Test (NPAT) survey. 12

cannot directly calculate voter utilities based on ideological proximity. Furthermore, NOMINATE scores are available for only one candidate, save for the few cases in which an incumbent is defeated by a challenger. Prior research, however, has shown that candidate platforms do tend to track each other in that Democratic and Republican candidates although divergent are both more conservative in more conservative districts (Ansolabehere, Snyder and Stewart 2001; Burden 2004). Thus, we believe the availability of only one of the party s candidate location for each race nonetheless enables us to approximate the dynamics of cross-district shifts in House candidate positioning depicted in Figure 1. We estimate separate sets of models that include either the Democratic or Republican NOMINATE score as a predictor. For each party, we use either the NOMINATE score of the winning candidate of that election or the score of the district s previous representative (i.e., representative who was in office on election day), whichever is available for the party. 11 Note that we do not make distinctions among different voter types (e.g., V 2 vs. V 4 ) in our empirical analysis. Measurement problems would likely arise from attempting to classify voters into such fine-grained groups, and introducing interactions in order to model split-ticket voting conditional on voter type would stretch our data beyond their limits. Our analysis therefore tests for general tendencies that we believe nonetheless reflect the dynamics in our theory. 12 Before introducing the estimated models, we review a couple of the expected relationships between House candidate positioning and ticket splitting. First, consider the influence of Republican House candidate positioning on possible vote profiles. As the candidate is increasingly extreme, we expect that voters will view her as less and less appealing. We may then be more likely to observe a Rd split, especially in comparison to a Rr straight-ticket vote. However, we might observe a decrease in Dr 11 We include all NOMINATE scores in this way to utilize as many observations as possible. One potential case to exclude is where a Democratic incumbent does not run for reelection and is replaced in the open seat election by a Republican, or vice versa. In this case, we are using the outgoing Democratic representative s NOMINATE score to estimate the ideological platform of the Democratic candidate. To justify this proxy, omitted analyses show a great deal of continuity within a district in the positioning of party members a strong predictor of the ideology of a new Republican (Democrat) representative in a district is the ideology of the previous Republican (Democrat) who held office in that district (see also Lee and Godbout 2010). As a robustness check, results that instead exclude these cases give identical substantive results to Tables 3 and 4 (essentially same coefficient estimates and no differences in statistical significance). 12 Although we only have one candidate s ideology in each race, using a member s NOMINATE score, while splitting the observations up by party as we do, likely captures the scenarios depicted in Figure 1. This is especially true for the time period of our data, given the recent trend over the past few decades of a steep increase in the presence of sorted districts, which are characterized by Democratic-leaning districts being represented by a Democratic representative, and vice versa. That is, more conservative GOP NOMINATE scores reflect increasingly conservative districts, which have increasingly conservative Democratic House candidates, and vice versa. 13

splitting compared to Dd straight-ticket voting, as those voters will now view d more favorably relative to r, who is too conservative. Now consider the influence of Democratic House candidate positioning in the same extreme district. As the candidate is increasingly conservative, we also expect to observe an increase in Rd split-ticket voting compared to Rr straight-ticket voting. Furthermore, we expect a decrease in Dr ticket splitting relative to Dd straight-ticket voting, as r is likely too conservative in the districts for potential Dr ticket splitters. [Table 2 about here.] [Table 3 about here.] We again present models for each straight-ticket baseline category in order to facilitate straightforward statistical inference for our comparisons of interest. As found earlier, the coefficient on Net President GOP utility again suggests that voters cast a vote profile that includes the Presidential candidate that is ideologically more proximate, which is consistent with sincere voting. 13 In Tables 2 and 3, the coefficient for NOMINATE is expected to be positive in column 2, indicating an increase in the likelihood of an Rd split-ticket vote relative to an Rr baseline, and negative in column 4, indicating a decrease in the likelihood of a Dr split relative to a Dd baseline. 14 This cross-cutting pattern of split-ticket voting is especially evident in Table 2, which uses the Democratic candidate s NOMINATE score. As the Democratic member is increasingly conservative, the probability of a voter defecting from an Rr straight-ticket vote to an Rd split increases. This voter represents our hypothesized V 4 type depicted in Figure 1. Increasing Republican extremism, however, negatively influences the probability of a Dr split-ticket voter relative to a Dd straight-ticket vote, which is the V 2 type. Thus, as predicted by the sincere, proximity voting model, increasing Democratic conservatism increases the likelihood of observing one type of split-ticket outcome but decreases the probability of another. 13 We do see, however, in Table 2 that the president utility coefficient is (unexpectedly) negative and significant for the comparison between a split Rd vote and a straight Rr baseline (column 2). This effect, however, is quite a bit smaller compared to the coefficients that support our predicted effects in columns 1 and 3. 14 Notice in Table 2 that the coefficient and standard errors for the GOP incumbent dummy variable are extremely large. This is due to the issue of separation (Zorn 2005). 25 out of the 848 observations have a GOP incumbent. Of those cases, there are zero cases of a Rd split-ticket vote. Multinomial logistic estimates that omit that variable are substantively the same. We unfortunately were not able to implement penalized-likelihood estimation for the multinomial logistic model to obtain a better estimate of the effect of GOP incumbency (Zorn 2005). But nonetheless, we are confident in our conclusions regarding our variables of interest (i.e., Democratic DW-NOMINATE score). 14

Results are less clear using Republican NOMINATE scores. We find evidence of the V 2 voter type. Voters are more less likely to cast a Dr split relative to a straight Dd vote in districts with more conservative Republican House candidates. This result corroborates one type of split-ticket voting highlighted by Burden and Kimball (2002, chapter 4). The effect is not quite as strong as for the model using Democratic NOMINATE scores, a point which we return to in a moment. We do not find evidence for the V 4 type (i.e., the coefficient in Table 3, column 2 is negative instead of positive, although statistically insignificant). The fact that the results are stronger when the Democratic NOMINATE score is used is not entirely unexpected. Recall that one candidate s the elected representative s NOMINATE score is being used in these models as a proxy for the likely locations of both House candidates, which are posited to track district ideology, as shown in Figure 1. One possibility is that Republican House candidate positioning may not be as good of a proxy as Democratic House candidate positioning for a few reasons. First, during the Congresses included in our analysis, House Republicans were more ideologically cohesively than were House Democrats. Among the districts represented in our data set, the average Republican NOMI- NATE score is more extreme than the average Democratic NOMINATE score, and the standard deviation is slightly lower. 15. Also, regressing NOMINATE scores on district presidential vote share a traditional proxy for district preferences produces an R 2 value that is much larger when predicting variance in Democratic NOMINATE scores compared to GOP NOMINATE scores (see also Stone and Simas 2010). 16 That is, on average, successful Democratic House candidates ideological platforms track more closely to district ideology than do successful Republican House candidates. This finding is consistent with other accounts of party behavior (e.g., Blessing and Jenkins 2010;?) showing that the Republican Party in this period recruited consistently conservative candidates who did not track as cleanly with Democratic positioning and district ideology as is depicted in Figure 1. One might still wonder about the negative coefficient for the GOP NOMINATE score in the second column of Table 3. One likely cause is the fact that especially conservative districts attracted particularly weak Democratic candidates. Thus, in increasingly extreme, conservative districts, voters were less and less inclined to vote for the Democratic House candidate. Omitted analyses suggests this is the potential cause. For both parties, low-quality challengers were more likely to enter in races with more extreme 15 This patterns holds true when examining all 435 districts. 16 R 2 is approximately 0.45 for Democrats compared to only 0.2 for Republicans. 15

incumbents. However, during this time period low-quality Democratic challengers were electorally less successful than low-quality Republican challengers, winning 30.8% of the vote compared to 36.1% (t-test difference statistically significant). In order to assess the substantive impact of House candidate positioning on split-ticket voting outcomes, we simulate the probabilities of vote profiles with all independent variables held constant except NOMINATE scores, which we vary from its minimum to its maximum. 17 For the average white, moderate, non-southern voter, increasing the Democratic NOMINATE score from the minimum to maximum ( 0.8 to 0.15) increases the probability of an Rd split-ticket vote relative to an Rr straight-ticket vote by 0.6 percentage points, which represents only a modest increase. There is, however, a regional effect that should be noted. The change in predicted probability among Southern whites is around 4 percentage points 18 A change in the Democratic NOMINATE score from its minimum to its maximum decreases the probability of a Dr split-ticket vote relative to a Dd straight-ticket vote by 26 percentage points. 19 The estimated effect of a similar change in GOP NOMINATE scores shown in Table 3 decreases the probability of a Dr split-ticket vote relative to a Dd straight-ticket vote by 5 percentage points. Although some of these changes in probabilities appear to be small, it should be noted that ticket splitting is a relatively low probability event overall, which provides perspective to these reported changes. 20 We can also assess empirically the additional implication of our proximity model for the two types of straight-ticket votes. Hypothesis 2 stated our expectation that as House candidates are increasingly conservative, the likelihood of a Dd straight-ticket vote should increase, whereas the likelihood of an Rr straight-ticket vote should decrease. This prediction is somewhat counterintuitive, since one might instead imagine more straight-ticket Republican voting in more conservative districts. We should expect a positive coefficient for NOMINATE in column 3 in both Tables 2 and 3, which reports the probability of a Dd vote compared to the Rr baseline, but a negative coefficient in column 6, which reports the 17 CLARIFY (King, Tomz and Wittenberg 2000) is used to simulate the probabilities of voting profiles reported in this section. 18 This reported value is obtained from an omitted split-ticket voting model including an interaction term between region and NOMINATE score. The model shown in Table 3 without an added interaction term produces an estimated increase in the probability of an Rd split among Southern whites of just over one percentage point. 19 The larger effect of NOMINATE on Dr ticket splitting, especially using the Democratic NOMINATE scores, is not driven by defections of Southern voters to the Republican Party. Coefficient estimates are nearly identical when omitting Southern respondents. 20 In our sample, 10.4% of tickets are split Dr and 7.3% are split Rd. 16

probability of an Rr vote compared to the Dd baseline. We observe precisely this pattern, although the coefficients do not reach conventional levels of statistical significance (we find stronger support with the model specification in the Appendix). Substantively, varying both party s NOMINATE scores produces quite large changes in predicted probabilities. Varying NOMINATE scores from its minimum to its maximum increases the probability of a Dd straight-ticket vote relative to an Rr straight-ticket vote increases by roughly 25 percentage points. This finding provides some suggestive support of Hypothesis 2, which further strengthens the case for the sincere voting model. The final relationship to assess, expressed in our additional observation, compares Dr to Rr voting and Rd to Dd voting. Because of the small expected effects and the fact that this type of splitting is not the focus of the proximity model (which leverages variation in utilities for House candidates), we do not emphasize this comparison. We find some evidence that the likelihood of an Rd split-ticket vote relative to a Dd straight-ticket vote decreases (especially in Table 3), and the relationship is worth considering given the substantive size of the coefficients (in particular Table 3). The results suggest the relationship between NOMINATE and vote choice is stronger for V 2 voters than for V 4 voters. 21 One substantive interpretation of this pattern is that for the moderate but liberal-leaning V 2 voters, the likelihood of casting a Dd straight-ticket vote greatly increases due to the fact that the Republican House candidate is too conservative (the upward slope in the Dd case might be even more sharp than predicted in Figure 2). Moderate, conservative-leaning V 4 voters, on the other hand, are not as quick to vote for the Democratic House candidate, who is increasingly appealing in more conservative districts (the upward slope for the Rd case may not be as sharp as predicted in Figure 2). There is also some evidence (in particular Table 2) that the probability of a Dr split-ticket vote relative to an Rr straight-ticket vote decreases as House candidates are more conservative, although this relationship again does not reach statistical significance. One substantive interpretation is similar to the one discussed for the Rd split relative to Dd vote. V 2 voters are especially sensitive to House candidate positioning, greatly decreasing the likelihood of casting a Dr split-ticket vote as the Republican candidate is increasingly conservative. Overall, the presented model estimates show evidence of the dynamics predicted by the sincere, 21 Recall from Figure 2 that probability of voting either Rd or Dd increases for all voter types as candidate conservatism increases. However, the relative differences vary by voter type. The increase in Dd outpaces the increase in Rd for V 2 voters, while the opposite is true for V 4 voters. This is what we mean by saying that the effect among V 2 voters appears stronger, since the overall effect in our model estimates shows a relative decrease in Rd voting relative to Dd. 17

proximity voting model. Changes in House candidate ideological locations increase the likelihood of ticket splitting for some voters, but decrease that likelihood for other voters (hypothesis 1). Furthermore, we find suggestive support for the proximity model s additional implication that the probability of casting a straight Republican versus a straight Democratic ticket varies predictably according to House candidate positioning (hypothesis 2). Conclusion In this paper, we analyze voting in House and presidential elections under the assumption that voters select candidates for the two offices sincerely, without regard to the potential mix of policy outcomes that might result from different combinations of party control of government. We present two sets of analysis that support the sincere model: (1) a direct test that simply accounts for candidate preference, and (2) a test of implications (cross-district variation) derived from the sincere voting framework. Our results, however, should not be interpreted as stating that voters always act sincerely. We believe, for example, that Duvergerian incentives lead voters to strategically defect from their top-choice in winnertake-all elections (e.g., Abramson et al. 1992; Burden 2005). Using respondent ideological placements, we demonstrated that a sincere voting framework explains a good deal of variation in vote choice and, consequently, observed patterns of split-ticket voting. Our initial evidence indicated that voters do in fact select candidates to whom they are ideologically more proximate in each race, independent of other elected offices on the ballot. Thus, in terms of weighing vote choices across levels of federal office, voters act sincerely. We incorporated stylized facts of House candidate positioning into our sincere, proximity-based voting model in order to derive hypotheses regarding variation in voting profiles across congressional districts. Connecting voting behavior to the specifics of an election (i.e., the candidates platforms) highlights the incentives that drive ticket splitting and explains how changes in district/candidate ideology can simultaneously increase the likelihood of one type of split-ticket while decreasing the likelihood of the other. Our theory posits that two ideologically identical voters situated in two different districts will cast a split ticket vote with different probabilities. The direction of the effect, however, is expected to differ between types of voters. 18