At Least Agree on the Important Things: The Impact of Issue Distance, Intracoalition Heterogeneity, and Salience on Voters’ Coalition Preferences

The 2021 German federal election led to the formation of the so-called traffic-light coalition between the Social Democratic Party, the Green Party, and the Free Democratic Party, which had never before been agreed upon at the federal level. Over a long period, German parties had competed for government in relatively clear and ideologically homogeneous camps. However, fragmentation of the party system made majorities for two-party alliances more and more unlikely, and party elites needed to reassess new partnerships. Most of these novel coalitions, like the traffic-light coalition, are also cross-cutting dimensions of political competition in Germany. This raises the question of how voters reflect upon these novel government alternatives and make up their minds about which of them they would like to see in office. In this paper, I argue that a nuanced view on issues rather than general ideology offers more precise insights on the origins of voters’ coalition preferences. Furthermore, as salience theory suggests, not every issue is equally important for every part of the citizenry. Therefore, it is expected that the effects of voter–coalition distance as well as intracoalition heterogeneity on specific issues are moderated by individuals’ saliency of the respective issues. These expectations are tested using data from the 2021 preelection cross-section survey of the German Longitudinal Election Study. The results emphasize the relevance of specific issues as well as salience in the formation of voters’ coalition preferences.


Introduction
In electoral systems with proportional representation (PR), it is seldom the case that one single party gains a majority of seats in parliament and can govern alone. Instead, parties need to agree upon alliances and form government coalitions to come into office and implement policies (Hobolt and Karp 2010). Hence, coalitions are decisive for legislation, and research shows that they are meaningful political objects for voters (Huber 2014).
Yet most of the research has focused on questions about how attitudes toward coalitions shape voting behavior. A growing body of literature challenged Downs's "pessimistic conclusion" (Blais et al. 2006) about voters' inability to incorporate coalitions in their decision-making process and found that electoral choices, especially in multiparty settings, are determined by voters' attitudes toward potential government coalitions (e.g., Cox 1997;Blais et al. 2006; Bargsted and Kedar 2009;Duch et al. 2010;Indridason 2011). However, considerably less is known about the origins of citizens' coalition preferences (but see Falcó-Gimeno 2012; Debus and Müller 2014;Plescia and Aichholzer 2017;Nyhuis and Plescia 2018). Given their importance for vote choices, a deeper understanding of the formation of these attitudes will lead to a more comprehensive insight into electoral behavior. Therefore, the focus of this paper is on the formation of attitudes toward possible future government coalitions.
Previous research identified two aspects that exert impact on voters' considerations about future government coalitions: First, historic regularities in coalition formation not only shape citizens' expectations about future governments Bowler et al. 2021), but voters also seem to favor familiar coalitions (Debus and Müller 2014). Second, coalition signals sent out by party elites impact voters' assessments and induce further considerations about potential government coalitions (Bahnsen et al. 2020).
But German coalition politics has undergone some major changes in recent history. Due to party system fragmentation (see Niedermayer 2008), majorities for the long-standing ideologically homogeneous alliances between the Christian Democratic Union/Christian Social Union (CDU/CSU) and the Free Democratic Party (FDP) on the one hand and the Social Democratic Party (SPD) and Alliance 90/The Greens (Greens) on the other hand became unlikely. Even a majority for the grand coalition of CDU/CSU and SPD, which has somehow been the "last-resort" option in recent history, is uncertain. Three-party alliances seem to be the only plausible option, but parties object to stating their favored coalition partners. This raises questions about how citizens react to the erosion of familiar patterns of coalition politics and how they evaluate potential coalitions in this context. In this paper, I argue that spatial considerations, which proved to be meaningful determinants in previous research (Falcó-Gimeno 2012;Debus and Müller 2014;Plescia and Aichholzer 2017), play an important role for voters' coalition preferences. Besides the distance between a voter and a coalition, which reflects the utility a voter can expect, the programmatic heterogeneity of the constituent parties of a coalition regards the fit of the potential partners and the functionality of a possible future government. However, because the most likely coalitions are cross-cutting dimensions of electoral competition, the more general perspective on ideology that previous research employed might miss important aspects of the context. Instead, a more nuanced view of more specific issue dimensions can give deeper insights into citizens' assessments of coalition governments. Furthermore, since voters are expected to act as well as to form opinions based on those topics they consider important (Giger and Lefkofridi 2014), the individual-level salience of an issue dimension should act as a moderating factor. To test these expectations, I used data from the preelection cross-section survey of the German Longitudinal Election Study (GLES). 1

The Origins of Voters' Coalition Preferences
Because a government coalition is ultimately responsible for the implementation of policies, spatial considerations should represent a decisive factor for voters' coalition preferences. Generally, two components can be deduced: voter-coalition distance and intracoalition heterogeneity. Certainly, these two factors are not entirely independent, and interdependencies seem plausible, but they constitute distinct determinants of attitudes toward a government. The voter-coalition distance represents the voter's utility from certain policy positions, i.e., how much a voter agrees with the policies a government implements. Intracoalition heterogeneity can be perceived as a predictor of the functioning and quality of a potential future government (Nyhuis and Plescia 2018).

Voter-Coalition Distance
The idea that the distance between a voter and a coalition is of importance for voters stems from the basic fact that, even though voters in multiparty systems cast their vote for a specific party, it is the norm that the government is formed by a coalition. Hence, a vote in a PR system does not unconditionally transfer into a vote for a given policy platform. Instead, a postelection bargaining process between parties comes into play and almost certainly will alter the government's position compared to the party's positions (Hobolt and Karp 2010).
Ultimately, voters in PR systems have a clear incentive to know about the policy positions of potential government coalitions and favor those alternatives closer to their own position. However, in his seminal work, Downs (1957, p. 163) expressed scepticism about citizens' abilities to determine concrete positions of coalitions and concluded voters would therefore neglect the coalition formation process in their decision-making.
Yet there are some approaches to refine the classic Downsian model and account for postelection bargaining and coalition formation in voters' decision calculus (see, e.g., Austen-Smith and Banks 1988;Linhart 2009;Duch et al. 2010). The basic argument is that voters do not only consider the positions of the parties alone but also take into account the coalitions that a given party might join and reflect on the potential bargaining outputs as part of the government formation process.
The challenge in the assessment of the positions of potential coalitions (e.g., in comparison to parties or candidates) is manifold. First, voters do not only need to know about the policy stances of the constituent parties of a coalition, but they must also anticipate the postelection bargaining process to come to a reasonable conclusion about a potential government coalition's position. Second, the number of possible coalitions a voter needs to assess is a function of the number of (parliamentary) parties and, consequently, a multiple thereof. Third, in most political systems in which consolidated preelectoral alliances are not the norm, a coalition-with the important exception of the incumbent one-forms only after the election and is purely hypothetical until then. In contrast to candidates or parties, which campaign to communicate their stances to the electorate, the expectation of a coalition's position must be formed under much higher uncertainty.
Considering these comprehensive challenges, scepticism about voters' capacities might not seem misplaced, but previous research has identified contextual factors as well as heuristics that facilitate reflections on coalitions and make them more approachable for larger parts of the electorate: In most PR systems, coalition formation follows stable historic regularities, which makes it easier for voters to identify plausible options and, even more important, to exclude implausible alliances from their considerations and thereby limit the choice-set . Polls should represent a similar heuristic for voters to reject coalitions with small numeric probabilities (Faas et al. 2008). In addition, coalition signals by party elites proved to be a valuable source of information for voters about which alliances may or may not be favored. As recent research by Bahnsen et al. (2020) indicates, signals even increase the weight of coalition considerations in voters' decision-making processes. In addition, recent findings from Bowler et al. (2022) suggest that voters also use heuristics such as programmatic proximity between parties to form their expectations about the most likely coalition formation.
Altogether, it seems reasonable to assume that voters can indeed assess possible postelection coalitions and form opinions about the policies they expect the coalitions to implement. In accordance with this, Bowler et al. (2020), as well as Fortunato et al. (2021), found that voters indeed hold elaborated perceptions of coalitions' policy positions and seem to use reasonable heuristics to get there. Evidence from previous research in Spain (Falcó-Gimeno 2012), Austria (Plescia and Aichholzer 2017), and Germany (Debus and Müller 2014) showed a significant influence of ideological proximity between a voter and a coalition on the voters' coalition preference. Taken together, voters' expectations of a coalition's policy position should impact their evaluation of the coalition in question.

Intracoalition Heterogeneity
It is reasonable to assume that voters' coalition preferences do not solely depend upon voter-coalition policy distances. The fit of the potential coalition partners-or in more formal terms, the programmatic heterogeneity between the constituent parties of a coalition-should also exhibit influence on the assessment of a multiparty alliance. This assumption primarily stems from theories of coalition formation at the elite level and especially from parties' policy-seeking motives (Axelrod 1970). Like voters, who receive more utility the closer the implemented policies are to their own position, parties tend to agree upon cooperation with another party whose positions are similar to their own stances (Martin and Stevenson 2001;Golder 2006).
The heterogeneity of a possible coalition should also not be irrelevant for voters. Greater distances between the parties lead to a larger range of potential policy outcomes and therefore to higher uncertainty about the actual position of a coalition, a situation that can be expected to be disliked by voters (Bartels 1986;Greene and Haber 2015). In addition, Fortunato (2019) found that voters rate parties in coalition governments lower when they perceive the party to be too compromising. Corresponding to that, Matthieß (2020) found that voters reward government parties if they fulfill their electoral pledges. Because it is easier in programmatic homoge-neous coalitions for parties to fulfill their pledges, and the necessity of large policy compromises is much lower, it can be expected that not only are member parties of such a coalition rated higher, but also the entire coalition is rated better.
However, only a few studies have analyzed the influence of intracoalition heterogeneity on voters' attitudes toward coalitions. Gschwend and Hooghe (2008) provide experimental evidence that voters are more likely to agree with a party's preelectoral coalition and to vote accordingly the higher the ideological congruence with the potential partner is. Likewise, Plescia (2017) observed a similar pattern using survey data from Italian regional elections, and Debus and Müller (2014) found this effect when investigating German survey data.

Dimensionality of Political Competition and German Coalition Politics
Previous research on the influences of spatial factors on coalition preferences focused on a general left-right ideological space. This one-dimensional approach captures a valuable heuristic of voters' assessments of the positions of parties and consequently of coalitions. However, I argue that a more nuanced view on more specific policy dimensions offers an adequate picture of German coalition politics and, therefore, more insights into voters' attitudes toward coalition governments. This approach follows arguments of previous research that political competition is best described by multiple issue dimensions (e.g., Kriesi et al. 2008;Dalton 2017). Following Benoit and Laver (2006), a one-dimensional approach is likely to neglect relevant aspects of political competition. An additional argument for more specific issues stems from contemporary research on representation (see, e.g., Thomassen 2012). As Giger and Lefkofridi (2014, p. 290) put it, "Broad ideological congruence between parties and voters neither equates nor does it necessarily imply similar positions on salient issues." To adapt this argument to coalitions, it is possible that one observes a low distance between a voter and a possible coalition on a more abstract ideological left-right dimension but misses discrepancies on more specific subdimensions. Because the relevance of considerations about possible government coalitions stems, among other factors, from the implementation of policies, it seems reasonable to take a deeper look at more specific issue dimensions rather than broad ideology. However, since there is no "true dimensionality" of political competition, the selection of the number of dimensions depends in part on the analysis itself (Benoit and Laver 2006, p. 110). These selected dimensions need to be detailed enough to map all important aspects of political interactions but at the same time be as parsimonious as possible so that they cause no redundancies (Benoit and Laver 2006, p. 14). I draw from previous research that identified social as well as economic policy as the most relevant dimensions characterizing political competition in Germany (see, e.g., Bräuninger et al. 2020). Moreover, in light of the increasing importance of environmental policies (see, e.g., Spoon et al. 2014), it seems necessary to rely on a third "environmentalism" dimension to map political competition.
In addition to these more general arguments for a multidimensional approach, German coalition politics and the developments in the recent past give further reason to take more specific issue dimensions into account. Over a long period, German parties competed for government in relatively clear and ideologically congruent camps.

K
The so-called black-yellow coalition of CDU/CSU and FDP provided a middle-right government alternative, while the red-green coalition of SPD and the Greens took the counterpart as a potential middle-left coalition. Eventually, this stable pattern in coalition formation made the assessment of coalition formation after the elections easy for voters and even enabled coordination in the German two-vote system (Pappi and Thurner 2002;Gschwend 2007;Shikano et al. 2009;Faas and Huber 2015;Huber 2017).
However, the proceeding fragmentation of the party system made majorities for two-party alliances more and more unlikely, while parties still objected to ideologically cross-cutting coalitions at the federal level. But instead of general ideological conflicts, disagreements on relatively specific policies seemed to have played a part in parties' difficulties to find new partnerships.
In the case of the 2017 German federal election, Bräuninger et al. (2019) observed that parties' stances on economic and social policy, as well as their positions toward immigration and the parties' weighting of these policies, had great explanatory power for the prediction of coalition formation. The differences between the CDU/CSU (especially the latter of the two "Union parties") and the Greens on the issue of immigration and large distances on economic policy between the FDP and the Greens can be one explanation for the failure of negotiations on a Jamaica coalition.
The polls in the run-up to the 2021 election predicted an equally complex situation regarding possible coalitions. Unlike previous elections, the somehow "last-resort" option, the grand coalition between the CDU/CSU and the SPD, was perceived as very unlikely to be agreed upon again. It seemed more than questionable that either of the two parties would join such a coalition as the junior partner and ensure chancellorship and the associated incumbency benefits (see ) for the major partner. As the formation of any two-party coalition appeared very unlikely, parties needed to consider three-party coalitions. The polls indicated almost certain parliamentary majorities for any three-party alliance of the CDU/CSU, SPD, FDP, and Greens. However, all of these potential government coalitions were cross-cutting the traditional camps of German party competition. The only exception to that was a left-leaning coalition of the SPD, the Greens, and the leftist party Die Linke. However, this coalition was anything but undisputed, especially among politicians and supporters of the Social Democrats, because of the (extreme) stances of Die Linke in certain policy fields, e.g., foreign policy.
As parties were forced to farewell the former two-party coalitions, they needed to find compromise with new partners with whom they might agree on some issues but disagree on other questions. Take, for instance, the so-called traffic-light coalition of the SPD (red), the FDP (yellow), and the Greens. On the one hand, on most sociocultural issues, such as same-sex marriage or drug policies, the liberal FDP has more in common with the Social Democrats and the Greens than with their longstanding first-choice coalition partner, the Christian Democrats. On the other hand, the clear liberal positions of the FDP on the economy, e.g., taxation plans, stand in contrast to the pledges of the other two parties. Consequently, a traffic-light coalition could be seen as congruent on one dimension and conflictive on the other dimension. Ultimately, a voter might favor this coalition on the grounds of its possible position and the programmatic homogeneity of the parties on the sociocultural dimension, but the voter might doubt effective cooperation of the parties on economic questions.
Based on the theoretical reflections about the impact of spatial distances on voters' coalition preferences and on the arguments for a multidimensional approach to capture political competition, I derive the expectation that, ceteris paribus, the closer that voters expect a coalition's policy position on a given issue to be to their own, the higher they rate this coalition.

H1
The greater the distance between the expected position of a coalition and a voter on a given issue dimension, the lower the rating of this coalition by that voter.
As argued above, the evaluation of a possible government coalition should depend not solely on the voter-coalition distance but also on the congruence a voter perceives between the potential partners. A coalition with a high degree of disagreement is likely to be dysfunctional. I expect that independent of the policy positions of a coalition, voters object to coalitions that are too programmatically heterogeneous because they want to avoid a conflictive government with an unexpected policy output.
H2 The greater the distance between the constituent parties of a coalition on a given issue dimension, the lower the rating of this coalition by a voter.
In addition to these distinct influences of distance and heterogeneity on coalition preferences, an interaction between them is conceivable. The reasoning behind this assumption arises from two lines of research: First, research on the role of uncertainty concludes that the utility of a party for a voter depends not only on policy distances but also on how certain a voter is about the position of the respective party; if a riskaverse voter is about to choose between two equally distant parties, they vote for the party whose position they are more certain about (see Bartels 1986;Gill 2005;Pappi and Bräuninger 2021). Second, previous research shows increased relevance of valence when candidates or parties ideologically converge (see, e.g., Green and Hobolt 2008;Franchino and Zucchini 2015).
Transferring these arguments to the realm of coalition politics, intracoalition heterogeneity is accompanied by uncertainty about a coalition's final stance. Under high ideological congruence or even consensus between the potential partners, voters' expectation formation about the coalition's position should be straightforward, since small ideological division fosters agreement. Heterogeneous positions toward a policy, however, extend the possible space of agreement, and the given issue might also become an object of the bargaining process. The coalition's final position might be influenced by various trade-offs in the coalition formation process. Additionally, as mentioned above, intracoalition heterogeneity might serve as a predictor of the functioning and quality of a potential future government. A programmatically heterogeneous government might be perceived as highly conflictual by voters and imply low valence (Nyhuis and Plescia 2018).
Ultimately, it seems reasonable to assume that a voter's coalition preference depends on the interplay of distance and heterogeneity. A voter on the right of the political spectrum, for instance, is not expected to prefer a middle-left coalition of K the SPD and the Greens even though the two parties are ideologically congruent, yet the expected position of this coalition is too distant. Furthermore, a potential coalition of the leftist party Die Linke and the radical-right Alternative for Germany (AfD) would certainly be objected to by the German median voter; even though the mean of the parties' positions might not be too distant, such a government coalition would be expected to be highly conflictual. Therefore, I expect an interaction effect of voter-coalition distance and intracoalition heterogeneity on voters' coalition preferences.

H3
The negative effect of voter-coalition distance (intracoalition heterogeneity) is contingent on the intracoalition heterogeneity (voter-coalition distance).

The Role of Salience for Coalition Preferences
If the political space is expanded and multiple dimensions come into play, spatial considerations become more complex. With every additional dimension of political competition, one implicitly assumes that voters reflect on their very own position on any of the dimensions, assess each party's stance, make up their minds about potential bargaining outcomes to reason the position of a given coalition, calculate the distance to the coalition's position, and ultimately add up each of these distances to conclude the potential utility if such a coalition were to come into office. This again raises the question about voters' ability and, to a certain extent, inclination to approach these efforts.
A quite straightforward answer to this question might be the conclusion that Iyengar and Kinder (1987, p. 64) famously put forward: "People do not pay attention to everything." A takeaway from this is that the realms of politics are indeed too complex for individuals to develop a comprehensive understanding of every facet, but citizens instead concentrate on those issues most important to them (Krosnick 1988(Krosnick , 1990. Krosnick (1990) outlined in his seminal work that society is divided into "issue publics," which are characterized by different levels of salience of issues. He defines salience as "the degree to which a person is passionately concerned about and personally invested in an attitude" (Krosnick 1990, p. 60). Thus, certain subgroups in a society are more invested in some issues than they are in other topics or other subgroups. If an issue is of higher relevance for people, Krosnick (1990) argues they will think about it more frequently, perceive higher polarization on this topic, and ultimately will form their political preferences upon this issue. The sources of the importance of an attitude are manifold. It might be the consequence of material self-interest, identification with a reference group, or personal values that will lead people to attribute importance to a certain issue.
As mentioned above, the focus on important issues does not mean that people are ignorant. Gathering information is costly and demanding. As a reaction to that, "people seem to employ a sensible strategy that minimizes the cognitive costs of deriving candidate evaluations while maximizing subjective expected utility" (Krosnick 1990, p. 82).
The reason for the impact of personal issue salience on preferences and behavior is that attitudes on salient issues are more accessible and might also become central to the self-concept (see, e.g., Lavine et al. 1996Lavine et al. , 2000. As Visser et al. (2003) showed, issue salience is highly motivational and induces people to protect such important attitudes, use and express them more frequently, act according to them, persuade others, and gather more information on an issue. Consequently, Holbrook et al. (2005) demonstrated that these motivational factors of importance enhance knowledge about the respective issue, and as people devote more cognitive resources to these attitudes, they become more memorable. Accordingly, Iyengar et al. (2008) found that in campaign contexts, voters seek more information about the topics they are interested in.
A large body of research has focused on the role of issue salience for political opinions and behavior. The underlying argument is that not only policy but also salience is relevant (Green and Hobolt 2008). In particular, the interaction of salience with the position toward an issue has been found to exert great explanatory power for vote choices (e.g., Fournier et al. 2003;Singer 2011;Lefkofridi et al. 2014;Ciuk and Yost 2016;Miller et al. 2017;Dennison 2020;Steiner and Hillen 2021). Moreover, research on representation demonstrated the relevance of the inclusion of individuallevel salience for the investigation of party-voter congruence (e.g., Thomassen 2012;Walgrave and Lefevere 2013;Giger and Lefkofridi 2014). Additionally, there is evidence that individual-level salience influences the importance that parties attribute to certain issues (e.g., Klüver and Spoon 2016;Neundorf and Adams 2018).
An illustrative example of the influence of salience is the investigation of vote choices by left-authoritarian voters in Western Europe. As, e.g., Lefkofridi et al. (2014) argue, no major party represents the positions of this subgroup of voters on both dimensions of sociocultural and economic issues. However, left-authoritarian voters overcome this supply gap to a certain extent by voting on the basis of the issue dimension that they attribute more importance to Steiner and Hillen 2021). For example, considering again an SPD-FDP-Greens coalition, a voter who emphasizes sociocultural issues might favor such a coalition because of the congruence of the parties on this dimension, while another voter might object to the traffic-light government because of the conflict on questions about the economy.
Beyond that, research on coalition formation illustrates the role of salience at the elite level. Not only does the success of the bargaining depend on the weighting of issues in question by the parties (see Bräuninger et al. 2019), but parties are also more likely to allocate portfolios on domains to which they attribute importance (Bäck et al. 2011). Furthermore, Greene et al. (2021) show that voters take this into account in their evaluation of government parties and reward the parties if they managed to receive their salient portfolios.
To put these findings on the impact of issue salience of voters' assessments of coalition governments into perspective, Plescia et al. (2022) found that Spanish voters' willingness to accept policy compromises in coalition bargaining depends on the importance they attribute to an issue. Compromise is perceived more negatively on the issues the voters are invested in than on those they do not care much about. Beyond that, to my best knowledge, there is no previous study examining the impact of salience on voters' coalition preferences.
K Taken together, issue salience does not only play an important role in the formation of government coalitions, but it also has cognitive as well as behavioral consequences at the individual level. When voters perceive an issue to be important, they are expected to gather more information on this issue and thereby get information on the party's stance on this policy. Furthermore, the individual salience makes this information more accessible and has clear motivational implications for evaluating a coalition based on the important information. This also concerns the expected influences of the voter-coalition distances and intracoalition heterogeneity. I expect that the influence of the distance between the coalitions' and the voters' policy positions on an issue is greater if the voters think the issue is important. If voters think an issue is not important, they should not care too much about the position of a future government on that issue. On the contrary, if they perceive a policy to be crucial, they should make up their mind about how a coalition would position itself on this policy and base their evaluation of this government alternative accordingly. Hypothesis 4 captures this potential interaction of policy distance (formulated in H1) and individual level salience: H4 If an issue dimension is salient to a voter, the effect of the voter-coalition distance on that issue dimension on the voter's coalition preference is greater.
Furthermore, the salience of an issue dimension should also have an impact on the effect of the perceived heterogeneity of the coalition partners. If voters simply do not care too much about a certain dimension, it seems less likely that they would base their assessment of a coalition on the functionality of the government in this policy field. But if voters attribute importance to a topic, I expect that they care whether a future government can find compromise on this issue. Similarly, the interaction effect of distance and heterogeneity should also depend on the salience of an issue for a voter.
H5 If an issue dimension is salient to a voter, the effect of the intracoalition heterogeneity on that issue dimension on the voter's coalition preference is greater.
H6 If an issue dimension is salient to a voter, the interaction effect of voter-coalition distance and intracoalition heterogeneity is greater.

Data and Methods
To test these expectations, I used data from the preelection cross-section survey of the German Longitudinal Election Study (GLES 2022). Interviews were conducted from 1 month before until the day before the federal election on 26 September 2021. The dataset contains answers from 5116 respondents. Additionally, I used data from the Comparative Manifesto Project (CMP) to obtain measures for party-specific salience on relevant issues (Volkens et al. 2021). The CMP data contain hand-coded information about parties' emphasis on specific issues, based on election manifestos.

Dependent Variable
The dependent variable of the analysis is the respondents' rating of a set of seven potential government coalitions: CDU/CSU-FDP; SPD-Greens; CDU/CSU-SPD; CDU/CSU-Greens; SPD-FDP-Greens; CDU/CSU-FDP-Greens; SPD-Greens-Left. 2 The desirability of each of these coalitions was measured on an 11-point scale from -5 ("not desirable at all") to +5 ("very desirable"). Because the expectations make claims about the general influence on coalition preferences and do not consider specific coalitions, I stacked the data set by the number of coalitions to test for these general hypotheses. In these stacked data, each observation is a respondent-coalition dyad, thus each respondent contributed seven observations. Since the dyads are clustered in respondents, the independence of errors in the models would be violated. Therefore, I computed clustered standard errors on the level of respondents.

Independent Variables
The central independent variables are the voter-coalition distance and the intracoalition heterogeneity and build upon the respondents' placement of parties on three issue dimensions as well as self-placement on the same scales. Respondents were asked to place each party on 11-point scales regarding taxation vs. social services, immigration, and climate change. 3 Afterward, they were asked to indicate their own positions on the same scales. It should be noted that respondents' projections of party positions might be biased due to affection and partisanship (see, e.g., Merrill et al. 2001;Dahlberg 2013), and the positions of alliances between parties a respondent likes might be equally distorted. But since the interest lies in the subjective perceptions of possible government coalitions, reliance on the subjective party placements seems more adequate than more objective measures.
The operationalization of the coalition positions is not trivial, and there is only scarce evidence about voters' prospective perceptions of coalitions' policy positions. On the one hand, it seems reasonable that voters employ Gamson's law and weigh each party's influence in a coalition by its seat share. On the other hand, it could be argued that voters view each party as a potential veto player in a cabinet and therefore expect the partners to have equal influence. Furthermore, research on coalition formation shows that parties are particularly assertive on issues that are salient to them (see, e.g., Bäck et al. 2011), and voters might attribute more influence in policy-making to parties that emphasize a respective issue (Fortunato et al. 2021).
2 Respondents were also asked about their ratings toward two coalitions under participation of the populist radical-right party AfD (CDU/CSU-AfD; CDU/CSU-AfD-FDP). I argue that because of the extremity of the AfD (see Arzheimer and Berning 2019), the assessment of such coalitions by voters is different from that for any other coalition. Therefore, the more general hypotheses about the origins of coalition preferences are not applicable, and I excluded them from the analysis. 3 Ranges of the scales are as follows: taxation vs. social services, 1="lower taxes and fewer social services" to 11="more social services and higher taxes"; immigration, 1="facilitate immigration for foreigners" to 11="restrict immigration of foreigners"; climate change, 1="politics should do much more to combat climate change" to 11="politics to combat climate change have already gone way too far." Recent research by Bowler et al. (2020) and Fortunato et al. (2021) suggests that voters apply a combination of these heuristics, but as Meyer and Strobl (2016) found, they might also be biased on partisan grounds. But drawing from findings on responsibility attribution, voters' perceptions of influence in coalition governments depends to a degree on party size (Angelova et al. 2016). Furthermore, voters' expectations about portfolio allocations are also informed by party size (Lin et al. 2017). Given this influence on related perceptions of government coalitions, it seems justifiable to account for the impact of party size on voters' cognition and operationalize a coalition's position as the seat-weighted average of the positions of the constituent parties. But since the evidence is mixed and there is need for further research on voters' perceptions of coalitions' policy positions, I replicated the analysis with different operationalizations of coalitions' positions as a robustness check: First, I used the unweighted averages of party positions. Second, I additionally weighted the positions of the constituent parties by the party-specific salience of the respective issues from the CMP data. 4 The distance between a respondent and a coalition on an issue dimension was then measured as the absolute difference between a respondent and a coalition. This variable ranges from 0 (respondent and coalition have the same position) to 10 (respondent and coalition take the two extremes at the scale), and higher values indicate greater distance.
To measure intracoalition heterogeneity on an issue, I followed the approach by Debus (2009) and used the (salience) weighted ideological heterogeneity. This measurement is based on the Euclidean distance between all pairs of the constituent parties of a possible coalition and weights the distances between the parties by the party-specific salience. It additionally accounts for the number of member parties of the respective coalition. This way, potential divergences in emphasis that the parties place on the given issues are reflected in the heterogeneity measure. If, for example, members of a possible two-party coalition show divergent positions on environmental policies, but one party stresses this issue whereas the other is more silent about it so that conflict on this specific issue seems rather unlikely, the weighted ideological heterogeneity would take lower values than if both parties were equally invested in this issue and the coalition could be perceived as highly 4 To measure party-specific salience using the CMP data, I followed the approach by Neundorf and Adams (2018) and used the sum of items 401-416 for economic salience and item 501 for salience of environmental policies. I differed from their measure of salience of immigration since they conceptualize it as a valence rather than a positional issue. However, the GLES item on immigration is formulated as a positional issue. For the sake of comparability between the individual-level and party-level data, I used the sum of the CMP items 601 (national way of life: positive) and 608 (multiculturalism: negative) used by Neundorf and Adams (2018), as well as 602 (national way of life: negative) and 607 (multiculturalism: positive). It should be noted that there is considerable debate about the CMP data, e.g., the document selection, divergence between salience theory and the coding of two-sided items concerning an issue, as well as the scaling approach of party positions (see Lowe et al. 2011;Gemenis 2013). However, since the CMP data was used here to measure salience and not party positions, the latter critique seems not to be problematic here. Furthermore, since the salience measure was computed by summing up the frequencies of positive and negative statements, it reflects a measure of issue importance more in accordance with salience theory. Moreover, since I only employed data for the German case, neither data quality nor comparability should be an issue here. conflictual. Overall, higher values on this variable indicate higher programmatic heterogeneity. To calculate the distances between the parties in a coalition, I relied on respondents' party placement in the GLES survey mentioned above. The partyspecific salience came from the CMP data.
Regarding individual-level issue salience, respondents were asked to indicate their personal importance of each of the three issue dimensions on a five-point scale ranging from 1, "very important," to 5, "not important at all." Because of the ordinal scale of this variable, I recoded answers into dummy variables for each of the three dimensions, which take the value of 1 if respondents indicated that a dimension is "very" or "somewhat important" to them. Since there is some debate about the adequate measurement of individual-level issue salience via open-ended or closedended questions (see, e.g., Miller et al. 2017), I further used answers to the openended question about "most important problem" as an alternative measurement in a robustness check. Thereby, I assessed respondents' issue salience if they mentioned economic issues, immigration, or climate change as the most (or second most) important problem. Using the open-ended question represents a more conservative measurement of issue salience since respondents need to proactively mention an issue as most important to them. In fact, the share of respondents indicating an issue as the (second) most important problem is significantly lower than those who ascribe importance to it in the closed question. 5 However, one must be cautious in comparing these two measures directly, because the importance of an issue might diverge from the perception of an issue to be a problem (see Wlezien 2005).

Controls
In addition, I controlled for certain other determinants that are expected to influence voters' coalition preferences. Since the "learned familiarity" (see Debus and Müller 2014) with coalitions increases the evaluation of a coalition, I included a dummy variable to control for whether a coalition had previously been formed at the federal level (as is the case for the coalitions of CDU/CSU-FDP, CDU/CSU-SPD, and SPD-Greens). 6 I further controlled for the influences of party and politician evaluations (see Plescia and Aichholzer 2017) by incorporating a dummy variable that indicates whether the most-liked party (based on scalometer ratings) is part of the coalition as well as the rating of the top candidate of the major party. Additionally, I controlled for standard sociodemographic characteristics of the respondents: age, gender, and education.

Statistical Models
To test the hypotheses, I estimated linear regression models. Since I used the data as a stacked data set with respondent-coalition dyads as the level of analysis, I computed clustered standard errors at the level of respondents to account for the nested structure of the data and violation of the independence of errors. Hypothesis 3 is assessed via an interaction term between voter-coalition distance and intracoalition heterogeneity. To test hypotheses 4 and 5, I included interaction terms between the voter-coalition distance (H4) and the respondents' salience on each dimension, as well as between the intracoalition heterogeneity (H5) and the salience. Hypothesis H6 was tested via a three-way interaction term between voter-coalition distance, intracoalition heterogeneity, and respondents' salience on each dimension. To be able to trace back the additional explanatory power of the independent variables as well as of the respective subdimensions of political competition, I included them successively and compared information criteria as well as coefficients between the different models.

Inference Criteria
Regarding inference criteria for the coefficients in the model, I relied on conventional levels of p-values (0.001; 0.01; 0.05). To evaluate the interaction terms, I additionally plotted predictions from the model for different levels of the covariates with 95% confidence intervals.

Reliability and Robustness Testing
To evaluate the robustness of the results, I employed different model replications that consider different approaches to the operationalization of the central independent variables: Voter-coalition distance: I replicated the analysis with coalition positions as unweighted averages of party positions as well as party-specific salience as an additional weight. Individual-level issue salience: I used answers to the open-ended question about "most important problem" as an alternative measurement. I assessed respondents' issue salience if they mentioned economic issues, immigration, or climate change as the (second) most important problem.
Section A in the supplementary material provides summary statistics for the different operationalizations of the independent variables.
To put the analysis on the origins of coalition preferences in the context of electoral choices, I estimated a conditional logit model with respondents' vote intention as the dependent variable, ratings of the parties as choice-specific determinants, and leader evaluations as individual-specific variables. In a second step, I added the ratings for coalitions as individual-specific determinants. Ultimately, this approach does not provide a fine-grained test for all the potential influences of coalition preferences, but it can test whether coalition ratings, in general, influence voting decisions independently from evaluations of parties and candidates (see Blais et al. 2006 for a similar approach).

Missing Data
Drawing from research using similar data on previous federal elections, it is possible that a significant share of respondents were not able to address or didn't know about the parties' positions on the issue dimensions (see, e.g., Giebler et al. 2021;Pappi and Bräuninger 2021). To avoid estimation problems due to listwise deletion, I followed the approach by Giebler et al. (2021) and used hot deck imputation for missing data on the placements of the parties. As indicators for the imputation, I used respondents' placements of the party on the other issue dimensions as well as their left-right placement of the party. 7 As a robustness check for this imputation method, I estimated the models without imputation using listwise deletion.

Assumption Violation/Model Nonconvergence
Other estimation strategies were possible: It would be possible to not use the data as a stacked data set and to estimate the models for each coalition separately. Furthermore, it would be possible to employ a y-hat approach for the control variables. Another estimation strategy could be to not use the scalometer ratings as the dependent variable but to look at respondents' most liked coalition (highest scalometer ratings) and estimate a conditional or mixed logit.

Results
Turning to the multivariate analyses, Table 1 in the appendix reports the results from the regressions models. For better comparability, all independent variables were rescaled to range from 0 to 1. The comparison of the coefficients for distance and heterogeneity between models 1 to 3 suggests that political competition in the realm of coalition politics is indeed multidimensional in the perception of the voters. Adding variables mapping further dimensions leads to only slight changes in the size of coefficients of the present determinants and does not affect their levels of statistical significance.
Model 3 includes the main effects of voter-coalition distance and intracoalition heterogeneity on each of the three dimensions. Five of the six effects, except for the one for a coalition's heterogeneity on the climate issue, exhibit the expected negative influence on the coalition rating and reach levels of statistical significance. This finding is in accordance with hypotheses 1 and 2 because both a larger distance between a voter and a coalition as well as larger discordance between the constituent parties of a potential coalition decrease the evaluation of the respective multiparty alliance.
Hypothesis 3 predicts a positive coefficient of an interaction term between distance and heterogeneity; that is, when the heterogeneity of a coalition is low, the negative effect of voter-coalition distance is intensified. As model 4 shows, all three coefficients of the interaction terms on the issue dimensions exhibit the expected positive sign. However, only the coefficient on the issue of taxation vs. social services is statistically significant. To investigate these interaction effects in greater detail, Fig. 1 displays linear predictions of the coalition ratings with low, average, and high programmatic heterogeneity for varying levels of voter-coalition distance. Starting with the left panel in Fig. 1, the significant interaction between voter-coalition distance and intracoalition heterogeneity is observable. Coalitions with a low degree of differences among their partners were rated significantly higher than those with average or high levels of programmatic heterogeneity when a coalition's position was perceived to be near a respondent's. With an increase in voter-coalition distance, these differences diminish because of a steeper incline for the low heterogeneity graph than for the average and the high heterogeneity one. However, as the insignificant coefficients of the interaction terms for the issues of immigration and climate change in model 4 already suggested, such a result cannot be found for these two dimensions. Although there is a slight difference in the slopes for the different levels of heterogeneity, confidence intervals for the predictions overlap, indicating Fig. 1 Effect of voter-coalition distance on coalition ratings by intracoalition heterogeneity. Linear predictions with 95% confidence interval based on model 4 in Table 1 a nonsignificant effect. Eventually, hypothesis 3 can only be partly confirmed concerning the issue of taxation vs. social services but cannot be confirmed for either immigration or climate change.
To assess hypotheses 4 and 5, model 5 in Table 1 incorporates interaction terms between individual-level salience of an issue and both voter-coalition distance and intracoalition heterogeneity. The hypotheses predict that the negative effects of distance and heterogeneity are greater if an issue is found to be important; thus, the coefficient of the interaction term in the model is expected to have a negative sign. Figures 2 and 3 graph these potential interactions. Considering the left and middle graphs in Fig. 2, no significant differences in the effects of the voter-coalition distance contingent on issue salience can be observed for the issues of taxation vs. social services and immigration. This finding suggests rejection of hypothesis 4.
However, for the issue of climate change, the expected effect emerges. The graph shows a significantly steeper slope for voters invested in the issue than for those who are not. When climate change is a salient topic for voters, their evaluation of a coalition is influenced more by their congruence with the coalition's stance on the issue than for those voters to whom the topic is not important. This result is in accordance with hypothesis 4.
Regarding the interaction effect of salience and intracoalition heterogeneity, the insignificant coefficients of the interaction terms for the issues of taxation vs. social services and immigration in model 5 do not support hypothesis 5. Yet for the former issue, the left graph in Fig. 3 depicts a pattern that is generally in line with expectations. The figure shows a significant difference in coalition ratings for lower levels of programmatic heterogeneity dependent on issue salience. If a coalition is perceived to be more consensual on the issue of taxation vs. social services, voters who ascribe importance to this topic rate this coalition higher than voters to whom the issue is not important. Because of the steeper slope for the former, this difference dimin- Fig. 2 Effect of voter-coalition distance on coalition ratings by issue salience. Linear predictions with 95% confidence interval based on model 5 in Table 1 K Fig. 3 Effect of intracoalition heterogeneity on coalition ratings by issue salience. Linear predictions with 95% confidence interval based on model 5 in Table 1 ishes with higher levels of programmatic heterogeneity. However, no such effect can be observed for the issue of immigration. Furthermore, the positive coefficient in model 5 as well as the right graph in Fig. 3 for climate change show an interaction between salience and heterogeneity that stands in contrast to the predictions of hypothesis 5. While one can observe a clear negative effect of programmatic heterogeneity on coalition ratings for voters to whom climate change is not important, Fig. 3 displays a positive effect for voters to whom the issue is salient. A possible explanation for this contrary finding is discussed in the nonregistered section below. Overall, these findings suggest rejection of hypothesis 5.
Assessing hypothesis 6 requires a three-way interaction between distance, heterogeneity, and salience, which is incorporated in model 6 in Table 1. To illustrate, Fig. 4 graphs the effect of voter-coalition distance on coalition ratings dependent on varying levels of programmatic heterogeneity and salience. The graphs for the issues of taxation vs. social services and immigration do not support the assumption of hypothesis 6. Both graphs show a decrease in effect size of the voter-coalition distance on coalition ratings with higher levels of intracoalition heterogeneity. This effect is more pronounced on the issue of taxation vs. social services than on immigration, which is in line with the results from model 4 and Fig. 1. However, no clear differences regarding issue salience can be observed. Turning to the three-way interaction on the issue of climate change, a moderation by salience can be found. Consider first the graph for voters to whom the issue is salient: As expected, on low levels of intracoalition heterogeneity, the voter-coalition distance exerts a negative influence on coalition ratings. With an increase in heterogeneity, this effect diminishes. On the contrary, this is not the case for voters to whom the issue was not important. However, the robustness of this finding must be questioned. Section D in the supplementary material reports the results for model 6 with different oper- Fig. 4 Effect of voter-coalition distance on coalition ratings by intracoalition heterogeneity and issue salience. Linear predictions with 95% confidence interval based on model 6 in Table 1 ationalizations of the relevant independent variables. The effect of the interaction term there does not reach statistical significance.
Lastly, coefficients of the theoretically plausible control variables exhibit influences in the expected direction and reach statistical significance. A coalition is rated higher if it has been formed at the federal level and includes the voter's preferred party. Furthermore, higher ratings for the candidate of the major party-in other words, the potential chancellor-increase the evaluation of this coalition. The sociodemographic controls indicate a negative effect of a respondent's age and a positive effect of education on coalition ratings.

Robustness Checks
Assessing the robustness of the findings, all models were estimated using alternative operationalizations of the central independent variables. The results are reported in Sect. C in the supplementary material. Except for the nonrobust finding regarding hypothesis 6 described above, there are no sizeable differences observable. To further put the findings of electoral behavior into perspective and to examine whether vote choices are generally influenced by coalition preferences, Sect. D in the supplementary material reports results from a conditional logistic regression with respondents' vote choice as the dependent variable and coalition ratings as the independent variables. The results suggest that even in a complex scenario, as occurred in the 2021 federal election, voters' coalition preferences did significantly influence their voting behavior.

Nonregistered Analysis
Considering the counterintuitive results for the positive effect of intracoalition heterogeneity on coalition ratings on the issue of climate change, some descriptive results might provide the first explanation. Figure 5 shows respondents' self and party placements. In the figure, one can observe a sizeable difference in self-positioning on the climate issue dependent on individual-level salience. Those invested in the topic take, on average, a clear position toward rigorous combat against climate change. In contrast, people to whom the topic is not important opine that measures against climate change have gone too far. Furthermore, the figure shows that respondents for whom the issue is salient perceive higher party polarization. This pattern matches previous findings discussed above, in that issue salience promotes information seeking and, consequentially, knowledge about an issue, which seems to facilitate the recognition of differences in political supply.
To put this finding in context, Fig. 6 displays the relationship between votercoalition distances and coalition ratings on the three issue dimensions separately for respondents to whom the respective issue was salient or not. All six panels of the figure show the expected negative relationship. In addition, Fig. 7 plots the association between intracoalition heterogeneity and coalition ratings. Again, the expected negative relationship can be observed for the issues of taxation vs. social services and immigration, independent of individual-level salience. Furthermore, this finding holds for the issue of climate change for respondents to whom this issue was not Coalition ratings and voter-coalition distances. Means of voter-coalition distance and coalition ratings with 95% confidence intervals. The line displays linear predictions with 95% confidence intervals from bivariate regressions with clustered standard errors at the respondent level important. However, the lowermost right panel of Fig. 7 shows that coalitions including the Greens feature higher programmatic heterogeneity on the climate issue than the two coalitions without this party. Nevertheless, those respondents to whom the issue of climate change was important rated the more incongruent alliances higher than one would expect under the assumption of a negative relationship between heterogeneity and coalition rating. A possible explanation for this might be the issue ownership of the Greens on the issue of climate change. Voters who care about climate change might first and foremost want government participation of the party most capable of handling the issue (see, e.g., Neundorf and Adams 2018) and do not care too much if this might involve intracoalition conflict. Section E in the K Fig. 7 Coalition ratings and intracoalition heterogeneity. Means of intracoalition heterogeneity and coalition ratings with 95% confidence intervals. The line displays linear predictions with 95% confidence intervals from bivariate regressions with clustered standard errors at the respondent level supplementary material reports an unregistered test of this ad hoc assumption. I estimated models for two subsets of respondents who mentioned climate change as the (second) most important problem: The first model builds on those respondents who did not mention the Greens as best able to handle the problem, and the second model builds on those who did. Further, I included an indicator if a coalition incorporates the Greens. In both models, the intracoalition heterogeneity exhibits the expected negative influence on coalition ratings, which might hint at issue ownership being one part of the explanation of the counterintuitive finding from Fig. 4.

Discussion and Concluding Remarks
In the run-up to the 2021 German federal election, voters were confronted with a novel complexity in postelection coalition formation. Majorities of the long-standing ideologically homogeneous two-party alliances were unlikely, and feasible coalitions were cross-cutting dimensions of political competition. Building on previous research on the formation of voters' coalition preferences (Falcó-Gimeno 2012; Debus and Müller 2014;Plescia and Aichholzer 2017), this contribution analyzed the influence of spatial considerations, taking a multidimensional perspective on coalition politics. The findings suggest that a nuanced view on issues might be an interesting approach for the study of attitudes toward coalitions. While not all expectations have been met on each of the three issues under examination, the findings in support of the assumptions proved robust.
First, the analyses provide clear support that the nearer the coalitions' stance on an issue is to their own position, the better the voters evaluate the coalitions. In addition, voters seem not only to contemplate how a future government might represent their own stances but to reflect upon possible conflict between the potential partners. In particular, the findings for the socioeconomic dimension indicate that voters are sensitive to the programmatic heterogeneity of possible coalitions. Furthermore, both factors seem to interact such that considerations about issue positions exhibit greater influence on coalition preferences when the coalition at hand is more homogeneous. As research shows, a mismatch between parties decreases the chance of coalition formation, and this might also play a part in voters' preference formation: The position of an unfeasible coalition does not matter too much, which eventually facilitates considerations about more likely alternatives. Of course, these assessments are not necessarily accurate (this surely should be an object of further research), but it speaks to the ability of voters to cope with complex scenarios by eliminating unlikely outcomes.
Moreover, since not every issue is expected to be equally important for every citizen, issue salience was expected to be a moderating factor. The results of such moderation are mixed, and assumptions have to be overruled regarding the issue of immigration. However, the findings for socioeconomic issues and especially for climate change do provide support for the expectations. Climate change is not equally important for every citizen, and eventually, for those voters who do not care too much about it, it is irrelevant what stance a future government might take. In contrast, those invested in it want a government that represents their position. Results for the socioeconomic dimension suggest that this might also be true for intracoalition conflict; that is, if someone cares about an issue, they want to see coherence between government parties, but if the topic is not important, conflict over it becomes a lesser concern. These findings have important implications for how voters perceive coalition politics. It suggests that their assessment differs depending on what is personally important to them. If a coalition is expected to perform unitarily in favor of the voters on those issues important to them, they might be forgiving toward unfavorable policies and/or conflict on other topics.
Certainly, these findings come with some limitations that should be addressed in further research. First, they provide only a cross-sectional perspective. It seems K promising to investigate the effects of salience as a moderating factor for coalition preferences in a longitudinal design to be able to trace back intrapersonal changes in coalition preferences to potential changes in individual salience. Second, as mentioned above, the results do not support the assumptions on every issue dimension examined in this analysis. This might suggest, for example, that from the perspective of voters, the issue of immigration might not have been as crucial for coalition politics as the socioeconomic dimension or the issue of climate change. However, one cannot be sure that the analysis in this contribution does not neglect other relevant dimensions. It seems necessary to focus on the dimensionality in greater detail and replicate the analysis with different issue dimensions. Third, coalition positions and programmatic heterogeneity in the analysis build upon voters' placements of the constituent parties. While this might be a lesser concern for the latter measure, it would be promising to measure voters' perceptions about coalitions' positions directly. While it is possible to approach these perceptions and test the robustness with different operationalizations, there is only limited evidence about how voters perceive a coalition's policy position (see, e.g., Meyer and Strobl 2016;Bowler et al. 2020;Fortunato et al. 2021). Fourth, the unregistered ad hoc analysis gives reason to investigate the impact of the participation of the issue-owner on voters' coalition preferences. Finally, since the argument for a nuanced view on issues and salience is based on the complex context of the 2021 election, it would be interesting to investigate whether the conclusions hold for earlier elections with more preelectoral clarity in coalition formation.   Standard errors in parentheses (clustered at respondent level) *p < 0.05, **p < 0.01, ***p < 0.001
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Conflict of interest R. Welz declares that he has no competing interests.
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