Electoral Institutions and Intraparty Cohesion

I.  Introduction

Parties and their elites control candidate selection and play an important role in shaping the ideological composition of legislatures and policy outcomes. In many cases, such as in Europe and most parliamentary systems, parties hold nearly complete authority to decide the composition of their candidate lists. However, our understanding of the determinants of candidate selection is still quite limited (see, e.g., the conclusion in Dal Bò and Finan 2018 and the references therein). This paper focuses on electoral rule disproportionality as a determinant of candidate selection, empirically examining its relationship with parties’ incentives to nominate a more or less cohesive list of candidates.

We refer to electoral rule disproportionality as the expected distortions generated by the electoral rule in favor of the election winner (Taagepera 1986). In proportional rules, a party’s seat share in the elected body (e.g., council or parliament) is in expectation (almost) identical to its vote share. Conversely, disproportional electoral rules generate distortions in the mapping of vote shares to seat shares that in expectation favor the election winner. These distortions can be attributed to various specific institutional characteristics, among which is the size of the elected body (Lijphart 1995; Herron, Pekkanen, and Shugart 2018). Indeed, in (very) large bodies, a party’s seat share in the elected body is, in expectation, (almost) identical to its vote share. That is, the electoral rule is proportional. Conversely, in small bodies, distortions are expected to give advantage to the election winner, making the electoral rule more disproportional. How does the magnitude of such expected advantage for the election winner affect parties’ choices when nominating their lists?

We inform our empirical approach by relying on a well-grounded conceptual framework in which parties present a list of candidates “tethered by a rubber band to the ideology espoused by the parties whose label they run on” (Grofman 2008). On the one hand, parties have incentives to obtain high vote shares so that they can influence the implemented policy in their preferred direction. Parties can attain this by adopting a more pluralistic approach, akin to a catch-all party. This involves including a diverse set of candidates in their lists, thus attracting a broader spectrum of voters with diverse ideological leanings (Kirchheimer 1966). On the other hand, electing candidates that adhere to a variety of ideologies can be harmful for the party since they may promote policies far from the party’s ideology. Under this trade-off, what is the optimal degree of a party’s ideological cohesion? Given that disproportional electoral rules are expected to favor the election winner, they strengthen parties’ incentives to become electorally appealing and hence propose a rather heterogeneous list of candidates. In contrast, relatively proportional electoral rules offer weaker incentives for an increased vote share, leading to the formation of ideologically cohesive lists.

Our empirical analysis focuses on Finnish municipal elections. This setup offers the opportunity to establish a meaningful identification strategy and utilize a novel dataset that records individual candidates’ policy positions. Causal evidence is obtained by focusing on quasi-experimental empirical evidence due to municipalities’ council size being determined solely as a step function of their population. That is, we use changes in the council size as a proxy for changes in the rule’s disproportionality, allowing for a regression discontinuity design (RDD). Data on parties’ ideological cohesion is obtained by leveraging a unique dataset recording the individual candidates’ policy positions in 2008 and 2012. These data come from the voting aid application of the Finnish public broadcasting company, YLE, and are further linked to electoral data and other candidate-level information. The questions in the voting aid applications allow us to construct two cohesion indexes, one using all available questions and one focusing on candidates’ redistribution preferences.

We start our empirical analysis by showing that council size serves as a reliable proxy for changes in the rule’s disproportionality (sec. III.D). That is, our first set of results validates our proxy by showing that, within our dataset, realized distortions in favor of parties securing high vote shares are more pronounced in small councils than in large councils. Consequently, this implies that the distortions imposed by the rule in our setting decrease with council size. The magnitude of the effect of crossing the threshold is a decrease of approximately 21%–26% relative to the mean value of the outcome, or 40%–67% of the outcome standard deviation, depending on the measure of distortions. While this result aligns with theoretical predictions and is not the primary focus of our study, this paper, to the best of our knowledge, is the first to offer causal evidence regarding the impact of council size on realized distortions. Indeed, within the existing literature, this relationship has been regarded as a folk theorem, with supporting arguments primarily being theoretical or based solely on correlations (Benoit 2000; Herron, Pekkanen, and Shugart 2018).

Our main results in section III.E show that, in the elections for smaller councils, competing lists tend to be less ideologically cohesive than in the elections for larger councils. The magnitude of the effect of crossing the threshold translates into a decrease in our two cohesion indexes by 7% relative to the mean value of these outcomes, or 20%–30% of the outcome standard deviation.

As our RDD identifies only the total effect on cohesion, we use our rich data to perform covariate balance tests and do not observe evidence of other jumps. For instance, our empirical setting permits us to focus on the effect of council size on intraparty cohesion without worrying about potential confounding effects through a change in the number of parties or candidates (Rae 1967; Taagepera and Shugart 1989; Cox 1990). Furthermore, no other policy changes take place at the thresholds that determine the council size. We also show that our results are not consistent with an alternative mechanism in which candidates optimally reposition in response to changes in the council size. Admittedly, we cannot be perfectly sure there is no other channel through which the council size could influence cohesion. Nevertheless, the electoral rule disproportionality is a plausible channel since our empirical results are in line with our conceptual framework and our balance tests do not reveal other evident determinants of cohesion. We also show that there is no sorting across the thresholds, which is natural as the municipal population is not self-reported. Last but not least, the results are robust to further batteries of robustness and validity checks. Here of particular interest is our novel use of placebo cutoff tests to assess the appropriate level of clustering in the optimal bandwidth selection.

The paper is structured as follows: In the “contribution” section just below, we present related literature and highlight our contribution. In section II we propose a conceptual framework to guide our empirical analysis. In section III we present our estimation strategy and the evidence. In section IV, we conclude. All supporting material, further discussion of our data and empirical results (e.g., robustness), and a formal analysis of our conceptual framework appear in the appendix.

Contribution.—Our estimates on the effect of electoral institutions on parties’ ideological cohesion constitute a novel finding. In a broader context, evidence regarding the causal effects of electoral institutions on any outcome remains relatively scarce (Shugart 2013). Typically, researchers have had to rely on cross-country or panel variation leaving room for potential confounding. In contrast, we leverage plausibly as-good-as-random variation within a country by utilizing the change in council size as a proxy for electoral rule disproportionality and join scholars exploiting subnational variation to identify causal effects of various dimensions of electoral institutions (see, e.g., Eggers 2015; Sanz 2017).

As Shugart (2013) and Buisseret and Prato (2017) argue, we still have a limited overall understanding of the mechanisms linking electoral institutions and the behavior of political actors. We contribute to this literature by proposing a potential mechanism through which electoral institutions could influence parties’ candidate selection on ideology. Our theoretical framework builds on recent literature, modeling proportional representation (PR) as a system of power sharing, as compared to majoritarian winner-take-all elections (Herrera, Morelli, and Palfrey 2014; Herrera, Morelli, and Nunnari 2016; Matakos, Troumpounis, and Xefteris 2016; Herrera, Llorente-Saguer, and McMurray 2019), and extends knowledge on parties’ cohesion across electoral institutions (Carey 2007; Buisseret and Prato 2022).

Closest to our setup, Matakos, Troumpounis, and Xefteris (2016) propose an electoral competition model in which two parties optimally choose their platforms on a unidimensional policy space (i.e., each party selects a unique point on the unit interval) under different levels of electoral rule disproportionality. Their main result suggests that polarization (i.e., the distance between parties’ platforms) decreases as electoral disproportionality increases, since parties have incentives to increase their vote share by converging toward the median. In our setup instead, parties propose an interval of policies (i.e., a list) that takes into account parties’ preferences over the overall composition of the elected body. In this setting, we introduce a personal vote dimension and characterize the optimal length of parties’ lists as the electoral rule disproportionality varies.¹ While Matakos, Troumpounis, and Xefteris (2016) provide cross-country evidence on the correlation between the electoral rule disproportionality and between-party polarization, we focus on a within-country setting and obtain causal evidence on the effects of council size as a proxy of the electoral rule disproportionality on intraparty cohesion.

Overall, our work contributes toward a better understanding of politicians’ characteristics in representative democracies.² While the elected officials’ characteristics and policy positions are known to matter for policy outcomes in several environments (see, e.g., Chattopadhyay and Duflo 2004; Lee, Moretti, and Butler 2004; Jones and Olken 2005; Washington 2008; Besley, Montalvo, and Reynal-Querol 2011)—including the context of our empirical exercise and via an intraparty channel (Hyytinen et al. 2018a)—different institutions seem to elect politicians with dissimilar traits (Best and Cotta 2000; Meriläinen 2022). Variation in electoral institutions has been offered as one potential explanation for differences in political selection (Carey and Shugart 1995; Galasso and Nannicini 2011; Gagliarducci and Nannicini 2013; Beath et al. 2016; Galasso and Nannicini 2017), with the present paper being, to the best of our knowledge, the first to provide causal evidence on electoral institutions affecting political selection on ideology. This result, hence, complements a long literature highlighting electoral institutions as a key determinant of the economy and the political system in representative democracies.³

II.  A Conceptual Framework

Electoral rules define the allocation of a number of seats available in an elected body (e.g., a council or parliament) to parties competing in an election. That is, electoral rules define a mapping from vote shares to seat shares. Generating a fully proportional mapping in which seat shares and vote shares coincide is practically impossible due to distortions emerging when dividing a discrete number of seats. However, specific features of the electoral rule generate diverse distortions. A large literature focuses on such specific characteristics of electoral rules (Herron, Pekkanen, and Shugart 2018).⁴ Among those, one is the size of the elected body, the focus of our empirical application. Imagine that only one candidate is elected. One vote more than the opponent is enough and the distortion in the mapping from votes to seats is maximized. Instead, when many candidates are elected the seat share allocation is expected to generate less distortion.

In our theoretical framework, we abstract from the exact source creating distortions in the vote to seat share mapping. We follow conventional terminology by referring to the electoral rule disproportionality as the expected distortions generated by the rule in favor of the election winner and discuss a channel through which electoral rule disproportionality could affect parties’ intraparty cohesion. Our argument is based on standard assumptions of the electoral competition literature, and while presented informally here, it is derived in full mathematical detail in appendix A1. In the appendix, we also detail modifications that would not affect the intuition behind the result presented (app. A1.1). However, let us clarify that our main result essentially depends on the following key premises: On the voters’ side, our model requires that a personal vote dimension be present.⁵ In our benchmark model, voters vote for the party that includes in its list the candidate closest to their ideal point. In the appendix, we show that our results are robust when permitting voters to also care about the average ideology of a given list or introduce some voters that choose the list that offers them higher expected utility. On the parties’ side instead, our model requires that, ceteris paribus, parties prefer to nominate candidates who share the parties’ ideology, and parties have full power in nominating their party lists.⁶

The electoral rule and disproportionality.—To fix ideas and provide meaningful comparative statics, our conceptual framework below presents the simplest case of a linear electoral rule (Taagepera 1986). This rule serves as a continuous approximation of the D’Hondt rule present in our empirical setting (Flis, Słomczyński, and Stolicki 2020), and links with our empirical measures of realized distortions. In the appendix, we present further details on the D’Hondt rule and obtain theoretical results for the latter as well as a larger family of electoral rules than the linear rule.

To formalize the electoral rule and its degree of disproportionality, consider a two-party election in which party j obtains vote share $v_j\ge 0$ and party −j obtains vote share $v_{-j}=1-v_j\ge 0$. The electoral rule in our model is mapping each party’s vote share v_j into a seat share $s_j(v_j)\ge 0$ with $s_j+s_{-j}=1$. The linear rule is formally defined as follows:

$$s_j(v_j)=\{\begin{array}{cl}0& \text{if }{v}_j\le \frac{n-1}{2n},\\ \frac{1-n}{2}+n{v}_j& \text{if }\frac{n-1}{2n}<v_j\le \frac{1+n}{2n},\\ 1& \text{if }{v}_j>\frac{1+n}{2n},\end{array}$$

with $n\ge 1$ (see fig. 1).

We define the electoral rule disproportionality as the expected distortions generated by the rule in favor of the election winner, formally defined as follows:

$$D={\int }_{0.5}^1(s(v_j)-v_j)d{v}_j\text{.}$$

For the linear rule in which $s(v_j)\ge v_j$, we have that $D=0.125-(0.125/n)$. This makes evident that the electoral rule disproportionality is increasing in parameter n. This is illustrated in figure 1. When $n=1$, parties’ seat shares accurately represent parties’ vote shares and the disproportionality is equal to zero. The extreme case of maximal disproportionality occurs in a winner-take-all election in which $n\to \infty$.

The election, parties, and voters.—Consider an election in a unidimensional policy space in which two parties ($j=L$, R) strategically choose the ideological heterogeneity of a continuum of candidates (list) competing in the election under the party’s label. That is, candidates’ ideologies are just numbers on the real line, and a list of candidates is given by a closed interval containing the party’s ideal policy. For example, in figure 2, the two parties propose lists [0.2, 0.4] and [0.8, 0.9], respectively.⁷

Voters’ preferred policies are uniformly distributed on the same policy space. Voters are voting for the party that included the candidate closest to their preferred policy in its list. In the example of figure 2, all voters to the left of the indifferent voter (located at 0.6) vote for party L, and all voters to the right of the indifferent voter vote for party R, implying vote shares $v_L=0.6$ and $v_R=0.4$.

The elected body.—Parties’ lists and seat shares s_L and s_R determine the distribution of ideologies in the elected body. The represented ideologies coincide with those of the nominated candidates, and each ideology has an equal weight within each party.⁸ Take for example party L in figure 2A. Given that $n=1$ this party is obtaining seat share $s_L=0.6$, and each of the ideologies in [0.2, 0.4] is represented in the elected body with an equal weight (i.e., $0.6/\left(0.4-0.2\right)$). In contrast, in figure 2B, since $n=3$, party L is obtaining $s_L=0.8$, and each of the proposed ideologies [0.2, 0.4] is represented in the elected body with a higher weight than before (i.e., $0.8/\left(0.4-0.2\right)$).

Parties’ payoffs.—We assume that parties are policy motivated and their payoffs depend on the overall distribution of ideologies in the elected body. Specifically, we consider that parties evaluate each ideology t represented in the body using a quadratic disutility function, with their overall aim being to minimize the average disutility from the represented ideologies. Formally, the payoff of party $j\in \{L,R\}$, given the elected body, is

$$U_j([{\underset{\_}{x}}_L,{\overline{x}}_L],[{\underset{\_}{x}}_R,{\overline{x}}_R])={\int }_0^1-{(x_j-t)}^{2}f(t)dt,$$

where f(t) is the density of the represented ideologies as previously discussed and illustrated in figure 2, and x_j denotes the party’s ideal policy.

Predictions.—Parties propose a list of candidates running for a seat in the elected body (e.g., council or parliament) aiming at maximizing their payoff. So what determines parties’ incentives to propose a more or less cohesive list of candidates?

A party has incentives to expand its list toward moderate grounds since the indifferent voter moves in its favor and the party attracts more votes. Any expansion toward moderate grounds in search of a higher vote share should be counterbalanced by the inclusion of more extreme candidates too, so that parties make sure that the elected candidates are not too moderate compared to the party’s ideal policy. Hence, parties benefit when increasing the ideological heterogeneity of their candidates by increasing their vote share and hence their seat share. However, proposing a heterogeneous list of candidates comes at a cost: the ideologies represented in the elected body may be too different from those parties advocate and, thus, negatively affect parties’ payoffs, despite parties’ optimally balancing their lists.

The above trade-off and the incentives to propose a more or less cohesive list of candidates depend on the electoral rule disproportionality. Recall that, as the rule becomes more disproportional, the expected advantage for the election winner is increasing. That is, disproportional rules reward high vote shares more generously in terms of seat allocation than proportional rules. Therefore, parties’ incentives to become less ideologically cohesive are increasing in the electoral rule disproportionality since the expected benefits of doing so overweight the associated cost. The following comparative static result provides our main theoretical prediction formally presented in the appendix.

Figure 3 illustrates prediction 1 plotting the ideology of the two most extreme candidates in each list, highlighting how parties’ lists become less ideologically cohesive as the electoral rule disproportionality increases. Prediction 1 provides the main testable prediction of our theoretical model. In our empirical setting, we are using council size as a proxy of the electoral rule disproportionality and the above prediction implies that parties’ lists of candidates are predicted to be more ideologically cohesive as the council size increases.⁹

III.  Empirical Evidence

We first describe the institutional details (sec. III.A), data of the empirical setup (sec. III.B), and then detail our identification strategy (sec. III.C). The same identification strategy is then used twice. First, we validate the use of council size as a proxy of the electoral rule disproportionality (sec. III.D). Second, we present our main results on the effect of the council size on parties’ ideological cohesion (sec. III.E). Finally, we discuss alternative mechanisms that could potentially explain the effect of council size on cohesion instead of the electoral rule disproportionality (secs. III.F and III.G) and provide further discussion on our methodology and robustness results (sec. III.H).

D.  Council Size and Disproportionality

Note that the degree of disproportionality of an electoral rule—indicating the rule’s tendency to favor parties obtaining high vote shares—is conceptually distinct from the precise advantage it confers on those parties in a specific election.¹⁹ However, given a large enough sample of electoral results, a more disproportional rule should be associated with a greater average advantage in favor of parties obtaining high vote shares. Indeed, in this section, we illustrate that the realized distortions favoring such parties in the mapping between vote shares and seat shares are, on average, more pronounced in smaller councils (see, also, Lijphart 1995; Herron, Pekkanen, and Shugart 2018). That is, we validate that council size is a good proxy of the electoral rule disproportionality.²⁰

1.  Empirical Measures of Distortions

We use two established empirical measures of realized distortions in a certain election: (i) the slope index, directly linking to the linear rule presented in our conceptual framework, and (ii) a version of the Gallagher index. Both indexes capture the distortions in the mapping of parties’ vote shares to parties’ seat shares and take larger values the higher the distortion.²¹ In total, we have 505 observations at the municipality-year level for which we compute the two indexes as our main dependent variables.

The slope index first proposed by Cox and Shugart (1991) is constructed as follows: For each municipality-year observation, we regress the difference $s_j-v_j$ on v_j. Then, we define the slope of the line obtained from this regression as the slope index. The advantage of the slope index is that it captures the size of the distortions alongside whether they favor large or small parties. The slope index is also linked to the way we have modeled the electoral rule disproportionality in our conceptual framework using the linear rule.

Figure 4 illustrates how the slope of the regression line captures not only the size of the realized distortions but also the direction. On the left, we depict one municipality-year observation for which the distortions are small and the slope of the regression is relatively flat (0.011). In a pure PR rule, the slope would be zero. On the right, we depict another observation for which the slope is positive and relatively large (0.27), pointing to distortions favoring parties obtaining high vote shares. That is, the slope of the line used as our slope index indicates whether distortions favor parties obtaining high vote shares (positive slope), parties obtaining low vote shares (negative slope), or the absence of distortions (flat line).

We employ the modified Gallagher index as a second index to guarantee robustness of our results to alternative measures of realized distortions given that the early debate on the “best” way to capture the latter is still open (e.g., Lijphart 1995). The modified Gallagher index in municipality i in year t is defined as

$$\text{M}{\text{G}}_{it}={\left\{\frac{1}{2}\sum _{j=1}^p{[\frac{s_j}{{\left({\sum }_{j=1}^p{s}_j^2\right)}^{0.5}}-\frac{v_j}{{\left({\sum }_{j=1}^p{v}_j^2\right)}^{0.5}}]}^2\right\}}^{0.5},$$

where $j=1$, … , p denotes the p different parties running in municipality i in year t. The difference in the summation term represents the distortions when a party j that obtains vote share v_j is allocated a seat share s_j. The value of the index is increasing in the level of distortions. In a pure PR system with no distortions, the index takes value zero since this difference is zero for all parties. Notice that, while the modified Gallagher index (as most indexes proposed in the literature) does well in representing the level of distortions in the vote-to-seat-share mapping, it remains silent on the direction of these distortions.²²

2.  Distortion Results

We begin this RDD analysis with a graphical visualization of the jumps at the pooled cutoff. In figure 5, we report the results for both indexes of realized distortions. The results are very similar for both indexes and both of them jump down at the cutoff.²³

In table 1, we report the nonparametric RDD results on the effect of the council size on realized distortions. As for the main results, we report the conventional local linear MSE-optimal coefficients. For statistical inference, and because of its superior coverage properties, we report confidence intervals based on the bias-corrected coefficient and the associated robust inference by Calonico, Cattaneo, and Titiunik (2014). We also report both the nonclustered results and those clustered at the municipality level. In line with the properties of the D’Hondt rule (see app. A1.1), the negative coefficients imply that distortions are smaller as the council size increases. All the coefficients have an expected negative sign. They are statistically significant at the 5% level for the modified Gallagher index and (barely) insignificant for the slope index. The magnitude of the effect of crossing the threshold translates into a decrease in the slope index (modified Gallagher index) by roughly 21% (26%) relative to the mean value of the outcome, or 40% (67%) of the outcome standard deviation.

	(1)	(2)
	A. Slope Index
Conventional local linear RD coefficient	−.023	−.023
95% confidence interval with bias correction and robust inference	[−.063, .007]	[−.062, .007]
Observations within main bandwidth	267	268
MSE-optimal bandwidths (main/bias)	807/1,385	811/1,409
Clustered bandwidths and standard errors	No	Yes
Outcome mean (standard deviation)	.108 (.057)
	B. Modified Gallagher Index
Conventional local linear RD coefficient	−.012	−.012
95% confidence interval with bias correction and robust inference	[−.022, −.003]	[−.023, −.002]
Observations within main bandwidth	239	240
MSE-optimal bandwidths (main/bias)	714/1,097	724/1,090
Clustered bandwidths and standard errors	No	Yes
Outcome mean (standard deviation)	.047 (.018)

While it is a well-known fact in political science that council size (or district magnitude) serves as a proxy for electoral rule disproportionality (see, e.g., Carey and Shugart 1995; Carey and Hix 2011), and this association is well established at a theoretical and descriptive level, there has been, to our knowledge, a lack of causal evidence on this relationship. Thus, our paper makes an additional independent contribution through these results, even if they are not its primary focus.

E.  Main Results: Council Size and Intraparty Heterogeneity

We now analyze how the council size influences intraparty cohesion. Guided by our theoretical framework, we are expecting that lists become less heterogeneous as the council size becomes larger (prediction 1).

1.  Empirical Measures of Cohesion

Our main outcome variables are two indexes of candidate heterogeneity, based on candidates’ responses to questions present in the voting aid application. The all-questions index is constructed using all available responses. The redistribution index focuses only on a subset of the questions focusing on taxation and redistribution (see app. A4 for the subset). The benefit of the comprehensive index is that it avoids selecting on questions. However, its drawback is that perhaps some of the questions are less relevant for the voters and the interpretation of this index is more complex. Therefore, we also focus on the redistribution index that is policy relevant and matches a classic left-right dimension in political economy.

We measure ideological heterogeneity using Euclidean distances (scaled by the number of questions) for both indexes.²⁴ That is, we first compute for each candidate the distance between their response and their local party mean response for each question, and take a square of that. Then we sum these squared distances over all the questions included in the index and take a root of the sums of those squares. Finally, we divide this sum by the number of questions each year to reduce residual variance due to the fact that the number of questions differs by year.²⁵ Our scaling makes not only the mean but also the entire distribution more comparable across the years, which is useful in the RDD analysis for computing optimal bandwidth and avoiding the need to control for a year fixed effect. If the distance is zero for a candidate, their ideology coincides with the local party mean. The larger the distance is, the more this candidate deviates from the local mean. We present descriptive statistics of the indexes in table A10 and their histograms in figure 6.

For the analysis, we include only the parties with more than five candidates responding to the YLE voting aid application at the municipality-party-election level.²⁶ This leaves us with 14,999 candidate–election year, 1,184 party–election year, and 475 municipality–election year observations.²⁷

2.  Cohesion Results

We begin the main RDD analysis by graphical visualization of the jumps at the cutoff. In figure 7, we report the results for the two heterogeneity indexes using a pooled RDD and observations aggregated to municipality-year level. Both heterogeneity indexes jump down at the threshold.²⁸ That is, parties become more ideologically cohesive as the council size increases.

We present the nonparametric regression results in table 2. Overall, the evidence is in line with our conceptual framework: The estimate is always negative indicating that party cohesion increases (that is, our dependent variable decreases) as the council size increases.

	All Questions		Redistribution
	(1)	(2)	(3)	(4)
	A. Candidate-Year Level Analysis
Conventional local linear RD coefficient	−.012	−.009	−.023	−.021
95% confidence interval with bias correction and robust inference	[−.018, −.008]	[−.019, −.003]	[−.043, −.012]	[−.043, −.009]
Observations within main bandwidth	2014	4256	3589	4357
MSE-optimal bandwidths (main/bias)	408/820	693/1,143	588/1,019	679/1,118
Clustered bandwidths and standard errors	No	Yes	No	Yes
Outcome mean (standard deviation)	.136 (.029)		.292 (.101)
	B. Municipality-Party-Year Level Analysis
Conventional local linear RD coefficient	−.009	−.008	−.020	−.020
95% confidence interval with bias correction and robust inference	[−.017, −.004]	[−.018, −.001]	[−.044, −.004]	[−.042, −.006]
Observations within main bandwidth	348	417	382	363
MSE-optimal bandwidths (main/bias)	617/1,072	711/1,152	663/1,100	651/1,100
Clustered bandwidths and standard errors	No	Yes	No	Yes
Outcome mean (standard deviation)	.137 (.015)		.293 (.042)
	C. Municipality-Year Level Analysis
Conventional local linear RD coefficient	−.006	−.006	−.028	−.028
95% confidence interval with bias correction and robust inference	[−.016, .003]	[−.015, .002]	[−.060, −.007]	[−.058, −.009]
Observations within main bandwidth	243	242	161	160
MSE-optimal bandwidths (main/bias)	813/1,191	813/1,206	558/956	550/958
Clustered bandwidths and standard errors	No	Yes	No	Yes
Outcome mean (standard deviation)	.136 (.013)		.292 (.032)

Panel A of table 2 reports the analysis at the individual candidate level. Especially in this specification, clustering (optimal bandwidth selection and inference) at the municipality level is the most reliable approach as our treatment has no variation within the municipality-year level. To confirm that this does not give us excess power, we repeat the analysis at the municipality-party-year (panel B) and municipality-year (panel C) level in table 2. These aggregated outcomes are calculated as means over the individual candidate distances aggregated to the respective level. The results are robust to these modifications.²⁹

The effect of crossing the threshold in table 2 translates into a decrease in the heterogeneity indexes by roughly 7% (respectively, 7%) relative to the mean value of the outcome. This effect also translates into a decrease of 20% (respectively, 30%) of the outcome standard deviation for the redistribution index (respectively, the all-questions index).

Notes

We are grateful to James Adams, Manuel Bagues, Peter Buisseret, Alessandra Casella, John Duggan, Olle Folke, Alexander Fouirnaies, Anthony Fowler, Bernard Grofman, Tasos Kalandrakis, David Kang, Eva Mörk, Tuomas Pekkarinen, Carlo Prato, Johanna Rickne, Jim Snyder, Stephane Wolton, and the editor and anonymous reviewers for their constructive comments and suggestions. For valuable feedback we thank participants in the Conference on Research on Economic Theory and Econometrics and conferences of the American Political Science Association, European Economic Association, European Political Science Association, Midwest Political Science Association, Workshop on Political Economy and Political Science, and Società Italiana di Economia Pubblica, as well as seminar audiences at Bocconi, Chicago Harris, Columbia, Harvard, Helsinki Center of Economic Research, King’s College London, Lancaster, Leicester, London School of Economics, Padova, VATT, and Zurich. This research is funded by the European Union (Tukiainen, European Research Council, INTRAPOL, grant 101045239). Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them. This paper was edited by Anna Dreber Almenberg.

¹ Our results would not be qualitatively distinct from those of Matakos, Troumpounis, and Xefteris (2016) if we entirely removed the personal vote element. In the appendix we provide extensions of our main setting guaranteeing robustness of our results when voters also care about the lists’ mean ideology or compare the expected utility obtained by the two lists.

² The focus of our paper is on intraparty heterogeneity at the candidate level. Nevertheless, our main result transcends the stage of candidate selection (and list composition) and rises to the ideological composition of the elected council (see table A6).

³ The literature on electoral institutions is vast. For some representative examples among many others, we refer the reader to studies on the effect of electoral institutions on polarization (Cox 1990), turnout (Blais and Carty 1990; Herrera, Morelli, and Palfrey 2014), campaign spending (Iaryczower and Mattozzi 2013), and corruption, redistribution, public spending, and the provision of public goods (Lizzeri and Persico 2001; Milesi-Ferretti, Perotti, and Rostagno 2002; Persson, Tabellini, and Trebbi 2003; Persson, Roland, and Tabellini 2007). For more references see therein as well as Taagepera and Shugart (1989), Lijphart (1995, 1999), Persson and Tabellini (2002, 2005), and Grofman (2008).

⁴ Even in the class of proportional representation rules, the exact allocation method decisively affects the seat allocation. For instance, while the D’Hondt method present in our empirical setting “tends to increase the advantage for the electoral lists which gain most votes to the detriment of those with fewer votes” (Kotanidis 2019, 1), other methods generate less disproportional results (e.g., Hare-Niemeyer and Sainte-Laguë methods; see Schuster et al. 2003). Additionally, further explicit distortions in favor of the election winner, aimed at strong governments, can be introduced through the presence of a minimum vote threshold to obtain representation, a bonus to the winner of the election, or others (Herron, Pekkanen, and Shugart 2018).

⁵ A long-standing literature on personal vote has found that many voters condition their electoral choices on individual candidates’ characteristics, attributes, and promises (proposals) in a variety of countries and institutional contexts (for a summary see seminal contributions such as King 1991; Carey and Shugart 1995; Cain, Ferejohn, and Fiorina 2013). This, in turn, generates strong incentives for candidates to seek and cultivate their “personal” vote. Such incentives are further intensified in open-list multimember district PR systems, such as in Finland (see, e.g., Carey and Shugart 1995). Moreover, in Finnish municipal councils there is no ruling coalition and the role of parties as legislative teams is relatively weak, with several voters liberated to adopt a candidate-oriented perspective in deciding how to vote. For example, in the 2017 Finnish Municipal Election Survey a majority of the respondents stated that candidates were more important than parties in determining their vote (Borg 2018). Personal vote is also important in Finnish parliamentary elections with 42%–51% of the voters voting based on the candidate instead of party in surveys covering five parliamentary elections up to 2011 (see, e.g., Borg 2012, table 18.2).

⁶ The party-centered process of candidate selection is highly relevant for the Finnish context (even at the local level). While it is possible to run as a candidate independently of parties if the aspiring candidate can collect 10 signatures from local eligible voters in support of the candidacy, this is very rare in practice: In the 2012 municipal elections only 2.2% of candidates were independent.

⁷ In our benchmark model parties propose non-overlapping intervals. One could relax this assumption without affecting the direction of our results. Consider party L proposing interval [${\underset{\_}{x}}_L$, ${\overline{x}}_L$] and party R proposing [${\underset{\_}{x}}_R$, ${\overline{x}}_R$] with ${\overline{x}}_L>{\underset{\_}{x}}_R$. Now all the voters in [${\underset{\_}{x}}_R$, ${\overline{x}}_L$] are indifferent between the two parties and, hence, randomize their vote. As ${\overline{x}}_L$ increases, then the vote share of party L still increases but at a slower pace than in our model. Thus, the incentives to extend the list and to gain votes as the disproportionality increases are still present.

⁸ Here we assume that elected ideologies are uniformly distributed in the parliament despite the vote distribution being nonuniform. Considering the continuous list as an approximation of a discrete list of equidistant candidates, this assumption requires that once the party elects more than two candidates, the two extreme and hence most voted candidates be definitely elected with the remaining seats distributed among the interior candidates with equal probability. For completeness of our argument, in app. A1 we show that our argument holds for other distributions.

⁹ In app. A1.1 we provide further theoretical details on the link between the electoral rule disproportionality and council size under the D’Hondt method present in our empirical setting.

¹⁰ The council sizes by municipal population are as follows: population of less than or equal to 2,000 (council size of 13, 15, or 17), 2,001–4,000 (21), 4,001–8,000 (27), 8,001–15,000 (35), 15,001–30,000 (43), 30,001–60,000 (51), 60,001–120,000 (59), 120,001–250,000 (67), 250,001–400,000 (75), and over 400,000 (85).

¹¹ Open lists are frequently encountered in national and subnational elections around the world using a PR system. For instance, at least 40 countries, including many western European democracies, use an open-list PR system when electing the single or lower chamber of their national parliament (Wall 2021).

¹² Parties can form pre-electoral coalitions and propose a joint list of candidates. The allocation of seats takes place at the coalition list level.

¹³ Finland was one of the first countries to introduce voting aid applications. They have gained popularity, with surveys indicating that approximately 40% of the Finnish electorate used an application prior to the 2007 parliamentary election, with 15% of the users claiming that they had no favorite candidate and followed the application’s recommendation (see Wagner and Ruusuvirta 2012 and references therein).

¹⁴ Also the 2017 election data are available but the council size rule was no longer binding in those elections.

¹⁵ Figure A12 reports the histograms of the share of respondents by municipality and by party.

¹⁶ Regression discontinuity at population thresholds is a common approach to isolate causal effects. See, e.g., Ferraz and Finan (2009), Egger and Koethenbuerger (2010), Fujiwara (2011), Gagliarducci, Nannicini, and Naticchionia (2011), Pettersson-Lidbom (2012), Brollo et al. (2013), Gagliarducci and Nannicini (2013), Eggers (2015), and Bordignon, Nannicini, and Tabellini (2016). For a recent literature review and possible issues with the use of RDD at population thresholds see Eggers et al. (2018). We carefully address the concerns they raise. Similarly to us, Sanz (2017) and Lyytikäinen and Tukiainen (2019) use population thresholds to study political consequences of electoral systems.

¹⁷ In the reported results, the bandwidth is optimized after pooling the data. However, the results are robust both to optimizing at each cutoff before pooling and to controlling for the cutoff fixed effects (not reported).

¹⁸ However, the main results remain statistically significant in the nonclustered specifications even if we include the merged units and the larger municipalities, but as expected, the point estimates are closer to zero (table A5). The results are also robust to limiting the sample further to the one to three most densely populated cutoffs.

¹⁹ As an illustration, consider elections using the linear rule with $n=3$ as explained in our conceptual framework (see fig. 1B) and two scenarios: one in which the winner gets 55% of the vote and another in which the winner gets 65%. With the same rule, the 55% vote results in a 65% seat share, while the 65% vote results in a 95% seat share. That is, while the disproportionality of the rule in both scenarios is the same, the realized distortions vary.

²⁰ According to our conceptual framework, the disproportionality of a D’Hondt rule that elects a k-member council is decreasing in k (see the relevant subsection in app. A1.1).

²¹ If parties have formed a pre-election coalition (roughly 15% of the lists in our sample) and, thus, run as a single joint list in the election, we define the list as a single party when calculating the distortions. This is to reflect the actual vote share to seat share mapping. When analyzing party cohesion, the RDD analysis on party cohesion could as well be conducted at the party level. While for consistency we report in the paper our cohesion analysis only at the coalition level, the results are similar at the party level.

²² The modified Gallagher index builds on the simpler Gallagher index (Gallagher 1991), possibly the most standard measure of distortions, defined as $G_{it}={\left[(1/2){\sum }_{j=1}^p{(s_j-v_j)}^2\right]}^{1/2}$. Koppel and Diskin (2009) formalized the concerns by Taagepera and Grofman (2003) on the Gallagher index showing that the modified version of the Gallagher index satisfies relevant properties that the Gallagher index does not (e.g., Dalton’s principles of transfers, scale invariance, orthogonality).

²³ We show that the results are similar when using a linear fit both for the whole sample and when limiting the sample within the MSE-optimal bandwidth in figs. A5 and A6.

²⁴ There are obviously many other ways one could calculate similar indexes. We have the luxury of using this simple and transparent metric as our interest is only in the static relative position of a candidate in relation to their party. Moreover, we cannot use, e.g., Mahalanobis or similar standardized distance measures at the within-party level because, by construct, they would force all the lists to be about equally cohesive.

²⁵ We also implement a correction by multiplying the distance by $n/(n-1)$, where n is the number of respondents. This correction is similar to one used in computing sample variance.

²⁶ The probability that parties have more than five respondents does not change at the cutoff. The RDD effect (MSE-optimal point estimate) on an indicator for “party has at least five candidates” is 0.02. This is small in magnitude and not statistically significant (robust and bias-corrected 95% CI is [−0.096, 0.138]).

²⁷ Note that, because we impose this minimum of five responses, we have 30 fewer observations at the municipal level than in the previous disproportionality analysis (sec. III.D).

²⁸ We show that the results are similar when using a linear fit both for the whole sample and when limiting the sample within the MSE-optimal bandwidth in figs. A5 and A6.

²⁹ In table A1, we show that these results are robust to using a more flexible specification in which we include cutoff-specific fixed effects, allow different linear trends in the running variable around each cutoff, and optimize the bandwidths for each cutoff separately before pooling the data.

³⁰ As is common in the literature, we compute the effective number of parties (lists) by the inverted Herfindahl index of vote shares of party lists.

³¹ However, this does not occur and lists usually include fewer candidates than the maximum permitted. Only 3.4% of lists are full in our sample. Typically only larger parties in larger municipalities do fill the lists completely.

³² We study absolute changes so that possible changes in opposite directions do not cancel each other out in the estimation.

³³ For indicative evidence refer to the cases of Italy regarding welfare state reforms (Ceron, Curini, and Negri 2019) and Germany during the 1980s and the low internal cohesion of the Christian democrats (Zohlnhöfer 2003).