Pre-Electoral Coalitions and the Distribution of Political Power

Pre-electoral coalitions (PECs) can be an effective strategy for parties to increase their chances of winning elections, but they may also distort electoral results and policies away from citizens’ preferences. To shed light on how PECs shape post-electoral power distribution, we study the causes and consequences of PECs in Finland where elections use an open-list proportional representation system, and parties may form joint lists. We document that PECs are more common between parties of equal size and similar ideology, and when elections are more disproportional or involve more parties. Using difference-in-differences and density discontinuity designs, we illustrate that voters punish coalescing parties and target personal votes strategically within the coalitions, and that PECs are formed with the particular purpose of influencing the distribution of power. They increase small parties’ chances of acquiring leadership positions, lead to more dispersed seat distributions, and sometimes prevent absolute majorities. PECs can thus enable a broader representation of citizens’ policy preferences.


Introduction
Political parties are often viewed as coalitions of like-minded individuals that seek to implement policies that might not otherwise garner enough support. As such, parties assume the responsibility of safeguarding the platforms they articulate during election campaigns and establishing mechanisms to regulate the decisions of elected officials McCubbins 1993, 2005;Levy 2004). However, instead of running on their own, parties across the world are increasingly joining forces before elections (Golder 2005(Golder , 2006bPowell 2000). Pre-electoral coalitions (PECs) between political parties can be an effective strategy for parties to increase their chances of winning elections, but they also have the potential to dilute party ideology and policy platforms. Thus, they may pose a challenge to the conventional role of political parties as intermediaries between citizens and the state.  (Benoit 2000). PECs can be formed without any commitment to a joint policy manifesto after the election. Moreover, the coalition partners' party labels remain visible in the ballot. These small barriers to entry to forming coalitions make such agreements frequent and yields rich large-N data for our study.
We begin our empirical analysis by studying how different contextual factors correlate with the presence of PECs at the municipal election level. This analysis confirms that hypotheses formulated by Sona Golder in her seminal work (Golder 2005(Golder , 2006a also apply to the Finnish case. More specifically, PECs are more likely when more parties are present and when the electoral system at the local level is very disproportional. These correlations suggest that PECs are formed both to signal the likely voting coalitions after the election and to exploit the electoral returns to scale. To better understand the motivations behind PEC formation, we study the various effects of PECs which is our main contribution. An advantage of considering the Finnish open list municipal elections is that we observe the vote count for each candidate, and thus, for each party separately even when the party is part of a PEC. We leverage party-level data on both coalition formation and electoral outcomes to examine the effect of coalition formation on electoral support and distribution of political power. Our difference-in-differences analysis suggest that parties that join PECs face puzzling consequences. Coalescing negatively affects vote and seat shares, on average. This contradicts the motivation behind larger candidate lists to save electoral costs (Montero 2016; Osborne and Tourky 2008)-we later discuss the possibility of reverse causality.
Voter punishment of coalitions is targeted particularly to coalitions with large ideological heterogeneity. We also find that PECs encourage intra-list strategic voting as voters from smaller coalition partners pool their votes into fewer candidates, hence increasing their electoral chances in the within-list competition against candidates from larger coalition partners. Strategic voting seems to benefit smaller parties within the coalition, which might explain why asymmetric coalitions occur less frequently. We also find that some parties are willing to form PECs and give away important leadership positions to their smaller partners.
Given these negative repercussions of electoral alliances, what could be driving parties' decisions to form such coalitions? Our work highlights a novel bargaining power hypothesis by which coalitions are strategically formed to influence the overall distribution of seats; more specifically, to influence the probability that any party obtains an absolute majority of seats and gains full political control of the municipality. In order to identify the role of PECs on the likely government composition, we use a density discontinuity design. The results suggest that PECs are an efficient tool for preventing absolute majorities when the largest party is close to obtaining more than half of the seats. 1 This same rationale to coalesce is at the core of the study by Frey, Gabriel, and Montero (2020). They document that in Mexican mayoral elections, parties are willing to compromise ideology and form an electoral alliance to remove an entrenched incumbent party from office.
The case of the Alavieska municipality in Northern Finland in the 2012 election illustrates our point. Four ideologically diverse parties (the National Coalition Party, the Left Alliance, the Christian Democrats, and the Finns Party), as depicted in Figure 1 below, formed an electoral 1 Even in the UK with a first-past-the-post system, there have been recent calls for a united front to defeat the Tories: "to defeat a common enemy, parties should set aside differences and cooperate." See an editorial "The Guardian view on a progressive alliance: divided they fall" in The Guardian (December 13, 2020), available online at https://www.theguardian.com/comm entisfree/2020/dec/13/the-guardian-view-on-a-progressive-alliance-dividedthey-fall (accessed January 20, 2021). alliance to prevent the Center Party from obtaining an absolute majority of the seats. The municipality had been dominated by the Center Party for years, and the spokesman for the Left Alliance, Timo Takkunen, stated that they "wanted to make sure that the policies reflect the opinions of all inhabitants and not only the those of the Center Party supporters." 2 In the end, the coalition did not obtain its objective, possibly due to the lack of ideological cohesion.
Another interesting example occurred in the municipality of Karvia. In the 2012 election, two ideologically close parties, the Social Democratic Party and the Left Alliance, formed a PEC that ensured the Center Party did not get a majority of the seats. The last elected candidate was from the Social Democratic Party, and the first non-elected candidate was from the Center Party. Had the PEC not formed, the Center Party would have obtained one more seat and reached an absolute majority of the local council seats.
In the next section, we introduce the institutional context of our study. We then lay out our central theoretical considerations and empirically testable hypotheses. After describing our data, we present our empirical findings on the correlates of PEC formation and the effects of electoral alliances on coalescing parties. Prior to our final concluding section, we discuss the robustness of our findings in considering dyadic data with all possible two-party combinations.

Left
Right Ideology L e f t A l l i a n c e ( -1 . 8 1 ) G r e e n P a r t y ( -1 . 1 8    After the election, the newly elected council appoints a municipal executive board where parties are represented according to their seat shares in the council. The council elects by majority rule the chairman of the municipal board, which is considered to be the most important local political office, and the chairman of the council, which is considered to be the second-most important position. 6 The council can also set up committees to deal with different functions of the local government. No official ruling coalition government is formed after the election, though sometimes parties may form informal coalitions. Councils vote on an issue by issue case, and post-electoral voting coalitions may change from one vote to another.

Theoretical Considerations
We study the strategic formation of PECs and how PECs affect voting behavior and other electoral outcomes. We group our arguments into causes and consequences of PECs and discuss how these can be used to understand the boundaries of political parties.

When Are Pre-Electoral Coalitions Formed?
Taking cues from the work by Golder (2005Golder ( , 2006a,b) on pre-electoral coalitions, we are first interested in how the local election level circumstances might shape parties' incentives to form joint lists. This initial set of hypotheses, and the corresponding empirical analyses, can be seen as a sanity check for our study vis-à-vis the previous work on PEC formation.
alphabetically within party lists. Parties are allowed to move away from alphabetical order but this rarely happens. The mechanical benefit of forming a coalition relies on the fact that bigger parties benefit from the apportioning of votes to seats. The key driver of this effect is the degree of disproportionality in each district which depends on the particular distribution of vote shares in the municipality, the electoral rule, and the council size. Parties in municipalities with particularly disproportional representation should have the largest incentive to form a PEC (see Blais andIndridason 2007 andParigi andBearman 2008).
Whether two parties decide to join forces also depends on the characteristics of each party and not just the electoral context. A factor that might encourage two parties to form an alliance is a shared ideology (Allern and Aylott 2009;Debus 2009;Golder 2006b;. For example, Golder (2006b) argues that coalitions amongst ideologically close parties should be more acceptable to voters of these parties and should result in smaller expected policy costs for the parties. 8 7 See also Gschwend and Hooghe (2008) and Eichorst (2014) for examples of studies arguing that PECs provide cues to the voters with regards to the future government composition. Moreover, Gschwend, Meffert, and Stoetzer (2017) use a survey experiment to show that providing voters with coalition signals increases the importance of coalition considerations and decreases the importance of party considerations in voters' decision-making. 8 For empirical evidence backing up this argument, see for instance Gschwend and Hooghe The similarity between coalition partners might not only concern their ideology but also their expected vote share. Asymmetry within coalitions should negatively affect the likelihood of forming an alliance as there might be more difficulties in agreeing a joint platform when bargaining between unequal partners. Bigger parties might feel smaller parties' ideology is over-represented in the coalition and smaller parties might feel their wishes are silenced by the bigger partner in the coalition.
In all, we should expect more PECs in a municipality when there are more parties, the degree of disproportionality is largest, when there are similar parties (in terms of ideology and expected vote share).

Consequences of Pre-Electoral Coalitions
Our second group of arguments is related to the consequences of PECs. We focus on three key outcomes: votes, seats, and control of the municipality (via leadership positions and by obtaining an absolute majority of councillors). If PECs reduce campaigning and candidate selection costs (Montero 2016;Osborne and Tourky 2008), we should observe such coalitions having more resources to attract votes. However, the opposite might hold true as voters might dislike their party identity diluted within a coalition. Seeing the specific candidates citizens are voting for (recall that Finland has an open-list PR electoral system) allows us to identify which parties gain or lose from forming a coalition. This characteristic also makes it possible to investigate whether voters are sophisticated (Downs 1957;Duverger 1954): voters of small coalition partners could pool their votes to fewer candidates who can then compete with the candidates from larger coalition partners on the list.
Votes are simply the means to seats and leadership positions. What is the effect of PECs on seats? Whilst joining a PEC could harm parties' vote shares, it is possible that the mathematics of apportionment improves the party's seat allocation. The D'Hondt seat allocation rule implemented in Finland favors larger lists (Benoit 2000). When looking at leadership positions, we should expect coalition parties to get a share of portfolios proportional to the seats they contribute to the coalition (Gamson 1961). This means that small parties within a PEC could sometimes get important nominations that would usually be reserved for larger parties. 9 Finally, our novel key proposition is that PECs can be used as a way to influence whether a list obtains an absolute majority of seats. Obtaining an absolute majority in Finnish municipalities is critical as councils make decisions based on simple majority. Moreover, an absolute majority typically allows the winner to appoint both the board chairman (equivalent to the mayor of the municipality) and the council chairman (equivalent to the speaker of the local council). Avoiding this concentration of power might be driving many parties to coalesce. PECs might prevent a rival party obtain an absolute majority or might help coalescing parties reach such threshold. 9 In Finnish municipalities there are no stable ruling government coalitions, indicating that small parties cannot access leadership positions via the post-electoral bargaining in exchange for agreeing to participate in a coalition government. However, Carroll and Cox (2007)

Data and Variables
The main body of our data consists of election results for all Finnish local elections held between 1996 and 2012, obtained from the Ministry of Justice. We report the detailed summary statistics on our data in Appendix Table A1. We restrict our analysis of PEC formation and their effects to registered political parties and rule out all independent (local) groups, because they are not allowed to form PECs. 10 We examine the votes and seats of all registered parties and obtain 11, 063 observations at the local party-election year level. Around 16% of observations are part of an electoral coalition.
We complement the election results with information from two data sources. First, we use data on the party of local political leaders (council and board chairmen) for the years 2000-2012 from the Finnish Association of Local Authorities (Kuntaliitto 2013).
Second, we measure party ideology with the voting aid application from the public broadcasting company YLE. Voting aid applications are interactive online surveys that election candidates can fill before the election. Voters can then answer the survey and find the candidate who best matches their policy preferences (about 40% of Finnish voters use these surveys, so politicians are well incentivized to accurately represent their platform). Our voting aid application data come from the 2012 municipal election. These data contain a number of questions related to 10 This means dropping 6.4% of the local party-election year level observations. However, these observations are correctly accounted for in measurement when needs be, for example, when defining absolute majorities or number of parties. Independent groups comprise merely around 3.4% of all candidates.
the local public sector and answers to these questions from roughly half of the candidates. 11 Using these data, we compute a measure of parties' economic ideology, which is arguably the most important area of policy-making in Finnish local politics. 12 For some of our analyses, the unit of observation is at the municipality-election year level. We have 1, 914 such observations. In 692 of these cases, there is at least one PEC in the municipality.
The municipality-level data serve us to test both the causes and consequences of PECs. When looking at the conditions under which PECs are more likely to form, our signaling hypothesis is easily tested with the number of parties in the municipality. We use the (lagged) modified Gallagher index to capture disproportionality when we assess the disproportionality hypothesis (see Koppel and Diskin 2009). 13 This measure captures the difference between the percentage 11 The respondents are slightly more likely to be female and younger than non-respondents.
Respondents total vote shares and winning probabilities are also somewhat higher. This selection may lead to small amount of error in measuring party level ideology, but these errors do not systematically concern any single party and are unlikely to impact our analysis. 12 We use principal component analysis to compress these data into a single measure of economic ideology. For further details, we refer to Appendix B. 13 The modified Gallagher index is formally defined as where s p is the vote share of party p in municipality m at time t, and v p is its vote share. Note that our analysis is not robust to considering the effective electoral threshold as a measure of disproportionality following Golder (2006b); see Appendix Table C3.
of votes and the percentage of seats that each party receives. The larger the number, the more disproportional the representation in a particular municipality.
The level of political polarization at the local level might also influence the likelihood of coalitions. We measure ideological dispersion in municipalities at a point in time as follows:

Causes of Pre-Electoral Coalition Formation
We start by evaluating how the characteristics of the political environment within the municipality shape coalition formation. This part of our empirical investigation is descriptive and complements and supports Golder's work on PEC formation (Golder 2005(Golder , 2006b). Because we are using municipality-level variables, our analysis deviates from that of Golder (2005Golder ( , 2006b) who uses dyadic data to test for these hypotheses. 14 We use municipality-election year level data and OLS to estimate the connection between the presence of PECs and different variables characterizing 14 Given that the theoretical predictions concern the political context in the municipality instead of the characteristics of potential coalition partners, aggregated data is better-suited than dyadic data to this study. the electoral conditions. We multiply the dependent variable by 100 so that the estimation results can be interpreted as percentages. 15 Results are summarized in Table 1 below. Notes: The dependent variable is an indicator for at least two parties forming a PEC, multiplied by 100. Standard errors clustered at the municipality level are reported in brackets. The estimation sample only includes municipalities that have at least three political parties. *, ** and *** denote statistical significance at 10%, 5% and 1%, respectively.
Consider first the signaling argument that suggests that an increase in the number of parties should be associated with an increased likelihood of having electoral coalitions. The coefficient of Number of parties is systematically positive and statistically significant, suggesting that having one more party is associated with a 7 to 9% increase in the probability that a municipality has a PEC. 15 We use OLS, as it is straightforward to interpret the estimation results as marginal effects. In Appendix Tables C1 and C2, we use probit and logit models, respectively, on a dummy outcome variable and obtain similar results.
We also find support for a higher likelihood to form an alliance when the electoral system is more disproportional. Note that PECs affect the values that our disproportionality index gets. To avoid any biases that could arise from this, we use the lagged disproportionality metric. 16 With large ideological differences, the incentives to obtain higher seat representation increase thus we should expect a higher likelihood of PECs. However, we do not find a significant positive correlation between the level of polarization and the propensity to coalesce. Contrary to Golder (2005), we do not observe that a disproportional electoral system should increasingly affect the likelihood of PECs when there are many parties in the municipality (column 2) nor when the municipality is very polarized (column 4).

Pre-Electoral Coalitions and Electoral Outcomes
We now zoom into political parties and ask what are the actual effects of joining a PEC at the party level, and whether coalitions benefit or hurt political parties' electoral performance. To do so, we estimate a standard generalized differences-in-differences specification at the local party level: Here PEC mpt is a dummy for party label p belonging to a PEC in election t in municipality m, α mp is a local party label fixed effect (that is, municipality times party fixed effect), α t is an election 16 In the appendix, we present and discuss results from a specification with municipality and year fixed effects which hold all time-invariant municipality-level characteristics and time-specific common shocks constant (Appendix Table C4).
year fixed effect and ε mpt is the error term. The estimate of our central interest isβ . It tells us the effect of forming a PEC on the outcome y mpt .
In this setting, the treatment group consists of those parties that switch from not having a PEC to having one, or from having PEC to not having one. The control group are those parties that maintain the status quo. The standard identifying assumption in a difference-in-differences strategy is that the outcomes in the coalescing parties would have evolved in the same way as before, had they not formed a PEC. And identically in this generalized setting, the outcomes of parties that had a PEC before, but dissolved it, would had evolved in the same way had they maintained the PEC. If this common trends assumption does not hold (e.g., because there are unobservable, time-varying factors driving the PEC formation that also affect our outcomes of interest), the estimates ought to be treated just as conditional correlations. We substantiate the existence of parallel trends in our robustness checks. A crucial time-variant factor that may shape both the outcome and propensity to join a coalition is party size: parties become less likely to coalesce the larger they are, but larger parties also tend to fare better in elections and the subsequent bargaining process. Thus, all our regressions control for party size, which we measure as the seat share the party obtained in the previous local election, Seat share mp,t−1 .
In order to analyze heterogeneous effects of electoral coalitions, we interact PEC mpt with ideological differences within the coalition and the party p's seat share in the previous election in some of our specifications. The former variable is simply computed as the distance between party p's ideological position and the position of the party within the coalition that is most ideologically distant.
We report the party-level difference-in-differences results in Table 2. Perhaps surprisingly, we find that voters seem to punish parties for forming coalitions (column 1). This is at odds with the Both results on votes and seats suggest that some parties might have a poor judgement when forming coalitions, as they do not seem to anticipate the negative consequences of such coalitions, in particular the ideologically asymmetric ones. Alternatively, parties might be strategically coalescing to influence the overall distribution of power in the municipality rather than seeking individual gains. We investigate this possibility in the next section.
In column (5) we see that joining a PEC-that is, in the Finnish case, forming a joint list with another party-leads to a less dispersed within-party personal vote distribution (using the Herfindahl index of the within-party personal vote shares as the dependent variable). The interaction between joining a PEC and party size has a negative effect on vote concentration, indicating that smaller parties within coalitions are the ones whose voters concentrate votes more. 18 This might also explain why PECs with asymmetric party size are not commonly observed.
Finally, we analyze the impact of forming a PEC in the assignment of leadership roles at the municipal level. Column (6) in Table 2 shows that coalescing large parties are less likely to obtain the top position in local government: the board chairmanship. This might be a sign of the 18 The result is robust to controlling for partners' candidate shares to address endogenous candidate entry (Appendix Table C7).
concessions big parties need to commit to forge coalitions with smaller parties. Finally, column (7) shows instead that coalescing large parties are more likely to obtain the council chairmanship.
In the Online Appendix, we show that these conclusions are robust to (i) restricting the sample to parties that are part of an electoral coalition at some point of time, (ii) controlling for party-specific linear time trends, (iii) inclusion of additional control variables, and (iv) estimation approach of de Chaisemartin and D'Haultfoeuille (2020) which takes into account the staggered nature of our treatment and units moving between the treatment and control groups.

Pre-Electoral Coalitions and Distribution of Power
We do not seem to find evidence that being part of a PEC brings major electoral benefits to any party. However, there might be effects that are not observed at the individual party level. We conclude our empirical analysis by asking what are the effects of PECs at the municipal level.
By doing so, we tackle our argument that PECs could affect the distribution of power and, most importantly, affect the likelihood of absolute majorities in the council.
We again estimate a difference-in-differences specification, yet now aggregating our data to the municipality-election term level. The regression central to our interest takes the following form: PEC mt is now defined as a dummy that is equal to one if there is a PEC in municipality m in election t. δ m and δ t are municipality and time fixed effects, respectively, and µ mt is the error term.
Our estimation sample covers all municipalities that are observed at least twice.
Do PECs alter the number of parties that obtain representation in the municipality? Do they affect the concentration of the seat distribution in the municipality as captured by the Herfindhal Index? Do they influence the seat share of the biggest party in the municipality? Or do they change whether a party obtains an absolute majority of seats? All of these questions help us understand the overall distribution of power in the municipality and whether PECs have an effect on it.  Notes: Coalition is an indicator variable that gets the value 1 if there is at least one PEC in a municipality, an 0 otherwise. Seat concentration refers to a Herfindahl index of the seat shares of the parties that are represented in the local council. All regressions include year and municipality fixed effects. Standard errors clustered at the municipality level are reported in brackets. *, ** and *** denote statistical significance at 1%, 5% and 10%, respectively.
We present additional robustness checks in the Online Appendix. Our estimates are robust to controlling municipality-specific time trends, supporting the parallel trends assumption. Moreover, the estimation results remain largely unchanged when we follow the estimation procedure proposed by de Chaisemartin and D'Haultfoeuille (2020).

Detailed Analysis of Close Elections
While the reduction in the maximum seat share is quite small, it could be critical for the largest party to obtain an absolute majority in close elections. We address this possibility using a density discontinuity test. We follow an approach typically used in regression discontinuity design settings to test for potential manipulation of the running variable. To operationalize this test, we adapt the testing strategy proposed by Ma (2018, 2020) by implementing a robust bias-corrected density test. This means that we find a local polynomial fit for the density curve on both sides of the threshold and then calculate the jump in density at the cutoff point.
The density test results can be found in Table 4 which reports the density test statistics, associated p-values, as well as a test for a difference in estimated discontinuities. A negative test statistic implies a jump downwards at the cutoff. 19 We conduct the test using different degrees of 19 Formally, the test statistic is given by polynomials, and we also vary the window around the cutoff point. 20 We find that there is a downward jump in the density of maximum seat share at the 50% cutoff when there are PECs.
Most of the density test results in the case of no alliances suggest no statistically significant jump at the threshold. Moreover, the density discontinuity test statistic is usually positive, unlike in the PEC sample. We also report the differences in discontinuities and test whether they are statistically significant. While the differences always have an expected (negative) sign, they are significant only for two of the specifications.
We then construct a placebo distribution of the largest party seat shares. We do so by taking municipalities that had PECs but distribute the seats according to the D'Hondt rule as if there were no alliances. The placebo distribution shows no hints of discontinuities close to the absolute majority threshold, as we verify more formally in Appendix C. This suggests that these PECs were able to prevent absolute majorities. As a further validity check, we explore covariate smoothness at the 50% seat share cutoff. We report and discuss these results in detail in Appendix C (see Appendix Table C12).
We visualize the key conclusion from the density discontinuity test in Figure 3. The graph shows a non-parametric density fit under three scenarios: when there are no PECs (Panel A), when at least one PEC has been formed (Panel B), and a placebo test (Panel C). There is no jump at the cutoff when there are no PECs or when we look at the placebo distribution, but the density has a downward jump at the 50% seat share cutoff in municipalities that do have PECs.
3.660 (70) 2.603 (37) (135)  Notes: The density test is conducted using rddensity package in Stata. T p (h) denotes the manipulation test statistic using pth order density estimators with bandwidth choice h = (h − , h + ). We employ uniform weighting (rectangular kernels) and vary the degree of local polynomials used. Moreover, we use two alternative ways to compute the optimal bandwidthsĥ p . In Panel A, we use different bandwidths on different sides of the cutoff (bandwidth selection procedure comb), and the same bandwidth on both sides of the cutoff in Panel B (bandwidth selection procedure sum). N − (N + ) is the effective number of observations on the left-hand (right-hand) side of the cutoff.

Discussion and Concluding Remarks
We study the logic of PEC formation and their effects. We begin by analyzing the process descriptively, but more importantly, we then provide some of the first causal evidence of the direct benefits and costs of forming PECs for political parties.
The two parts of our analysis are like two matching pieces of a puzzle. First, the descriptive analyses reveal that PECs are more likely to occur (possibly to signal the intention for future cooperation) when there are more parties in an election. Analyzing the causal effects of PECs at the level of local governments shows that they, indeed, shape the distribution of political power and influence which parties govern. Second, we find evidence suggesting that parties are more likely to coalesce in more disproportional electoral environments. Looking at the vote and seat share effects of PECs helps us understand why. Third, the expected coalition size and size asymmetry matter as well. The party-level results offer a rationale for why parties avoid asymmetric coalitions: they  Taken together, our results indicate that coalition formation is not driven by purely vote-seeking motivations. Policy motivations appear to be more prevalent than the motivation to gain office, at least in part, because ideological proximity is an important determinant of PECs. Furthermore, PECs do not have a large impact on seat shares. Most importantly, we find that PECs affect the 21 As an additional "reality check," we construct a dyadic data set comprised of all party pairs and examine which ones become actual coalition partners in Appendix D. Echoing the results that we show in the main text, we find that (i) coalitions are formed to maximize the probability of obtaining an absolute majorities of seats, (ii) parties avoid asymmetric coalitions, and (iii) ideologically distant parties are less likely to coalesce. overall distribution of power by preventing absolute majorities from forming, thus ensuring that decision-making power is not concentrated.
Whether PECs should be allowed or not has been debated throughout the world. For instance, countries such as Estonia and Holland ban formal pre-electoral agreements. One argument against electoral coalitions has been that they may distort the electoral result and policies away from citizens' preferences. However, our findings imply that PECs give parties an opportunity to guarantee a broader substantive representation of citizens' policy preferences, by preventing absolute majorities. That said, PECs may play a different role in different electoral systems. This calls for more comparative research.

A Descriptive Statistics
Our data set, obtained from the Ministry of Justice, covers all local elections held between years 1996 and 2012. We report the summary statistics on our data in Table A1. Panel A focuses on the party-level data. Around 16% of the parties are part of an electoral coalition. We see that the parties that are part of an electoral alliance are smaller both before and after the election than parties that do not belong to an pre-electoral coalition. Furthermore, they have more concentrated within-party vote shares, as measured by the Herfindahl index.
Using the party-level data, we construct a data set of all possible two-party dyads to study what parties are more likely to coalesce with each other. These data are summarized in Panel B. Out of around 30,000 potential coalition pairs, only about 4% become actual coalitions. Coalitions are more likely to actualize when parties are ideologically closer to each other. Furthermore, coalitions that are expected to be larger are less likely to form. Asymmetry of the party size does not appear to play a major role.
We also use data that are collapsed to the municipality level. We report the descriptive statistics for our municipality-level data in Panel C. These data are composed of 1, 914 municipality-year observations. In 692 cases, some kind of electoral alliance has been formed.
The modified Gallagher index is formally defined as where s p is the vote share of party p in municipality m at time t, and v p is its vote share.
Importantly, it satisfies some relevant axiomatic properties (e.g., Dalton's principles of transfers, OA3 scale invariance, orthogonality). We use the lagged value in our analyses, as PECs could influence the current-term disproportionality.

B Measuring Party Ideology
We measure party ideology using so-called voting aid application data from the Finnish public broadcasting company Yle. Voting aid applications are interactive questionnaires, the purpose of which is to assist voters in finding a candidate with similar policy preferences to theirs.
Candidates fill out the survey before elections, after which voters can take the same survey to find a suitable candidate. The voting aid applications include a number of claims mostly related to the size of the public sector and redistribution, such as: "Privatizing public services makes them more efficient and saves money" and "We have paid too little attention to marginalization of children and teenagers". A stronger agreement with the first claim is associated with a more right-leaning ideology, whereas the stronger agreement with the latter two claims is related to a more liberal ideology. Overall, the data contain seventeen claims. The candidates would give their answers on a 1-5 scale (from "completely disagree" to "completely agree" where the middle option was "I do not agree or disagree").
We employ a principal component analysis to compress the survey responses into a single measure of economic policy preferences. This is a commonly used approach to extract a one-dimensional measure of ideology from survey data (Ansolabehere, Snyder, and Stewart 2001;Heckman and Snyder 1997). See also Matakos et al. (2019) for further information and as an example of another study using these data. The first principal component captures the left-right dimension of economic ideology and explains about 15% of the variation in the data. We focus on this dimension of ideology, as it is more central for decision-making in local governments.
OA6 Table B1 reports results of the principal component analysis alongside with the questions included in our data. Claims where a stronger agreement implies more right-wing attitudes get larger positive values, whereas the opposite is true for claims where a stronger agreement is in line with more left-wing preferences. We multiply the resulting principal component by minus one in order to have a smaller score for left-wing parties. That is to say, the resulting ideology measure is the smaller the more liberal is a candidate. Table B2 reports summary statistics by party.

C Robustness and Validity Checks
This appendix contains a number of auxiliary robustness and validity checks.

C.1 Further Tests of the Disproportionality and Signaling Hypotheses
We use a linear probability model to empirically assess the disproportionality and signaling hypotheses. However, our results are robust to using non-linear probit and logit models that taken into account the binary nature of the dependent variable (see Tables C1 and C2).
In the main text, we measure disproportionality of the local electoral environment with the modified Gallagher index. Table C3 presents regression results where we measure disproportionality with the effective threshold instead. Columns (1) and (3) do not suggest that there is a relationship between PEC formation and electoral system disproportionality. If anything, there is an inverse relationship between disproportionality and PEC formation when there are very few parties (column 2). As the number of parties increases, this negative relationship gets diluted. Other than that, the regression results echo those that we report in the main text.
We present results from a specification with municipality and year fixed effects which allow us to hold all time-invariant municipality-level characteristics and time-specific common shocks constant in Table C4. Given that many features of the local political context are rather persistent, including municipality fixed effects leaves us with considerably less identifying variation. Indeed, while we still find a strong relationship between the presence of PECs and the number of political parties, the result we have for disproportionality vanishes.

C.2 Additional Difference-in-Differences Results
This subsection presents additional difference-in-differences results. We start by visualising the interaction effects in Figures C1 and C2.
We have also re-estimated our party-level specification only using a sample of parties that belong to a PEC at least once during the time period included in our data. This allows us to address the caveat that parties that join a PEC at least once may be very different from those that never join a PEC. These regression results are presented in Table C5. The results remain mostly unchanged.
Joining a PEC leads to a lower vote share (column 1), and the effect is driven by parties that join more ideologically dispersed PECs (column 2). This negative effect carries on to seat shares (columns 3 and 4). Becoming a part of a PEC also leads to a more concentrated vote distribution (5). Finally, there is no statistically significant evidence that joining a PEC would matter for postelectoral bargaining outcomes (columns 6 and 7). Qualitatively, the point estimates suggest that parties that are part of a PEC become more likely to acquire the board chairmanship and less likely to get to nominate the council chairperson.
We then rerun our regressions including group-specific linear time trends. Note that the estimation sample differs slightly from that used in our main text, as we can now only include parties that are observed at least three times. Table C6 shows that the party-level results remain unchanged. Coalition formation appears to influence vote shares negatively, and this effect is larger when the coalition is ideologically dispersed. However, the regression coefficients are not statistically significant (columns 1 and 2). We do not see any effects on seat shares (columns 3 and 4). Even when controlling for the trends, we find that coalition may induce strategic voting that is more prevalent among smaller parties (column 5). Finally, we show suggestive evidence OA11 that smaller parties become more likely to acquire the board chairmanship after joining a PEC in column 6, while the opposite is true in the case of council chairmanship (column 7).
Moreover, we introduce additional control variables that aim at capturing the level of party popularity-namely, the number of candidates per council seats-and its change between two subsequent elections. Introducing these controls in our estimations does not change our conclusions; see Table C7.
Note that we have estimated conventional TWFE models. Recent work on difference-in-differences has suggested that under some conditions such estimation approach can yield biased results. This can happen in particular with a varying treatment timing and if the treatment goes on and off (for some units). The newly proposed methods to deal with these issues are not suited to estimate interaction effects, especially because these the interactions involve continuous and time-varying variables, but we are able to assess the robustness of those specifications that do not include interactions. Table C8 shows that our estimates of the effect on vote share are still negative and statistically significant, albeit slightly smaller in absolute terms, when we follow the approach of de Chaisemartin and D'Haultfoeuille (2020). 1 However, there is virtually no effect on seat share. These findings are nevertheless qualitatively in line with our main arguments here.
We then turn into assessing the robustness of the municipality-level difference-in-differences analyses. In Table C9, we can see that the positive effect on the number of parties persists after controlling for the municipality-specific linear time trends (column 1). Seat shares also become less concentrated, and this effect is statistically significant (column 2). We lose the statistical 1 We conduct these analyses using the did_multiplegt package on Stata.
OA12 significance of our point estimates in column 3 where we show the effect on the largest party's seat share, but the magnitude of the point estimate remains very stable. Finally, we do not see any clear effect on there being an absolute majority (column 4).
We also rerun our estimations following de Chaisemartin and D'Haultfoeuille (2020). Similar to the party-level analyses, we have municipalities that enter and exit the treatment group and the timing of this varies. Table C10 shows that our estimation results remain largely unchanged when we use the estimation procedure proposed by de Chaisemartin and D'Haultfoeuille (2020).

C.3 Placebo Density Test
We provide more detailed results for the placebo density test in Table C11. As in the main text, we conduct the test following . We construct the placebo seat shares using the data from municipalities that had PECs. We use the D'Hondt rule and redistribute the seats as if there were no PECs. There appear to be no jumps at the cutoff, as there should not be.
This gives further support for our claim that coalitions among smaller parties may indeed prevent the largest party from obtaining an absolute majority when the election is very close.

C.4 Covariate Smoothness
In this section, we present RD estimates on different covariates to explore if there is something special about the 50% maximum seat share threshold. We estimate the following specification: y m,t−1 = α + β 1[Seat share margin mt > 0] + f (Seat share margin mt ) + ε mt .
(1) Notes: The dependent variable is an indicator for at least two parties forming a PEC. Standard errors clustered at the municipality level are reported in brackets. The estimation sample only includes municipalities that have at least three political parties. *, ** and *** denote statistical significance at 10%, 5% and 1%, respectively. Notes: Vertical lines mark the average number of candidates per seat. Dashed lines are 95% confidence intervals. We also show the distribution of the moderator (lagged party seat share) Figure C1. Interaction effects of pre-electoral coalition and party size.

OA14
Here, Seat share margin mt is the distance between largest party's seat share and in municipality m at time t. The treatment of interest is an indicator variable for the largest party having an absolute majority. We run local linear regressions within MSE-optimal bandwidths, and allow for different slopes on different sides of the threshold. Besides the conventional estimation, we follow the robust bias-corrected approach proposed by Calonico, Cattaneo, and Titiunik (2014). Effectively, this means that we fit a second-order polynomial within the optimal bandwidth for the local linear specification. We run the covariate smoothness test for seven different pre-treatment covariates, y m,t−1 . Table C12 shows the RDD estimates. In Panel A, we use data from municipal elections that do not have any PECs. There is no robust evidence that any of the covariates would systematically have jumps at the 50% seat share cutoff. Panel B shows regression results using data from municipalities that had at least one PEC. The point estimates are again convincing that there are no discontinuities in predetermined covariates. As we are interested in the difference in discontinuities, what is perhaps even more important in our setting is that there appear to be no massive differences between the estimates for municipalities with and without PECs. Finally, Panel C shows the RDD estimates using a placebo running variable: largest party's seat share that has been computed assuming that there are no PECs. The results from this placebo analysis are again good news for us. We do not detect any robust evidence of discontinuities at the threshold. This analysis comes with the caveat that the largest party seat share does not satisfy the requirements of a proper regression discontinuity design; the running variable ought to be continuous. For instance, Meriläinen (2019) discusses this issue further.

D Lessons from Dyadic Data
This appendix discusses the lessons we can draw when we use dyadic data. We also describe these data and our variables in detail before proceeding to the analysis. For each pair of parties we define Coalition size as the sum of parties' lagged seat shares. If a party did not run in t − 1, its size is coded as zero. Variable Asymmetry captures the asymmetry amongst coalition partners, i.e. the absolute value of the difference in party sizes divided by the 2 Parties that form coalitions with more than two parties are accounted for multiple times in our data. Analysing specifically larger coalitions would explode the number of potential coalitions and lead to unstable very rare events analysis. The drawback is that we do not learn whether larger coalitions are formed with different logic than two-partner coalitions.

D.1 Dyadic Data and Variables
OA16 sum of party sizes. We code this variable as zero if both parties had zero seats in the previous election. The resulting metric varies between zero and one, a higher value reflecting a more asymmetric coalition.
The dummy variable Majority is equal to one if both parties would expect to obtain an absolute majority based on their past seat shares. This allows us to test the hypothesis that asymmetric coalitions may form if they are likely to obtain an absolute majority and a full control over policy-making . In order to capture the relevance of the critical 50% threshold, we also define a variable capturing how far the coalition is from such a threshold: Distance from majority is defined as |50% − Coalition size|. This measure captures whether coalitions are close to achieving an absolute majority. Interacting it with Majority results in a piecewise linear fit that allows us to evaluate whether the propensity to coalesce peaks when the coalition is likely to reach an absolute majority of seats (while it does not need to overshoot that threshold). Finally, we measure the ideological (in)compatibility of two potential coalition partners by the difference in their ideologies. 3 We call this variable Ideological range.
3 Comparing realized and non-realized coalitions reveals that coalitions are more common among ideologically close parties (see Table A1 for summary statistics). However, it seems that their expected size is smaller than the size of potential two-party coalitions that did not form. There appear to be no differences in terms of asymmetry. We will return to these comparisons below in a more sophisticated regression framework.

D.2 Estimation Results
We start by asking whether expecting to reach a majority of seats (or being close to it) is associated with the probability of two parties forming an alliance. Table C13 presents findings from a number of regression models that we estimate using OLS. 4 Column (1) first regresses an indicator variable for two parties forming a PEC-multiplied by 100 to allow interpretating the estimates as percentages-on the Distance from majority variable, an indicator for the coalition reaching an absolute majority of seats and an interaction of these two terms. The coefficient for reaching a majority of the seats (based on the previous election's seat shares) is positive but not statistically significant. The positive and significant coefficient for Distance from majority and the negative and significant coefficient for it's interaction with Majority shows that the propensity to coalesce peaks when the dyad can just about form a majority. This is natural as when the distance is large, it is likely that one party could reach an absolute majority of seats on its own-and thus would not need to coalesce with anyone. This specification demonstrates coalitions not wanting to maximize seat share but instead maximize the probability of obtaining an absolute majority of seats.
In column (2) we examine the role of the size of the expected coalition, size asymmetry, and their interaction. Given the negative coefficient of Coalition size, we can conclude that PECs are less likely to form between large parties. Similarly, as we predicted, similarly sized parties are more likely to coalesce. The interaction term tells us that only when the coalition size is large enough can we expect asymmetric coalitions (i.e. a large party coalescing with a small one). In column (3), we replace coalition size with the dummy variable indicating whether the two parties 4 We obtain similar results if we use probit and logit models (see Tables C14 and C15). OA18 together can reach an absolute majority of the seats. Once again, size asymmetry is negatively correlated with the probability of two parties forming a PEC, two parties of a similar size are also less likely to coalesce if they expect to get a majority of the seats together, but this negative association is diluted by size asymmetry. In other words, two parties that expect to get an absolute majority of the council seats become more likely to join forces the more different their electoral support is.
Last, we investigate the role of ideology in PEC formation. We find strong support for the prediction that ideologically proximate parties are more likely to coalesce in column (4) where we regress an indicator for two parties belonging to the same PEC on their ideological distance.

D.3 Robustness Checks
Our main analysis of the dyadic data uses a linear probability model to estimate marginal effects.
In Tables C14 and C15, we show that the qualitative conclusions remain unchanged even if we use non-linear probit and logit models.
Furthermore, the analysis in the main text does not include any additional covariates in the analyses that we conduct using the dyadic data. However, the conclusions from this investigation remain unchanged if we control for municipality and election year fixed effects. We show this in Table C16.
Column (1) first regresses an indicator variable for two parties forming a PEC on the difference between the dyad's expected seat share distance from majority, an indicator for the expected seat share being enough to give the parties more than half of the seats, and an interaction of these two terms. We see that when two parties do not expect to get a majority of the seats, a coalition is OA19 more likely to realize between them the smaller was the sum of their seat shares in the previous election. The coefficient of Ma jority is positive (although not statistically significant), indicating that a coalition between two parties is more likely if their expected joint seat share is more than 50%. However, the interaction term had a negative regression coefficient-i.e. two parties are less likely to form a PEC the larger they are, if they expect to get a majority.
In column (2), we examine the role of expected coalitions size, size asymmetry, and their interaction. Given the negative coefficient of Coalition size, we can conclude that PECs are less likely to form between large parties of a similar size. Similarly, size asymmetry decreases the propensity of two parties coalescing. In column (3), we replace coalition size with an indicator variable for the two parties together acquiring an absolute majority. As before, size asymmetry is negatively correlated with the probability of two parties forming a PEC. Two parties of a similar size are also less likely to coalesce if they expect to get a majority of the seats together, but this negative association is diluted by size asymmetry. That is to say, two parties that expect to get more than half of the council seats become more likely to join their forces the larger is their size difference.
We investigate the role of ideology in PEC formation in column (4). We find strong support for the prediction that ideologically proximate parties are more likely to coalesce. The larger the ideological incompatibility between two parties, the less likely it becomes that they form a PEC. Notes: The dependent variable is an indicator for at least two parties forming a PEC. Standard errors clustered at the municipality level are reported in brackets. The estimation sample only includes municipalities that have at least three political parties. *, ** and *** denote statistical significance at 10%, 5% and 1%, respectively. Notes: The dependent variable is an indicator for at least two parties forming a PEC, multiplied by 100. Standard errors clustered at the municipality level are reported in brackets. The estimation sample only includes municipalities that have at least three political parties. *, ** and *** denote statistical significance at 10%, 5% and 1%, respectively. Notes: The dependent variable is an indicator for at least two parties forming a PEC, multiplied by 100. Standard errors clustered at the municipality level are reported in brackets. The estimation sample only includes municipalities that have at least three political parties. *, ** and *** denote statistical significance at 10%, 5% and 1%, respectively. Notes: Vertical lines mark the average number of candidates per seat. Dashed lines are 95% confidence intervals. We also show the distribution of the moderator (ideological distance) Figure C2. Interaction effects of pre-electoral coalition and ideological distance.  (6) is Herfindahl index of withinparty vote share concentration. Regressions control for the number of candidates relative to the council size, and year and party group fixed effects. Standard errors clustered at the party group level are reported in brackets. *, ** and *** denote statistical significance at 1%, 5% and 10%, respectively. Notes: Vote and seat shares are measured in percentages. Chairmanship is an indicator variable that gets the value one if the party holds either board or council chairmanship (or both). The dependent variable in column (6) is Herfindahl index of within-party vote share concentration. Regressions control for the number of candidates relative to the council size, and year and party group fixed effects. Standard errors clustered at the party group level are reported in brackets. *, ** and *** denote statistical significance at 1%, 5% and 10%, respectively. Notes: Vote and seat shares are measured in percentages. Standard errors clustered at the party group level are reported in brackets. *, ** and *** denote statistical significance at 1%, 5% and 10%, respectively. Notes: Coalition is an indicator variable that gets the value 1 if there is at least one electoral alliance in a municipality, an 0 otherwise. Herfindahl refers to a Herfindahl index of the seat shares of the parties that are represented in the local council. All regressions include year and municipality fixed effects. Standard errors clustered at the municipality level are reported in brackets. *, ** and *** denote statistical significance at 1%, 5% and 10%, respectively.

Notes:
Coalition is an indicator variable that gets the value 1 if there is at least one electoral alliance in a municipality, an 0 otherwise. Herfindahl refers to a Herfindahl index of the seat shares of the parties that are represented in the local council. All regressions include year and municipality fixed effects. Standard errors clustered at the municipality level are reported in brackets. *, ** and *** denote statistical significance at 1%, 5% and 10%, respectively.  Notes: The density test is conducted using rddensity package in Stata. T p (h) denotes the manipulation test statistic using pth order density estimators with bandwidth choice h = (h − , h + ). We employ uniform weighting (rectangular kernels) and vary the degree of local polynomials used. Moreover, we use two alternative ways to compute the optimal bandwidthsĥ p . In Panel A, we use different bandwidths on different sides of the cutoff (bandwidth selection procedure comb), and the same bandwidth on both sides of the cutoff in Panel B (bandwidth selection procedure sum). N − (N + ) is the effective number of observations on the left-hand (right-hand) side of the cutoff.

Notes:
The dependent variable is an indicator for two parties belonging to a PEC, multiplied by 100. Standard errors clustered at the election level are reported in brackets. *, ** and *** denote statistical significance at 10%, 5% and 1%, respectively. Table C14. Dyad-level determinants of PEC formation (probit model). (1) (2) (3) Notes: The dependent variable is an indicator for two parties belonging to a PEC. All specifications control for municipality and election year fixed effects. Standard errors clustered at the election level are reported in brackets. *, ** and *** denote statistical significance at 10%, 5% and 1%, respectively. Notes: The dependent variable is an indicator for two parties belonging to a PEC. All specifications control for municipality and election year fixed effects. Standard errors clustered at the election level are reported in brackets. *, ** and *** denote statistical significance at 10%, 5% and 1%, respectively. Notes: The dependent variable is an indicator for two parties belonging to a PEC, multiplied by 100. All specifications control for municipality and election year fixed effects. Standard errors clustered at the election level are reported in brackets. *, ** and *** denote statistical significance at 10%, 5% and 1%, respectively.