Incumbency

Analyses of the incumbency advantage have peaked in recent years. Although research has been conducted on incumbency for several decades in political science (e.g., Gelman and King Reference Gelman and King1990), pioneering work by Lee (Reference Lee2008) has led to a renewed interest in the question of how being elected in election t affects the reelection probabilities of a candidate in election t + 1. There is strong evidence that candidates benefit from being the incumbent (a summary of the existing literature is provided by, e.g., de la Cuesta and Imai Reference de la Cuesta and Imai2016). While many of these studies focus on the case of single-member districts for examining incumbency effects, there is also increasing evidence that incumbency is beneficial in open-list PR system (e.g., Dahlgaard Reference Dahlgaard2016).

How is the analysis of the incumbency advantage relevant for the discussion of female representation? The basic idea is rather simple. Since men are strongly overrepresented in almost every parliament in the world, it will become more challenging for women to increase their level of representation as incumbents are more likely to be reelected (Schwindt-Bayer Reference Schwindt-Bayer2005). Therefore, incumbency has been described as a “mechanism of reproduction for male dominance (understood … as the numerical over-representation of men in politics)” (Chiva Reference Chiva2017, 82).

However, it is important to differentiate between incumbency as a mechanism that solely hinders the creation of a gender-balanced parliament and as a mechanism that disadvantages women (or favors men). The differentiation of these two concepts is crucial. The first concept of hindering female representation is closely related to the idea of path dependency and makes no claim about whether the incumbency advantage is stronger for men than for women. Instead, this argument simply implies that the incumbency advantage is solely unfavorable to female representation as it increases the probability that existing patterns of descriptive representation will be reinforced. Put differently, the argument implies that once women are sufficiently represented, they are equally likely to benefit from the incumbency advantage, but becoming the incumbent is harder for women than for men. The results reported by McGregor et al. speak in favor of this explanation, as they indicate that “[f]emale candidates perform very well in wards with a female incumbent candidate, but men and women are equally likely to support female candidates in these settings” (Reference McGregor, Moore, Jackson, Bird and Stephenson2017, 142). Similar results are reported by Allik (Reference Allik2015) for the case of Estonia.

The second mechanism is quite different, as it raises the question of whether the incumbency advantage might be particularly strong for men. If this is the case, then it is not just that men are more likely to be reelected, but also that women are less likely than male incumbents to hold their seats. The research regarding the gender specificity of the incumbency effect is mixed. Some authors have found evidence for a particular disadvantage of female incumbents. Chiva (Reference Chiva2017), for example, provides a comparative analysis of incumbents’ rerunning and reelection probabilities in Central and Eastern Europe. Her findings suggest that female incumbents are often equally likely to rerun for parliament but show lower proportions of being reelected compared to male incumbents (Chiva Reference Chiva2017, 95). She argues that this might be caused by “party gatekeeper's [(un)]willingness to place women candidates in winnable seats or positions.” This assumption is not unwarranted, as previous research has shown that list placement is a particularly important factor for electoral success, even in open-list PR systems (Jankowski and Marcinkiewicz Reference Jankowski and Marcinkiewicz2019). Even more importantly to support this argument, Fiva and Rohr (Reference Fiva and Røhr2018) find a strong effect of incumbency on future list placement in party-centered systems.

Others, however, have found that incumbency might be particularly beneficial for women. Bhavnani (Reference Bhavnani2009) exploits a natural experiment in India to analyze how the election of women affects the future patterns of female representation in the same district. The random assignment of certain districts to elect only female candidates allows for such an analysis. The results clearly demonstrate that the election of women has a positive effect on future female representation. The treated districts were more likely to elect women in the future, and more women ran for parliament in those districts. In a similar vein, Shair-Rosenfield and Hinojosa (Reference Shair-Rosenfield and Hinojosa2014) argue that the presence of female incumbents can decrease the amount of gender bias in elections and within parties. By demonstrating their qualification as a politician, becoming an incumbent helps women to overcome an otherwise existing prejudice against female candidates among voters and party leadership.

Building on these different perspectives on how incumbency might affect female representation, we ask how female incumbency affects the probability of female representation in open-list PR systems. Our focus is on list placement and, more specifically, list leadership. Becoming the list leader in an election is an important signal to the electorate. The candidate placed at the first ballot position is the party front-runner; such placement reflects the highest level of endorsement of a party for this candidate (Folke, Persson, and Rickne Reference Folke, Persson and Rickne2016). Moreover, being placed at the first ballot position is a very strong predictor of getting elected to parliament (Faas and Schoen Reference Faas and Schoen2006). This obviously holds true in closed-list PR systems, but in open-list PR systems as well, ballot position effects for the top-placed candidates are so strong that being placed first is an important prerequisite for getting elected (Marcinkiewicz Reference Marcinkiewicz2014). Therefore, our empirical analysis focuses on the effects of electing a female candidate on the probability of having a female candidate as the list leader in the following election. It is important to note at this point that we focus on cases in which only one candidate from the party list was elected to parliament. It is also important to highlight that we focus only on the gender of the list leader in the next election and do not directly control for whether the incumbent is the candidate who reruns at the top of the party list. This is due to the fact that our data do not allow us to match individual candidates between the elections. Focusing on the gender of the list leader in the next election, however, is in line with our research question of how gender representation patterns are affected by a female incumbent. We also want to highlight that we think that the rerunning incumbents largely account for the potential effects.Footnote ¹

We expect that incumbents have an advantage over other candidates because they remain politically active for the next several years, have the chance to build local political networks, and are well informed about local problems. Therefore, their position within the party should be strengthened, and they should have more influence on their list placement in the next election (Folke, Persson, and Rickne Reference Folke, Persson and Rickne2016). Moreover, parties should often have a strategic incentive to nominate the incumbent to the first ballot position in the hope that this candidate will attract more votes. Consequently, we expect that once a woman (man) is elected to parliament, this party list is more likely to have a woman (man) at the top of the list in the next election. This constitutes our first hypothesis:

Empowerment

The previous section was concerned with the effects of electing a woman on the future career prospects of this particular woman. We were not concerned with the effect of electing a woman on the overall future selection patterns of female candidates. Such a process is commonly referred to as the “empowerment” effect.

Empirical evidence suggests that political engagement of females may motivate other women to become involved in politics as well. A number of studies relying on data from India report the existence of a substantive empowerment effect (e.g., Bhavnani Reference Bhavnani2009). In districts that were reserved for female candidates at a certain point in time, other women were also more likely to win in the following elections. Also, the overall number of female candidates increased. In general, it may be concluded that in districts where females contested the election, subsequent increases in different forms of political engagement by women can be observed. The phenomenon of empowerment has been analyzed both in the temporal (as was done by Bhavnani Reference Bhavnani2009) and in the spatial context (Broockman Reference Broockman2014; Gilardi Reference Gilardi2015). In the former case, the increase in political engagement by females is expected to be found in the period following female candidacy or electoral victory. The latter approach attempts to identify the spillover effects on neighboring districts.

The evidence in favor of the empowerment effect, however, is not uniform. Wolak (Reference Wolak2015) finds in her experimental study that women's political engagement is insensitive to the gender of the candidate. A study by Broockman (Reference Broockman2014) relying on data from U.S. state legislative elections demonstrates that the patterns observed in industrialized countries may be different from what could be observed in the Indian context studied by Bhavnani (Reference Bhavnani2009). In the case of U.S. state elections, no positive empowering effect of female candidacy could be identified. Broockman (Reference Broockman2014) tests the empowerment effect by analyzing whether the election of a woman in a single-member district has an impact on the probability of nominating a woman in spatially proximate districts in the next election. More differentiated results are offered by Gilardi (Reference Gilardi2015), whose analysis stretches over a period of 40 years. Using data from municipal elections in the Swiss canton of Zurich, Gilardi (Reference Gilardi2015, 966) demonstrates that spatial spillover of the empowerment effect is substantive in the first elections after women were granted voting rights. It becomes weaker over time, however, and in the end disappears. Finally, Foos and Gilardi (Reference Foos and Gilardi2017) conduct a field experiment to test whether female politicians can function as a role model for other women and motivate them to become politicians. Their results suggest that female role models can acutally demotivate other women to become politicians. One explanation for this finding is that other women might feel intimidated when seeing how many obstacles lie in the way of a female career in politics.

Since we examine a party-list-centered system, we can avoid analyzing the impact of electing a woman on the probability of nominating more women in regionally proximate districts. This type of spatial spillover was the focus of the studies by Broockman (Reference Broockman2014) and Gilardi (Reference Gilardi2015), who discuss examples of majoritarian voting systems. We believe that the composition of the party list in the same district in the next election provides an even more interesting and convincing case for analysis (temporal spillover). As already explained with regard to the incumbency effect, we expect that being the only elected candidate from a list gives the incumbent more influence in the internal hierarchy of the party in the future. Therefore, the incumbent should be more likely to secure herself a better placement in the next election. If the empowerment effect exists, it should have a strong effect on the list composition directly within the district (and not only on candidates in proximate districts).

The empowerment effect should be more likely to occur in the context that we analyze, as the “costs” of nominating additional women are relatively low in PR systems compared with majoritarian systems. Being placed close to the bottom of the ballot paper is associated with a very low election probability. This is drastically different than in single-member districts, where only one candidate per party is nominated. Bluntly put, if a party member wants to run for parliament in PR systems, she or he can easily be added to the party list without significantly lowering the electoral chances of the most preferred candidates of the party too much. In a single-member district, in contrast, only the most powerful candidate in the intraparty selection process is eventually nominated. In these cases, some women might be more motivated to run for election, but they ultimately do not appear at the ballot paper because they have lower chances during the selection process. Therefore, analyzing the gender composition of party lists in PR systems should provide a better testing ground for empowerment effects. Of course, we cannot fully exclude the possibility that we are analyzing cases in which more candidates wanted to run for office than positions on the list were available. However, the number of candidates who were not selected to the list as well as the ratio of potential candidates to the number of available seats should be drastically lower in PR systems compared with majoritarian systems.

Following the idea of empowerment, we expect that the election of a woman in election t will lead to an increase in the number of female candidates in election t + 1. We use two different outcome variables to test this effect: the raw number of women on the party list in election t + 1 and the proportion of women in election t + 1.Footnote ² Therefore, our second hypothesis is as follows:

Contagion

The third objective of our study is to examine the effect of female electoral success on selection decisions by other political parties. We expect that the election of a woman from one party may encourage other parties to nominate more women to their party lists. If this is the case, we can speak of the existence of a specific kind of spillover effect that Matland and Studlar (Reference Matland and Studlar1996) describe as “contagion.” The contagion effect differs from the empowerment effect addressed in the previous section because of its external character. The success of a woman appearing on one party list is expected to have impact on other parties. Matland and Studlar (Reference Matland and Studlar1996) theorize and find empirical support that such effects are particularly strong under PR systems—the case we are focusing on. They argue that contagion should appear as the election of women “may demonstrate that there is no electoral penalty associated with women candidates” and because “parties feel increased pressure to respond by more actively promoting women themselves” (Matland and Studlar Reference Matland and Studlar1996, 712). This explanation is followed by Broockman (Reference Broockman2014, 192), who suggests that the success of a woman running for office may motivate party elites to decrease their bias against female candidates. The positive example of a female legislator representing one party may motivate elites of other parties to be more supportive of female candidates.

There is also the possibility that the candidate selection process has a strategic character. While deciding who should be placed on the list, party leaders must take into consideration decisions made by the leaders of other parties. If at time t one party managed to get a female candidate elected to the parliament in a given district, leaders of other parties may be compelled to place in a prominent position on the party list a candidate who is similar to that successful candidate. The electoral victory of a female candidate may indicate that voters in a given district are less biased against female candidates. Therefore, other parties might see it as an electoral advantage to gain votes by nominating a woman to the top of their list as well. Finally, one might expect that there is variation in the contaigon effect, depending on whether a left-wing or a right-wing party elected a woman in the previous election. More specifically, we expect a “contagion from the right” (Matland and Studlar Reference Matland and Studlar1996, 710), meaning that the election of a woman from a right-wing party will have a stronger contaigon effect. The reason for this expectation is simple: in contrast to more left-wing parties, Polish right-wing parties put less emphasis on the representation of women in parliament or are even directly opposed to the idea of gender parity (see the debate on the implementation of a gender quota in 2011 as described in Gwiazda Reference Gwiazda2015). Therefore, right-wing parties should care less about the gender of competing candidates, also because their voters might be less likely to vote for female candidates. (Both Jankowski and Marcinkiewicz Reference Jankowski and Marcinkiewicz2019 and Górecki and Kukołowicz Reference Górecki and Kukołowicz2014 demonstrate that women of right-wing parties in Poland often receive fewer votes than men.) For left-wing parties, however, increasing the share of women is often an important issue. Thus, left-wing parties can be expected to be particularly inclined to nominate a woman in cases in which a right-wing party has a female incumbent. In doing so, left-wing parties avoid being perceived as potentially less female-friendly than right-wing parties. Consequently, we formulate two hypotheses:

Data Set

Our data cover various elections in Poland, all using the same version of the open-list PR system. The Polish open-list PR system in its current form remained virtually unchanged between 2001 and 2015 and allows voters to cast one vote for a candidate appearing on a certain party list. Preference voting is compulsory, which means that voters cannot simply confirm the list order provided by the parties but have to cast their vote for a specific candidate (Marcinkiewicz and Stegmaier Reference Marcinkiewicz and Stegmaier2015). The party magnitude is determined based on a seat allocation method (in most cases the D'Hondt method) given the vote shares of the parties in a district. Candidates are elected based on the number of preferential votes received. This version of the open-list PR system is applied in national, regional, county, and local elections in larger municipalities (and, prior to 2011, in medium-sized municipalities; see Górecki and Kukołowicz Reference Górecki and Kukołowicz2018).

We combine data from all of these levels for all elections held since 2001. The raw data cover 64,106 unique lists. However, we restrict our sample to the party lists of the four major Polish parties: the right-wing populist Law and Justice party (PiS), the centrist/liberal Civic Platform (PO), the conservative-agrarian Polish People's Party (PSL), and the left-wing Democratic Left Alliance (SLD). Other parties are not considered, since they were not continuously represented in most of the analyzed (local, county, regional, and national) representative bodies for the whole period of analysis and usually existed for only a short period of time. Of course, it would be interesting to analyze the effects for these smaller lists as well. However, even when some of those lists reran in the next election, they often used different party names and thus matching lists between the elections becomes quite challenging. There is also no party registry that could be used to match identical lists. As we have to remove these smaller parties, the number of unique party lists in our data set is reduced to 24,185.

Regression Discontinuity Design

We are interested in estimating the causal effect of electing a single woman to parliament on future female candidate selection patterns. However, the relationship between electing a woman in election t and female selection patterns in election t + 1 is obviously endogenous. A woman who has won by a large margin might be particularly qualified as a politician, and she is both more likely to receive preferential votes and to become the list leader in the next election. In order to overcome this problem, we make use of the regression discontinuity design.Footnote ³

The RDD can be applied to cases in which a continuous variable (commonly referred to as a “scoring,” “forcing,” or “running” variable) with a known cutoff value determines treatment assignment. Using the RDD, we are able to estimate the causal effect of the treatment under the plausible assumption that subjects cannot fully control their placement on the running variable. Consider the simple case of a two-candidate election as an example (Lee Reference Lee2008). The treatment of being elected is assigned only to the candidate with a positive vote margin—that is, the candidate who received more votes. However, candidates cannot fully control how many votes they receive in an election. This implies that there is a certain amount of “randomness” in the observed election outcome for each candidate. Since the cutoff at which the treatment is assigned is fixed, the treatment is “as-if” randomly assigned around the cutoff. Put differently, when two candidates compete against each other and the race between the candidates is decided by only a few votes, then both candidates basically have the same probability of winning the election. In short, the RDD exploits the “as-if” random assignment around the cutoff of the continuous variable as a natural experiment. It should be noted, however, that the causal effect of the treatment can only be observed around this threshold and is thus “local.”

In order to apply the RDD to the case of open-list PR elections, we have to make some tough decisions and restrict our data set to an “estimation sample” for which causal effects can be identified (compare, e.g., Folke, Persson, and Rickne Reference Folke, Persson and Rickne2016). Speficially, we have to focus on cases in which only one candidate has been elected in election t. Moreover, we use cases in which the two candidates with the highest number of preference votes were of different genders. Then we estimate the vote margin between these two candidates as a measure of closeness between the top two candidates.Footnote ⁴ The vote margin is defined with regard to the female candidate, meaning that it is positive if and only if a woman was elected and negative if a man was elected (in this case, the woman was a runner-up). Eventually, this implies that for very small vote margins, it was basically as-if randomly assigned whether a male or female candidate was elected to parliament from that list. Therefore, these lists are comparbale and differ only with regard to the gender of the elected candidate. Put differently, we focus on cases that resemble the situation of a single-member district in which only one candidate is elected. The main difference is that our outcomes are different from the single-member district case because we cannot only analyze the effects with regard to a single candidate but to a whole list of candidates in the next election.

We acknowledge that the decision to focus only on lists with a party magnitude of one and where the top two candidates were of different genders makes our data set less representative. In fact, we are left with 2,978 observations—a rather small subset of our full data set. In this regard, our research design reflects the trade-off between using as many observations as possible in an analysis that does not necessarily allow for identifying causal relationships or using only those observations that can be used for identifying a causal effect. Recent work on causal inference has often advocated the latter position (Keele Reference Keele2015), and we follow this strand of research. However, we are aware that our estimates provide only a causal effect for a specific sample of cases. Still, it should be mentioned that this is—to our knowledge—the first time that the empowerment hypothesis has been tested for the case of PR systems using a causal identification strategy.

One might think of other modeling strategies to apply the RDD. For example, one might want to give up the restriction to focus on lists with a party magnitude of one and focus on lists on which a woman was barely elected or not elected, ignoring whether male candidates were elected as well. While this is possible, we opt against such a strategy for theoretical and methodological reasons. Theoretically, this approach strongly weakens the assumed mechanisms underlying the “empowerment” or “role model” argument. Under this alternative modeling startegy, the elected woman would be, by defintion, the last elected candidate. This woman is the potentially weakest incumbent as she received the smallest number of preference votes among all elected candidates. Methodlogically, this alternative approach is also problematic because the running variable becomes imbalanced around the threshold. The reasons for this aspect are rather technical and related to the nonlinearity between ballot positions and the number of preference votes. Put bluntly, when we focus on lists with more than one elected candidate, then the number of lists for which one women was elected by a close margin increases, while the number of lists on which a woman was not elected by a close margin decreases. This eventually results in an imbalanced running variable that violates the McCrary test as the density of the running variable is no longer continuous around the threshold (see the next section for details).

Estimation of the RDD

While the basic setup of the RDD is rather simple, the estimation of the local average treatment effect is a bit more complex, as potential pitfalls have to be taken into account (see, e.g., Lee and Lemieux Reference Lee and Lemieux2010). First, while the treatment is “as-if” randomly assigned around the threshold, the treatment effect is usually identified by running local linear regression analyses inside a certain estimation window around the threshold using the running variable as a predictor. By using a triangular kernel, more weight is given to observations close to the cutoff, and less weight is given to observations more distant from the cutoff. Observations outside the estimation window do not contribute to the result, as they are assigned a weight of zero. Second, a crucial question is how the estimation window is determined (for an overview, see Cattaneo and Vazquez-Bare Reference Cattaneo and Vazquez-Bare2016). The dominant approach is to use the Imbens and Kalyanaraman bandwidth selector (Imbens and Kalyanaraman Reference Imbens and Kalyanaraman2012; IK) or the more flexible method developed by Calonico, Cattaneo, and Titiunik (Calonico, Cattaneo, and Titiunik Reference Calonico, Cattaneo and Titiunik2014; CCT). Both estimators minimize the mean squared error. We use both approaches in our analysis, but we report—if not explicitly mentioned differently—the results based on the CCT bandwidth selector. Third, as demonstrated in Calonico, Cattaneo, and Titiunik (Reference Calonico, Cattaneo and Titiunik2014), statistical inference is biased in conventional RDD analysis, and thus we report the results using the bias-correction method for p-values developed by CCT.

Fourth, the RDD is based on the assumption that subjects cannot fully control their placement on the running variable. This assumption can be tested by two different procedures. First, when subjects cannot fully control their placement on the running variable, then candidates should not be able to select themselves systematically into the treatment or control group (e.g., Caughey and Sekhon Reference Caughey and Sekhon2011). This means that the number of observations around the threshold should be fairly similar. This can be tested empirically by controlling for discontinuity in the density of the running variable (McCrary Reference McCrary2008) with the expectation of finding no such discontinuity. The second way to control for the validity of the RDD is by estimating the RDD on predetermined outcomes. For example, the treatment should only have an effect on outcomes measured for election t + 1, but it cannot have an effect for outcomes in election t. Therefore, we can expect predetermined outcomes to be fully balanced around the threshold and not display any discontinuities. In the next section, we present these analyses and demonstrate the validity of the RDD for our case. Finally, the robustness of the RDD results can be strengthened by running placebo analyses. For this purpose, we estimate the RDD using hypothetical cutoffs with the expectation of finding no effects for these cases.

Validity Checks for the RDD

As described in the previous section, we now present validity checks for the RDD. First we control for the density in the running variable. For this purpose, we use the approach developed by Cattaneo, Jansson, and Ma (Reference Cattaneo, Jansson and Ma2017), which improves on the McCrary test (Reference McCrary2008). As explained earlier, the RDD is only valid when there is no sorting around the threshold, implying that candidates cannot systematically select themselves in the treatment and control group. This assumption is fulfilled in our case, as demonstrated in Plot a of Figure 1. The p-value of the test is .8987 and thus does not allow us to reject the null hypothesis of no discontinuity in the density of the running variable. Plots b–f in Figure 1 display the results of applying the RDD to predetermined outcomes in election t (instead of election t + 1, as we will do later in the empirical analysis). There is no discontinuity at the cutoff for any of these outcomes, which again strengthens our confidence in the validity of the RDD.

Figure 1.

Validity checks for the RDD. Plot a displays the density of the running variable for the control group (gray) and treatment group (black) based on the procedure developed in Cattaneo, Jansson, and Ma (Reference Cattaneo, Jansson and Ma2017), which is comparable to the McCrary (Reference McCrary2008) test. There is no discontinuity in the density around the cutoff (vertical dashed line). Plots b–f display the effect of the treatment on predetermined outcomes. As expected, predetermined outcomes are not affected by the treatment. The vote margin in plots b–f is only displayed for the range –0.5 to 0.5 to increase the clarity of the plots.