Electoral Systems and Strategic Learning in Spain and Portugal? The Use of Multilevel models

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1 Electoral Systems and Strategic Learning in Spain and Portugal? The Use of Multilevel models Patrick Vander Weyden & Bart Meuleman Paper presented at the 58th Political Studies Association Annual Conference Democracy, Governance and Conflict: Dilemmas of Theory and Practice 1-3 April 008 Swansea University Patrick Vander Weyden Address: University of Ghent, Faculty of Poltical and Social Sciences, Department of Political Science, Universiteitstraat 8, 9000 Gent, Belgium Bart Meuleman Address : OE Centrum voor Sociologisch Onderzoek, Parkstraat 45 - bus 3601, 3000 Leuven, Belgium 1

2 Abstract This paper examines the interaction effect between time (successive elections) and district magnitude on three dependent variables: disproportionality, the number of participating parties (as an indicator of strategic elite behaviour) and the effective number of electoral district parties (as an indicator of strategic voter behaviour). It is assumed that when implementing a new electoral system both voters and party elites must learn to experience the functioning of the electoral system over time; it is only with the passage of time that they will behave strategically. If the hypothesis holds, this also means that the effects of the electoral system should vary over time. Our hypotheses are tested by using multilevel models. Our analyses were carried out at district level and two country cases (Spain and Portugal) were carefully selected. There seems to be an independent time-effect on all our three dependent variables. However, strategic learning as a result of mechanical effects of the electoral system at the district level seems to be absent. Keywords: electoral systems, strategic learning, strategic voting, multilevel models, time. Word count: 7950

3 INTRODUCTION Besides proposing the effect of the electoral formula as an explanation for the disproportional nature of certain electoral systems and number of parties in the party system, there is a tendency within the literature, following Taagepera and Shugart (Taagepera and Shugart, 1989), to regard district magnitude as the most important feature of an electoral system when accounting for the above-mentioned phenomena (Cox, 1997; Gallagher, 1991; Ordeshook and Shvetsova, 1994). Thus, the hypothesis that the smaller the district magnitude, the greater the disproportionality and the fewer the number of parties has been repeatedly tested empirically within the field of research (e.g. Rae, 1971; Taagepera and Shugart, 1989; Liphart, 1994). The effect of time in research on the effects of electoral systems is, however, discussed only marginally. Yet, a good case can be made out for including the variable of time in the analyses. It can be assumed that voters as well as party elites (whether consciously or unconsciously) need to go through a learning process if they are to grasp the full consequences of a new electoral system. As a result of experiences with large mechanical effects (measured, for example, through disproportionality) of the electoral system in the first election under a new electoral system, it could be supposed that both voters and party elites will behave strategically (psychological effects) in the next elections. One can expect the disproportionality and number of parties to be particularly high during the first elections in small districts and to decrease in subsequent elections because party elites and voters alike will behave strategically due to experiences with the strong mechanical effect of the electoral system. Party elites can achieve this by collaborating and submitting lists together. Small parties could also consider not submitting any lists in smaller districts as the effort is out of proportion to the chance for success (strategic party elite behaviour). By becoming acquainted with strong mechanical effects in the first election(s), voters can (re)direct their votes to the most relevant parties (strategic voting behaviour in a broad sense). In other words, the effect of district magnitude should be greater in later election(s) than in first election(s) (hypothesis to be tested). If we believe that there is such a thing as a learning process about the effect of the electoral system and that strategic behaviour is a consequence of a learning and experience process, then this also implies that the effects of electoral systems are not the same in all election periods. That is why it is meaningful and necessary to introduce time as a variable and test this hypothesis. Most analyses of the effects of electoral systems consider the effects as a static datum. After an electoral system has been implemented, one apparently expects the effects to be the same in the first elections as in later ones. This does not mean that the problem is not theoretically recognized. A few authors (Cox, 1997, ; Liphart, 1994, 88; Reed, 1990; Shugart, 199; Taagepera and Shugart, 1989, 65) are aware that the implementation of (new) electoral systems involves a learning process. Nevertheless, the empirical testing of this learning process has until now been left unexecuted. Even if one is conscious of a learning process, one assumes that this learning process occurs only during the first election(s) and that afterwards a kind of stabilization of the effect of the electoral system takes place. Liphart, for example, compares the latest election results under an old electoral system with the results of the second and third elections under a new system in one single country. He uses this method of working to measure the impact of a new electoral system (Liphart, 1994, 78-94). Although this is a very creditable attempt to measure the effect of a new electoral system, it remains a 3

4 fairly static measurement that does not reflect the evolution of effects at various election periods. HYPOTHESES In this paper, we will test the medium range psychological (strategic) effects of electoral systems (district magnitude) on party systems (number of parties). The basic hypothesis can be formulated as follows: the stronger the functioning of the electoral system (the smaller the district magnitude), the greater the disproportionality and the fewer the number of parties. By a strong electoral system we mean a system with (very) small district magnitudes, M (number of seats to be distributed per district). Also electoral formulas can determine the strength of the electoral system. These formulas will be left out of the scope of this paper. Through a careful case selection we hope to be able to keep the possible effect of the electoral formula constant (see further on). When we include the time factor (and thus medium range effects) in the analysis, our basis hypothesis can be further refined into the following three subhypotheses: 1. The smaller the district magnitude, the greater the disproportionality. This effect is the largest in the first elections and decreases in subsequent elections. This effect of time (number of elections) should be the strongest in the smallest districts. Measuring the pure mechanical effect of electoral systems is far from easy because of the endogeneity of the mechanical effect as Benoit illustrated. Party elites and voters can anticipate the mechanical effect. Measuring the mechanical effect by using the number of parties winning seats or disproportionality indicators as dependent variables are overestimating the mechanical effect (Benoit, 00). Thus measuring disproportionality means measuring psychological as well as mechanical effects of electoral systems. By introducing time and variations over time in our analysis we use an alternative way to disentangle the endogeneity of the mechanical and psychological effects. However, using indicators of disproportionality, is still a rough estimate of psychological effects. To disentangle strategic behaviour of party elites and voters we will test two additional hypotheses.. The smaller the district magnitude (and thus the larger the mechanical effects), the more strategically party elites will behave. In other words, we can expect party elites to offer fewer labels to voters (number of participating parties, see further operationalization). This strategic elite behaviour should become stronger as the number of elections increases (learning process). 3. The same reasoning can be applied to strategic voting behaviour. The smaller the district magnitude, the more strategically voters will behave. In other words, we can expect voters to concentrate their votes on the most relevant party labels, which should reduce the effective number of electoral parties (see further operationalization). This strategic voter behaviour should become stronger as the number of elections increases (learning process). LEVEL OF ANALYSIS An important point of discussion in research on the effects of electoral systems is the level of analysis. Duverger s dependent variable, the number of parties, is a variable at national system level (Duverger, 1951 [1976]). However, the mechanical as well as the psychological effects occur first and foremost at district level. At district level, votes are converted into seats and it is at this level that strategic or non-strategic voting behaviour and strategic party elite behaviour in relation to the electoral system is relevant to an important extent. Research in the line of Duverger has mainly focussed on the national level by, for instance, analyzing the relation of average district magnitude to national party systems (Blais and Carty, 1991; 4

5 Bogdanor and Butler, 1983; Coppedge, 1997; Farrell, 1997; Liphart, 1994; Taagepera and Shugart, 1989). Although theoretically the problem is acknowledged (Benoit, 001; Benoit, 00; Cox, 1997; Leys, 1959; Sartori, 1976; Sartori, 1994; Taagepera and Shugart, 1989), only very few studies work with electoral district data (Cox, 1997; Shugart, 1985; Gschwend, 007). Yet, by carrying out analyses at district level, we gain a theoretically and methodologically more accurate insight into the psychological, strategic functioning of electoral systems (electoral formula and district magnitude). Moreover, interfering variables, which are beyond the scope of the definition of electoral systems but which can play a role when analyses are conducted at national level, are excluded. An example of such an interfering variable is malapportionment. Malapportionment occurs when geographical units (electoral districts) are allotted a share of seats not equal to their share of the population (Monroe, 1994). Since all mechanical effects of electoral systems occur in the first place at the district level, especially in systems with one primary district (like it is in the case of Spain and Portugal), logically, psychological consequences of the mechanical effect should be observed at the district level. Take for example two districts, district A with magnitude equal to and district B with magnitude equal to 40. The mechanical effect of the electoral system will be strong in district A and will be very weak in B. As a consequence, it will be easier for political parties to gain a seat in district B compared to district A, keeping all other variables equal. Logically we can expect that smaller political parties are strategically more interested to present a list in district B, since the chance to win a seat is higher in district B. Moreover, voters in district A should know, if they vote strategically as a function of the mechanical effect of the electoral system, that only two seats are distributed and that voting for a prospectless smaller party will be a wasted vote. So voters in smaller districts are expected to vote more strategically than in districts with higher district magnitudes. Finally both district psychological effects should result in a lower number of parties in districts with a small district magnitude compared to districts with a high number of seats to be distributed. That is basically what we mean with the psychological district effects of electoral systems. It is the effect on voters and party elites at district level as a consequence of mechanical effects of the electoral system at district level. Of course national system variables can cause psychological pressure and strategic behavior on voters and party elites, but we do not consider these national system variables as direct consequence of the mechanical effect of the electoral systems. In other words, our definition of strategic voting (psychological effects) is restricted to the immediate impact of the mechanical effects of electoral systems. The level of analysis we will employ in this contribution is the district level. This means that it is at the district level that the operationalization of our variables, case selection and data collection will take place. OPERATIONALIZATION OF VARIABLES DISTRICT MAGNITUDE The electoral systems variable is operationalized through one feature of electoral systems, viz. district magnitude, M. District magnitude is defined as the number of seats to be distributed per district. District magnitude, M, will further be transformed as the logarithm of M, log(m). In all our analyses, we will use this logarithm of M to refer to district magnitude. The reason for this transformation is that in the statistical models we use, the relation between dependent and independent variables is supposed to be linear (assumption of linearity). The degree of change in the dependent variable produced by changes in the independent variables is assumed not to vary with the value of the independent variable. However, exploratory analyses pointed out that the relation between the dependent variables we are planning to use 5

6 (LSq, DNv and p see below) and district magnitude is not linear, but rather exponential in nature. This problem was tackled by taking the logarithm of district magnitude. The relation between the logarithm of district magnitude and our dependent variables indeed turns out to be linear. By making use of the natural logarithm of district magnitude the assumption of linearity is satisfied. Using the logarithm of district magnitude is in line with other research results (Benoit, 00; Ordeshook and Shvetsova, 1994; Taagepera and Shugart, 1989). NUMBER OF PARTIES In recent years, academic descriptions of party systems have been emphasizing the calculation of the relative share of national votes (Laakso and Taagepera, 1979), following Rae s fractionalization index (Rae 1971). Especially in comparative studies of electoral system effects on party systems (see e.g. Taagepera, 1989; Liphart, 1994; Cox, 1997) but also in studies describing and explaining party systems in specific cases (Chhibber and Kollman, 1998; Moser, 1999; Olsen, 1998), the effective number of parties is used as standard measure. The effective number of electoral parties is calculated as follows: N = V n i 1 V with Vi representing party i s relative share of national votes. Since we will make our calculations mainly at district level, we will refer to the effective number of electoral district parties with the term DN V. Basically, this method of calculating boils down to weighing parties by means of their own relative electoral importance. i Besides the effective number of electoral district parties measure, we will include the absolute number of participating parties (p) as a dependent variable, following other authors (Ordeshook and Shvetsova, 1994). We will, however, retain only the total absolute number of parties and not employ any other measures, such as e.g. counting only those participating parties who won more than 1% of the vote. The reason is theoretical. If we want to know about the strategic behaviour of party elites as a function of the electoral system, then all parties must be counted. Not counting the smallest parties would exclude any strategic behaviour of precisely those parties of whom such behaviour could be expected. DISPROPORTIONALITY The two most commonly used disproportionality measures are the Loosemore-Hanby index (D-index) and the Least Square index. For the sake of comparability of our results with existing research, we have to make a choice between the Loosemore-Hanby index and the LSq-index. The main drawback of the Loosemore-Hanby index is that it overestimates disproportionality in elections with a lot of (small) parties (Liphart, 1994, 60). As we will indicate further on in this paragraph about case selection and data collection, one of our basic assumptions is that when analyzing data we start from full election results. This means that small parties will be kept as small parties; they will not be included in the other category. This also requires frequently involving a great many (small) parties in the analyses. The Loosemore-Hanby index (notation: D-index), however, is disseminated fairly generally within 6

7 the field, although in the last decade the LSq-index has become more popular in scientific circles. As mentioned before, since we work with full data, the D-index leads to distortions if there are a lot of parties involved. This is why we decide in favour of the LSq-index. Furthermore, as regards our data, the relationship between the LSq-index and the D-index is very strong with a correlation coefficient of 0,939 (statistically significant at <0,01). The maor advantage of the LSq-index is also that it weighs the differences. Big vote-seat differences outweigh smaller ones. Thus, we opt for the Least Square index (LSq). This index squares the percentages of the vote-seat differences for each party and then adds up these squared vote-seat differences. This sum is divided by and from this number the root is finally extracted (Gallagher, 1991, 40) or: LSq = ( v s ) i i CASE SELECTION AND DATA COLLECTION Before going more deeply into the specific selection of cases, it must be made clear that we can only select those countries that have a fairly stable electoral system. This is a prerequisite if we are to examine time (learning) effects. Moreover, by excluding those cases that changed their electoral system, we can partly control the problem of endogeneity. When certain countries change their electoral system, this is always done by the existing party system and parties. In other words, the electoral system can be considered as a dependent variable of the existing party system. By merely selecting those cases that have an unchanged electoral system, we partially exclude the impact of a particular party system on the choice of electoral system. If we select countries with a stable electoral system, the next question is of course how many elections we need to test our hypothesis. To analyse an evolution and learning process, we decided that at least four elections are necessary. Less than four elections would imply that a non-linear evolution, which is the case in some of our results (see further), would be difficult to detect. We can further try to reduce the problem of endogeneity by selecting new democracies. New democracies are understood to mean countries that organize elections for the first time after a period of non-democratic regime, where several parties are able to take part in free elections and all seats to be distributed during the elections are engaged in the battle. Still, the problem of endogeneity cannot be solved completely because in order to implement new democratic electoral legislation an embryonic pre-democratic party system may already have left its mark on the choice of a new electoral system. An additional criterion for the selection of cases was that we had better select countries with a comparable electoral formula. Since we included ust district magnitude as a feature and are thus mainly interested in the influence of district magnitude, a pure analysis seems only possible if the electoral formula is kept constant. This is especially important if we are to compare countries, for within the country cases the electoral formula remains constant. The reason for this is that in most countries the same electoral formula is used in all districts. On the basis of the above criteria, it was hard to find countries which kept there electoral system over more than four elections. Most post-communist countries changed their electoral 7

8 system. Although electoral systems were up till very recently stable institutions in traditional European democracies, newer democracies tend to change their electoral institutions more often. Trying to find other countries worldwide which meet our criteria lead to the same conclusion. Either they changed their electoral system or either not enough elections were conducted under the new rules. Taken into account this empirical reality and to stand by our selection criteria, we selected Spain and Portugal as country cases. Both of these countries use the D Hondt system as electoral formula. Spain had its first democratic elections, after a non-democratic period, in 1977 and Portugal in The two countries have a relatively stable electoral system with only marginal adustments on district magnitude. In addition, by selecting districts in Spain and Portugal, there is a fairly wide variation on the independent variable, district magnitude. Spain comprises 5 districts (provinces), of which 58 percent of the district magnitudes are smaller or equal to 5, while in Portugal this is the case for merely 15 percent out of the 0 districts. The median district magnitude for Spain is 5 and for Portugal it is 7. Less important but worth mentioning is that both countries use a closed party list system. The next important question is of course whether our cases Spain and Portugal are relevant cases to explore our hypothesis. This question lead us to the possibility of strategic voting in systems of proportional representation. Irwin and Van Holsteyn showed in their work that voters, even in hyper proportional systems like the Netherlands, consider strategic voting under certain circumstances (Irwin and Van Holsteyn, 003). Also Gschwend finds in his different studies evidence for strategic voting in PR systems (Gschwend, 004). Coming back to our two country cases, Gunther finds overwhelming evidence, using survey data, that because of the small district magnitude in Spain, Spanish voters vote strategically (Gunther, 1989, ). Although to a lesser extent, recent research shows that in Portugal too, voters seem to vote strategically as consequence of district magnitude (Gschwend, 007). The question is not whether there is strategic electoral behaviour (as a consequence of the district magnitude) in Spain and to a lesser extent in Portugal but whether there is strategic learning over time (different elections), and that is our central hypothesis in this study. An additional argument for analyzing time effects in PR systems is that strategic voting needs more experience, more knowledge of political institutions in comparison to for example first past the post systems. Therefore, we can conclude that our cases Spain and Portugal are not only best possible comparable cases but also valid cases to test our hypothesis. As our level of analysis is concentrated on the district level, we also collected our data at district level. This concerns first of all the election results. We decided to collect the data in as much detail as possible. This meant including in our database the number of votes won by each party, regardless of the strength of the party. For Portugal we took the first seven democratic elections covering the election period 1975 till 1987 (1975, 1976, 1979, 1980, 1983, 1985, 1987). The reason for excluding more recent elections (elections from 1991) is that the number of seats to be distributed (M) changed significantly in 1991 from 46 to 6 with of course important consequences on the district magnitude in a large number of districts. As mentioned before, keeping our electoral system variable constant is essential to analyze strategic learning effects. To keep the number of elections in both country cases equal, we decided to include for Spain also the first seven democratic elections between 1977 en 1996 (1975, 1976, 1979, 1980, 1983, 1985, 1987). The Spanish data come from the Ministry of Internal Affairs (Ministerio del Interior) and the Portugese data were provided by the Ministry of Internal Affairs. 8

9 and 7 elections held between 1977 and 1996 (1977, 1979, 198, 1986, 1989, 1993, 1996) form the dataset. For Portugal we included 7 elections organized between 1975 and 1987 (1975, 1976, 1979, 1980, 1983, 1985, 1987), which APPLICATION OF A MULTILEVEL MODEL For 7 different districts, we have information on 7 consecutive elections at our disposal. The nature of this dataset is clearly longitudinal: for each of the 7 different districts, we have repeated measurements at 7 time points. The data exhibits a hierarchical structure, in the sense that election results are nested within districts. This brings along a specific methodological issue. Analyzing all observations (election results at various points of time) within one district as if they were independent, is a fundamental violation of the assumptions underlying the general linear model. Conventional statistical tools, such as regression analysis or analysis of variance, assume all observations to be independent of each other. If the assumption of independent observations is violated, then the estimates of the standard errors of conventional statistical tests become too small, which can result in pseudo- significant results (Hox, 1995). In the data under study, the dependency of the observations within districts is very strong. The intra-class correlations 1 of the dependent variables LSq, p and DNv equals 0.76, 0.40 and 0.48 respectively. This means that between 40 and 76 per cent of the variance can be attributed at the district level. Ignoring this large portions of variance could bias our conclusions seriously. Thus, our data requires appropriate statistical techniques that can handle the hierarchical structure of the data. In the past, various authors have tried to by-pass this methodological problem by analysing the data at aggregated level (i.e. averaging individual observations over the clusters they are part of). However, this analysis strategy has maor drawbacks. Among others, the number of observations is limited seriously since cluster averages are used in the analysis. By consequence, aggregated analysis lack statistical power (Kreft and De Leeuw, 1998). Instead, we opted for a statistical tool that was developed with the explicit goal of handling the hierarchical data structure we are confronted with, namely multilevel modelling (Hox, 1995; Hox, 00; Kreft and De Leeuw, 1998; Sniders and Bosker, 1999). Sometimes, this technique is also referred to as random effect or mixed modelling (Verbeke and Molenberghs, 000). Multilevel models render it possible to distinguish various levels of analysis. The analysis of longitudinal data can be seen as a special case of multilevel modelling: Less obvious applications of multilevel models are longitudinal research and growth research where several distinct observations are nested within individuals (Hox, 1995; Verbeke and Molenberghs, 000). The longitudinal aspect of the analysis is expressed by including time as a variable in the model, which allows to model evolutions over time. Technically, the differentiation between several levels of analysis is obtained by specifying so-called random effects, such as cluster-specific intercepts or regression slopes. As a consequence, variance at the different levels is introduced. As a result, the average correlation (expressed in intra-class correlation) between observations within one single cluster is higher than the average correlation between observations of various clusters. With this, the assumption of independent observations is relaxed. 1 The intra-class correlation coefficient expresses the ratio of the variability between the districts to the total variability. Higher values point to a higher level of variability within the districts and thus to a greater need for controlling this variance. In order to calculate this coefficient the total variability is subdivided into the variability between the districts and the variability within the districts. The intra-class value lies between 0 and 1 (Kreft & De Leeuw 1998, Sniders & Bosker 1999). 9

10 In this case, a distinction can be made between election results at various time points (the individual level) and the districts they are nested within (the group level). The districts are considered as subects for which several observations (elections) are available. Obviously, the districts and elections are grouped within two countries, and therefore not completely independent. But as we are dealing with a too limited number of countries, the national level could not be introduced as a separate level of analysis. Instead, we incorporated the countries as fixed effects in the models. This is ustified, since we are explicitly interested in comparing results between countries. On the basis of, amongst other things, explorative plots, we decided to use random intercept models only. This means that our models include district-specific intercepts, but that regression slopes are equal for all districts (within one country). To clarify this, a typical example of the models that we use in this article is given here. Y i = 0 + b0i ) + time + country + β1 + β + country time + β1 ( β time + ε (1) i b0i with ε i ~ N(0, σ ) 0 ~ N(0, σ ) () Dependent variable Y i contains information on the -th election for district i. This dependent variable is seen as a function of the time ( time ). By including this time-effect, the evolution over the time series is modelled. In this example, a linear time-effect is specified. In the analyses, it might turn out necessary to add quadratic time effects. Depending on the specific research question, a country effect (country), other independent variables ( β 1 and β ) and interactions effects with time ( country time, β 1 time ) can be included in the model. Given our specific research hypotheses, we are highly interested in these interaction effects with time. After all, an interaction between time and district magnitude would evidence the presence of strategic learning effects. The intercept of the function, ( β 0 + b0i ), consists of two components: a common intercept for all districts ( β 0 ) and a district-specific deviation from this common intercept ( b 0 i ). This random intercept is a normally distributed random variable, with mean zero and variance σ 0. Precisely the inclusion of this random component allows variation at the district level. Individual error term ε i describes the variation at the individual (election) level. This individual error component is normally distributed with mean 0 and residual variance σ. RESULTS We used the SAS procedure PROC MIXED for the estimation of all models (Verbeke & Molenberghs, 000). Robust variance estimation (the so-called sandwich estimate) is implemented to guarantee that standard errors for fixed effects are not biased by misspecifications of the covariance structure (Verbeke & Molenberghs, 000, 6). To facilitate the interpretation of the effects, the following coding schemes were used: table 1 10

11 THE EFFECT OF DISTRICT MAGNITUDE AND TIME ON DISPROPORTIONALITY District magnitude is hypothesised to have a negative effect on disproportionality (see hypothesis 1 in paragraph ). Apart from this effect of district magnitude, we have special interest in the interaction between time and district magnitude. The effect of time should be strongest in the smallest districts, where mechanical effects play a more decisive role. This puts more pressure on voters and party elites to behave strategically. If we want to draw correct conclusions on the expected relations, it is important to include the necessary control variables in the model. The electoral formula may be an important explanatory variable. Since we are including in the analysis district cases solely from Spain and Portugal and the electoral formula remains constant for these two countries, electoral system can be excluded from the analysis. National differences are accounted for by taking up a dummy-variable that indicates the country the district is situated within. Based on theoretical arguments, one could say that the effective number of electoral district parties (DNv) has an effect on disproportionality. The higher the effective number of electoral parties, the more parties are ineligible for distribution of seats, which will increase disproportionality. However, district magnitude logically precedes the number of effective parties in our theoretical model, since we assume DN V to be influenced by district magnitude (psychological effects). By consequence, we do not have to control for DN V in order to estimate the total effect of district magnitude on disproportionality. table From table, following regression equation can be deduced: LSq = time country log( m) ( country time ) [ log( m ) time ] The intercept is equal to This means that, on average, the value of the disproportionality index equals when time, country and log(m) are zero. Given our coding scheme, this is the case in the first election in Spanish districts with log(m) equal to the mean of all districts (the district magnitude was standardised prior to analysis). A significant country-effect was found: in Portugal, the disproportionality index is on average points lower than in Spain. The different results between Spain and Portugal can be explained by the lower average and median district magnitude in Spain. The results also reveal a significant negative effect of time (-0.651). This means that in Spain, with each additional election, the disproportionality-index decreases by In Portugal, the time effect is less strong than in Spain, but still negative ( = -0.04). Finally, we come to the effect of district magnitude. If log(m) increases with one standard unit, the LSq-index is found to decrease by This strong significant effect confirms the hypothesized negative relation between district magnitude and disproportionality, and is in line with other research results (Liphart, 1994; Taagepera and Shugart, 1989). More important however is that any empirical evidence for an interaction between time and district magnitude is absent, as the estimated interaction term is far from significant. This means that the decrease of disproportionality over time is found in small and large districts alike. Or phrased differently, the statistically significant effect of district magnitude on disproportionality is not bound by time. Our multilevel model is quite successful at explaining 11

12 the observed differences in disproportionality. The proportions of explained variance (R²) at the election level and at the district level equal and respectively (Sniders & Bosker, 1994). This means that our model accounts for 56 per cent of the differences in disproportionality between elections, and for 69 per cent of the differences between the districts in the study. Based on this analysis, we conclude the following: 1. This analysis confirms our hypothesis that there is a negative relation between district magnitude and disproportionality: the larger the logarithm of district magnitude, the smaller the disproportionality measured by the LSq-index. The results are telling nothing new and confirm the results of other research (Liphart, 1994; Taagepera and Shugart, 1989).. However the introduction of time as variable shows some new empirical and theoretical insights. There is a negative effect of time on disproportionality, as measured by the LSqindex. Over the elections, the disproportionality is shown to decrease but 3. our analysis doesn t show an interaction effect of time and district magnitude on disproportionality. These results are a strong indication that the electoral system effects, due to strategic behaviour of voters and elites, would vary over time, cannot be confirmed. Instead, the effect of district magnitude is proven to be stable over time. Or, in other words, disproportionality decreases over time for small and large districts equally. This is a very important conclusion and an indication that voters as well as party elites do not learn strategically as a result of the strength of the electoral system (variations in district magnitude). The fact that disproportionality is decreasing over time, independent of district magnitude, does not exclude strategic behaviour, however. National systems variables (such as visibility of political parties and party strength at the national level) can cause strategic behaviour as well. It would be very interesting to introduce national system variables in our analysis, but in our kind of analysis with a careful case selection (to keep electoral systems characteristics constant over time) we ust don t have enough country cases. What we can hypothesize here is that the electoral system characteristics at district level do not have a maor impact on strategic learning behaviour at that district level. In the following paragraphs we will further explore the results of our analysis on disproportionality by trying to analyse separately the learning process of the party elites and voters over time. THE EFFECT OF DISTRICT MAGNITUDE AND TIME ON THE NUMBER OF PARTICIPATING PARTIES: STRATEGIC ELITE BEHAVIOUR Party elites are expected to behave strategically in districts with strong mechanical effects. Previous research and paragraphs showed that strong mechanical effects occur in districts with a small district magnitude. New and small parties might be less inclined to push forward candidates and/or lists in districts where there is strong mechanical effect. In these districts, a stronger tendency for cartel formation and cooperation should also be observed. Thus, we may assume that, if this hypothesis is confirmed, the number of participating parties in small districts should be lower than in large districts and should decrease over time stronger in large districts than in smaller districts. To test these hypotheses, we estimate a model with the number of participating parties as the dependent variable. Apart from the effect of district magnitude, we are interested in time effects. From explorative analyses, we could deduce that the number of participating parties 1

13 does not evolve over time in a linear way. There are indications for a quadratic relation between p and the time variable. For this reason, we decided to include a quadratic time factor to the model. Interactions with time and country are also included in the model. table 3 p = time time country log( m) ( country time ) ( country time ) (log( m) time ) (log( m) time ) The overall intercept is Consequently, the average number of participating parties equals in Spain (country = 0) at time point 0 and with log(m) equal to 0 (thus equal to the mean of all districts together as this variable was standardised). In Portugal, roughly five parties less participated at time point 0, as the effect of the variable country equals This difference is statistically very significant. The effect of time on the number of parties is somewhat harder to interpret because of the quadratic factor. Both the first-order and the quadratic time effect are significant, which indicates that the evolution is not linear but parabolic. In the case of Spain, the number of parties increases up to approximately the fourth election and then starts to decrease again. The time curve for Portugal, on the other hand, has a rather flat course. Per standard unit of increase of log(m), the number of participating parties increases by.489, all other variables being kept constant. This confirms our hypothesis that, as the districts become larger, the number of participating parties increases. The interactions between district magnitude and first order and quadratic time effects are not statistically significant. Therefore, we are inclined to conclude that the quadratic time effect does not depend on the district magnitude. In other words, the effect of district magnitude on the number of parties is equal for all time points in the analysis. It cannot be concluded that party elites start to behave more strategically over time. At least, this is true when the number of participating parties is used as indicator for strategic elite behaviour. The proportions of explained variance are almost identical to those of the previous model. The election-level R² equals 0.53, the district-level R² Over 50 per cent of the differences between elections and almost 70 per cent of the differences between districts have been explained by our model. The three main conclusions that can be drawn from this analysis are: 1.There is an effect of district magnitude on the number of participating parties. If the district magnitude increases, so does the number of participating parties. In small districts the number of participating parties is significantly smaller..under control for all other variables, a quadratic effect of time on the number of participating parties is found. The number of participating parties seems to increase in first elections after which a decrease in the number of participating parties is observed. This is especially the case for Spain. In Portugal, the parabolic trend is less pronounced. 13

14 3.Any interaction between district magnitude and time is absent. Consequently, the effect of district magnitude on the number of participating parties is stable over time. Or phrased differently, the learning process (effect of time) of party elites does not depend on district magnitude. The analysis of strategic learning elite behaviour (indicated by number of participating parties) as a consequence of the strength of the electoral system could not be confirmed. The number of participating parties is increasing during the first elections and is decreasing during the next (quadratic function) but this evolution takes place independently from district magnitude. As pointed out earlier these findings are new and illustrates that parties do not learn and do not need time to learn as a function of the strength of the electoral system. Thus, the decreasing pattern of participating parties over time cannot be explained by the psychological interpretation of the mechanical electoral system effect by party elites as such. Of course, this does not exclude strategic party elite behaviour. On the contrary, national characteristics and strategic party elite behaviour at the national level can probably explain the reduction in participating parties over time. Furthermore, what has been showed here is that if there is some kind of strategic elite behaviour at the district level, it is present immediately at the first election because our analysis clearly shows that the effect of district magnitude on the number over participating parties is constant over time. If this interpretation is correct, which is reasonable in the light of our results, it means that party elites can make the right estimations of the mechanical effects even before the first elections has been held. THE EFFECT OF DISTRICT MAGNITUDE AND TIME ON THE EFFECTIVE NUMBER OF ELECTORAL PARTIES: STRATEGIC VOTING BEHAVIOUR. If strategic learning behaviour occurs as our hypotheses state the effective number of electoral district parties (DN V ) should be smaller in small districts compared to large districts (Liphart, 1994, 7), and the effective number of electoral parties should decrease stronger in smaller districts over time as more elections are organized. We can assume that voters get acquainted with the mechanical operation of the electoral system and adapt their voting behaviour by concentrating their votes on the relevant parties at district level. To test this hypothesis, we estimate a multilevel model with DNv as dependent variable. Again, we pay attention to evolutions over time and a possible interaction effect between time and district magnitude. Unlike the previous model, a quadratic time effect was proven to be unnecessary. We estimated two different models. In a first model, we solely include district magnitude, time, country, an interaction effect between time and country and an interaction effect between time and district magnitude. This model allows us to estimate the total effect of district magnitude on the number of electoral district parties. In a second model we also include the number of participating parties as a control variable. Indeed, there is reason to believe the number of participating parties acts as an intervening variable on the relation between district magnitude and the effective number of parties. In the last paragraph, we found district magnitude to influence the number of participating parties. Furthermore, based on theoretical grounds it can be expected, there is reason to believe that the effective number of electoral district parties is influenced by the number of participating parties. Thus it is theoretically and methodologically useful to add the number of participating parties, p, to the model, since this allows to distinguish strategic voting behaviour by voters from strategic elite behaviour. Under control for p, the direct effect of log(m) on DNv is estimated. 14

15 table 4 The first model results in the following regression equation: DNv = time country 0.46 log( m) ( country time ).017 (log( m ) time ) 0 The estimated intercept is Analogously with previous models, this can be interpreted as the average value on the dependent variable when all other variables have score zero. The estimated number of effective parties equals almost 3.6 for Spanish districts of average size at the first election. In Portugal, the number of effective parties is roughly 0.7 lower. In Spain, time has a significant negative effect on the effective number of electoral parties. At each additional election, the number of effective parties decreases with In Portugal, on the other hand, the number of effective parties seems to increase slightly over time ( = 0.057). Important for testing our hypothesis is that district magnitude has a significant effect on the effective number of electoral parties. The greater the district magnitude, the larger the number of electoral district parties. More important however is again, the interaction effect between time and district magnitude is found to be insignificant. The effect of district magnitude remains constant over time. However, finding an effect of district magnitude on the effective number of parties is not a watertight guarantee that voters behave strategically. After all, the relation might be mediated by the number of participating parties, which would mean that the observed effect is rather due to strategic behaviour of party elites. To rule this alternative explanation out, the number of participating parties is added as a control variable in a second model. This second model leads to the following results. table 5 DNv = time country log( m) ( country time ) (log( m) time ) p First of all, we notice that under control of among other variables district magnitude - the number of participating parties indeed had a significant effect on the effective number of parties. On average, each additional participating party leads to an increase of 0.04 effective electoral parties. The largest part of the model parameters do not change substantially by adding the control variable. There are two exceptions on this. The effects of both district magnitude and country are reduced seriously under control of the number of participating party. Concretely, this means that the effects of these variables are partly at least- mediated through the number of participating parties. In part, district magnitude is found to have an effect of the effective number of parties because district magnitude influences the number of participating parties because a larger number of participating parties leads to an increased number of effective parties. Thus, part of the effect of district magnitude on the effective number of parties is due to party elite and not voting behaviour. However, even under control of the number of participating parties, the effect of district magnitude remains statistically 15

16 significant. This means that the effect of district magnitude cannot be explained completely by the supply of party labels (strategic party elite behaviour). More than half of the effect should be ascribed to (strategic) voting behaviour. For the country effect, an analogous interpretation can be made. The finding that the effective number of parties is smaller in Portugal can partly, but not completely, be accounted for by its smaller number of participating parties. Even though this is not the main focus of the analysis, it would be interesting for further research to explore more into details the lower number of participating parties and number of effective parties in Portugal. Since the average and median district magnitude is higher in Portugal, one could expect more parties in Portugal than in Spain. One possible explanation for these counterintuitive outcomes in Portugal and Spain can be found in the more complex cleavage structure and regional differences in Spain. Portugal could be considered as a cultural more homogenous country. We do not believe in a deterministic approach of effects of electoral systems. Electoral systems are only one variable which can explain the number of political parties in the party system. Other (national system) variables like cleavage structure, important issues, charismatic leadership could be relevant too. What we do in this contribution is looking to the effects of electoral systems at district level. Saying this does not mean that we exclude the possibility of the impact of other variables explaining the differences between number of parties. Compared to the model for the other dependent variables, the explanatory power for the effective number of parties is substantially lower. The second model (with the number of participating parties) accounts for 14.6 per cent of differences between elections and for 14.4 per cent of differences between districts. This rather low explanatory power can be explained by the fact that time and especially district magnitude have less influence on the effective number of political parties than on disproportionality or the number of participating parties. By consequence, other elements that are not included in the model determine the effective number of political parties. From the above discussion of our two analyses, the following conclusions can be drawn: District magnitude also has a significant effect on the effective number of electoral district parties. Moreover, we do not have any indications that this effect might vary over time, because a significant interaction effect between time and district magnitude is absent. However under the control of all other variables, time seems to have a fairly strong effect on the effective number of electoral district parties (DN V ). These results are similar to those of the other analysis in which the number of participating parties is the dependent variable. This means that if there is a psychological effect of the electoral system (district magnitude) on voters, it is present at the first election because the effect of district magnitude under control of the number of participating parties is constant over time. We cannot observe a strategic learning effect on voters as a consequence of the mechanical effects of the electoral system. This conclusion does not exclude strategic learning behaviour of voters, since there is an independent effect of time on the decreasing nature of the effective number of elective parties. This last result is harder to interpret. It means that other variables should be added to the model in order to explain the decreasing trend during the first elections. A possible explanation can be found in national system variables such as the number of parties in government, the number of significant parties in parliament, national party organisation and party visibility in national covered media. Because of these national variables it is possible that voters in the district redirect their votes to the national visible parties. This process takes time and that may be the reason why the effective number of parties is decreasing over time. Anyhow, our analysis is showing very clearly that voters do 16