My dependent variable is the existence (or absence) of an electoral reform, and its different types. For an extensive definition and typology of electoral reform, see Chapter 3.140 The identification of a case of electoral reform without specifying the direction in which the rules of the game change is clearly insufficient. On this basis, it is very useful to distinguish between permissive and restrictive reforms, which decrease and increase the overall disproportionality produced by the electoral rules, respectively (Taagepera and Shugart 1989). In general, disproportionality can be defined as “the deviation of parties’ seat shares from their vote shares”
(Lijphart 1994: 57). Further details of all the episodes of electoral reform identified are given in the Appendix 1 to this thesis.
4.4.2. Independent variables
The first key independent variable is the level of party system fragmentation, which is captured by the effective number of electoral parties in the current term (ENEP). This index was first introduced by Markku Laakso and Rein Taagepera in 1979, and indicates “the number of hypothetical equal-size parties that would have the same total effect on fractionalization of the system as have the actual parties of unequal size” (p. 4). Its exact operationalization corresponds to the inverse of the sum of the square of all parties’ vote shares,141 and ranges from 1 to infinity
139 My logic would also call for at least a higher-level interaction of democratic age with party system fragmentation*electoral disproportionality and party system fragmentation*electoral volatility. Unfortunately, I do not have a sufficient number of cases to test them.
140 Sources: Birch (2003), Birch et al. (2002), Bowler and Grofman (2000), Colomer (2004a), Gallagher and Mitchell (2005a), Golder (2004), Grofman et al. (1999), Grofman and Lijphart (2007 [2002]), the Inter-Parliamentary Union (n.d.), Johnson and Wallack (2010 [2003]), Jones (1995 and 1997), Lijphart (1994), Lundell and Karvonen (2003), Negretto (2009), Payne (2007), Remmer (2008), Renwick (2011), Shugart and Wattenberg (2001), Shvetsova (1999), Wills Otero and Pérez-Liñán (2005), Zovatto and Orozco Henríquez (2008), and electoral laws of each country.
141 To be more precise, the formula is:
127 (in fact, to the number of parties that obtain at least one vote).142 In the past two decades, the effective number of parties “has become the most widely used measure” of party system size (Lijphart 1994: 70) because it considerably improves on the merits of other previous measures of party system fragmentation. First, it is comparable across very diverse country cases. Moreover, it weights the count of parties by their relative electoral strength, and, hence, takes into account their “coalition” and “blackmail” power (Sartori 2005 [1976]). Maurice Duverger (1964 [1954]:
207-208) clearly had the concept of effective parties in mind when discussing party systems (see also Clark and Golder 2006: 680). However, using it also entails potential problems that cannot be ignored.143
I also include in the models the value of the Gallagher’s Index of electoral disproportionality in the current term. This measure is calculated according to the following formula: Disproportionality Index (DI) = √ ∑ where vi is the percentage of vote obtained by party i and si is the percentage of seats obtained by party i.144 This index can range from 0 to 100 (Gallagher 1991). The disproportionality index not only helps me to test hypothesis 2, but also seeks to control for the presence of ceiling or floor effects.145 The third independent variable of interest is electoral volatility, which is measured on the basis of the Pedersen’s Index in the current term (Pedersen 1979). This index is created by adding the net difference (i.e., in absolute terms) in the percentage of votes obtained by each of the parties in a
ENEP = __1__
n pi2, i=1 where pi is the percentage of votes obtained by party i.
142 Source: Golder (2004) complemented by Gallagher’s dataset
(www.tcd.ie/Political_Science/Staff/Michael.Gallagher/ElSystems/index.php).
143 One such potential problem corresponds to the “other” and “independent” categories. In this chapter, I correct the effective number of electoral parties by using the least component method of bounds suggested by Taagepera (1997). This operation essentially requires calculating the effective number of electoral parties treating both categories as a single party (smallest effective number of parties), then recalculating the effective number of parties as if every vote in the “other” and “independent” categories belonged to a different party (largest effective number of parties) and taking the mean. The incidence of independent candidacies is only high in Russia and Ukraine.
144 Source: Gallagher’s dataset (www.tcd.ie/Political_Science/Staff/Michael.Gallagher/ElSystems/index.php).
145 One could argue that there is a ceiling and floor effects problem in my analyses because extremely permissive (restrictive) systems, that produce a high (low) party system fragmentation, cannot become more permissive (restrictive). The introduction of the Gallagher’s Index of Disproportionality seeks to fix this problem by trying to control for the degree of permissiveness of the current system. As a robustness check, I also show some additional results in which the “extreme” systems (i.e., FPTP and PR systems with a single-national district) have been excluded.
128 given pair of elections and dividing it by two, and ranges from 0 to 100.146 Scott Mainwaring, Peter Mair and Joshua Tucker kindly shared their data on electoral volatility with me.147
Summing up, I do not examine the long-term effect of any of these variables on electoral reform. In fact, it could be argued that the effect of these explanatory factors occur mostly over a series of two or three elections. However, this issue is far from having been completely demonstrated in the literature. Moreover, the way in which party system fragmentation, electoral disproportionality and electoral volatility should be theorized and calculated to affect the likelihood of electoral system change in the long-term (e.g., averaging their value in the last three elections) and the limited data availability lead me to exclude this idea from the empirical analysis.
Finally, I also include in the models as an additional independent variable the duration of the current democratic period. A regime qualifies as democratic if all of the following conditions are met: one, direct or indirect election of the effective executive; two, election of the legislature;
three, multiple parties are legally allowed; four, existence of parties outside of the ruling coalition; five, the alternation rule is not violated; and six, at no time during their current tenure in office the incumbent (person, party, military or hierarchy) unconstitutionally closed the lower house of the national legislature nor rewrote the rules in their favour.148
4.4.3. Control variables
I use the following two controls: first, Henisz’s political constraints index; second, the real GDP per capita; and third, the ideology of the party in government. The rationale behind the first control seems straightforward because it is necessary to take into account the number of potential veto players that can block the reform of the electoral system (Tsebelis 1990). In this regard, the higher the number of veto players that exist, the more difficult the electoral reform becomes.
Henisz’s index (2000 and 2002) measures the feasibility of policy change, i.e. the extent to
146 To be more precise, electoral volatility is calculated according to the following formula:
TV = ½ Σ | ∆ pi |,
where the variation in vote share for each party is ∆ pi = pi(t + 1) - pi(t), i = 1, ..., n.
147 Ideally, the amount of available voters in Bartolini and Mair’s sense (1990) would have been proxied by some other more precise measure (i.e., the proportion of non-identified citizens with a party). However, the lack of appropriate data in this respect has led me to employ Pedersen’s Index as a second best option.
148 Source: Cheibub et al. (2009).
129 which a change in the preferences of any one political actor any lead to a change in government policy. The index is composed from the following information: the number of independent branches of government with veto power over policy change, counting the executive and the presence of an effective lower and upper house in the legislature (more branches leading to more constraint); the extent of party alignment across branches of government, measured as the extent to which the same party or coalition of parties control each branch (decreasing the level of constraint); and the extent of preference heterogeneity within each legislative branch, measured as legislative fractionalization in the relevant house (increasing constraint for aligned executives, decreasing it for opposed executives). The index scores are derived from a simple spatial model and theoretically range from 0 to 1, with higher scores indicating more political constraint and thus less feasibility of policy change.149
In addition, I introduce economic performance as a second control variable whose omission could bias the estimation of the coefficients of the main independent variables. Because electoral outcomes are shaped by economic performance in contemporary democracies (van der Brug et al. 2007), the real GDP per capita (in 1,000s) is added to the models.150 If the economy performs poorly, parties in power will probably lose votes in the following election. This should make them more likely to reform electoral rules in a permissive direction. Real GDP per capita is a chain index obtained by first applying the component growth rates between each pair of consecutive year, ‘t-1’ and ‘t’ (t = 1951 to 2007), to the current price component shares in year
‘t-1’ to obtain the domestic absorption (DA) growth rate for each year. This DA growth rate for each year ‘t’ is then applied backwards and forwards from 2005, and summed to the constant price net foreign balance to obtain the Chain GDP series.
Finally, the ideology of the government may be of importance as a control variable as well (Bol 2011; Bowler et al. 2011). In particular, it might be interesting to distinguish between left-wing and right-wing cabinets. As previous works have shown, left-wing parties should be more likely to support electoral reform than righ-wing parties. The ideology of the executive is proxied by the parties’ orientation with respect to economic policy using the following criteria:
149 Source: Henisz (2010).
150 Source: Heston et al. (2012).
130 the variable takes value 1 for parties that are defined as conservative, Christian democratic or right-wing; 2 for parties that are defined as centrist; and 3 for parties that are defined as communist, socialist, social democratic or left-wing.151
4.4.4. Econometric technique
Event history data for discrete time processes generally record the dependent variable as a series of categorical outcomes denoting whether the events occurred or not at the observation point. In fact, discrete time data look a lot like Binary dependent variable Time-Series Cross-Section (BTSCS) data when we want to explain a dichotomous outcome (Beck et al. 1998). The only real difference between the discrete time duration models and other types of continuous time survival specifications is that in the former duration data is disaggregated into discrete time units (Bernardi 2006). Like in the OLS world, none of the models that belong to the familiar world of categorical dependent variables (logit, probit, multinomial logit/probit…) takes account of the problem of time dependence. If there is time dependence, models such as these produce estimates that are consistent but inefficient and with wrong standard errors (Poirier and Ruud 1988). In fact, if serial correlation (time dependency) is high, simulations by Beck and Katz (1997) have shown that the standard errors from a normal categorical dependent variable may be underestimated by 50 per cent or more. In order to deal with time dependence, I will do two things. First of all, I will estimate all the models with several additional parameters or cubic splines (Beck et al. 1998) even though they will not be shown to save space. Smoothing functions such as cubic splines are attractive alternatives to temporal dummies when tackling serial correlation because they consume fewer degrees of freedom. Beck et al. (1998) argue that cubic splines are probably the most appropriate and flexible way to deal with temporal dependence in discrete time duration models. Additionally, I will employ robust standard errors clustered by legislative term. This second operation not only seeks to address serial correlation but also attempts to correct for possible problems of heteroskedasticity.
Summing up, I will first test the hypotheses by way of a set of seven multinomial logistic regressions, since the dependent variable has more than two discrete and unordered categories (Long 1997). The observation is the country-year, and the time-period will go from 1945 to
151 Source: Beck et al. (2001).
131 2010. I will deal with duration dependence by including cubic splines in all the specifications (Beck et al. 1998). However, I will also follow David Carter and Curtis Signorino’s recommendation (2010) as a robustness check, and all the models will be rerun including a cubic polynomial transformation of time (t, t2 and t3).152
Finally, as an alternative to the BTSCS models that I have covered, I will specify several Cox models. The main characteristic of these transition rate models with continuous time is that the specific distributional form of the duration times is left unspecified. In other words, there is no need to assume that the duration times have a particular distribution. What we only care about is how a set of covariates moves the baseline hazard up or down. Because of the strong assumptions of parametric models about the shape of the hazard, parametric models are not as widely used outside the social sciences as is the Cox model (Box-Steffensmeier and Zorn 2001).
An important issue involved in model specification concerns treating permissive reforms as being subjected to different risks than restrictive electoral system changes. This feature points one to a competing risks framework, which makes it possible to explore separately the factors that increase the likelihood that politicians will modify the electoral system through either of these events.