How fractionalisation and polarisation explain the level of government turn-over

Abstract

This article seeks to explain to what extent government composition changes in cabinet formations: it examines why some party systems tend to see wholesale turn-over (where all government parties were previously in opposition) and others only see partial turn-over (where some of the government parties were previously in government). This distinction has been described by many prominent political scientists. Yet there is limited research into the underlying causes. This article examines the importance of both party system characteristics and conditions specific to the cabinet formation: it finds that specifically the interaction between number of parties in a party system and their distribution over the political space matters for the level of party turn-over in government.

Appendix

This Appendix examines four issues:

• (1) a different visualisation of the main interaction relationship (see footnote 6 in the article);

• (2) an alternative operationalisation of the Government–Opposition Vote Differential (see footnote 3 in the article);

• (3) an alternative operationalisation of the GTI (see footnote 4);

• (4) and an alternative operationalisation of turn-over that incorporates the ideological difference between the government and the opposition (see footnote 1).

First, we examine Fig. 3 in Appendix. It shows the marginal effect of polarisation on the GTI for increasing effective numbers of political parties. It supports the same substantive conclusion as Fig. 2 in the paper: when the effective number of political parties is low, polarisation has a significant negative effect on the Government Turn-over Index. In the mid-range there is no significant effect of polarisation. When the number of political parties is high, polarisation positively affects the Government Turn-over Index. This effect becomes significant when the effective number of political parties is greater than seven. Substantially, the conclusions are the same as those described in the paper, although the level of uncertainty is greater for these marginal effects.

Fig. 3

Marginal effect of polarisation as the effective number of political parties increases. Based on Model 1 in Table 3 (in the article)

Second, we examine the Government–Opposition Seat Differential. Where the Government–Opposition Vote Differential looks at the difference in votes between the previous government and opposition, this measure looks at their seats.

$$\Delta_{s} = \mathop \sum \limits_{i = 1}^{n} S_{i,t - 1} \cdot G_{i, t - 1} - \mathop \sum \limits_{i = 1}^{n} S_{i,t - 1} \cdot (1 - G_{i, t - 1} )$$

(A.1)

where S_i,t−1 is the share of the seats the respective party got in the previous election.

Models 1, 2 and 3 in Table 4 in Appendix show the results. They are quite similar to those in Table 3 (in the paper). As shown in Models 1 and 2, there is a significant effect of the effective number of parties on the level of government turn-over in the model without and with polarisation. As Model 2 shows, polarisation in itself does not affect the level of alternation. The coefficients for the interaction are almost identical (and statistically indistinguishable) to those in Model 3 in Table 3 (in the paper). The key differences are in the size of the effect of the government–opposition differential; the seat differential (Δ_s) appears to have a weaker effect than the vote differential (Δ_v). At the same time, electoral volatility has a stronger effect in these models than in the paper. It seems likely that the vote differential (Δ_v) picks up on some of the variance that in the Models in Table 3 Electoral Volatility picked up. All in all, the alternative operationalisation of the Government–Opposition Differential does not markedly change the conclusions.

Table 4 Alternative operationalisations (beta and logistic regressions)

Next, we examine an alternative operationalisation of the dependent variable, the GTI. In the paper, all cases where the government composition did not change (where the GTI was zero) were excluded from the analysis. The reason for this is that the expectations that apply to different levels of government turn-over does not apply to why government stay in power. Models 4, 5 and 6 look at GTI_All, that is at alternative operationalisation, which does not exclude the cases where GTI did not change. This more than doubles the number of cases. This means that a large share of the variance is between the cases where there is no change and where there is some change. These analyses support the expectation that different patterns apply here: only the Post-election Dichotomy and Electoral Volatility have significant effects in Models 4, 5 and 6: the higher the electoral volatility the higher government turn-over is and the government formed after an election have a higher level of government turn-over, compared to governments formed during the term (which includes government change where for instance only the PM changes). The key variables of the paper (polarisation and its interaction with fractionalisation) do not affect this new variable at all. Model 7 provides an explanation for this pattern. It looks at GTI_Any, that is a measure that looks at whether there is any kind of alternation for all cases. In other words, it checks whether the GTI_All is equal to zero, if it has, it has value zero, if not, it has value one. These results are strikingly similar to those for GTI_All. Note that here logistic regression is employed so the coefficients are not directly comparable to other models presented in the paper or the appendix: here we also find significant effects for the Post-election Dichotomy and Electoral Volatility. What is also interesting is that there is a positive effect for fractionalisation, which is significant in Model 7. This implies that government turn-over at all is more likely in multiparty systems as opposed to two-party systems, while in the paper the finding is that fractionalisation leads to lower levels of government turn-over (in terms of the GTI). In two-party systems if there is alternation, which is marginally less likely than in multiparty systems, it is wholesale alternation, while in multiparty systems alternation occurs more often but then it is partial alternation. Wholesale alternation is the only option two-party systems, but it requires a change in the composition of parliament, while partial alternation can occur in a multiparty system if one junior government party is traded in for the other. Combining these results explain why in Model 4 fractionalisation has no effect on the GTI_All. Models 8 and 9 also show no effect of polarisation (other than reducing the N and weakening the effect of fractionalisation), which means that change of government is not more likely to occur in systems where parties stand far apart.

It appears to be the case that while the hypotheses discussed in the paper can explain the variance between 0.01 and 1, it cannot explain cases where the GTI_all is zero. There appears to be a different mechanism beneath the zero values and the other values. A zero-inflated negative binomial model is specifically meant for a situation where the theoretical mechanism beneath the generation of the zero values is different from the mechanism that generates the other values and where the distribution of the other values is not normal. There is one drawback, however, is that it is not meant for values bounded between zero and one. We address this by multiplying GTI_All with 10 into GTI₁₀. Models 10, 11 and 12 (in Table 5 in Appendix) show clearly that the mechanisms behind the generation of the zero values (lower half) and the other values (upper half) is different. Note that the signs in the lower half of the table are flipped compared to Models 7, 8 and 9, because it now predicts whether the value is zero: it decreases the likelihood of both non-alternation and wholesale alternation. Model 10 shows the same pattern for fractionalisation we observed above. The models indicate that electoral volatility makes non-alternation less likely: when the distribution of seats is similar to the outcome where the previous government was formed, it staying in power is more likely. Changing a government just after elections also makes non-alternation less likely: the only time non-alternation is picked up as a government changes is after elections. The mechanism for non-zero values shown in Table 5 in Appendix completely conforms to findings elsewhere in the paper, including the significant interaction between polarisation and the effective number of political parties.

Table 5 Alternative operationalisations (zero-inflated negative binomial regressions)

Table 6 Alternative operationalisations (OLS regressions)

Finally, we look at an alternative way to approach alternation, namely by looking at the ideological distance between the current and the previous government. The IA, which is employed by Tsebelis (2002), Tsebelis and Chang (2002) and Zucchini (2010), looks at the absolute difference between the ideological position of governments on basis of the average position of their most extreme parties in the government:

$$IA = \left| {\frac{{\hbox{max} \left( {LR_{G,t} } \right) - \hbox{min} \left( {{\text{LR}}_{G,t} } \right)}}{2} - \frac{{\hbox{max} \left( {LR_{G,t - 1} } \right) - \hbox{min} \left( {{\text{LR}}_{G,t - 1} } \right)}}{2}} \right|,$$

(A.2)

where LR_G is the set of left right positions of the parties in government (at t and t − 1). The seat-weighted IA is the same idea but it looks at the average position of all parties in the government, weighted by their seat total. In terms of the variables introduced in the paper,

$$IA_{sw} = \left| {\frac{{\mathop \sum \nolimits_{i = 1}^{n} S_{i,t} \cdot LR_{i,t} \cdot G_{i, t} }}{{\mathop \sum \nolimits_{i = 1}^{n} S_{i,t} \cdot G_{i, t} }} - \frac{{\mathop \sum \nolimits_{i = 1}^{n} S_{i,t - 1} \cdot LR_{i,t - 1} \cdot G_{i, t - 1} }}{{\mathop \sum \nolimits_{i = 1}^{n} S_{i,t - 1} \cdot G_{i, t - 1} }}} \right|.$$

(A.3)

This is another way of thinking about government turn-over. In the theory section, we essentially considered four cases:

• (1) when polarisation is high and the number of parties is high, the GTI would be high;

• (2) when polarisation is low and the number of parties is high, the GTI would be low;

• (3) when polarisation is high and the number of parties is low, the GTI would be high;

• (4) and when polarisation is low and the number of parties is low, the GTI would be high.

The expectation would need to be different for situation four when it comes to IA and the IA_sw: if polarisation is low, the IA cannot be high, because the government would be formed by the parties that, given the polarisation, stand close together. Consider the situation in Malta where the Labour Party and the National Party are very close together and therefore the polarisation is very low. In this situation one cannot expect a high IA, while one can expect a high GTI. There is no sound basis to expect an interaction relationship, it is still included in the model for consistency’s sake.

The analyses for the IA and IA_sw (Table 6 in Appendix) support broadly the same conclusions: ideological alternation is higher when a government is formed after an election (as opposed to during the parliament’s term), when Government–Opposition Vote Differential is lower and when electoral volatility is higher. As expected but contrary to the findings for the GTI, polarisation has a strong direct effect on the level of ideological alternation and the effective number of parties does not affect the level of ideological alternation. The interaction for the IA_sw is visualised in Fig. 4 in Appendix. It shows that at low levels of fractionalisation, low polarisation is associated with low levels of ideological alternation; while for the same levels of fractionalisation, high polarisation is associated with high levels of polarisation are associated with high levels of ideological alternation. When the number of parties becomes higher the uncertainty becomes such that the two are no longer distinguishable. That is when the number of parties is high the polarisation matters less, contrary to the pattern for the GTI.

Fig. 4

Seat-weighted ideological alternation as a function of the effective number of parliamentary parties at different levels of polarisation. Notes Black lines are the predicted level of alternation for different effective numbers of parliamentary parties for non-polarised systems (Polarisation at 0.23) and the grey lines are the predicted level of alternation for different levels of the effective numbers of parliamentary parties for polarised systems (Polarisation at 7.35). Based on Model 12 in Table 6 in Appendix. The dashed lines are 90% confidence intervals