Formateur optimization – the neglected part of coalition-directed voting

In most parliamentary democracies, elections are the first of several stages determining the composition of the government and the identity of the prime minister. This process, though nuanced and varied between countries, generally includes three steps.Footnote ¹ First, a formateur is chosen based on parties’ seat share and the institutional arrangements in place. Second, potential partners are typically approached, leading to the formation of a coalition. Third, cabinet members are assigned portfolios (Cox Reference Cox, Herron, Pekkanen and Shugart2018; Kedar Reference Kedar2012). Vast literature has demonstrated that voters in such systems take into account this coalition formation process when making their vote choice, so that coalition-based considerations affect voting sometimes even more than party-based considerations (Blais, Aldrich, Indridason et al. Reference Blais, Aldrich, Indridason and Levine2006; Cox Reference Cox, Herron, Pekkanen and Shugart2018, Reference Cox1997; Duch May and Armstrong Reference Duch, May and Armstrong2010; Hobolt and Karp Reference Hobolt and Karp2010; McCuen and Morton Reference McCuen and Morton2010).

The types of coalition-directed strategic voting voters engage in are closely related to the abovementioned stages of government formations, each stage providing voters with different incentives to engage in policy voting (Kedar Reference Kedar2012). Voters thus engage in coalition-directed voting to influence either who will be the formateur; who will be available as partners to the possible formateur(s); or the balance of power within a likely coalition. Cox (Reference Cox, Herron, Pekkanen and Shugart2018) outlined these pathways as three potential strategies for coalition-directed voting: formateur optimization, partner optimization, and policy balancing (see also Gschwend and Meffert Reference Gschwend, Meffert, Arzheimer, Evans and Lewis-Beck2016). We first discuss policy balancing and partner optimization, the more well-known and well-studied forms of coalition-directed voting, followed by a discussion of formateur optimization and how it varies from the other two.

Policy balancing is a strategic voting behavior adopted by voters who perceive the composition of the next coalition as a foregone conclusion and are certain about the identity of the next formateur. Instead of focusing on changing the coalition’s formation, they aim to influence the allocation of ministerial portfolios within the coalition by altering the seat shares of its constituent parties. This strategy is also commonly called ‘coalition-targeted Duvergerian voting’ (Bargsted and Kedar Reference Bargsted and Kedar2009). The core idea behind policy balancing is that voters seeking to impact government policy will strategically vote for a party they believe will enter the coalition and wield ministerial influence.

Empirical studies provide strong evidence for this form of strategic voting. Bowler et al. (Reference Bowler, Karp and Donovan2010) found that voters tend to abandon their preferred party if they perceive it as unlikely to join the expected coalition. Similarly, Herrmann (Reference Herrmann2008) documented comparable patterns in Austria. Bargsted and Kedar (Reference Bargsted and Kedar2009) showed that in Israel, voters who believe their preferred party has little chance of entering the post-election coalition are inclined to support the ‘lesser of evils’ among the viable coalition partners. Cox (Reference Cox, Herron, Pekkanen and Shugart2018: 268) refers to this phenomenon as ‘policy balancing by out-voters’, where voters from outside the expected governing bloc strategically shift their support to moderate coalition parties to temper the anticipated government’s policies. Cox (Reference Cox, Herron, Pekkanen and Shugart2018) also identifies another variation called ‘policy balancing by in-voters’, in which voters who support the anticipated coalition cast their votes for more extreme coalition partners to influence the coalition’s policy direction in their preferred ideological direction (Kedar Reference Kedar2005; Reference Kedar2012).

Partner optimization, in contrast, focuses on shaping the composition of the next coalition by influencing the availability and strength of potential coalition partners. A well-known example of this strategy is ‘threshold insurance’ or ‘rental voting’, where supporters of a major party temporarily vote for a smaller, allied party that risks failing to meet the electoral threshold. This ensures the smaller party’s survival and availability as a coalition partner. Studies by Gschwend (Reference Gschwend2007) and Meffert and Gschwend (Reference Meffert and Gschwend2010) provide empirical evidence of threshold insurance voting, highlighting cases where large-party supporters strategically lend their votes to secure the parliamentary presence of their preferred junior partners.

Formateur optimization, also referred to as sequential voting, refers to voters who vote to affect which party gets the first opportunity to form a government and thus, most likely, who will be the next prime minister (Cox 2018; Reference Cox1997). The most straightforward way to influence the identity of the formateur is by voting for his/her party, under the assumption that the larger the party’s seat share, the greater the likelihood that its leader will be appointed as formateur. Indeed, in many cases, the formateur is the leader of the largest party in parliament (Bäck and Dumont Reference Bäck and Dumont2008; Martin and Stevenson Reference Martin and Stevenson2001).

While at first sight this strategic behavior might seem very different from the classic Duvergerian strategic voting, a careful look allows adapting the Duvergerian logic to this strategic behavior as well. Instead of looking at the potential loss in votes ‘wasted’ on a party that did not make it into parliament – as in the case of the classical strategic voting, or at the potential loss in votes ‘wasted’ on a party that did not make it into the coalition – as in the case of ‘coalition-targeted Duvergerian voting’ (Bargsted and Kedar Reference Bargsted and Kedar2009), it is possible to take this logic one step further and apply it to formateur voting – looking at the potential loss in votes ‘wasted’ on a party that did not become the formateur’s party. In this scenario, voters weigh their choices in light of how their decisions might impact the identity of the head of government, just as they would weigh the trade-offs in a Duvergerian system, where the objective is to avoid ‘wasting’ a vote and ensure their desired outcome within a two-party structure.

Cox (Reference Cox, Herron, Pekkanen and Shugart2018) argues that formateur optimization is most likely when there is high uncertainty regarding the identity of the next formateur but minimal uncertainty about possible future coalition compositions. However, he also argues that formateur selection precedes coalition formation in voters’ strategic considerations. The sequencing reasoning suggests that voters first assess the likelihood of their preferred formateur’s success before considering coalition partnerships. Consequently, even under high coalition uncertainty, the formateur consideration remains primary. Findings from Harsgor et al. (Reference Harsgor, Itzkovitch-Malka and Tuttnauer2023) support this reasoning, showing that the effect of coalition expectations is significant only among voters who are certain about the formateur race outcome. This further reinforces our decision to focus on formateur uncertainty, as it shapes the initial stage of voters’ strategic calculations.

An important question that arises in the context of formateur optimization is how to conceptually and analytically distinguish it from other types of coalition-oriented voting, such as partner optimization and policy balancing. For partner optimization, the differentiation is rather easy, as, by definition, partner optimization involves voting for non-formateur-coalition-partner-parties rather than voting for formateur parties. A more complex differentiation is that between policy balancing and formateur optimization as both are forms of strategic voting in which voters may choose to vote for a formateur party instead of their preferred non-formateur party. The distinction between the two is thus analytical and is based on the different conditions and the distinct motivations they are driven by.

Formateur optimization focuses on voters who prefer non-formateur parties but strategically vote for a formateur party to influence which party will have the first opportunity to form the next government. This behavior typically occurs in situations of formateur uncertainty, where there is close competition between potential formateur parties. In these cases, voters shift their support to the potential formateur party they believe has the best chance of leading the government, prioritizing the goal of ensuring that their preferred coalition leader forms the government.

Policy balancing, on the other hand, occurs when voters are confident about which party will form the next government and instead seek to influence the internal distribution of power within the anticipated coalition. In such scenarios, voters might opt to vote for the assumed formateur party rather than their preferred non-formateur party, but their goal is different – they aim to shape the balance of power and the allocation of ministerial portfolios within the coalition. A notable example of this can be seen in Bargsted and Kedar (Reference Bargsted and Kedar2009), where voters in Israel, confident that a particular coalition would form, strategically voted for the formateur party because it represented the most moderate option within the coalition. In these cases, the choice to vote for the potential formateur party is driven by the desire to moderate government policies rather than to influence the identity of the next formateur (which is assumed to be certain).

Nonetheless, the theory we set forth in our paper suggests that formateur optimization is not restricted to cases of high formateur uncertainty and is expected to occur also under low formateur uncertainty, contingent on voters’ preferences. This further complicates the differentiation between formateur optimization and policy balancing, as in cases where formateur uncertainty is low and supporters of a non-formateur party shift their vote for a formateur party. However, we move forward with the assumption that the group of voters for which formateur optimization and policy balancing is indiscernible is rather small. We base this assumption on studies documenting policy balancing, for example: Bowler et al. (Reference Bowler, Karp and Donovan2010) or Herrmann (Reference Herrmann2008), which show that for the most part, policy balancing does not involve strategically voting for the formateur party, but rather voting for non-formateur expected coalition partners. It is only in a very specific political conjecture, such as the case of Israel 2009, where this was not the case. Considering this discussion, we assume that a non-formateur party’s supporter who strategically votes for a formateur party engages in most cases in formateur optimization, and not policy balancing.

While partner optimization and policy balancing have been extensively studied, formateur optimization remains largely unexplored. This is quite surprising given the central role prime ministers play in shaping coalition structures, portfolio allocations, and policymaking. Also, the growing trend of personalization, which shifts the focus from parties to party leaders, further underscores the importance of studying this type of consideration that voters might hold. Only a few studies empirically examine formateur optimization voting behavior, focusing on a particular country at a particular time (see Felsenthal and Brichta Reference Felsenthal and Brichta1985; Harsgor et al. Reference Harsgor, Itzkovitch-Malka and Tuttnauer2023; Indridason Reference Indridason2011; Nachmias and Sened Reference Nachmias, Sened, Arian and Shamir1999). Nonetheless, it is important to note that such studies find evidence for the existence of formateur optimization voting. For example, Indridason (Reference Indridason2011) shows that voters have incentives to attempt influencing policymaking after elections through the identity of the formateur. Other studies suggest that formateur considerations may affect vote choice. Kedar (Reference Kedar2012:10) stresses the importance of examining the selection of the formateur as a possible venue for coalition-directed voting, noting that ‘voters may desert a favorite small party and instead support a larger party if they think this party may be the largest or the one chosen to lead the government’. Abramson, Aldrich, Blais et al. (Reference Abramson, Aldrich, Blais, Diamond, Diskin, Indridason, Lee and Levine2010) also note that tactical voters in PR systems may be motivated by their desire to influence the identity of the formateur.

Most recently, Harsgor et al. (Reference Harsgor, Itzkovitch-Malka and Tuttnauer2023) provide empirical evidence for formateur optimization in the Israeli case, driven by formateur uncertainty. Focusing on a particular case of vote-switching in repeat elections, they show that voters are more likely to switch their vote to affect the identity of the next formateur, the higher the formateur uncertainty is. However, Harsgor et al. (Reference Harsgor, Itzkovitch-Malka and Tuttnauer2023) focus on one specific context of repeat elections and the inclination of vote switching between elections rather than strategic voting per se. They do not develop the role of uncertainty in formateur optimization to a broad comparative context and do not develop theoretically the different conditions in which uncertainty works. In addition, they measure formateur uncertainty in one way only and do not provide an extensive examination of voter preferences nor offer a comparative framework to understand formateur optimization. Thus, a deeper examination of the impact of formateur uncertainty on formateur optimization and its potential interaction with other factors is greatly needed.

Determinants of formateur optimization: Theoretical expectations

Formateur optimization inherently involves trade-offs that can be effectively framed using insights from spatial voting models (Enelow and Hinich Reference Enelow and Hinich1982; Reference Enelow and Hinich1984; Hinich and Pollard Reference Hinich and Pollard1981). These models assume that voters evaluate parties based on their ideological proximity, deriving the highest utility from parties closest to their own policy preferences.Footnote ² In the context of formateur optimization, however, voters face a unique decision: whether to prioritize ideological alignment by supporting their most-preferred party or to vote strategically for a party likely to influence coalition formation as the formateur. This decision involves balancing costs and benefits.

The costs of formateur optimization stem from the ideological distance between the voter’s most-preferred party and the expected formateur. Voting for a party that is ideologically farther away entails a sacrifice in utility derived from policy alignment. In spatial terms, this cost can be conceptualized as the ‘distance penalty’ that voters incur when deviating from their ideal point on the policy spectrum.

The benefits, on the other hand, arise from the potential to influence the identity of the next formateur. By supporting a viable formateur, voters can influence coalition outcomes, potentially ensuring that the overall government’s policy orientation is closer to their preferences. In this framework, the utility gained from successfully influencing the formateur – and, by extension, the coalition – is weighed against the utility lost from not supporting the most ideologically proximate party. Spatial voting models, therefore, provide a clear structure for understanding these trade-offs: voters maximize their overall utility by balancing the ideological cost of their vote with the strategic benefit of influencing coalition dynamics.

However, it is important to note that while spatial proximity plays a central role in structuring these trade-offs, the utility may also stem from non-ideological considerations, such as perceptions of party competence, leadership, or the desire to block an undesirable formateur from gaining power. For instance, a voter might support a centrist party expected to act as a formateur, even if it is ideologically distant, to block the formation of a government led by a party they strongly oppose. Similarly, identity-based considerations, such as shared ethnicity, religion, or regional affiliation with the expected formateur, may generate utility for voters independent of ideological alignment. This broader conception of utility acknowledges that voters may prioritize coalition outcomes or the identity of the formateur over strict ideological alignment. Thus, formateur optimization voting reflects a complex calculus where spatial and non-spatial factors combine to inform voter decision-making.Footnote ³

Our hypotheses aim to address the abovementioned gap by exploring the conditions that enable formateur optimization. We specifically focus on theoretically developing the concept of formateur uncertainty and its interactions with voters’ preferences.

Our first hypothesis seeks to directly assess formateur optimization as a function of formateur uncertainty. As could be expected, we examine this mechanism within the subset of non-formateur parties’ supporters, positing that when there is high uncertainty regarding the formateur, these voters are more inclined to engage in formateur optimization, thus voting for a formateur party instead of their most favorable non-formateur party. As stated earlier, the rationale behind this expectation is straightforward – when the race between the potential formateurs is close, voters are more motivated to strategically endorse a formateur’s party in the hope of influencing the selection of the next formateur, compared to when the formateur’s identity is more or less certain.

Following this preliminary hypothesis, we delve into more complex expectations concerning the interplay between formateur uncertainty and voter preferences. We present two such expectations: the first addressing voter preferences regarding his/her most preferred party and the second addressing voter preferences regarding the identity of the next formateur.

In general, the literature finds that the intensity of the voter’s preference for a party is expected to have consequences for their willingness to engage in strategic voting (Abramson et al. Reference Abramson, Aldrich, Blais, Diamond, Diskin, Indridason, Lee and Levine2010). Studies show that voters who identify with a party are reluctant to desert their first party of choice, as the cost of deserting this party is sizeable (Gschwend Reference Gschwend2007; Niemi Written and Franklin Reference Niemi, Written and Franklin1992). Furthermore, the distance – in terms of ideology or favorability – between one’s preferred party and a possible strategic vote choice has been found to affect the likelihood of strategic voting (Daoust and Bol Reference Daoust and Bol2020). How do such calculations influence formateur optimization strategic voting? Our next hypothesis addresses this question, explaining how the gap in favorability between the voter’s most preferred party and her most preferred formateur party moderates the relationship between formateur uncertainty and formateur optimization.

We expect that the larger this gap, the less likely voters will be to engage in formateur optimization. When the gap between how much a voter likes her most preferred party and how much she likes her favorite formateur party is large – she will be less likely to strategically vote for a formateur party, as the cost of deserting the preferred party is higher compared to when the gap is small. Put differently, we expect voters to be less sensitive to formateur uncertainty when there is a large gap in affection between their most preferred party and their preferred formateur party.

While H1 and H2 echo the view of high uncertainty as a necessary condition for formateur optimization, H3 presents further progress in the conceptual understanding and the empirical examination of formateur optimization. Here, we argue that formateur uncertainty is not a necessary condition for formateur optimization. Even when it is relatively clear who will end up as the government formateur, some voters may be inclined to engage in formateur optimization. In this context, we distinguish between voters who are certain about the victory of their preferred formateur candidate and voters who are certain that their preferred candidate will lose. This approach integrates voters’ preferences for the government formateur with their expectations regarding the election’s outcome, allowing us to explore the possibility that the effect of expectations on voting may be contingent on preferences. Consequently, it aids in providing a more precise understanding of the circumstances under which voters are inclined to engage in formateur optimization.

We begin by reaffirming that influencing the formateur’s identity is important for voters in coalition government systems. Voters confident that their preferred candidate will become the prime minister can feel safe enough to shift their focus to other coalition-directed strategies, such as partner optimization and policy balancing. Conversely, voters who believe their preferred candidate is likely to lose might not see formateur optimization as a worthwhile behavior, as it is neither a vote for their most preferred party nor a vote that they think is likely to change the formateur outcome. However, these voters may still be motivated to engage in formateur optimization, as demonstrated before (Harsgor et al. Reference Harsgor, Itzkovitch-Malka and Tuttnauer2023).

The reason voters may vote for their preferred formateur party rather than their most-preferred non-formateur party is what we call a ‘Puncher’s Chance’ perspective. Borrowed from sports, a ‘Puncher’s Chance’ is a boxing idiom that indicates an improbable yet possible outcome, specifically referring to a boxer who is outmatched yet still has the capacity to win if they can land one or two clean heavy punches (Jones Reference Jones2013). Thus, even with slim chances of influence, such voters may still see value in supporting their preferred candidate as a final effort or hope.

This kind of ‘Puncher’s Chance’ behavior is in line with voting in general. Voters frequently participate in electoral acts even though they know they have minimal chances of altering the outcome. As Blais and Young (Reference Blais and Young1999) and Blais (Reference Blais2000) noted, the act of voting itself has a negligible effect on election results. Yet, as Duffy and Tavits (Reference Duffy and Tavits2008) observe, voters often overestimate, even subconsciously (Blais and Rheault Reference Blais and Rheault2011), the likelihood that their vote will be pivotal, acting as if their individual contribution could sway the outcome. If a non-formateur party supporter votes strategically for a formateur-candidate party she expects to lose, i.e., not end up as the formateur; she risks losing both the benefit of voting for her most preferred party and the benefit from having her preferred formateur elected. However, assuming that voters hold great value in the identity of the next prime minister, who will greatly affect the country’s policymaking for the next 4–5 years, such a risk may be worth taking.Footnote ⁴

This leads us to hypothesize that the likelihood of formateur optimization among voters with low uncertainty about the formateur’s identity hinges on whether the voter believes their preferred candidate will win or lose. If the voter anticipates a win for their preferred candidate, formateur optimization will decline as voters have little to no incentive to strategically vote for the formateur’s party instead of their most preferred non-formateur party. This is because such voters can have the best of both worlds: they can vote sincerely for the party they feel closest to and have their preferred candidate as formateur. However, if the voters think their preferred candidate is about to lose, they may still be motivated to support this underdog in hope for the improbable, keeping formateur optimization akin to cases of high uncertainty. We thus hypothesize:

Figure 1 is an illustration of H3. The figure depicts the difference in the likelihood of engaging in formateur optimization between voters who expect their preferred formateur candidate to win and those who expect their preferred candidate to lose, across varying levels of uncertainty regarding the identity of the next formateur.

Figure 1. The effect of voter expectations and preferences on formateur optimization.

The graph demonstrates a nonlinear relationship centered around the point of complete uncertainty (50%), where voters are maximally unsure whether their preferred PM will win or lose. Importantly, in cases of complete uncertainty, preferences for one candidate over another become meaningless. That is, when uncertainty about the winner in the race for formateur is maximal, it is unlikely that voters can articulate specific expectations regarding the identity of the winner. Thus, under conditions of complete uncertainty, we do not distinguish between different expectations about the outcome and therefore leave this segment of the graph blank. However, at other levels of uncertainty, the two can coexist – individuals can hold expectations even when they lack full certainty or have low confidence in those expectations. This distinction aligns with psychological and political science research on probabilistic reasoning and belief formation. For example, Tversky and Kahneman (Reference Tversky and Kahneman1992) demonstrate that people often form expectations even under uncertainty, relying on heuristics and incomplete information. Similarly, research on electoral forecasting (e.g., Kayser and Leininger Reference Kayser and Leininger2016; Murr Reference Murr2011) suggests that voters develop expectations about election outcomes even in situations where uncertainty is significant.

Following this logic, as we move from complete uncertainty to high uncertainty, it is possible to differentiate between voters with different expectations regarding the winner. Nevertheless, when formateur uncertainty is high, different expectations regarding the perceived winner do not translate into differences in the likelihood of formateur optimization. This is because, under high levels of formateur uncertainty, both groups of voters are inclined to vote strategically to affect the identity of the next formateur regardless of their political preference for a specific formateur, and thus the likelihood of formateur optimization peaks for both groups.

As formateur uncertainty decreases and the race for formateur becomes less competitive – moving away from the center of the x-axis toward either end, right or left – voters are less motivated to engage in formateur optimization. However, the effect of formateur uncertainty on voters’ likelihood to engage in formateur optimization is contingent on the combination of voters’ expectations and preferences. This is why the slopes on either side of the 50% mark diverge. Voters who believe their preferred PM is likely to lose (left side) are less sensitive to changes in the level of uncertainty in the prime ministerial race and are likely to engage in formateur optimization even when formateur uncertainty is low. In contrast, voters who believe that their preferred PM will win (right side) are more sensitive to such changes, and thus for them the likelihood of formateur optimization declines sharply as certainty increases. Put differently, formateur uncertainty matters less for voters who expect their preferred candidate for formateur to lose compared to those who expect their preferred candidate to win.

Empirical strategy

Our empirical strategy is twofold. First, we conduct a cross-national analysis using the broadest available survey data in order to establish the relationship between formateur uncertainty, preferences, and strategic voting. This analysis allows us to take advantage of the variation in real-world political competition – specifically, how tight the race was in each election cycle – and use it as an independent variable instead of having it remain constant, as with case studies. In a second step, we analyze six pre-election surveys in a single country, Germany, to delve deeper into the perceptions of individual voters, leveraging specific questions about the electoral race and its outcomes that were not available in the comparative setting.

Before we dive into the specifics of our research design, we wish to address a few key challenges involving the study of formateur optimization. The first and most complex challenge is that of empirically distinguishing between different forms of strategic voting. Unfortunately, existing datasets do not include direct questions about voters’ motivations to vote. However, even if such questions were available, it would still be challenging to disentangle overlapping motivations, as voters often pursue multiple goals simultaneously. For example, a voter might aim to influence the formateur while also considering ideological representation or coalition policy outcomes. This makes it very hard to use empirical measures to isolate distinct types of coalition-oriented voting behavior.

Instead, we argue that the question of distinguishing between different forms of coalition-directed voting – such as voting to influence the formateur versus voting to achieve policy balancing – is primarily a conceptual and analytical question. As a result, we rely on the analytical definitions discussed above. We classify voters who are non-formateur party supporters but cast their vote for a formateur party as engaging in formateur optimization. We believe this decision is justifiable, since, as we explain above, the possible overlap between formateur optimization and policy balancing is minor and may exist only in cases of low formateur uncertainty and in a very specific political conjecture.

Another key challenge in studying formateur optimization is the measurement of uncertainty. The CSES surveys do not provide information on voters’ assessment of uncertainty in the formateur race. Thus, we rely on post-election outcomes to infer the level of uncertainty about the formateur’s identity before the elections. This allows us to measure uncertainty using an objective measure that does not include voters’ subjective evaluations; however, such a measure exists only at the system level. Contrarily, the German survey, on which we will further elaborate, provides some individual-level information on uncertainty. Specifically, the survey asks respondents whether they think it is clear who will win the election approximately one week before the vote. While this does not directly measure uncertainty about the formateur, it provides an indirect indication of voters’ perceptions regarding the likely outcome of the election, which we use in our analysis. We further discuss the advantages and disadvantages of the measurement approaches in the concluding part of the paper.

Main analysis: Cross-national design

The German case

To investigate the mechanism underlying our findings in the cross-national analysis, we compiled a dataset of German pre-election survey responses. This dataset complements the cross-national one and differs from it in several ways. First, it includes questions that more directly get at the respondents’ perceptions and expectations regarding the race between the two largest parties and for the eventual prime minister. As such, it allows us to directly test for H3. Second, the surveys were conducted before each election (rather than after the elections as with the CSES data), making the measurement of respondents’ affect toward the parties independent from the eventual electoral results. Third, the surveys allow for individual-level variation regarding formateur uncertainty, as they include voters’ subjective expectations regarding electoral outcomes.

Results

As we did in the comparative analysis, we focus on non-formateur party supporters, that is, those who gave the highest thermometer score to parties other than the CDU, CSU, and SPD. In a bivariate analysis, we find that those who are uncertain of the results are more likely to make a formateur vote (14%) than those who are certain about the winner (10%), with the difference being statistically significant (p =.03). We then turn to the regression analysis. Table 2 presents five models, all including our controls and year fixed effects. In Model 1, we use the formateur uncertainty measure as the main independent variable. In contrast with the bivariate test, it does not come out statistically significant. The next four models all include the formateur expectation measure that combines voters’ expectations regarding formateur uncertainty with their preference for formateur.

Table 2. Determinants of formateur optimization in Germany 1998-2021

Standard errors in parentheses.

⁺ P < 0.1, *P < 0.05, **P < 0.01, ***P < 0.001.

When we use this measure in Model 2, we find a negative effect for those who are certain that their preferred formateur candidate will win. As we expected, compared to those who are uncertain of the results of the election, those who are certain their preferred formateur will win are less likely to make a formateur vote. In contrast, the difference between the uncertain and those who expect their formateur candidate to lose is insignificant and substantively small. This means that voters who expect their preferred formateur will lose are indistinguishable from those who see the race as close in their likelihood to perform formateur optimization. These findings, which support H3, are graphically presented in Figure 4.

Figure 4. The effects of formateur uncertainty and preferences on formateur optimization.

Note: Predicted probabilities based on Model 2 in Table 2. Vertical capped lines represent 90% confidence intervals.

To reinforce H3, we include in Model 3 only voters who are certain of the formateur race outcomes. The coefficient for ‘preferred wins’ denotes here the effect of expecting the preferred formateur to win, compared to expecting the rival to win. The effect is negative and substantial: holding all other variables to their observed values, the difference between expecting to win and expecting to lose is associated with a 7.5 percentage points decrease in the likelihood of formateur optimization, down from 14.8% to 7.3%.

In Model 4, we explore how the different levels of macro-level uncertainty, captured by the gap between the two largest parties as represented in the pre-election polls, condition the effect of the individual’s expectations and perceptions. First, we find that an increase in the electoral gap – meaning lower formateur uncertainty – is associated with a decrease in the likelihood of formateur voting among those who are uncertain of the outcome, as the coefficient for the gap shows. This echoes our findings from the cross-national analysis (Model 2 in Table 1). Moreover, when we compare those who expect their preferred formateur candidate to win and those who expect their preferred candidate to lose, we find the effect is strong and significant for the former (p =.007) but not the latter (p =.126). This means that as formateur uncertainty decreases, those who expect their preferred formateur candidate to lose are more prone to engage in formateur optimization compared to those who expect their preferred formateur to win. These findings, again, echo the findings of the cross-national analysis (Models 4 and 5 in Table 1).

Finally, in Model 5, we return to H2 and introduce the interaction between the formateur expectations and the drop in thermometer scores between the respondent’s ‘sincere choice’ and their preferred formateur. Figure 5 shows the effect of expecting the rival formateur to win (left) or the preferred formateur to win (right) and provides further, albeit more nuanced, support for H2. We find that the negative effect on the likelihood of formateur optimization is significant only for those who expect their preferred formateur to win, and only when the thermometer drop to the formateur party is small (applicable to 81% of respondents who expected to win). For those who expect the rival formateur to win, the interaction is insignificant across the whole range of the thermometer drop variable.

Figure 5. The marginal effect of formateur uncertainty conditional on thermometer drop, by voters’ preferences and expectations.

Note: Marginal effects of formateur expectation based on Model 5 in Table 2. Gray bars depict the percentage of cases for each value on the x-axis. Vertical capped lines represent 90% confidence intervals.