Do voters want their parties to be office- or policy-seekers in coalition negotiations?

Abstract Do voters want their party to be office- or policy-seekers in coalition negotiations? This question has been left unstudied in political science research so far. While existing research shows that policies matter for voters when forming their preferences for coalitions, in this study it is argued that voters find it at the same time important that their preferred party gains offices. Specifically, voters’ office-seeking considerations are expected to increase the more indifferent they are to the policy content of a coalition agreement. To test this assumption, an original conjoint experiment among Green Party voters in the context of the German federal election in 2021 has been conducted. The findings demonstrate that voters’ office-seeking considerations become more important the more similar coalition agreements are with regard to their policy content. These findings have important implications for the understanding of voters’ preferences regarding coalitions.

understanding of the party-and institutional-level factors that affect government formation.
Yet, we know less about the question of which preferences voters have regarding the coalition formation process.Existing studies demonstrate that voters are aware of potential coalitions and can quite accurately predict which coalitions might be formed after an election, even in complex multi-party systems (e.g.Armstrong and Duch 2010;Hobolt and Karp 2010).It has also been shown that voters take these potential coalitions into account when they cast their ballot (e.g.Bargsted and Kedar 2009;Blais et al. 2006;Gschwend et al. 2017).Studies directly addressing voters' coalition preferences demonstrate that voters favour coalitions where coalition partners are ideologically closely aligned, indicating that policy-seeking factors are key for understanding coalition preferences (Debus and Müller 2014).Additionally, it is also important to voters 'whether coalition governments will be able to govern effectively' (Plescia andAichholzer 2017: 268, Nyhuis andPlescia 2018).
While these studies have highlighted which parties the voters want to join a coalition with their preferred party, they do not address the problem that voters can hardly predict how the entire government formation process will play out.Particularly in ever-more fragmented and polarised multi-party systems, voters (and political actors) do not know beforehand which specific government is going to be formed following an election.Even historical patterns of coalition formation (Armstrong and Duch 2010) might not be a good heuristic anymore.
In recent years, there have been various cases in which parties were forced to form 'atypical coalitions' , that is coalitions that have never been seen before (at least not at the national level).Recent governments formed in Israel, Germany, and Austria are cases in point.This is mainly so because traditional coalitions fail to get a majority of seats in parliament and, thus, parties have to look for new coalition partners.In other words, parties need more ideological flexibility when forming a coalition.This development has also consequences for analysing voters' preferences towards coalitions.While it is certainly interesting to see which coalitions a voter would like to see formed, the most preferred coalition options may not be arithmetically feasible of holding a majority in parliament. 1  Therefore, we suggest that it can be equally informative to analyse voter preferences beyond the question of which parties should form the coalition.
When forming a coalition, each party has to make concessions to its coalition partners.Standard theories on coalition formation indicate that such compromises have to be made with regard to two factors (Strøm and Müller 1999): First, parties care about how many and also which cabinet positions they get (office-seeking).Second, parties want their policy proposals to be implemented by the coalition (policy-seeking) in order to show voters-and especially party supporters-that they represent their interests effectively (Fortunato 2019b) as well as to be rewarded by voters for the fulfilment of electoral pledges made in manifestos and during the campaigns (see e.g.Thomson et al. 2017;Werner 2019).As parties are unlikely to get everything they wish for in a coalition, voters' preferences for coalitions might depend on the specific outcome of the coalition negotiation process (see, e.g.Martin and Vanberg 2020).This assumption holds even more true in situations in which a party might have the option to choose between different coalition partners.For example, a centrist party might have the option to join a center-right or center-left coalition. 2Should such a party join a coalition in which it is more likely to succeed with regard to policyor office-seeking aspects?In this paper, we address exactly this question from the perspective of voters.While it is well known that it matters to voters whether their parties will be able to implement their most important issues in a coalition (Matthieß 2020;Plescia et al. 2022), we do not know whether voters also care about offices in coalition negotiations.
This study, thus, is the first to analyse to which extent offices matter for voters' coalition negotiation preferences and we ask the following research question: Do voters want their party to be office-or policy-seekers in coalition negotiations?
While we argue that voters will generally be in favour of coalition agreements that address their policy preferences, we also assume voters to be office seekers.Voters in general are not well informed about politics (Achen and Bartels 2016;Lupia 2016), and thus might lack important information to predict whether certain coalitions will be able to implement specific policies.Potential coalitions are a salient topic in the public and are highly present in the media before elections.Not only the question of which parties are likely to join the government after the election is discussed, but also potential ministerial portfolio allocations.This is not surprising because '[p]ortfolio allocation certainly is the most straightforward indicator of the payoffs parties bargain for when entering a coalition government' (Bäck et al. 2011: 441).Since voters are frequently exposed to debates about portfolio allocation, we expect them to perceive winning offices in coalition negotiations as crucial indicators for their preferences.We further argue that office-seeking motives become more relevant the more indifferent a voter is towards two coalition agreements.In other words, if a voter is indifferent between two coalition agreements, the more she wants to increase office-seeking aspects.If, however, a voter clearly prefers the policies of a potential coalition agreement ' A' against the policies of a potential coalition agreement 'B' , then potential cabinet positions can hardly compensate for this factor and should not have an effect on voter's preferences for coalition agreement ' A' .
In order to test these expectations, we rely on an original conjoint experiment conducted in the context of the federal elections in Germany in 2021.The experiment was conducted with a sample of 989 voters of the Green Party.The Green Party was in a strategically favourable position before the German federal elections in 2021 as virtually no reasonable coalition could have been formed without it.Given the character of the Green Party as a niche party with party supporters that possess greater policy-seeking orientation (Lehrer 2012) and given the multiple options of the Green Party for potential coalitions after the elections, their voters' preferences especially with regard to office-seeking are highly interesting.In the conjoint experiment, we presented the respondents with two different coalition agreements varying with regard to the office-seeking and policy-seeking dimensions.However, we did not mention any party labels to avoid biases stemming from party or ideological preferences.The respondents then had to choose which of the two coalition agreements the Green Party should sign after the election.
To analyse the extent to which offices and policies matter to the voters in coalition negotiations, we make use of an innovative measure.As we are interested in the effect of policy-and office-seeking attributes on the probability of a profile for being selected in combination, we use two measures.First, we estimate the policy congruence between a voter and a conjoint profile.We further estimate the policy advantage of one of the conjoint profiles over the other, and then calculate which of the two profiles is closer to the policy preferences of the voters and, thus, has a policy advantage.Second, we also estimate the relative office advantage of one of the displayed profiles over the other in order to analyse to which extent offices matter to a voter.We refer to these two measures as Relative Policy Advantage (RPA) and Relative Office Advantage (ROA).
We find empirical support for our theoretical expectations: First, voters are more likely to select a coalition agreement when the policy profile matches voters' policy preferences.Second, we demonstrate that the more voters are indifferent between two coalition agreements -i.e. the more the policy-seeking aspects of these agreements are similar -the more important become voters' office-seeking considerations.More generally, we find that policy-and office-seeking considerations reinforce each other but that policy-seeking preferences seem to be more relevant to voters.These findings have important implications for our understanding of voters' preferences regarding coalitions and coalition agreements (see e.g.Blais et al. 2006;Duch et al. 2010;Gschwend et al. 2017;Meffert and Gschwend 2010;Plescia 2022;Plescia et al. 2022), and provide important insights into the current difficulties and challenges of government formation and representative democracy.By highlighting the thus far understudied aspect of the importance of both policies and offices in coalition negotiations, we not only contribute to the growing literature on voters' coalition preferences but also get one step closer to 'a model of the coalitional voter' to better 'understand how voters perceive and think about coalition policymaking' (Fortunato 2021: 15).

Voters and coalition negotiations
Previous studies have mainly addressed voters' coalition preferences before elections using observational data.Particularly in multi-party systems, where coalition bargaining is common, voters often are aware of potential coalitions that might be formed after an election (Meffert and Gschwend 2010).This is probably less the case the more fragmented party systems become and the more potential coalitions are on the table (Laver and Benoit 2015).Preferences for certain coalitions are mainly explained by the ideological positions of the voters, the potential coalitions, and the involved parties.The closer the position of the voter is to the parties in a potential coalition, the more likely the voters are to support this coalition (Debus and Müller 2014;Falcó-Gimeno 2012).
If voters are aware of potential coalitions, they also already consider potential coalition negotiation outcomes as important when casting their ballot (Blais et al. 2006).Several studies indicate that voters do not always vote for their preferred party, but are also willing to vote strategically for another party (Hobolt and Karp 2010).Hence, some voters vote for their preferred coalition rather than their preferred party (Duch et al. 2010;Gschwend et al. 2017;Meffert and Gschwend 2010).
While all of these studies shed light on coalition preferences before elections, there is also research that focuses on voters' reactions to coalition formation and the performance of coalitions once they are in office.There is evidence that voters, on the one hand, learn about the policy positions of the parties in the coalition, especially when there are intra-coalitional disputes about certain issues (Spoon and Klüver 2017), and that government participation also affects voters' perceptions of parties' policy positions.Voters perceive coalition partners to be ideologically closer to each other than would be warranted based on expert judgments of parties' manifesto contents (Adams et al. 2016(Adams et al. , 2021;;Fortunato and Adams 2015;Fortunato and Stevenson 2013).
On the other hand, voters also consider the performance of their party while they are in government when casting their ballot in the next elections.As Fortunato (2019a) demonstrates, voters also punish their party when they make compromises in coalitions.Voters want their preferred party to prevail in negotiations with coalition partners.In other words, '[v]oters do not care for compromise and cooperation between coalition partners in the policy-making process and they are willing to punish parties for these behaviors' (Fortunato 2021: 20).This mainly applies to less informed and less politically interested voters, as these lack the understanding that compromises are important in coalitions (Fortunato 2019a).
Moreover, voters also consider their party's pre-electoral pledges and whether the party was able to implement these as part of the coalition (Belchior 2019;Duval and Pétry 2020;Thomson 2011;Werner 2019).Thus, government parties 'are able to prevent bigger electoral losses if they show better performances in keeping their pledges' (Matthieß 2020: 789).Related to that, and as demonstrated by Plescia (2022), voters react to coalition agreements signed by their party.The findings indicate that the more parties move away from their position when entering a coalition, then 'the more likely voters are to decrease their party preferences as they will derive a lower utility from voting for them' (Plescia 2022: 9).
Overall, these studies indicate that voters not only are aware of the policy positions of the parties that are part of a potential coalition but also that they care about what parties promise before elections and about the policy concessions parties make during coalition negotiations. 3A less researched question, however, is which preferences voters have towards specific coalition agreements their party would be able to sign once deciding which coalition to join.

What affects voters' preferences towards coalitions and their agreements?
Voters hold parties, especially those in government, accountable for delivering on their electoral promises.Particularly voters that identify strongly with a party-which is also guiding their voting decision in the first place-are less biased in perceiving pledges as being unfulfilled (Belchior 2019).Consequently, we expect voters to be quite confident with regard to their preferred party's success in fulfilling electoral promises once this party enters government.
Previous studies argue that, in general, coalitions are most likely to be formed when the parties involved are ideologically close to each other (Martin andStevenson 2001, 2010).This is due to the parties' strong interest in implementing their policies during the legislative term.Thus, it is important how close the parties are positioned to each other regarding certain policies (Bräuninger et al. 2019;Debus and Müller 2013).Parties, however, have to make certain concessions when they become part of a coalition.In coalition bargaining processes some parties are more successful in enforcing their policy positions than others, which leads to more beneficial coalition agreements for some parties, e.g.mainstream parties, than others (Bäck et al. 2011;Klüver and Bäck 2019).
Voters' preferences towards certain coalitions are likely to rely on the policies that a party might be able to implement during the legislative term in this coalition as well (Armstrong and Duch 2010;Plescia and Aichholzer 2017).Thus, similar to parties' considerations, voters' coalition preferences are driven by the ideological and programmatic closeness of the positions of potential coalition partners to their preferred party (Duch et al. 2010;Falcó-Gimeno 2012;Plescia and Aichholzer 2017).Voters are in favour of coalitions where their preferred party is able to implement their policies, and voters thus are unwilling to support coalitions where the most important policies of their preferred party cannot be implemented (Debus and Müller 2014;Gschwend and Hooghe 2008;Plescia 2017).
In line with the theoretical arguments made by Fortunato (2019bFortunato ( , 2021) ) and Martin andVanberg (2011, 2020), who highlight the 'dilemma of coalition governance' (Martin and Vanberg 2011: 3-4), where coalition parties must cooperate and make compromises to govern effectively but simultaneously must signal to their party supporters that they are not tainting the party brand by too much accommodation, we thus argue that voters-like political actors-want as many preferred policy proposals implemented as possible (see e.g.Strom 1990;Strøm and Müller 1999).From this policy-seeking perspective, we expect that if voters would be confronted with two potential policy outcomes (that is, coalition agreements), they will choose the policy outcome that is closer to voters' policy preferences, even when accounting for potential office-seeking considerations (that is, portfolio allocations).Therefore, our first hypothesis reads as follows: H1: Voters' policy-seeking considerations will be more important than office-seeking considerations, the more the policy outcomes (that is, coalition agreements), match their policy preferences.
However, we also expect voters to consider whether their preferred party will be able to implement their most important policies.This seems to be most likely when the preferred party obtains offices.Even though '[g]etting into cabinet does not assure a party's supporters their preferred outcomes' , at least it 'allows that party the opportunity to bargain for them' (Fortunato 2021: 44).Voters, therefore, should also face a similar trade-off as partisan actors between policies and offices in coalition negotiations (Bassi 2021;Evans 2018;Sened 1996) by considering offices at least as a necessary condition for getting the chance to implement their preferred policies.
Parties do not only have to make concessions regarding policies but also offices and voters also possess not only preferences regarding which policies should be implemented but also have specific views on (a) which portfolios a party should try to gain when entering government and (b) which politicians should lead these ministries (Martin and Vanberg 2020;Nielsen 2020).This is particularly important as cabinet ministers are able to dictate policies in their area of expertise-or as Laver and Shepsle (1996) point out, cabinet ministers act as 'policy dictators' .Although voters are often uninformed about the specific details of the policy-making process, the power of ministers in office over their policy area is also well known to the public (Duch and Stevenson 2013).This is so because potential election and government formation outcomes are the favourite toys of the media when reporting on electoral campaigns.It is thus widely discussed in the public which coalitions might form and how the portfolios could be allocated among potential coalition partners.Furthermore, voters also have (implicit) knowledge of 'Gamson's Law' , that is the allocation of portfolios proportional to the seat weights a party brings to a coalition (Lin et al. 2017) because this more or less one-to-one proportionality of seats brought to the coalition and a party's number of portfolios is most of the time the actual outcome for government formation processes in modern democracies (e.g.Ariotti and Golder 2018;Bäck et al. 2009;Cox 2021;Ecker and Meyer 2019;Warwick and Druckman 2006).
Moreover, gaining influential offices means that parties are winners of the coalition negotiation process.Since we know that winning an election is generally an important determinant of voters' satisfaction with politics (e.g.Anderson and Guillory 1997;Anderson and LoTempio 2002;Banducci and Karp 2003;Singh et al. 2011), we also expect that winning influential offices in coalition negotiations by their party is important to voters.When the preferred party is able to gain offices, we expect that the party's voters perceive themselves as winners as well.In contrast to elections, where electoral winners sometimes are hard to identify, it is easier to assess who is among the winners in coalition negotiations.We expect that it is most likely that voters see their party as the winner when they gain as many offices as possible, that are preferably offices related to the party's policy focus.Observing the allocation of portfolios is a rather simple heuristic that voters use to assess if one's preferred party has negotiated successfully by at least receiving the share of portfolios that corresponds to its relative size (Lin et al. 2017).Thus, we expect voters to be office-seeking in the sense that they should strongly prefer coalitions where their preferred party holds influential offices.
Even though the spoils of offices are easier to observe for the large majority of voters than the less visible policy outcomes written down in coalition agreements (Martin and Vanberg 2020), we argue that especially coalition party supporters' distaste of policy compromises (Fortunato 2019b(Fortunato , 2021))-which is sometimes framed with an anti-elitist connotation as 'parties selling out their policy principles for obtaining a seat at the cabinet table'-trumps their office-seeking preferences.Consequently, we argue that even though both factors may simultaneously play a role when voters and party supporters must decide between two potential policy outcomes (that is, coalition agreements as a result of successful government formation processes), the trade-offs between these two factors vary.If coalition agreement ' A' is ideologically closer to the ideological position of a voter than coalition agreement 'B' , then this voter is more likely to choose ' A' over 'B' , regardless of the respective portfolio allocations associated with these coalition agreements.Yet, the more indifferent coalition agreements ' A' and 'B' are with regard to the policy content, office-related factors such as the portfolio allocation should matter more for the voter.Therefore, we stipulate the following hypothesis: H2: Voters' office-seeking considerations increase, the more indifferent they are between two policy outcomes (that is, coalition agreements).

Research design
We first describe our case selection highlighting why we are focussing on Green Party voters in the weeks before the German federal election in 2021.Subsequently, we present the experimental design before we lay out our rationale for an attribute-level analysis to investigate hypothesis 1 and for the trade-off analysis for assessing hypothesis 2.

Case selection
In order to test our hypotheses, we make use of a conjoint experiment integrated in an online survey among 989 Green voters in Germany.We fielded the survey in mid-September 2021 and, thus, in the week prior to the German federal election in 2021.The sample for the survey was provided by the professional sample provider respondi.Green voters were identified by a screening question at the beginning of the survey where the respondents were asked to indicate their vote choice in the upcoming general election.Additionally, we included quotas for sex (50% male and 50% female respondents) and age (in groups for respondents under 35 years, between 35-55 years, and older than 55 years).We did not include additional quotas as this would have made the inclusion of a large number of Green voters more challenging.The used quotas ensure a certain degree of heterogeneity with regard to gender and age.Reflecting the general composition of Green party voters, the respondents in our sample tend to be better educated than the average German population.For example, approx.65% of the respondents have a university entrance diploma.
The case of Green voters in Germany is particularly suitable for testing our hypotheses.In general, the German multi-party system makes coalition bargaining after elections necessary, as no party is realistically able to gain an absolute majority in parliament. 4Hence, coalition formation processes are already extensively discussed among parties and the public before the elections.Moreover, the federal election of 2021 provides a particularly well-suited example for addressing our research question for several reasons.
First, one prominent factor in the government formation literature could be almost entirely ruled out before the government formation process in this specific case: the incumbency factor (see Martin and Stevenson 2010).Both the CDU/CSU and the SPD made it crystal clear that they will not govern together following the election.Additionally, this time -unlike in 2017 -the polls unequivocally showed that several other three-party coalitions would obtain an absolute majority in parliament, indicating that there would be no need for Christian and Social Democrats to return to the 'grand coalition' as a last resort as they were forced to in 2017/2018 (see Bräuninger et al. 2019).
Second, for the first time in German national politics, there has been a realistic chance that none of the two mainstream parties dominating German party competition-CDU/CSU and SPD-would win the elections.Instead, the Green Party was the most important competitor in the general election (see Debus 2021;Faas and Klingelhöfer 2022).Throughout the electoral campaign, all realistic coalition options discussed in the media and-more importantly-by political actors involved the Greens in some way: a two-party coalition with the CDU/CSU, or three-party coalitions either including CDU/CSU and the FDP, SPD and FDP, or SPD and The Left.Thus, potential Green voters could have been very confident that their preferred party would end up in government following the elections, but it was very uncertain in which of the various potential coalitions this would be the case.
Consequently, we focus on Green voters in our sample, as we are particularly interested in their coalition preferences regarding their preferred party to engage more in office-or policy-seeking.Focussing on one party is also necessary to create a consistent experimental design: When analysing all voters, the content of the experimental design would need to be adjusted to every group of voters.Each party and its voters have other issue preferences and different preferences for certain offices.Thus, a design that is suitable for analysing all parties simultaneously is probably unfeasible.
Finally, the case of the Green voters provides us with an ideal testing ground for the extent to which voters are policy-or office-seeking in coalition negotiations.The Greens are very well known for their policy positions, as they are the clear issue owner with regard to environmental issues in Germany.Although offices, and particularly the chancellorship, were prominently discussed in the media in 2021 (Faas and Klingelhöfer 2022), the Greens were considered to be more policy-seeking and less oriented towards offices in general.

Experimental design
In order to test our hypotheses, we conducted a paired-choice conjoint experiment. 5Conjoint experiments have become a standard approach in political science research for addressing multidimensional decision-making problems (Bansak et al. 2021b;Hainmueller et al. 2014).In the experiment, respondents were asked to decide between two hypothetical coalition agreements both in which the Green Party would be included.The respondents were informed that the Greens have to conduct coalition negotiations with other parties in such a case.Such negotiations may involve questions of political personnel (e.g.chancellorship and portfolio allocation) and policies (e.g. the future direction of environmental policy).After this, the conjoint was presented to the respondents and they had to select between two profiles (i.e.coalition agreements) and, thus, indicate which coalition agreement they think the Green Party should sign.By using this experimental design, we are able to circumvent one important aspect of why voters are often disappointed and dissatisfied with their parties when confronted with the results of policy negotiations: '… voters may always imagine some counterfactual where the result of policy negotiation is getting everything they want and blame their representative for failing to deliver' (Fortunato 2021: 43).By forcing the respondents to choose between two profiles they did know exactly what the result of policy negotiations is.
As it is common practice in conjoint experiments, the conjoint profiles (i.e. the two coalition agreements) were completely randomised, meaning that for each attribute every level was chosen randomly (Bansak et al. 2021b).The hypothetical coalition agreements differed with regard to the offices the party could gain and with regard to certain policies they seek to implement.The presented offices as well as policies are based on the issue focus of the Green Party.As the Green Party mainly focuses on issues related to the environment and climate it is most likely that they aim to get ministries related to these issues to support their issue ownership with the respective portfolios (Ecker et al. 2015;Krauss and Kluever 2022).We, thus, included whether the Greens receive the Ministry of Environment, the Ministry of Agriculture, or a newly founded Ministry of Climate.The establishment of the latter was one of the key parts of the Green Party's election campaign (Faas and Klingelhöfer 2022).In addition, we also included whether the chancellor is from the Green Party.We have, thus, four office-related attributes.Each of these attributes was either 'yes' or 'no' , where 'yes' indicates that the Greens will get this office.
With regard to the policies selected for the conjoint experiment, we make use of six salient policies of the Green Party during the election campaign.We identified these issues based on the Green Party manifesto.These are (1) a general speed limit on highways, (2) mandatory solar plants for new buildings, (3) making agricultural subventions conditional on high standards of animal housing, (4) a cap on rents, (5) phase-out from Coal Energy, and (6) limitations to arms exports.The first four issues have binary levels, 'yes' or 'no' , indicating whether the Green Party was able to implement its policies in the coalition agreement.For the phase-out of Coal Energy, we provide four different years, reflecting public debates about this issue which highlighted that other parties wanted to rely on coal energy for a longer time period.For the limitations on arms exports, we provide three levels to account for existing heterogeneity within the Green Party and the public on this issue (see e.g.Hofmann 2021).The three levels are: 'general ban of arms exports' , 'arms exports only to established democracies' , or 'no general ban on arms exports' .The exact wording of all attributes and levels used in the conjoint experiment are presented in Table 1. 6 We deliberately decided not to include with how many or with which other parties the Green Party would form a coalition.In doing so, we are able to prevent that respondents use potential confounding factors -such as ideological closeness to other parties, portfolio calculations, or considerations regarding other party leaders' policy stances -into account when selecting one of the two profiles.Furthermore, we did not give respondents any information on the relative size of parties, that is the electoral results, to mitigate the potential confounding factor that voters do not see coalition party influence as proportional (Bowler  et al. 2020). 7 Each respondent had to complete five tasks.We, thus, have a total of 9,890 observations (= 989 respondents × 5 tasks × 2 profiles).Repeating the task is standard practice in conjoint experiments and increases the power of the study.As Bansak et al. (2021b, 27) state an 'important advantage of conjoint designs is that one can obtain many more observations from a given number of respondents without compromising validity than a traditional survey experiment, where within-subject designs are often infeasible due to validity concerns' .However, conjoint experiments tend to be quite complex.Thus, it is reasonable to assume that further increasing the complexity of conjoint designs, for example by increasing the number of tasks, might influence the response quality.Addressing these concerns, recent research shows that even complex conjoint experiments with many tasks and several attributes do not lead to low-quality responses (Bansak et al. 2018(Bansak et al. , 2021a)).In addition, one has to consider that the observations are nested at the respondent level.As described in Hainmueller et al. (2014: 20), clustered standard errors can be used to address this aspect and we follow their recommendation.

Analytical strategy
We start with the results of the attribute analysis to assess to what extent voters engage in policy-seeking when faced with two potential coalition agreements that match their policy preferences to a varying extent (H1).Subsequently, we present the results of the trade-off analysis which assesses to what extent the policy indifference of two potential coalition agreements affects voters' office-seeking considerations (H2).

Attribute level analysis
We first investigate the effect of the individual attribute levels on the probability that a respondent selects a coalition agreement.Thus, we follow Leeper et al. (2020) and estimate Marginal Means which reflect the probability that a conjoint profile is chosen conditional on an attribute level averaged over all other attributes.A potential problem of this approach is that the effect of the policy attributes probably depends on the policy preferences of the respondent.Although it is reasonable to assume that most Green voters will support the policies advocated by the Green party, there is no guarantee that this is the case for all respondents and for all issues.A respondent might disagree with the Green party on the speed limit on highways but still vote for the Green party.But this respondent will probably prefer a coalition agreement in which the Green Party is unsuccessful in their attempt to implement a speed limit on highways.Thus, using the 'raw' attribute levels which only indicate whether a policy was implemented or not, might underestimate the effect of the policy outcomes as some respondents might prefer when a certain policy of the Greens is not implemented.This concern does not mean that using the 'raw' attribute levels is not interesting.After all, the Green Party promoted such policies during its election campaign and wanted them to be implemented.Thus, by comparing the office and policy attributes, we can compare the effect of policy issues as desired by the Green Party while ignoring the actual preferences of their voters.Therefore, the first part of our empirical analysis assesses the effects of the attribute levels on the selection probability as is common in conjoint analysis.
However, in the second step of the analysis, we also incorporate the preferences of the respondents into the analysis.To do so, we recode the values of the 'raw' attribute levels in the conjoint experiment with how much they align with a respondent's position on the respective issue.We asked all respondents prior to the experiment about their position on the policies that we later included in the conjoint experiment.These positions were measured on a five-point scale ranging from 'completely disagree' (1) to 'fully agree' (5).For example, if a conjoint profile was in favour of implementing a speed limit on highways, the 'raw' attribute level would be 'yes' .We replace the value 'yes' with how the respondent evaluates such a policy outcome.If the respondent strongly opposes a speed limit on highways this attribute level would receive a value of 'strongly disagree' because the outcome of the coalition strongly contrasts with the respondent's policy preference.For the phase-out of Coal Energy, we compute the difference between the years displayed in the conjoint experiment and the year which was indicated by the respondents for this policy in the pre-treatment questionnaire.We then create groups depending on the number of years between a respondent's indicated preference and the respective attribute level for the phase-out of coal energy.

Trade-off analysis: policy vs. office
While standard conjoint analysis is interesting for investigating the effect of each individual attribute on the probability that a profile is selected, we are not directly interested in the effect of individual attributes for H2.Instead, we are interested in the combined effect of office-or policy-seeking attributes.Therefore, we use a second type of analysis for directly analysing the overall effect of all policy and office attributes on the probability that a coalition agreement was selected.
The suggested approach first estimates the policy congruence between a conjoint profile (i.e. a coalition agreement) and the policy preferences of a respondent.We then use this metric to estimate whether a respondent is closer to the first or the second displayed conjoint profile.We use a similar measure for the office dimension by summing up the number of offices the Green Party would get according to the displayed conjoint profiles.Finally, we use both measures to analyse how the effect of the number of offices depends on the policy congruence of a respondent with the displayed profiles.
We measure the policy congruence between a voter and the displayed conjoint profiles as described already with regard to the attribute level conjoint analysis, but use numeric values for the level of congruence.For each policy j included in the conjoint experiment, the position of voter i gets a value of 0 when the voter 'fully agrees' with the position of the Green Party.When a voter 'rather agrees' with the position of the Greens, we assign a value of 0.25 and so forth.Complete disagreement with the Green Party position results in a value of 1.We refer to a voter's position as P i,j .Likewise, for each conjoint profile, the policy position of a profile k on issue j is given by P k,j .P k,j can only take values of 0 or 1, depending on whether the policy is part of the coalition agreement (= 1) or not (= 0).The overall policy congruence (S i,k ) between a respondent i and a conjoint profile k is then estimated as the sum of the policy congruence on each issue j as: For example, when a respondent fully agrees with the position of the Greens (P i,j = 0) and the position of the Greens is part of the coalition agreement (P k,j ), then S i,k equals 1.Likewise, when a respondent completely disagrees with the position of the Greens (P i,j = 1) and the position of the Greens is not part of the coalition agreement, then S i,k also equals 1.When a conjoint profile contains only policy attribute levels that perfectly match a respondent's preferences, then S i,k is 6.When a respondent disagrees with all positions of a coalition agreement, then S i,k is 0. Higher values, thus, indicate higher levels of policy agreement.We then estimate the Relative Policy Advantage (RPA) of the first conjoint profile over the second conjoint profile as: When both coalition agreements have the same policy congruence with the respondent, the RPA equals zero.Positive values indicate an advantage for the first conjoint profile and negative values an advantage for the second profile.As the RPA increases, the probability of selecting the first conjoint profile should increase.The theoretical range of this variable is from −6 to +6, but empirically we observe only values in the range from −4 to +4 as it rarely happens that one profile has perfect congruence with a respondent and the other profile has perfect incongruence with the respondent.Figure 1 displays the distribution of this variable.
For the four office-seeking attributes in the conjoint experiment, we assume that these are valence attributes and that all voters would like to have their party get as many offices as possible.We, thus, compute for each profile the number of offices that the party would get based on the levels of the four office-attributes.We then also estimate the difference in the number of offices between conjoint profile 1 and conjoint profile 2. The variable has a range from −4 to +4, indicating whether profile 1 or profile 2 would result in more offices for the Green Party.We refer to this variable as the Relative Office Advantage (ROA).
We then run a logistic regression analysis on a sample consisting solely of the first conjoint profiles.The dependent variable is whether the profile was selected or not.The independent variables are the relative policy advantage (RPA) as well as the relative office advantage (ROA) of profile 1.As our main hypothesis is that voters rely more strongly on office-factors when they are indifferent with regard to the policy-proposals, we include an interaction between the RPA and the ROA.The regression model, thus, is specified as follows:

Results
We first present the results of our attribute analysis to test hypothesis 1.Then, we turn to the policy vs. office analysis to test hypothesis 2.

Attribute analysis
Figure 2 displays the Marginal Means (MMs) of the attribute levels.MMs indicate the probability that a conjoint profile is selected given the respective attribute level averaged over all other attribute levels.Values above 0.5 indicate a positive effect on the selection probability.The four attributes at the top of Figure 2 display the office-related attributes.They confirm our expectation that voters are generally in favour of having more offices as the selection probability is higher when the Greens get the respective Ministry in the coalition agreement.Particularly the chancellor and the Ministry of Environment are seen as relevant, while the MMs for the Ministry of Agriculture and Climate are lower.
The MMs for the office-related attributes are comparable to most policy-related attributes.All other binary attributes show very much comparable MMs.In all cases, the MMs indicate that respondents prefer it when the Green Party is successful with their policies in the coalition agreement, which is not surprising and confirms the assumption that note: relative policy advantage (rpa) is estimated as the differences between the policy congruence of the first and second conjoint profile with a respondent.each policy congruence could take a value of 0 to 6, where 6 indicates perfect congruence and 0 complete disagreement.positive values of the rpa indicate that a respondent is closer to the first profile than to the second conjoint profile.Zero indicates indifference between both profiles.most voters support the policies of the Green Party.The only clear difference in the strength of the MMs can be observed for the phase-out of Coal Energy.This policy has much higher MMs, with earlier years being clearly preferred over later years.In general, these results indicate that individual policies -such as coal energy -can be more important, but there is so far little evidence that policies are more relevant than offices to voters.
This pattern is different when accounting for the policy preferences of the respondents.As explained in the methods section, we replaced the attribute levels with the policy congruence between the conjoint profile and a respondent.We then estimate the effects conditional on how strongly each attribute reflects a respondent's policy preference.The results are displayed in Figure 3.This analysis allows for a different conclusion.Respondents care about policies, but they care more about the implementation of their own policy preferences.As can be seen, the Marginal Means for the policy issues are now much larger, and usually larger than the MMs of the office-seeking attributes.Except for the cap on rents and mandatory solar panels, all policies are now clearly more important than the office-related attributes.Overall, this analysis demonstrates that voters care about their own policy preferences being implemented (H1).If one does not account for the diverging preferences of a voter and the party, then office and policy attributes are not necessarily more important than offices to the respondents.However, if one accounts for individual preferences, the pattern is different.

Policy vs. office analysis
While the previous section has provided first evidence for the claim that policies are more important than offices when they reflect a respondent's preferences, the analysis did not directly address the interaction and potentially reinforcing of office-and policy-related attributes.To answer this question, we plot in Figure 4 the results of the logistic regression analysis.In Figure 4A, the predicted probabilities are displayed.The y-axis displays the probability that a respondent will select the first conjoint profile.The x-axis depicts the Relative Policy Advantage (RPA) of the first profile over the second profile.When the RPA is positive, the first profile (coalition agreement) is closer to the respondent than the second profile.The three curves reflect different levels of the Relative Office Advantage (ROA), i.e. the difference between the number of offices that the party receives in the first and in the second coalition agreement.As can be clearly seen, there is a positive effect of the RPA on the selection probability.When the first profile has a clear policy advantage over the second, the first profile will almost always be chosen and vice versa.Importantly, this relationship is moderated by the ROA.When the RPA is close to zero, indicating that both profiles have similar levels of congruence, the ROA matters most, which means that in such cases offices are important to the voters.
In Figure 4B this effect is displayed based on first differences.It displays the difference in the predicted selection probability for the first profile when it has a ROA of 4 or −4, conditional on the level of the RPA.In other words, it is the difference between the blue and orange curves in Figure 4A.As can be seen, when the RPA is at zero (i.e. policy indifference between both profiles), the effect of the ROA is at 0.6.But the effect of the ROA decreases to 0.15 when the RPA is clearly positive or negative.
Figure 4C offers a more comprehensive visualisation of the relationship between the RPA and ROA.The contour plot shows the predicted probability of selecting the first conjoint profile for all combinations of the RPA and ROA.Again, the plot provides clear evidence for the relevance of the RPA.For example, even when the ROA is strongly negative a small positive value in the RPA still leads to a predicted probability of 0.5.In contrast, when the RPA is strongly negative, a predicted probability above 0.2 is never observed.Thus, our findings clearly show how policy congruence outperforms office-seeking motives.Office seeking is most relevant when coalition agreements are similar with regard to their policies, and when voters become indifferent towards two coalition agreements regarding their policies.Hence, also our second hypothesis is supported by the empirical findings.predictions and first differences were computed using the Zelig-package in r. the methodological approach for estimating these values is explained in more detail in King et al. (2000).each value is based on 5,000 simulations.Figure c) is a contour plot and show predicted probabilities for all combinations of the rpa and roa.[colour online only.]

Conclusion
Like Freddie Mercury, party supporters 'want it all and they want it now': they want their preferred party to govern alone and to implement all the policies they prefer.However, the real world is more complexespecially in political systems with proportional representation-and voters actually know this (Bowler et al. 2022).If at all, their preferred party is likely to end up in a coalition government.Assuming that voters want their preferred party to be in office but also keeping in mind that voters are disappointed when their party must make concessions and compromises (Fortunato 2021) and cannot push through all of its electoral promises, voters face a trade-off between policy-and office-seeking considerations when thinking about potential coalitions.This trade-off, however, has only implicitly gained attention in the literature so far (see e.g.Fortunato 2021; Martin and Vanberg 2020).
To shed light on this aspect, we focussed on Green party voters before the German federal election in 2021.We conducted a conjoint experiment where voters were forced to choose between two hypothetical coalition agreements which vary with regard to the policy content and the portfolio allocation.We demonstrate that our two theoretical arguments regarding voters' preferences in coalition negotiations find empirical support.First, voters are more likely to choose a coalition agreement, the more the policy profile matches their policy preferences.Second, we find that voters' office-seeking considerations become more important the more similar coalition agreements are with regard to their policy content.
These empirical findings contribute to the growing literature on voters' preferences regarding coalitions and coalition agreements (see e.g.Blais et al. 2006;Duch et al. 2010;Gschwend et al. 2017;Meffert and Gschwend 2010;Plescia 2022;Plescia et al. 2022) by highlighting the trade-off between policy-and office-seeking considerations voters are facing.This trade-off should become more and more important in the ever more complex bargaining environment political parties in modern democracies are competing in (see Laver and Benoit 2015).Single-party governments are more and more unlikely, and both minority and majority coalition governments are becoming the standard type of government constellations (see e.g.Thürk et al. 2021).Moreover, our findings also indicate that voters care about the policies that their preferred party is able to implement.While electoral campaigns are often focussed on individual politicians, such as the parties' front-runners, after the election voters might be more aware of the importance of policies and less likely to focus on single persons as well as on offices.Notwithstanding this, when forming their preferences towards certain coalitions at the beginning of the cycle of the coalition, offices are important to voters.Despite these crucial findings, at least four caveats and potentials for future studies remain.First, our study solely focussed on majority government constellations, at least implicitly.By conducting the conjoint experiment in Germany, a country where minority and single-party majority governments are highly unusual at all political levels (Bäck et al. 2013;Bräuninger et al. 2019;Gross 2023), we most likely deal with voters not considering these two government constellations as viable outcomes of post-election bargaining.Even though coalition governments holding a majority in parliament are quite common (see Thürk et al. 2021), our theoretical arguments should additionally be tested in countries with a tradition of minority governments or single-party governments.
Second, we focussed on voters of a party that has been campaigning as an opposition party, which has not been in government for more than two decades, and-given the Green Party's increasing electoral successes and participation in government in state and local politics in the past years (Bräuninger et al. 2019;Gross 2018)-is on the edge of moving from a niche party to a mainstream or dominant party, respectively (De Vries and Hobolt 2020;Meguid 2005).This probably makes the Green electorate a special case to test our hypotheses, as they might be more likely to focus on policies than offices due to their strong issue focus.Consequently, our theoretical arguments should be tested with regard to voters from government and dominant parties, respectively.
Third, we made the assumption that all voters and party supporters are well-or bad-informed about politics, in general, and multiparty government politics and policy-making processes, in particular, to the exact same extent.However, this is a rather simplistic assumption since there exist large differences between voters and party supporters regarding their political awareness (Martin and Vanberg 2020), and these differences are additionally affected by varying institutional, political, and electoral contexts (Fortunato et al. 2016).Green voters and party supporters display a higher degree of political awareness than voters and supporters of other parties (Dolezal 2010).Moreover, the conjoint experiment provided all information to the respondents.In reality, however, many respondents might not be that well-informed about the policies agreed upon in a coalition and rather focus on the portfolio allocation outcome as an information shortcut (Martin and Vanberg 2020).Consequently, our theoretical arguments should be tested with voters of other parties and in varying political, institutional, and electoral contexts.
Lastly, our findings may pave the ground for interesting new ways of analysing voters' preferences once parties are negotiating about forming multiparty coalition governments, when we turn away from 'just' focussing on voters' preferences and expectations on Election Day and the rather short period of government formation afterward, to the 'cycle of coalition' (Fortunato 2021).Because most voters 'want to have it all' (policy-wise) they reject cooperation and compromise in multiparty coalition governments and will be disappointed by their preferred party, the question is how large the disappointment must be to punish their party by switching their vote or by abstaining in the next election.Whereas tracking the level of voter disappointment over the cycle of coalition is a challenging task (requiring individual-level panel data), in an adapted version of our conjoint experiment scholars could (a) manipulate the allocation of portfolios to analyse at which point voters no longer consider the distribution of cabinet ministries (clearly observable) to be sufficient, even if their preferred party receives a lot of (less observable) side payments, that is policies that are close to the party's and voters' ideal points; and (b) manipulate the policy-related content of hypothetical coalition agreements to tease out at which point voters do not want to sacrifice policies any more for the spoils of offices.

Notes
1. We restrict our argument here to majority coalition governments since single-party majority governments, single-party minority governments, and minority government coalitions still are less common than majority coalition governments (Thürk et al. 2021).2. Assuming that other parties from the center-right and center-left are also interested in joining a coalition with the centrist party and that the centrist party does not belong to one of the two 'ideological camps' .3. For the sake of simplicity, our theoretical argument is based on the assumption that all voters are informed about politics to the same extent, thus disregarding the varying levels of political awareness between and within the different groups of voters and party supporters (see e.g.Fortunato et al. 2016).We discuss potential ways of refining this assumption to capture the varying levels of voters' political awareness in the conclusion.4. Of course, minority governments would be a possible outcome of government formation processes in Germany but never happened at the federal level and are also very uncommon at the sub-national level (see Bräuninger et al. 2019;Debus and Gross 2016). 5.The experiment was not pre-registered.Future studies could test and corroborate our findings based on a pre-registered design.6.The exact wording of the introduction to the conjoint experiment as well as the decision screen presented to the respondents can be found in the online appendix.7. This, of course, simplified the real-world constellations Green voters were facing because joining a coalition as "junior partner" with CDU/CSU and FDP, two parties from the right-wing ideological camp, would definitely result in a different coalition agreement than the one agreed upon with the SPD and the FDP, where the Greens and the SPD -two parties from the left-wing ideological camp -would have more influence during coalition bargaining.We discuss this in the conclusion in further detail.

Figure 1 .
Figure 1.Distribution of the relative policy advantage variable.

Figure 2 .
Figure 2. Marginal means of conjoint attribute levels.note: Marginal Means are displayed.Horizontal lines are 95% confidence intervals.

Figure 3 .
Figure 3. Marginal means of conjoint attribute levels recoded as agreement with respondent.note: Marginal means are displayed.Horizontal lines are 95% confidence intervals.

Figure 4 .
Figure 4. effect of policy closeness and offices on selection probability.note: in all figures, the x-axis displays the relative policy advantage (rpa) of the first conjoint profile over the second conjoint profile.positive values indicate that the first conjoint profile (i.e.coalition agreement) was closer to a respondent's policy preferences than the second profile.negative values indicate the opposite.Figure a) displays predicted values on the y-axis, i.e. the probability that a respondent selects the first profile in the conjoint experiment.'relative office advantage' (roa) measures the difference in the number of offices in the first and second conjoint profile.positive values indicate that profile 1 has more offices than profile 2 and vice versa.Figure B) displays first differences on the y-axis, i.e. the differences between the blue and the orange line from Figure a. predictions and first differences were computed using the Zelig-package in r. the methodological approach for estimating these values is explained in more detail inKing et al. (2000).each value is based on 5,000 simulations.Figurec) is a contour plot and show predicted probabilities for all combinations of the rpa and roa.[colour onlineonly.] Figure a) displays predicted values on the y-axis, i.e. the probability that a respondent selects the first profile in the conjoint experiment.'relative office advantage' (roa) measures the difference in the number of offices in the first and second conjoint profile.positive values indicate that profile 1 has more offices than profile 2 and vice versa.
Figure B) displays first differences on the y-axis, i.e. the differences between the blue and the orange line from Figure a.

Table 1 .
attributes and levels used in the conjoint experiment.