Introduction
In US general elections, ballots cover many different races. In some states, one can circumvent race-by-race voting by ticking a single box at the top of the ballot that automatically registers a vote for every candidate from a particular party in partisan races. This is known as the Straight Ticket Voting Option [STVO], Master Lever or Partisan feature.Footnote 1
To STVO or not to STVO is a controversial question. For example, in the run up to the 2016 general election, Michigan’s GOP-held legislature passed a bill banning STVO—but the Democratic party immediately challenged that decision. In the end, the Supreme Court sided with the Democrats; straight-ticket voting was reinstated just before the election and, unexpectedly, brought more Republicans into power.Footnote 2
Despite heated political debates surrounding STVO and confusion about its consequences, no theoretical model exists that clarifies which party benefits from it, how it impacts candidate selection and the effect it ultimately has on policy; this paper helps fill the gap. Using a pre-election competition model a là Downs [1957], we incorporate the two-principals paradigm into a standard probabilistic voting model [Hinich 1978; Lindbeck and Weibull 1987]. For each contested office, parties nominate candidates who maximise vote share discounted by the distance in their positions from party bliss points. The trade-off both parties face is therefore the choice between increasing vote share by fielding candidates who are better aligned with voters and maintaining ideological purity or party unity over the political agenda.
In an election with STVO, voters must first decide whether to use the option or instead go through the ballot and vote in each race individually. At the time of the decision, voters only observe candidates’ political positions and party affiliations. Going through the ballot is costly for the voter, therefore the trade-off he faces is between fine-tuning the choices in every race, on the one hand, and saving his time and effort by using the STVO, on the other.
Specifically, if the voter does not use the STVO and goes through the ballot, he solves a sequence of utility maximisation problems, choosing the candidate who delivers greatest utility in each race. Voters’ utility from electing a candidate has three components: first, a measure of distance between the candidates’ and the voter’s political positions [voters prefer candidates who are closer to them ideologically]; second, a bonus for the candidate’s affiliation with a party if the voter is its partisan; third, an idiosyncratic shock that captures the voter’s valuation of the candidate’s quality. The latter is observed only if the voter goes through the ballot. Thus, if a voter uses the STVO, his party choice is based on the expectation of total utility from the party’s candidates, conditional on the voter’s own political positions and partisanship status.
We start by formally exploring STVO’s effect on the position of candidates in each party. Since going through the ballot is costly, voters who are nearly indifferent between voting a straight ticket and making partisan exceptions in a small number of races will be most tempted to use it.Footnote 3 Thus, introducing STVO diverts partisan voters away from positional voting. This impacts politicians’ positions in two different ways. First, because many voters “buy in bulk”, individual candidates’ characteristics such as political positions and quality matter less. Consequently, politicians are more inclined to cater to their party’s political agenda, and not their constituency. We label this STVO effect the party loyalty effect. Second, non-partisan [swing] voters become relatively more important in determining electoral outcomes so politicians align with them in order to win their support.Footnote 4 We call this the swing voter effect.
More specifically, the optimal candidate’s platform on an issue is a convex combination between the party’s bliss point and the position of the average voter in the constituency with a drift proportional to the covariance between the swing voter propensity and political positions. Introducing STVO strengthens the multipliers on the party’s bliss point and covariance and weakens the multiplier on the average voter’s position. Intuitively, STVO leads to an unequivocal increase in partisan votes, meaning both parties can more readily “afford” to put forward candidates who are ideologically closer to their respective bliss points [party loyalty effect]. Meanwhile, non-partisan, positional [or swing] voters become more decisive in electoral outcomes, so politicians’ platforms change to accommodate them [swing voter effect].Footnote 5 The STVO’s combined effect is thus determined by the level of partisanship in a state and the distribution of political positions among partisan and swing voters.
Proposition 1 establishes that STVO can have an asymmetric effect across party—e.g., it may make one party’s candidates more moderate in equilibrium, while candidates from the opposing party become more extreme. This result aligns with available data. According to Fig. 1’s right-hand graph, voters in STVO states do not systematically differ from voters in non-STVO states [apart from perhaps a few recent observations]. Yet Fig. 1’s left-hand graph suggests STVO correlates with right-wing Republican senators but has no visible relationship to the positions of senators from the Democratic party. [See also Gorelkina et al. 2019 for additional evidence supporting this conclusion.]
Fig. 1
Voters’ and senators’ positions with and without STVO. Note: Left-hand graph shows average senatorial positions by party and STVO status. Right-hand graph displays self-declared average voter positions by STVO presence. Senators’ positions correspond to the first dimension of DW-NOMINATE, a multidimensional scaling application developed by Poole and Rosenthal [2015]. Voters’ positions are the first dimension of Enns and Koch [2013]’s dynamic scale of voters’ policy “moods”. Data on the presence of the STVO on state ballots are from Gorelkina et al. [2019]. All positional data are projected onto a left [0] right [100] axis. State-level data on voters’ partisanship and positions calculated at the beginning of each Congressional term. See Gorelkina et al. [2019] for a full description of the data used to generate each graph
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Proposition 2 examines the impact STVO has on vote shares. In the model, the Republican party’s vote share increases as more voters become Republican partisans, and as the average voter’s views tend to the right; the opposite holds for the Democratic party. The first effect of the STVO is to reinforce the impact of partisanship on vote shares. In contrast, the STVO diminishes the effect of the average voter’s position as it brings the swing [non-partisan] voter to the forefront. When the STVO is available, fewer partisan voters elect by position as they pull the partisan lever instead; thus, the fraction of swing [non-partisan] voters among those who do elect by position increases. Swing voters become more decisive in determining electoral outcomes.
With Proposition 3 we show that the expected position of the election winner is subject to the compound effect of the STVO on candidates’ positions and vote shares. Consistent with Proposition 2 that states partisanship is a more important determinant of vote share when the STVO is present, it also becomes a more important determinant of elected candidates’ platforms with the introduction of STVO. Elected candidates’ platforms hew more closely to the party that has more partisans in the state. The effect of partisanship advantage acts on all issue dimensions and is reinforced by the STVO. Furthermore there are spillover effects between the issues. The STVO induces a spillover effect in the covariance between partisanship and voters’ political positions when that covariance on one issue affects an elected official’s position on another issue. Thus, two constituencies that differ only on the covariance between partisanship and voters’ political positions on a single issue will nevertheless elect politicians that differ across all issue dimensions. Intuitively, issue spillovers are due to the correlation in parties’ bliss points: on each issue, parties are on opposite sides of the origin. This induces correlation across the positions of elected candidates and explains how the prolonged use of STVO has likely contributed to clustering in candidates’ political positions and sorting of the electorate [for empirical evidence, see e.g., Krasa and Polborn 2014a].
Our paper contributes to the literature in several ways. First, we are the first to formally model the link between a common element of ballot design and the positions of elected politicians. This work builds on research in several related contexts, including split-ticket voting and coattail effects. For example, Zudenkova [2011] shows that coattail voting is the outcome of an optimal re-election scheme through which voters incentivise politicians’ efforts; Halberstam and Montagnes [2015] find that the coattails in presidential elections have an adverse effect on ideological polarisation among candidates. Meanwhile, Chari et al. [1997] study split-ticket voting in an environment where the government finances its spending by uniform taxes. Focusing on the interaction between executive and the legislature when choosing policy, Alesina and Rosenthal [1996] show that some voters split the ticket in equilibrium.
Our study further emphasises the relationship between party identification and voters’ positions. Dziubiński and Roy [2011] and Krasa and Polborn [2014b] develop models of vertically differentiated candidates, where voters take into account not only the candidates’ political positions but also their fixed identities—e.g., cultural, religious, or social [partisanship in this paper]. In particular, they study the effects of ideological polarisation of voters on the candidates’ positions on economic issues; thereby polarisation results in voters’ party preferences hinging more strongly on cultural issues. This paper offers another insight into issue spillovers [when voters’ views on one issue affect the candidate’s campaign on another issue] by adopting a model where both issues are treated as different dimensions of the candidate’s platform, and the platform is endogenous. A voter’s partisanship status is exogenous but correlated with her political position. We show that issue spillovers may arise in this framework: a party may select a socially conservative candidate running in a socially liberal state, as long as social issues do not dominate the election. Such spillovers become stronger when straight ticket voting is facilitated [for example by the STVO], and by extension, when candidates’ party affiliation becomes more conspicuous or important to voters.
A recent survey article [Dal Bó and Finan 2018] stresses the importance of parties in candidate selection. However, our paper joins only a handful of studies that explore the effect of institutions on intra-party dynamics. Kselman [2017] compares the equilibria of different electoral systems and finds that open list proportional representation avoid the free-riding problem inherent in closed-list proportional representation systems. Buisseret and Prato [2018] focus on the conflict of party and individual politicians’ goals and show that flexible lists in proportional representation systems may weaken politicians’ incentives to cater to voters and focus on toeing the party line instead. Buisseret et al. [2019] study party nomination strategies in list proportional representation systems, focusing on candidate quality [human capital]. Motivated by insights from Hix [2002] and Carey [2007], we contribute to this earlier work by exploring a setting where candidates face two principals—the voter and the party—and uncovering how ballot design can have an asymmetric impact on candidate selection that depends on the correlation between voters’ partisanship and political positions.
Our model also sheds a new light on the classic median-voter theorem [Black 1948; Downs 1957] and provides an explanation for the possibly asymmetric effects of STVO. In particular, we show that while candidates chosen by parties are not at the median voter’s position, their platforms depend critically on the non-partisan voter, which is the source of asymmetry. The position of partisan voters—who tend to be more extreme—is less significant to the party’s choice of candidate in STVO states, since it takes partisan votes there for granted. On the one hand, the party’s relative disregard for partisan voters’ positions produces an effect similar to Downs’s original insight where extreme voters matter less to politicians. On the other hand, swing [non-partisan] voters—who are less sensitive to party labels when they vote—play a more decisive role in determining parties’ candidate choices, but their political positions may, in fact, be very far from the median voter. Theoretically, this swing voter effect creates an asymmetry absent from the original Downs model.
Finally, empirical motivation for theoretically exploring the effects of STVO comes from evidence of voter roll off and the importance of ballot design.Footnote 6 Of particular relevance are Schaffner et al. [2001], Hall [1999] and Gorelkina et al. [2019]: the first two papers show that roll-off is higher in elections featuring nonpartisan candidates; the third paper demonstrates an empirical link between the STVO’s presence and policy-making. More generally, we believe our findings are also useful for interpreting empirical research on the impact of ballot design, and especially those features facilitating straight-ticket voting.Footnote 7
The rest of the paper is organised as follows. In Sect. 2, we develop a simple probabilistic model of electoral competition. In Sect. 3 we solve the model with and without STVO and derive the impact it has on candidates’ platforms, vote shares and the expected platform of the election winner. Section 4 concludes.
Setup
Fix a US state and an election period and let the offices listed on a ballot be indexed by \[k\in {\mathcal {K}}\equiv \left\{ 1,2,\ldots , K\right\} .\] \[\mu \in \{0,1\}\] indicates the availability of a straight-ticket voting option [STVO], where \[\mu =1\] when the STVO is present and \[\mu =0\] when it isn’t. Our policy space is multi-dimensional and defined as the product of N unit-length intervals:
$$\begin{aligned} {\mathcal {P}}\equiv \left[ -\frac{1}{2},\frac{1}{2}\right] ^{N}\!, \end{aligned}$$
where N is the number of policy issues [e.g., economics or national defense]. Three types of actors are positioned within \[{\mathcal {P}}\]: voters, parties, and candidates.
Each party \[j\in \{R,D\}\] [Republican or Democratic] has a bliss point denoted by a vector of issue positions
$$\begin{aligned} Y_{j}\equiv \left[ Y_{j1},Y_{j2},\ldots , Y_{jN}\right] \in {\mathcal {P}}. \end{aligned}$$
Without loss of generality, positions are labelled so that the Democratic party’s bliss point is always to the left of the Republican party, i.e., \[Y_{Dn}0,\] then non-partisan status is associated with a more right-wing position on issue n compared to the rest of the state. Similarly, \[\bar{\sigma }_{n}0,\] \[\sum _{n}\omega _{n}=1\]] and reflects the dis-utility i experiences from electing a candidate whose views do not precisely mirror his own. The second component is a partisanship “bonus” \[00\]]. This implies the following.
Corollary 1
Introducing STVO increases the weight of the party’s bliss point, \[Y_{jn},\] and the effect of the swing-position covariance, \[\bar{\sigma }_{n}.\]
STVO influences candidates’ positions by diverting their partisan voters away from positional voting. On the one hand, this means that candidates’ positions have less of an impact on voters’ behaviour so parties can nominate more “loyal” candidates [party loyalty effect]. On the other hand, since swing voters are weighted more heavily among positional voters, parties will pay more attention to their particular preferences [swing voter effect]. We discuss these effects as they appear in Eq. [6]; a short derivation of the STVO’s total effect as a sum of both components is shown in Lemma C4 [Online Appendix C].
Party loyalty effect:To pin down the first effect, we focus on a state in which voters’ partisanship status and positions on issue n are uncorrelated [\[\bar{\sigma }_{n}=0\]].Footnote 17 In this case, the candidate’s optimal political position is a convex combination of the average voter and party bliss points. In the presence of STVO, the party can afford to choose a candidate whose views on the issue are closer to those of the party.
Swing voter effect:Now drop the assumption of zero covariance and suppose we are in a state with few partisan voters, so that the party loyalty effect is small. In this case, introducing STVO forces both parties to follow the direction of the swing voter. The reasoning is as follows. Assume that \[\bar{\sigma }_{n}>0\] so that holding more left-wing views on issue n is associated with being a partisan and, as a result, use of the straight-ticket option. In this case, STVO attracts left-wing voters, so the average position of those who go through the ballot—and judge the candidates by their political positions—shifts to the right. Hence, the candidate’s optimal position must satisfy the more right-wing swing voters when STVO is introduced. More generally, STVO makes swing voters more decisive in electoral outcomes so when \[\bar{\sigma }_{n}>0\] the swing voter effect is also positive [more extreme Republican candidate, more moderate Democrat], and vice versa for \[\bar{\sigma }_{n}