Electoral systems and the Sheriff of Nottingham

Abstract

Abundant research provides evidence that electoral systems have an impact on party system fragmentation. Taking up these findings, and adopting a dynamic approach, this article explores the effect of electoral refoms on electoral disproportionality. Specifically, it demonstrates that permissive changes in the electoral system improve the overall correspondence between vote-shares and seat-shares of parties. The explanation is that underrepresented parties in the parliament obtain more seats the more inclusive the electoral rules become. Likewise, disproportionality is higher after a restrictive electoral reform. The article employs my own data on electoral reforms from 59 established and new democracies between 1945 and 2010. Evidence is found not only that electoral reform has an effect on electoral disproportionality as measured with the Gallagher’s least squares index, but also that this impact is in turn conditioned by the size of the change in the rules and the level of democratic experience.

Keywords

Democratic age electoral disproportionality electoral reform least squares index

Introduction

Disproportionality is of course one of the major effects of electoral rules. For this reason, it has been at the core of an increasing literature which has measured it, has identified some of its main determinants, and has discussed its consequences for different political institutions such as party systems, parliaments or governments. In the last century, Douglas W. Rae (1971: 86), arguably one of the founding fathers of the science of electoral systems, emphasized the relevance of disproportionality as the main consequence of electoral institutions, graphically depicting them as the Sheriff of Nottingham, ‘apt to steal from the poor and give to the rich’. And, while most electoral systems share the same directional pattern of redistribution, there are still very important differences in its strength or degree (Rae, 1971: Ch. 9).

In the bulk of the literature on electoral systems, indices of disproportionality have been expressed as averages over a given number of elections, and their longitudinal evolution from one election to the other has been overlooked. Its fluctuations, however, are anything but negligible in countries that have reformed at least some of the components of the electoral system. For instance, disproportionality reached a historical minimum in the 1996 New Zealand general election by dropping from 18.19 percent down to 3.43 percent. This drastic reduction was largely caused by the adoption of a mixed-member proportional system (Vowles, 2008). The most striking contrasting case is the 1993 Polish parliamentary election. With 29 parties in the Parliament and a quite remarkable effective number of almost 11 legislative parties after 1991, the ruling centre-right parties passed a more restrictive electoral law (Benoit and Hayden, 2004). As a result, disproportionality reached a considerable 17.81 percent, that is, about 14 points more than two years before.

Do electoral system changes always generate the theoretically expected outcomes? While most electoral reforms might likely produce some consequences for disproportionality, under what circumstances do they have larger effects? The present article examines whether electoral reforms change the levels of disproportionality, and identifies which type of context tends to enlarge this impact. Although electoral reforms are messy processes and reformers seldom have a clear expectation about how they will change the structure of the party system (Pilet, 2007; Rahat, 2011; Renwick, 2010), I analyse whether electoral system changes influence the degree of disproportionality in the translation of votes into seats, and argue that the status of established democracies is particularly critical to shaping voters’ level of information about the functioning of the new electoral system but also to immunizing them against any sort of institutional change. Furthermore, I demonstrate that the size of the reform conditions its impact on the levels of disproportionality. This study is thus an attempt to fill some of the gaps observed in the literature by moving beyond country-specific explanations and considering evidence from 59 democracies with a total of 644 elections carried out under various rules and in different contexts. Moreover, my findings cross-validate previous analyses (e.g. Anckar, 1997; Lijphart, 1994) by adding new covariates (mainly, democratic age) and employing cross-sectional time-series models. In sum, I re-examine the issue of electoral disproportionality with new evidence and methods using a larger and richer dataset and more precise parametric estimations than previously.

The article is structured as follows. I discuss in the next section the analytical literature that defines and explains variations in electoral disproportionality, and elaborate a series of hypotheses that describe its main determinants. I then present my research design and conduct the corresponding empirical tests. Finally, section five concludes.

Effects of electoral reform on disproportionality

Electoral disproportionality has been defined by Lijphart as “the deviation of parties’ seat-shares from their vote-shares, [a] (…) prima facie (…) simple and straightforward concept’ (see also Taagepera and Shugart, 1989: 104). In other words, and following now Gallagher and Mitchell (2008: 602), ‘unless every party and independent candidate wins exactly the same share of the seats as they won of the votes –which of course never happens in real life – there exists a degree of disproportionality’. In contrast, Cox and Shugart (1991: 350) focus on a slightly different aspect, arguing that electoral disproportionality is related to ‘the extent to which different methods of PR favor large parties over small’.¹

Which factors determine electoral disproportionality? As expected, the permissiveness of the electoral system emerges as the most potentially important predictor among them. It is well established that electoral systems have an impact on the number of parties that receive votes or get into the Parliament (Cox, 1997; Duverger, 1954; Lijphart, 1994; Rae, 1971; Sartori, 1994; Taagepera and Shugart, 1989). However, the number of studies examining the effect of the rules of the game on electoral disproportionality is not very large. According to Gallagher (1991), there are five institutional sources of disproportionality: the electoral formula, the district magnitude, the legal thresholds, the possibility of malapportionment and the distribution of votes between the parties; while Cox and Shugart (1991) highlight the role played by compensatory seats, thresholds, malapportionment and the geographical distribution of party support. However, none of them empirically demonstrate these points.

Lijphart’s contribution (1994) constitutes one remarkable exception to this pattern when he finds that categorical ballots, explicit or implicit apparentement provisions, proportional formulas and large assemblies decrease electoral disproportionality. Moreover, and above all, he argues that the levels of electoral disproportionality respond very sensitively to the variations in the effective threshold. Likewise, district magnitude is recognized as the decisive factor by Taagepera and Shugart (1989: 124) and Carey and Hix (2011: 395). In contrast, Benoit (2000) finds evidence for a strong effect of the electoral formula. Finally, Anckar’s empirical analyses (1997) reveal that the Gallagher’s index of disproportionality is mainly affected by the district magnitude and the effective threshold. These findings are by no means surprising if we take into account the fact that the former concept gives rise to the latter indicator (Gallagher and Mitchell, 2008).

Building on these contributions, my expectation is that episodes of electoral system change will have an impact on levels of disproportionality. Evidence for the existence of this kind of relationship is not negligible (e.g. Anckar, 1997; Lijphart, 1994), but it is primarily focused on consolidated democracies. As it is well known at least since Duverger’s (1954) seminal contribution, the negative consequences of restrictive electoral rules on party system fragmentation result from two sorts of mechanisms. First, minor parties are typically awarded a much smaller seat-share than the share of votes they receive due to the operation of a mechanical effect (or proximal, according to Rae (1971: 67)). Second, electoral restrictiveness is expected to decrease the number of parties by generating incentives for strategic entry on the part of political entrepreneurs and tactical voting on the part of voters (Cox, 1997). Duverger (1954) and Rae (1971) coin the terms psychological and distal effects for these behavioural consequences of non-permissive electoral laws (primarily, a higher preference and, hence, propensity to vote for large parties).

The relationship between the number of parties and the levels of electoral disproportionality constitute the basis for my first hypothesis. Following Duverger, I argue that electoral reforms may provoke changes in the levels of disproportionality because they operate on party system fragmentation at the electoral and the legislative level through different means and, most importantly, at different points in time. The mechanical effect of electoral systems will decrease (increase) the effective number of parliamentary parties just after a restrictive (permissive) reform through the automatic application of the change in the electoral rules. In contrast, the psychological effect comes from the reactions of political actors to the expected consequences of the electoral reform. What I suggest is that this latter effect is slower than the former and, as a consequence, the levels of electoral disproportionality change. To sum up, I posit that levels of disproportionality will get higher (lower) in countries where a restrictive (permissive) electoral reform is adopted (H₁). Part of this impact stems from the fact that party system fragmentation is more elastic at the legislative rather than at the electoral level.

The second feature that is predicted to affect the levels of disproportionality is the size of the electoral reform. Consistent with the literature on electoral systems, I expect major rather than minor changes in the rules of the game to exercise a larger impact on the degree of deviation from perfect proportionality. It is well known that major reforms of national electoral systems remain rare (Katz, 2008; Nohlen, 1984). If one takes into account the fact that only major reforms can change the whole format of the party system, as I argue here, and that this type of institutional change needs the support of the party or coalition of parties in power to be passed, it is understandable that they are far from common. In contrast, mere fine-tuning of the components of the electoral system would give a smaller but more frequent possibility to politicians to change the levels of disproportionality even if they modified a decisive factor of the electoral rules such as the district magnitude. In short, I hypothesize that the effect of electoral reforms on the levels of disproportionality will be higher (lower) in case of major (minor) electoral system changes (H₂).

Finally, considerable differences between old and young democracies are expected, and not only with regard to the levels of disproportionality but also the impact of electoral reforms. Students in this field have argued that the crucial factor in observing political consequences of electoral laws is the availability of good information about the operation of the rules; and this kind of information is arguably worse in young democracies (Cox, 1997). Thus, the ability of citizens to recognize and act upon situations where voting for one’s sincere preference leads to a less desirable outcome – wasting their vote – heavily depends on the age of democracy (Horowitz and Browne, 2005). Voters’ (and elites’) inexperience with both the operation of the rules and the nature of party systems gives rise to expectations of a smaller psychological effect and, hence, a larger impact on disproportionality of electoral reforms in new democracies (Benoit, 2002). This predicted pattern would erode as the democracy matured (Duch and Palmer, 2002; Kostadinova, 2006; Tavits and Annus, 2006).

Yet, voting in a given election is on its own self-reinforcing (Dinas, 2010: 13). By repeating the act of voting, as van der Eijk and Franklin put it (2009: 179), citizens get locked into particular voting patterns. This idea of habit formation (Franklin, 2004) might hamper the psychological or distal effects of electoral reforms in old democracies. People under stable electoral rules acquire, over time, a ‘habit of voting’ (Franklin and Hobolt, 2011). Once such a habit has been obtained it is not easily lost, so the psychological effect of a change in electoral rules will be felt in the first instance only by those who have not yet acquired that habit – mostly younger voters. More importantly, voters in young democracies might be much more sensitive to electoral reforms because their process of partisan anchoring is not complete yet. This lack of habituation could counteract the aforementioned effect derived from voters’ (and elites’) political inexperience and poor information and leads to expect a smaller impact of electoral system change on disproportionality in non-established democracies.

In order to illustrate these points, let’s imagine, for example, two countries that adopt a more permissive electoral system. Countries A and B are young and consolidated democracies, respectively. As a consequence of the straightforward application of the new electoral rules, some parties – almost always the large ones – will be less ‘over-represented’ than they were, receiving a smaller proportion of seats than they did before the reform; and the opposite will hold for the small parties. This result will be common to both countries. But the dynamics at the electoral level will diverge to some extent in the two countries. While leaders of small parties and their potential supporters in both types of democracies will realize that the new rules provide incentives to run alone and vote for them, respectively, the time needed to elapse before they fully understand those new rules may be shorter in established democracies. That is why we should see a quicker adjustment of the behaviour of all political actors to the new electoral arrangements and, as a result, a smaller impact of institutional change on the levels of disproportionality in old democracies. However, this effect should be the opposite according to the potentially competing hypothesis of habituation. Citizens in established democracies are anchored to particular voting patterns. For this reason, we should expect lower rates of party-switching among them and, hence, a more considerable reduction in the levels of disproportionality as a result of permissive electoral system changes. Summing up, if the first explanation about the role of political information was right, electoral reforms should have their largest impact on electoral disproportionality in recently democratized countries; this effect would get smaller the older the democracy was (H_3a). In contrast, if partisan anchoring was the main mechanism driving the modifying effect of democratic experience, electoral reforms should have their smallest impact on electoral disproportionality in recently democratized countries; this effect would get larger the older the democracy was (H_3b).

Data and method

Sample

The dataset includes over 600 observations in 59 countries between 1945 and 2010, with more than 10 elections on average per country. The sample only includes democracies according to Przeworski’s (1991: 10) definition, and the cases analysed vary widely in the number of elections conducted and electoral reforms adopted, and the amount of variation that needs to be explained.² And while the levels of disproportionality are basically explained by the type of electoral system, the dispersion is a function of at least three factors: the average disproportionality, the number of elections and the frequency of electoral reforms. The structure of the data is cross-sectional time-series, but they are organized along elections rather than years. One could argue that electoral disproportionality should be studied with disaggregated data because national patterns of this phenomenon (as in party system fragmentation) derive from district-level outcomes (Cox, 1997). However, the lack of disaggregated data is not a problem for my research design as long as the mean disproportionality at the district level, contrary to what often happens with party system size, represents an upper bound for countrywide values of this variable. Hence, the difficulties in the calculation of the national party system fragmentation generated by the aggregation of the different local party systems do not exist here, and electoral disproportionality at the national level is at most equal to mean electoral disproportionality at the district level.

Measuring electoral disproportionality

My dependent variable is the change in the Gallagher’s index of disproportionality.³ The number of indices used for measuring electoral disproportionality has been remarkably high in comparative research, making its quantification a more difficult and controversial issue than for other standard political indicators (Lijphart, 1994: 57). Most of the indices share similar conceptual traits despite the quite different ways in which deviations have been operationalized. In either case, the canonical index in the literature is that of least squares (Gallagher, 1991). Not without reason, this index scored first in the evaluation of 19 measures of electoral disproportionality performed according to 12 criteria by Taagepera and Grofman (2003). Moreover, the fact that the least squares index takes into account both the total amount of vote–seat disparity and its size, together with my concern with how different electoral systems affect the distribution of seats among parties, leads me to choose it over the zoo of other indices.⁴

Defining electoral reforms

My main independent variable is the existence (or absence) of an electoral reform, and is coded in terms of its different types. I define an electoral reform as a change in the electoral system or group of laws ‘which govern the processes by which electoral preferences are articulated as votes and by which these votes are translated into distribution of governmental authority (typically parliamentary seats) among the competing political parties’ (Rae, 1971: 14; see also Massicotte et al., 2004). However, the identification of a case of electoral reform without specifying the direction in which the rules of the game change is clearly insufficient. That’s why I deem it necessary to distinguish between permissive and restrictive reforms, which are expected to respectively increase and decrease the ‘hospitality’ of the electoral system to small parties (Taagepera, 1998: 415). Given that the underrepresentation of these parties is the main source of disproportionality, making easier or more difficult their access to the assemblies and raising or reducing their seat-share should have an impact on it.

An electoral reform is coded as permissive (restrictive) in the following cases: first, the replacement of the formula by one that is more (less) ‘hospitable’ to small parties; second, a reduction (rise) in the number of districts; third, a rise (reduction) in the assembly size; fourth, a reduction (rise) in the legal threshold; fifth, the implementation (suppression) of an additional tier to allocate seats in PR systems; sixth, the rise (reduction) in the percentage of seats that are allocated in the PR tier in mixed systems; and seventh, the introduction (suppression) of linkage between tiers in multi-tier or mixed systems. Following Lijphart (1994), the change in the number of districts, the assembly size, the legal threshold or the percentage of seats allocated in the PR tier in mixed systems have to be of at least 20 percent to be considered as reforms. Further details of all the episodes of electoral reform identified and the sources used are given in an online appendix to this article.

Other independent variables⁵

First of all, I use Katz’s (2008: 58) stringent rules to limit the meaning of ‘major reforms of national electoral systems’ to the wholesale replacement of the electoral formula through which a strong president, or the chamber of parliament to which the national government is responsible, is elected. Accordingly, I consider major reforms those that concern the adoption of proportional, mixed-member or majoritarian systems when the electoral rules that were in use before the change belonged to the other two big families. However, the dichotomy proposed by Katz is a bit rough because it only takes into account changes in the electoral formula. For this reason, I opt for a differentiation based on changes of the district magnitude as well. District magnitude has been considered as ‘the decisive factor’ of electoral systems (Taagepera and Shugart, 1989: 124). In the same vein, substantial modifications in district magnitude are one of the criteria used by Jacobs and Leyenaar (2011) to define major electoral reforms. Specifically, following Carey and Hix (2011), a change in the number of seats per district is coded as relevant and, hence, involves a major reform if the mean district magnitude changes at least 20 percent and goes from lower or equal to eight to higher than eight seats; or the other way round. Otherwise, I code the reform as minor. As pointed out above, major reforms are expected to exacerbate the negative (positive) impact on electoral disproportionality of permissive (restrictive) reforms. In order to test this effect, I introduce two interactions, PermissiveReform*MajorReform and RestrictiveReform*MajorReform, whose coefficients should be negative and positive, respectively.

I also create the variable DemocraticAge, which is equal to the number of years since the transition to democracy.⁶ I do not have any clear expectation about the sign of the coefficient for this variable taken alone because it corresponds to the effect of this variable when there is no reform.⁷ Finally, I also include two additional interaction terms in the regression models, PermissiveReform*DemocraticAge and RestrictiveReform*DemocraticAge, in order to test the third hypotheses. I do not have clear expectations about these coefficients either. On the one hand, the lack of information in new democracies discussed above suggests that reforms will have a larger effect on electoral disproportionality there. Thus, the coefficients for the first of these interactions should be positive, whereas for the second should be negative. However, according to the habituation hypothesis, I expect a negative and a positive coefficient, respectively, for these interaction terms since I predict that a permissive (restrictive) reform will have a larger negative (positive) effect on electoral disproportionality as the democracy matures.

Estimation issues

As far as the estimation technique is concerned, I prefer to avoid employing panel-corrected standard errors (PCSEs). If I implemented them, I would implicitly assume that the observations are correlated across units, which seems inappropriate given the dependent variable under consideration: why would electoral disproportionality have to be correlated across countries? For this reason, I assume that electoral disproportionality is correlated within countries. Accordingly, the models are estimated using random effects models.⁸

There is a second technical reason for circumventing the use of PCSEs, and it relates to the asymptotic behaviour of the generalized least squares (GLSs) estimators. As is probably known, the use of PCSEs entails that the elements in the variances–covariances matrix are estimated across panels for each point in time. Therefore, they become efficient only as the repeated observations in time approach infinity. Beck and Katz (1995) consider T > 15 as the minimum acceptable threshold to achieve such properties. Unfortunately, the number of elections held since the abandonment of dictatorial rule is still small in new democracies. In contrast, the maximum-likelihood estimators used here achieve their asymptotic behaviour as the number of panels approaches infinity – in this sample, J = 59. This fact implies that there are sufficient units to achieve the desired behaviour (Gelman and Hill, 2007) and that PCSEs with GLSs estimators will be outperformed.

Finally, to estimate models with such a structure requires specific attention to time-series dependencies, i.e. autocorrelation, and possible problems of unit root (non-stationary). In order to account for the first problem, I have followed the strategy advocated by Beck and Katz (1995) and added a lagged dependent variable to the right-hand side of the equation. With regard to the latter, I refrain from using any solution because the plot of the data suggests that a process of unit root does not exist, and, moreover, I am already using a differentiated variable as dependent variable.

Findings

Before getting into the multivariate regression models, I tested whether I can infer the proposed association between electoral reform and changes in disproportionality using simple bivariate tools. I first computed the variation coefficient of electoral disproportionality for old and new democracies and plotted these against the number of electoral reforms per election for the period 1945–2010. Figure 1 shows the result and adds a line for the predicted values of an OLS regression of the dispersion in Gallagher’s least squares index on the institutional instability measure. This simple bivariate model returns a positive value for the number of reforms per election that is statistically significant at the 5 percent level. This finding is consistent with the first hypothesis: despite substantial variation around the regression line, disproportionality tends to have varied more in countries with a high number of electoral reforms.

Figure 1.

Dispersion in electoral disproportionality and electoral reforms.

Table 1 includes the descriptive statistics of the variables used and Table 2 displays the results of five econometric models with changes in Gallagher’s index of disproportionality.⁹ The most general finding from the specifications is that electoral reforms explain pretty well the fluctuations observed in the levels of electoral disproportionality. This overall impression bolsters the view of electoral engineers emphasizing the role of institutional change in accounting for variations in the degree of correspondence between the vote-share and seat-share of parties. Finally, the R-squared are not very high given the inclusion of a lagged dependent variable in the right-hand side of the regression equation. However, the low R² is a result of using changes in disproportionality as dependent variable and, hence, is not particularly indicative of a poor goodness of fit of the model.

Table 1.

Descriptive statistics.

Variable	Mean	SD	N
Δ Disproportionality	–0.12	3.89	644
Permissive reform	0.07	0.27	644
Restrictive reform	0.05	0.23	644
Major reform	0.04	0.21	644
Years of democracy (logged)	3.30	1.23	644
Effective number of electoral parties	4.13	1.79	644
Years after reform (logged)	1.36	0.94	644

Table 2.

Effects of electoral reforms on electoral disproportionality, new and established democracies (1945-2010).

	Model 1	Model 2	Model 3	Model 4	Model 5
Δ Disprop. (t-1)	−0.378***	−0.381***	−0.377***	−0.383***	−0.384***
	(0.034)	(0.034)	(0.034)	(0.034)	(0.034)
Permissive Reform	−3.117***	−2.753***	−2.098***	−2.884***	−5.992***
	(0.511)	(0.557)	(0.596)	(0.516)	(1.621)
Restrictive Reform	1.912***	2.326***	1.046	2.073***	−1.711
	(0.662)	(0.707)	(0.799)	(0.660)	(2.176)
Major Reform		−1.264	−1.625
		(0.769)	(1.867)
Permissive*Major			−1.881
			(2.152)
Restrictive*Major			4.007*
			(2.290)
Democratic Age(logged)				0.379***	0.241
				(0.138)	(0.148)
Permissive*Democracy					1.024**
					(0.511)
Restrictive*Democracy					1.209*
					(0.668)
ENEP	−0.089	−0.078	−0.062	−0.075	−0.097
	(0.078)	(0.078)	(0.078)	(0.078)	(0.078)
Constant	0.265	0.227	0.164	−1.150*	−0.565
	(0.348)	(0.348)	(0.346)	(0.623)	(0.659)

N (Observations)	585	585	585	585	585
J (Countries)	59	59	59	59	59
R²	0.23	0.23	0.25	0.24	0.25

Note: The dependent variable is the change in Gallagher’s index of disproportionality; all models are random effects with standard errors in parentheses; *** p<0.01, ** p<0.05, * p<0.1 (two-tailed tests).

More in depth, I receive broad support for the proposition that a permissive reform has a negative and statistically significant effect on electoral disproportionality (p<0.01). My models also yield a statistically significant positive effect of restrictive reforms on electoral disproportionality. In contrast to permissive modifications of the rules of the game, the coefficient for restrictive electoral system changes loses statistical significance in the interactive models. What do these estimates mean in substantive terms? Taking the coefficients from models 1, 2 and 4, a permissive reform decreases electoral disproportionality by about 3 points. This effect is in turn slightly less pronounced if we consider that the estimated coefficients for restrictive reforms vary from 1.912 to 2.326. Hence, as in Shugart’s (2008) work, I find that the impact of a switch from majoritarian to proportional is bigger than the other way round. In either case, I conclude that electoral engineering substantially influences levels of disproportionality.

My estimates partially support hypothesis 2 that predicts a positive association between the size of the reform and its impact on electoral disproportionality. The coefficient estimated for the interaction term Restrictive*Major has the expected negative sign and is statistically significant at the 10 percent level. In contrast, I do not obtain a statistically significant coefficient for the other interaction term (Permissive*Major). Taking the estimated effect for major restrictive reforms, an increase in the size of the institutional change increases electoral disproportionality by about 4 percent.¹⁰ To illustrate it, model 3 predicts electoral disproportionality in France in 1988 to increase slightly more than 4 percentage points after the re-introduction of the majority run-off system in 1986; and, in fact, it did because it went from 7.23 percentage points in 1986 to 11.84 percentage points two years later.

Model 5 in Table 2 shows the results for the third hypotheses. Briefly, this last specification demonstrates the existence of clear differences between old and new democracies. However, simply breaking down the sampled countries in these two groups is not enough to demonstrate the impact of democratic age on the levels of electoral disproportionality. In this sense, the coefficient of DemocraticAge is positive and statistically significant in Model 4. This is interesting because it means that consolidated democracies do not create by themselves less electoral disproportionality once I control for electoral system change and continuity. The absence of conditions favourable to electoral proportionality in new democracies (like a high number of lists) might be either overridden by the presence of permissive reforms there or concealed by the high correlation between democratic age and the emergence of new small parties.

Considering the interactions now in detail, I find some initial support for the idea that the effect of permissive reforms is higher in recently democratized countries. In this sense, the coefficient of Permissive is negative and statistically significant in Model 5 (p<0.01), indicating that permissive reforms in contexts of non-established democracies have relatively weak effects on electoral disproportionality. However, this seems not to be particularly robust, as the interaction term fails to reach statistical significance. Moreover, my findings for restrictive reforms are in line with the habituation hypothesis. First of all, this type of institutional change seems not to be consequential for electoral disproportionality in new democracies. Second, the effect of restrictive reforms increases with the number of years under democracy. Hence, this latter finding returns at least partial evidence in favour of the partisan anchoring hypothesis, according to which electoral reform leads to more variation in the levels of disproportionality in old democracies. Nevertheless, these in principle favourable results will have to be confirmed below by calculating substantively meaningful marginal effects and standard errors.

In effect, according to Brambor et al. (2006), the statistical significance of an interaction term cannot be evaluated through the p-value shown in the regression table. For this reason, it is necessary to graphically illustrate the marginal effect of my main independent variable (that is, electoral reform) on the levels of disproportionality over time. Figure 2 plots the conditional effect of the different types of reforms on the levels of disproportionality for a range of values of the modifying variable (i.e. the length of democratic rule when the reform is adopted). The graph on the left shows that the expected marginal effect of a permissive reform in a recently democratized country (that is, when the number of years of democracy is equal to zero) is huge (almost six percentage points) and negative. However, this effect, as predicted by the informational hypothesis, tends to drop towards zero as democracy matures, and does not produce any statistically significant change in the levels of disproportionality after about 100 years of democracy.¹¹

Figure 2.

Marginal effect of electoral reform on electoral disproportionality over democracy.

If we now turn to restrictive reforms, the graph on the right supports the habituation hypothesis that expects a positive association between the effect of this type of institutional change and the number of years under democracy. As predicted, the adoption of these new electoral rules does not significantly increase the levels of disproportionality when the reform takes place in the first democratic decades. Nevertheless, it can also be seen that restrictive changes in the rules of the game do significantly increase electoral disproportionality when the democracy has been in place long enough. Hence, this graph demonstrates that the extent to which the impact of constraining reforms is actually translated into higher levels of disproportionality depends on the presence of a large number of citizens locked into voting patterns typical of established democracies.

How can we explain these fluctuations in the levels of disproportionality after an electoral reform? In order to answer this question, I present some additional models in Table 3 showing that the link between electoral reforms and changes in disproportionality is caused by the different time of reaction the mechanical and the psychological effects have after a change in the rules of the game. The dependent variable is the change in index of disproportionality again and the main independent variables are two interactions between the reforms and the number of elections (logged) after them. The reported results demonstrate that the adoption of a new electoral system immediately affects the mechanical translation of votes into seats, but actors (i.e. the psychological effect) need some time to find out how the new rules work and to adapt their behaviours to this new institutional environment. Hence, what is crucial in a reform process is what happens in the immediately next election after it. In fact, the statistical significance of all the constitutive terms of the interactions regarding reforms suggest that it is only at that moment (i.e. when Time=0) that their effect on disproportionality is noticeable. Beyond that point in time, none of these institutional changes has an effect different from zero at the 0.05 level.¹²

Table 3.

Effects of electoral reforms on electoral disproportionality over time, new and established democracies (1945-2010).

	Model 1	Model 2	Model 3	Model 4	Model 5
Δ Disprop. (t-1)	−0.399***	−0.402***	−0.401***	−0.409***	−0.414***
	(0.035)	(0.035)	(0.035)	(0.035)	(0.034)
Time after the Reform (logged)	0.503***	0.562***	0.181	0.541***	0.614**
	(0.169)	(0.182)	(0.283)	(0.172)	(0.260)
Permissive Reform		−0.622*	−2.077***
		(0.354)	(0.698)
Restrictive Reform		0.888*	1.678**
		(0.454)	(0.808)
Permissive*Time			1.025***
			(0.371)
Restrictive*Time			−1.325**
			(0.598)
Major Permissive Reform				−1.441***	−4.654***
				(0.492)	(1.195)
Major Restrictive Reform				1.668***	5.678***
				(0.581)	(1.707)
Major Permissive*Time					2.075***
					(0.678)
Major Restrictive*Time					−3.328**
					(1.309)
ENEP	−0.036	−0.081	−0.092	−0.072	−0.073
	(0.087)	(0.087)	(0.080)	(0.088)	(0.089)
Constant	−0.888*	−0.712	0.035	−0.775	−1.176*
	(0.494)	(0.559)	(0.679)	(0.498)	(0.659)
N (Observations)	585	585	585	585	585
J (Countries)	59	59	59	59	59
R²	0.25	0.18	0.22	0.20	0.23

Conclusion

Do electoral reforms in the inter-party dimension always have the theoretically expected impact on the degree of disproportionality in the translation of votes into seats? It is well established that electoral systems evidently favour larger and more concentrated social groups at the expense of smaller and more dispersed ones. In other words, the rules of the game generally help parties that are already rich in votes, as the Sheriff of Nottingham favoured individuals already rich in power and wealth. Although the variables explaining party system fragmentation have been investigated extensively, considerably less is known about the determinants of electoral disproportionality. And this gap is particularly surprising giving the ubiquity of this phenomenon across different electoral systems. In fact, the effects of electoral laws upon the parliamentary representation of political parties behave as the Matthew’s Principle, producing a persistent bias in favour of strong and against weak competitors (Rae, 1971: 134).

Taking advantage of the relatively widespread implementation of electoral reforms during recent decades, and their huge heterogeneity in terms of the components of the rules that were modified and the countries in which they were adopted, I have shown in this article that changes in the features of the electoral systems generate fluctuations in the disproportionality of electoral outcomes. In particular, while permissive electoral system changes improve the overall correspondence between the vote-share and the seat-share that obtain each party, restrictive reforms worsen it. In general, the former have a stronger effect than the latter. These results are driven by what happens in the first election after the reform.

This study also shows the modifying effect of the size of the electoral reform and the number of years of democratic rule. Therefore, my article questions the validity of analyses that treat the effect of institutional change as essentially linear. Specifically, I have first provided evidence that only major restrictive reforms increase the levels of disproportionality. My findings, however, are less clear for major permissive reforms: while the estimated coefficient has the expected sign, it is not significant at the traditional levels of statistical confidence.

One of the main results of the article lies in the interaction between electoral reforms and democratic age. When permissive reforms are adopted in young democracies, the combination of the lack of information about the exact working of the new rules and the relative weakness of parties render voters less likely to electorally react to the new incentives generated by them. However, this pattern considerably changes over time. For example, in countries which have been democratic for more than 100 years, citizens, elites or both immediately update their behaviour after a permissive reform and subsequently minimize the effect of the electoral system change.

Building on the ‘habit of voting’ theory, I have also found that the positive impact of restrictive reforms on electoral disproportionality is primarily observed in established democracies. Hence, this type of institutional change widens the gap between the vote-share and seat-share of parties when it is adopted in consolidated democracies but not when the country in question has recently become democratic. Moreover, these results suggest that reforms in new democracies that should theoretically increase the disproportionality of the rules of the game will fail to achieve it.

Obviously, some of these unusual electoral system effects that we see in new democracies are not necessarily a direct result of their ‘newness’. Young democracies maintain one main characteristic –such as poorly established party systems – that distinguish them from most consolidated democracies. But there are many other features, for example high levels of social turmoil, that are also characteristic of new democracies. In fact, it is reasonable to think that institutions can only shape politics and, hence, really work in the direction theory predicts when society is quite stable. And even though social turmoil is more common in new democracies, we see periods of ‘social unrest’ in some consolidated democracies as well. Thus, should the ‘new democracy’ category be extended to old democracies that have experienced periods of important political change? Although I do not have a clear answer to this question, the expected impact on disproportionality of the major (and restrictive) reforms of Japan and Italy in the early 1990s leads me to think that the key variable is the age of democracy. However, this is an element of reflection that perhaps deserves more attention in the future.

The relevance of these results seems to contradict those who claim, as Shugart (2008: 51) did, ‘that the agenda of proportionality and number of parties is largely closed (…)’ and that there would only be room for some fine-tuning. In contrast, I think that my theoretical discussion and empirical evidence open up a further research agenda on how these episodes of electoral engineering are linked to fluctuations in the levels of disproportionality. Besides its intrinsic paramount relevance for the field of electoral systems, the establishment of the conditions that affect electoral disproportionality has important practical implications. For instance, and just to mention a few of them, the emergence of inaccuracies in the transformation of votes into seat-shares can entail the election of legislators that lack ideological congruence with their constituents (e.g. Golder and Stramski, 2010). Further, if rules repeatedly fail to produce a close correspondence between the numbers of votes and seats that obtain each party, considerable segments of citizens may stop participating in electoral politics (Franklin, 2004), feel less politically efficacious (Banducci and Karp, 2009) or simply experience less satisfaction with the democratic process (Listhaug et al., 2009). And there is also the stream of arguments which have been used in the normative debates on the advantages and disadvantages of electoral disproportionality. In this sense, while some scholars consider that proportionality is a desirable goal of electoral systems and a major criterion by which they should be judged (Lijphart, 1994), others have been traditionally emphasizing the convenience of hampering it (Hermens, 1941). In either case, my findings are good news from the point of view of normative democratic theory because they suggest that changes at the institutional level can have an impact on the levels of electoral disproportionality.

Finally, the findings presented in this article are not in and of themselves sufficient to provide a robust theory of the causes of changes in electoral disproportionality. Even reforms that have been designed to constrain the overall permissiveness of the electoral rules, such as many of the adopted in the last two decades in Israel, have not managed to produce the desired outcome. Hence, these examples highlight the inherent limitations of electoral engineers in fulfilling their expectations on institutional change. Moreover, voter coordination is more difficult when a high number of parties contest elections (Cox, 1997), so that what looks like erratic behaviour on the part of voters may really be driven by the actions of parties (Tavits and Annus, 2006). In this sense, what I have not identified yet is the causal effect of overcrowded ballots on electoral disproportionality. Additionally, without a way to randomly assign electoral reform, its effect cannot be distinguished from the potential – if any – impact of other variables leading to its adoption. Thus, future comparative studies are necessary in order to clearly specify the causal path between electoral reforms and levels of disproportionality and properly address this potential problem of endogeneity.

Footnotes

Acknowledgements

An earlier version of this article was presented at the European University Institute Workshop on ‘Politics and Representation’ (2011) and at the Spanish Political Science Association Conference (2011). I thank the participants at these two fora as well as Catherine de Vries, Mark Franklin, Peter Mair, José Ramón Montero and Pablo Simón for helpful comments and suggestions.

Funding

This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors.

Notes

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Electoral systems and the Sheriff of Nottingham

Abstract

Keywords

Introduction

Effects of electoral reform on disproportionality

Data and method

Sample

Measuring electoral disproportionality

Defining electoral reforms

Other independent variables 5

Estimation issues

Findings

Conclusion

Footnotes

Acknowledgements

Funding

Notes

References

Other independent variables⁵