Do electoral reforms tend to favour the incumbents? A quantitative analysis

Electoral reforms offer an opportunity to incumbents to change the rules strategically, for their own benefits. From this aspect, the low number of studies addressing the effect of incumbents’ potential strategic manipulations of the electoral rules is striking. Most research analyses single reform cases, offering an overview of the context, the negotiations, and the outcome of the reform process. Comparative research on strategic electoral manipulation, however, is scarce, and almost non-existent on non-transitional settings or established democracies. To fill this gap, the present study examines whether European electoral reforms have served the short-term interest of the incumbent parties, analysing data in 30 European countries of all relevant electoral reforms carried out between 1960 and 2011. Interestingly, the results do not support the assumption that incumbent parties generally benefit from carrying out a reform. Moreover, it finds no substantial differences in this regard between major and minor reforms, and neither the age of democracies nor the timing of the reform has a significant effect on reformers’ gains. The paper discusses possible explanations for the negative effect found, and it concludes that, apart from promoting self-interest and the unpredictability of the reforms’ effects, the most probable causes are the reformers’ alternative goals.


Introduction
In times of electoral reform, there is an obvious conflict of interest. The electoral system can be designed to help or harm actors' chances in the next election. This special form of bias has always generated considerable interest both from political scientists and the general public. However, there are few systematic quantitative papers addressing incumbents' actual gains or losses related to the modification of electoral rules.
The majority of relevant research analyses single reform cases, offering an overview of the context, the negotiations, and the outcome of a reform process (for example, Shugart and Wattenberg (2001) and Colomer (2016) offer numerous electoral reform case studies). Other studies focus on transition periods, which are characterized by extreme levels of uncertainty and are examples of decisions taken under the veil of ignorance. These studies include Western European cases after World War II and Eastern European ones after the fall of the Berlin Wall (Andrews and Jackman 2005;Birch et al. 2002;Kaminski 2002;Sgouraki Kinsey and Shvetsova 2008). They conclude that political actors, even if they had clear intentions, mostly failed to create an electoral law that served their interests. The authors argue that in each country the decision about the very first democratic electoral laws was characterized by extreme levels of uncertainty; therefore, political actors were unable to foresee what type of electoral system could be in their best future interests.
Other papers analyse more nuanced aspects of institutional changes, including the impact of fragmentation and volatility on preferences for electoral system types and the established parties' insistence on entry barriers when new parties are emerging (Bawn 1993;Colomer 2005;Núñez et al. 2017;Pilet and Bol 2011;Remmer 2008;Sebők et al. 2019;Shugart 1992).
While the literature's general assumption about moments of electoral change is that incumbents try to promote electoral rules that serve their interests (Bawn 1993;Bedock 2014;Benoit 2004;Norris 2004;Núñez and Jacobs 2016;Pilet and Bol 2011;Quintal 1970;Remmer 2008;Riker 1986), to the best of our knowledge, there are no quantitative works on the simplest and most straightforward aspect of this issue covering a large sample of democracies, namely, on reformers' gains in the future electoral results. To fill this gap, the present study examines whether European electoral reforms have served the short-term interest of incumbent parties in terms of reformers' future gains. We hypothesize that incumbent parties have indeed been favoured by the modifications of electoral laws.
To measure the extent an electoral system favours a party, a key concept we use is the difference between seat shares and vote shares, which we call disproportionality. Alternative dependent variables we use are seat shares and future office holding.
The surprising result of the paper is that empirical evidence does not support the well-established hypothesis that electoral reforms favour reformers. The effect of carrying out a reform on the change in the seat-vote disproportionality of incumbents, on the change of their seat shares and on their future office holding is consistently negative in different model specifications and, in many of our models, this effect is significant. Hence, in the last part, we discuss a set of possible explanations for the results. We argue that the two most probable explanations for this negative effect may be reformers' goals other than promoting their self-interest, and information incompleteness, which leads to severe miscalculations regarding the future effects of reforms. The significance of negative results in many of the models, however (especially those using future office holding as an independent variable), remains a puzzling question for future research.

Literature review
One can hardly overrate the role of electoral systems in the functioning of representative democracy. As Lijphart noted, "choosing the electoral system is one of the most important decisions-if not the single most important decision-of all the constitutional decisions facing democracies (1994,207)". Thus, the moments when electoral laws change are of particular importance for a political scientist. As no electoral system converts the popular will into seats in a neutral manner, all of them favour certain political actors over others. Therefore, moments of electoral reforms offer an opportunity to incumbents to change the rules strategically, to serve their benefits. As Birch describes, "[t]his type of conflict of interest would undoubtedly never be considered acceptable in the civil service, and not even in many private sector organizations, but it is accepted as a routine part of the democratic process in modern political systems" (Birch 2011, 86).
According to the rational choice theory, with insufficient political power and political interest, there could be no electoral reform. Reforming is costly-it involves decision-making costs, costs of voter affect (as after some impudent electoral engineering, at the polls voters may hold to account the reformers), costs of reciprocity (as reforms set precedents for future reforms), and information costs (the costs of correctly projecting the effects of a new system (Quintal 1970). The benefit of a reform is the legislative seat bonus the reformers gain in consequence of the reform. Considering these costs and benefits, political actors calculate whether reforming is possible and is worth it; based on the results, they then decide whether to reform the electoral system (Benoit 2004).
Sarah Birch's insightful analysis (2011) of electoral malpractices dedicates an entire chapter to the incumbents' strategic manipulation of the electoral law, presenting both quantitative and qualitative analyses based on election observation reports. She refers to such manipulation as the "oldest and best-established type" of electoral malpractice. She defines it as the manipulation of the electoral processes and outcomes to substitute personal or partisan benefit for the public interest (Birch 2011, 14) and as the "particularization of the electoral process" (Birch 2011, 26). Riker instead (1986) conceptualizes this practice as "electoral heresthetics", a special form of manipulation that politicians regularly use in a democratic competition. Thus, the distortion of electoral laws to the benefit of the incumbents can be regarded as a moment of normal democratic functioning, as malpractice, or as a borderline case between the two. Nevertheless, strategic manipulation of the electoral law is part of normal democratic functioning, even if the more severe cases certainly qualify as malpractice.
The dominant (rational) expectation in the literature is that electoral reforms are designed to favour the incumbent parties whenever an electoral law undergoes a substantial change (Bawn 1993;Bedock 2014;Benoit 2004;Núñez and Jacobs 2016;Pilet and Bol 2011;Quintal 1970;Remmer 2008). As Birch notes, "electoral system reform by legislatures involves a fundamental conflict of interest, in that it requires the current holder of a set of posts to determine the means by which those posts will be filled in the future (2011, 86)". Assuming that political parties are powermaximizers, this fundamental conflict of interest implies that incumbents promote changes in the electoral law that favour themselves and/or they prevent changes in the law that are harmful to them. Therefore, whenever an electoral reform occurs, we can reasonably expect it to favour the incumbents.
Taking a glance at empirical investigations, we find a number of studies that support the above rational choice hypothesis concerning institutional choices. Shugart (1992) analyses the relationship between the direction of electoral reforms and the effective number of parties (ENP) in the case of Western European electoral reforms. He points out that there is an upward trend in the ENP when electoral systems are reformed to be more proportional, while there is a downward trend in the ENP when electoral systems are reformed to be less proportional. Colomer's findings (2005) are similar in a worldwide context: multipartism precedes proportional representation, and high ENP leads from plurality to mixed or proportional systems.
Analysing recent Central European electoral reforms, Sebők et al. (2019) find support for the hypothesis that incumbents strategically manipulate the entry barriers of the electoral market to their benefits. Remmer (2008) investigates South American electoral reforms. She finds that incumbents facing declining support tend to increase the proportionality of electoral systems, and incumbents with electoral gains tend to pursue less proportional systems to fortify their position. Analysing West Germany's electoral system choices, Bawn (1993) concludes that these can be very well described as a product of a rational bargaining process of competing parties, that is, "institutional choices are political choices" (1993,986). Bol and Pilet (2011) show that parties' expected gain in seats has a positive effect on their support for electoral reform; however, this is only true for those parties that have spent more than 40% of the time in opposition over the 25 years preceding the reform process. These results are aligned with the rational choice framework, supporting the argument that political actors reform the electoral system when they have the power to do so and when reforming seems beneficial for them.
Nevertheless, it is important to note that even though self-interest is a key factor, it is certainly not the only component that influences institutional change. Moral constraints, opposing partisan interests, popular opinion, ideology, and values may also be influential (Bowler and Donovan 2013;Lijphart 1994;Renwick 2010). Supporting the role of values, Katz (2005) and Bol (2016) show that some electoral reforms have indeed been carried out by value-driven politicians who introduced reforms with the aim of enhancing democracy. Moreover, even if parties try to follow their self-interest, it cannot be taken for granted that their reform process will truly be 'profitable', as the consequences of electoral reforms are often uncertain and unpredictable. In line with this notion, some authors point out that reforms, even if planned to serve the interests of the incumbents, might not be beneficial for them (Kaminski 2002), as information incompleteness is persistent, and miscalculations of the reforms' effects are frequent. Similarly, Núñez et al. (2017) show that the emergence of new parties is a powerful explanation for reforms that reduce the openness of electoral systems. The authors argue that these post hoc reactions to newcomers suggest that politicians may not be able to anticipate electoral changes. A line of studies focusing on electoral reforms carried out after regime changes arrives at similar conclusions (Andrews and Jackman 2005;Birch et al. 2002;Sgouraki Kinsey and Shvetsova 2008), although these argue that while extreme uncertainty could have prevented reformers in transition periods from enacting reforms that serve their interest, in times with moderate levels of uncertainty, political actors are still expected to promote changes that serve their interests.
To summarize this section, although the literature considers other aspects as well that may influence electoral reforms, it is still a dominant view that self-interest is the central explanation. Consequently, electoral reforms are expected to be beneficial for reformers. Although generalizable evidence on a positive impact of reforms on incumbents' future electoral results is mostly lacking, reforms that are not beneficial for the incumbents are mostly regarded as exceptions or special cases which deserve unique explanations. To fill this gap, this paper aims to quantitatively test the hypothesis that contemporary European electoral reforms have served the short-term interest of incumbent parties.
Considering that electoral reforms are very different, ranging from minor modifications to complex reforms that completely change the formerly used procedure, our expectations may vary depending on the scale of changes a reform implies. As substantial modifications have the potential to induce higher volatility compared to former results, they may bring more benefits to reformers than smaller modifications, implying that incumbents should benefit more from major reforms than from minor ones. However, we could also argue that major reforms involve much more uncertainty; hence, their overall effect is much less predictable than that of minor ones. Additionally, while minor modifications are relatively frequent, major reforms are rare (Jacobs and Leyenaar 2011;Katz 2005;Norris 1995), which contributes to the unpredictability of the effect they produce. Considering this reasoning would lead us to expect minor reforms to be more beneficial for incumbents than larger ones, which is just the opposite of the expectation we discussed above. Nevertheless, pooling all kinds of reforms without differentiating between the scale of changes they imply may possibly mask systematic differences between the consequences of major and minor reforms. For this reason, besides testing the general effect of electoral reforms compared to cases when no reform occurred, we seek an answer to the question whether major electoral reforms are more or less beneficial for reformers than minor ones.

Data and variables
We use data from the Electoral System Changes in Europe project (Pilet et al. 2016), which covers all relevant electoral reforms in Europe between 1945 and 2011. We combine this dataset with the Comparative Political Data Set (CPDS, Armingeon et al. 2018a, b), which contains data on election results and socioeconomic indicators going back to 1960. Data on government composition comes from the supplement of the above database (Armingeon et al. 2018a). We also used data from the Polity IV project (Center for Systemic Peace 2014) about the year of democratization in each country.
Our analysis dataset includes 30 European democratic countries; observations are party-elections between 1960 and 2014. We excluded parties with no vote share, and reform cases that were implemented before the first democratic election in a given country. In total, we have 2990 observations, i.e. 2990 partyelections in 319 elections. In 84 of those election cases, the electoral system had been modified, meaning that reforms were relatively frequent in the period analysed. Naturally, not all changes carry the same weight. In our sample, the electoral formula (proportional, majoritarian, or mixed types) changed in six cases, as presented in Table 1. The mean district magnitude changes are summarized in Table 2. The mean district magnitude, calculated as the seats weighted district magnitudes of the electoral system's tiers, remained unchanged in 45 cases. The electoral system's mean district magnitude increased (became more proportional) in 16 cases. Appendix 1 gives the list of reforms included in the analysis.

Dependent variables
Most empirical studies examining the partisan bias of electoral institutions investigate the deviation of electoral results from proportionality or, when examining single cases, they investigate some specific forms of manipulations, such as gerrymandering (when constituency boundaries are drawn to produce disproportional results on the aggregate level) or malapportionment (when the numbers of voters in electoral constituencies strongly differ, thereby favouring a certain political side). Employing a comparative research design, in this paper we follow the first approach to assess the extent an electoral system favours a party.

The change in disproportionality between seat shares and vote shares (∆D)
Following the standard rational choice approach, we assume that parties aim at maximizing their seats (Benoit 2004;Colomer 2005;Quintal 1970;Rahat 2011).
For party i at election t , we define disproportionality ( D(i, t) ) as the share of seats ( S(i, t) ) minus the share of votes ( V(i, t) ), both in percentages: If larger than zero, disproportionality indicates that a party controls more seats in the legislature than its popular vote share would suggest. Disproportionality captures the extent the electoral system favours a party because the higher (lower) the disproportionality is, the fewer (more) votes the party needs to get a certain number of mandates. If the electoral system is perfectly proportional, then D(i, t) = 0 : Every party gets the share of mandates according to its share of votes. Parties with a positive disproportionality value have higher seat shares than vote shares. We measure the impact of the reform by the change in disproportionality ( ΔD ), that is the difference between the disproportionality after and before the reform, using the change in disproportionality ( ΔD ) variable for party i after election t: This variable shows how favourable the electoral system became relative to the previous electoral system. If it is positive, the next electoral system is more favourable for the party than the previous electoral system.
We chose this measure for two main reasons. Firstly, holding the voters' preferences constant, the seat share maximization problem and the disproportionality maximization problem are equivalents. Thus, disproportionality seems a natural alternative to seat share, while disproportionality can be better interpreted on its own than seat share. A higher seat share does not always signal a more favourable electoral system, but having higher disproportionality does. Secondly, using ΔD captures changes in both the voters' preferences and the electoral system rules. If we control for changes in electoral preferences, then disproportionality shows how favourable the rules are, and we can control for those changes with the party's vote share in t + 1. In addition, we also use two simpler alternative independent variables to arrive at more accurate conclusions and to prove the robustness of our results.

Difference in seat shares between election t and t + 1
An alternative independent variable we use is the difference between incumbents' seat shares in elections t and t + 1.
The logic behind operationalizing electoral success in this way is that the goal of the electoral reform could be the highest possible seat share. In theory, parties can have higher seat shares without having higher disproportionality. Therefore, we also consider this possibility.

Incumbent status in t + 1
One can argue that parties' objective is not maximizing disproportionality or seats, but rather to remain in government. Considering the differences between the goals of seat maximization and remaining in office, we also tested the effect of reforms on a binomial-dependent variable (entered office after the next elections-1, or not-0).

Being an incumbent when reforms occur: incumbent position*reform
Our hypothesis is that reforming the electoral system favours the incumbents, and we expect that reforms have a positive impact on the ΔD of reformers. To test this hypothesis, we consider whether party i reformed the electoral system after election t (and before election t + 1 ). This is measured with the interaction of two dummy variables: (1) whether party i was a government party after election t, and (2) whether a reform bill was passed between election t and t + 1 . Both variables feature in our regressions as controls.

Scale of the reform
We distinguish between major and minor reforms. To categorize the sample, we used the seminal work of Lijphart (1994) in the first place because it offers an easily applicable and straightforward framework to identify major reforms. 1 As the ESCE project does not include technical reforms, we used a dummy variable indicating major modifications (major reform-1, minor reform-0). 2 According to Lijphart (1994), major reforms include cases of significant changes in assembly size (more than 20%), in the average district magnitude (more than 20%), in the electoral threshold (more than 20%), or the change of the electoral formula.
To give an insight into what could constitute a minor change, minor reforms include (but are not restricted to) moderate changes in assembly size, local changes (e.g., change in the number of tiers in a single province or district), moderate change in the average district magnitude, change in the volume of deposit required by candidates, change in the colour or overall design of the ballot paper, changes in the representation of minorities, the regulation of vacancies, or the regulation of multiple candidacy.

Vote share in t + 1
To control for changes in electoral preferences, we use the popularity of parties in t + 1 measured in vote shares in some specifications. The descriptive statistics of all variables are summarized in Table 3.

Time since democratization
We operationalized the year of democratization as the first year of the last uninterrupted period when democracy scores were above 8 out of 10 in the Polity IV democracy scores database. We use two variables to measure the age of democracies: a continuous variable indicating the number of years since democratization and a dummy variable indicating new and old democracies (1-up to 10 years of democratic experience, 0-older democracies).

Time between reforms and the next elections
Many of the reforms we analyse are not regulated by a single reform package but by different bills introduced throughout the years; judicial reviews that cancel certain parts of reforms further complicate the operationalization of the variable. Hence, we applied a dummy variable to indicate whether a cabinet's last modification of the electoral law happened less than one year from the next election (1, otherwise 0).

Results
Firstly, we present the fundamental properties of ΔD and its relationship with various variables. The distribution of ΔD for reformers and non-reformers is shown in Fig. 1. We observe that reformers tend to have a lower ΔD . The mean ΔD for reformers is − 1.37, and the mean ΔD for non-reformers is 0.10, and − 0.81 for nonreformer government parties.  That is, even reformers' largest gains are modest compared to reformers' largest losses. This suggests that while some reforms are undoubtedly beneficial for the incumbents, the opposite is also rather frequent.
Comparing major and minor reforms, as Fig. 2 shows, their effect in terms of their benefits for reformers seems similar. This suggests that the differentiation between major and minor reforms might not be as important in predicting the gains of reform for reformers as we initially expected.
To offer a more detailed picture of the impact of electoral reforms on parties' disproportionality and seat gains, we control for the most important confounding factors in a set of linear regression models, presented in Table 4.
In Table 4, Models 1, 2 and 7 show the difference between cases of no reform and cases of reform in general. Models 3, 4 and 8 compare cases when either minor or major reforms occurred to cases of no reform. Models 5, 6 and 9 compare cases of major reform to all other cases (with no reform or minor reform happening). The dependent variable is ΔD (Models 1-6) and ΔS (Models 7-9). Models 2, 4 and 6 use an additional control variable, i.e., the vote share of parties in the next elections (Vote share(t + 1)). 3

Fig. 1 Kernel density plots of ΔD for reformers and non-reformers
3 Table 4 does not show the ΔS regressions with the Vote share(t + 1) control variable. The ΔS regressions with the Vote share(t + 1) control variable have the same parameters for the reform variables as the ΔD regression with the Vote share(t + 1) control variable. The ΔD linear regression equation is: where V(t) and V(t + 1) are the vote shares, X is the matrix of all the other explanatory variables, 1 , 2 are parameters, is a vector of parameters of the variables in X . Rewriting ΔD as S(t + 1) − V(t + 1) − S(t) + V(t) yields: According to our baseline model (Model 1), reforming has a significant negative impact. Reformer parties end up in a setting that is less favourable for them in terms of the disproportionality between seat shares and vote shares, when we pool all types of reforms and compare them to cases when no reform occurred. The effect remains negative but turns insignificant if we include vote share at the next elections as an additional control variable.
In those three models (Models 7, 8, and 9) where the dependent variable was the difference in seat shares from election t to election t + 1 , the reform does not appear to have a positive effect on the reformers' future seat shares, to say the least, as these results are consistently negative and significant. When analysing the effect of major reforms and that of major and minor reforms on ΔD separately, the results are insignificant, but again consistently negative. Figure 3 shows the marginal effects predicted by our baseline model (Model 1) for the interaction of the government/opposition status of parties and whether a reform occurred during the cabinet's term. It reflects that in the cases when no reform occurs, the prediction of ΔD for incumbent and opposition parties is statistically similar. Compared to these cases, when reforms do occur, there is a negative change in ΔD for incumbents, while ΔD changes positively for challengers. This reflects that incumbents are not favoured by their recent electoral reforms in terms of seat-vote disproportionality. Adding V(t + 1) − V(t) to both sides: Thus the ΔS regression has the same parameters for the variables in X (e.g., being a reformer party) as the ΔD regression: is the same in both the ΔD and the ΔS equations.

Table 4
Results of linear regression models

Model 9 ΔS
Party is in government (t)* There is a reform ( Table 4 (continued) Finally, to shed light on the consequences of reforming on office holding, we run logit models with parties' incumbent status in t + 1 used as a dependent variable. This aspect might be an even more important goal for parties than to maximize their seat shares. We construct our logit models in a similar fashion as we did the linear regression models, analysing first the effect of reforms in general (Models 1 and 2), then that of major reforms compared to all other cases (Models 3 and 4), and the effect of major and minor reforms separately, compared to the cases of no reforms (Models 5 and 6). The results are reported in Table 5.

Model 8 ΔS
In line with the negative effects presented in Table 4, the logit models in Table 5 show that reforms are not beneficial for reformers. Being a reformer party significantly harms the chances of being re-elected in almost all the models, whether there is a minor or major reform (except for the case of Model 4, referring to the effect of major reforms, where the relationship is insignificant). Moreover, unlike in our linear regression models, including vote shares in t + 1 does not affect the significance of the negative effect of being a reformer incumbent in Models 2 and 6.
We additionally tested in two aspects whether the inclusion of time could explain our results. First, former results suggest that transitional settings are characterized by extreme levels of uncertainty, therefore there could be a difference between reforms carried out in more established and less established democracies. We run a regression model predicting reformers' disproportionality gains including the years since democratization (Appendix 2). We have found no support for the assumption that the difference between the age of democracies is an important predictor regarding reformers' gains, whether we differentiate between recently democratized cases and older cases, or we use the years since democratization as a continuous variable.
Secondly, we considered the amount of time that passed between the reform and the next elections, as shorter time frames between reforms and elections might make it easier to predict the effect of a reform. According to our regression model (Appendix 3) that predicts reformers' disproportionality gains, the negative-insignificant  Table 4 relationship gives no support to the hypothesis that reforming in the election years is more beneficial. Actually, there is some indication that electoral reforms might be more harmful immediately before elections, but again, the relationship is insignificant.
To sum up, contrary to our main hypothesis, being a reformer party is not associated with future electoral success compared to leaving the electoral law intact. Reforming the electoral system when in office does not in general lead to a positive change in disproportionality, a higher seat share, nor to better chances for parties to remain in government. The results of the simplest descriptive statistics and Table 5 The results of logistic regressions estimating the effect of reforms on office holding Robust standard errors are in parentheses. Dependent variable: party is in government(t + 1) ***p < 0.01, **p < 0.05, *p < 0. Additionally, the type of reform (whether it is a major or minor modification), the age of democracy at the time of the reform, and the time between the reform and the next elections do not appear to be important predictors regarding the effect of the reform for reformer parties. That is, major modifications seem to be just as likely to be unprofitable for reformer parties as minor modifications, effects of modifications carried out immediately before an election are similar to the effects of those carried out during the first years of a cabinet, and parties in more established democracies conduct reforms very much like parties in young ones.

Discussion and conclusion
The rational choice theory predicts that, when shaping the rules of the game, electoral reformers are guided by their future interest. This implies that in moments of change in electoral institutions we can expect modifications that favour the incumbent parties. Contrary to this expectation, we have found that over the past decades, European electoral reforms have not served the interests of incumbents in terms of a positive change in their vote shares compared to seat shares, neither in terms of their future seat shares nor in their chances of being re-elected. Moreover, in many cases, the negative impact of the reform on incumbents' electoral results (on disproportionality, seat shares, and especially on re-election) was significant, reflecting that modifications in the electoral institutions actually favoured opposition parties. Major and minor reforms had similar impacts on incumbents' future electoral outcomes. The scale of reforms was not an important predictor in explaining their effect on incumbents' future electoral outcomes, suggesting that differentiating between major and minor reforms is not as fruitful in this regard as we suspected. The same applies for the age of democracy and the timing of the reform (up to one year preceding the next elections or earlier), which are insignificant predictors of reformer parties' future gains. The expectation that electoral reforms favour the incumbents relies on two basic assumptions. The first is that incumbent political parties aim to maximize their power, and the second is that they are able to effectively follow their self-interest. While such expectations are plausible, it is important to highlight that they are not unconditionally true, and in some cases, as we have noted, they certainly do not apply (see also Katz 2005, 63, on why incumbents change the rules at all). Here we discuss in more detail the most plausible explanations of the relationship we have identified and offer some tentative answers.
The first exception is the case of technocratic or caretaker governments, which do not generally seek to maximize their future power, although they sometimes carry out institutional reforms. Certainly, there are electoral reforms designed by non-partisan governments, nevertheless, as we have concentrated on parties and the partisan impact of reforms, in our sample there are no reforms carried out by nonpartisan governments, which means that technocratic or caretaker governments are not responsible for the results we have found.
Secondly, there are moments when parties may not want to maximize their seat shares. In the case of a severe crisis, for example, incumbent parties might not want to remain in power for another electoral cycle. However, in times of crisis, voters are likely to automatically punish the incumbents (Lewis-Beck and Stegmaier 2000), and parties have plenty of other non-winning strategies to choose without sacrificing their future chances. This means that the fact that parties do not intend to maximize their seat shares at all times does not explain why they should put their chances in the future elections at stake.
Thirdly, incumbents may not effectively control the majority of seats or the proportion of seats that is necessary to tailor a system to their needs. However, in these special cases-when governing coalitions require external support, coalition members cannot reach an agreement or when party discipline is low-we simply could not expect reforms to happen. In most of these cases, the opposition still cannot modify the electoral law without the support of governing parties, which means that this aspect is unlikely to be the general explanation for the negative correlation we have found. Thus, not controlling enough seats to modify the electoral system could better explain why certain reform processes fail, and it is not a satisfactory answer to why reforms implemented are harmful to the incumbents.
Fourthly, in some cases, governments change the electoral law to meet the requirements of judicial reviews or referendums. As Renwick's (2010) analysis of European electoral reforms shows, although these two kinds of reforms do happen, they are relatively rare compared to majority-imposed reforms. Therefore, although they are definitely part of the story, these exceptions are also unlikely to be the main explanation for the negative effect we have found.
Fifthly, while certain modifications might have a lasting effect on the electoral competition, as Katz argues (2005), the electoral advantage is only one aspect of politics, and decisions about electoral institutions are not isolated events. Incumbents might engage in elite pacts, or they might truly follow certain ideologies and democratic ideals when designing electoral institutions. Hence, instead of following their self-interest, they may aim at introducing a more proportional system by improving the representation of minorities or introducing gender quotas. Therefore, we cannot exclude the possibility that other goals (ideological or simply utilitarian) are even more important for some incumbents, and that, in exchange for other gains or for following their ideals, they may carry out electoral modifications that are not advantageous for them.
Lastly, assuming that reformers introduce modifications that favour themselves presupposes very detailed and correct information about the electorate's preferences and about the mechanisms that transform votes into seats. This means that incumbent actors should be completely informed about the present situation and the conditions characterizing a future situation; they should also have complete information and a full understanding of the functioning of the highly complex process that turns votes into seats. In our views, these assumptions are rather unrealistic due to the obvious lack of information that characterizes political processes. Without complete information, even if electoral institutions are designed to serve the interests of incumbents, they do not necessarily reach this aim. As Shvetsova (2003) argues, under incomplete information, even if reforms are "endogenously selected", their ex-post effect is often "exogenous". Uncertainty seems to be crucial in explaining why parties oppose reforms (Andrews and Jackman 2005;Pilet and Bol 2011), and it also seems an important factor in explaining why they implement reforms that prove to be harmful for them.
To sum up, we argue that these last two aspects, i.e., that incumbents follow alternative goals when reforming and miscalculations that stem from the lack of information, may be the most probable causes of the negative effect we have found. Both are ideas contrary to the heart of the rational choice theory, which leads us to reinforce Rahat's conclusion (2011) that, on its own, the rational choice approach may not be the best framework to investigate electoral reforms.
Therefore, the contribution of this paper is twofold. Empirically, it falsifies a hypothesis that is widely shared by both scholars and common wisdom, namely, that electoral reforms generally serve the interests of reformers. Theoretically, the paper suggests that the answer offered by the rational choice theory to explain electoral reforms is far from complete. This gives support to a conclusion similar to Rahat's (2011). However, we have to stress that we have analysed the consequences of reforms in terms of future gains counted in seat shares, seat-vote disproportionality, and future office holding, hence our analysis cannot claim anything specific about reformers' intentions. We can only say that if reformers' intention was to follow their interests, their success rates were poor.
We are aware that our negative results will not change deeply rooted beliefs and rational expectations about electoral reforms that generally favour the incumbents. Expecting strategic manipulations by the incumbents in times of electoral reforms certainly remains a plausible hypothesis whenever a reform happens. However, it needs to be emphasized that even if some specific reforms have undoubtedly been designed to favour the incumbents-and they succeeded-analysing a full sample of European electoral reforms over six decades and considering future seat shares, seat-vote disproportionality and office holding, we have not discovered any general pattern of successful strategic electioneering.

Declarations
Conflict of interest On behalf of all authors, the corresponding author states that there is no conflict of interest.
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