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Public Choice

Erschienen in:

01.03.2015

Strategic electoral rule choice under uncertainty

verfasst von: Konstantinos Matakos, Dimitrios Xefteris

Erschienen in: Public Choice | Ausgabe 3-4/2015

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Abstract

We study electoral rule choice in a multi-party model with office-motivated parties and electoral outcome uncertainty. We show that when all dominant parties (parties with positive probability of winning the election) have sufficiently good chances of winning, they agree to switch from the PR rule to a more majoritarian one in order to increase their chances of forming a single-party government. We identify the exact degree of disproportionality of the new rule and we prove that it is increasing in the expected vote share of the smaller parties (parties with zero probability of winning otherwise). The necessary and sufficient conditions for such collusion in favor of a majoritarian rule are: (a) the high rents from a single-party government and (b) sufficient uncertainty over the electoral outcome. Our theoretical predictions regarding the degree of the disproportionality of the electoral rule are supported by empirical evidence.

Vorheriger Artikel Legitimacy and the cost of government

Nächster Artikel The rule of law and constitutionalism in Muslim countries

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One exception can be the case of nationalist parties (e.g., Sinn Fein or the Scottish nationalists) which have territorially concentrated electoral support and, hence, they might also prefer the simple plurality rule.

Riera (2013) also records 128 cases of major and minor electoral reforms from 1945 to 2010. More than a third of them (46) were unambiguously majoritarian in nature. Moreover, two thirds of those majoritarian reforms took place after 1990 in those newly established democracies.

As in Andrews and Jackman (2005), the term electoral uncertainty implies that elections are competitive and contested by both dominant parties.

Transitions from a majoritarian to a more proportional rule usually do not require any strategic coordination. Consider the following case: under a majoritarian rule (such as FPTP) it is very likely that a single party commands the majority in the parliament. On the one hand, if this party is expected to be the winner of the election the majoritarian rule is maintained (or even reinforced). On the other hand, if the party is expected to lose and has the necessary votes to enact a reform a more permissive electoral rule will be introduced. In both cases, electoral rule reform is the outcome of a single-agent payoff maximization program without involving any strategic interaction (see Appendix B and also Ergun 2010).

Here we need to clarify that in our framework, parties in favor of electoral rule reform need only have expected utility gains and not necessarily realized ex post seat gains (as in Benoit 2004). This is so because parties’ expected utility incorporates something more than mere seat gains: the increase in the probability of forming a single-party government for the parties favoring the reform. In the presence of electoral uncertainty this is utility enhancing for both, in expected terms.

Fernández-de-Córdoba and Penadés (2009) also study the choice of electoral institutions (from a broad set of rules) by parties that try to maximize the minimum number of seats for a given share of votes. Their analysis shows that the maximin choice is the D’Hondt rule, generally equivalent to the Droop formula. The scope of our analysis is different as we focus on dominant parties’ incentives for strategic coordination, driven by their desire to form a single-party government.

This type of proportionality distortion is an ordinary one as it gives a permanent advantage to the big parties (the largest of which will always receive the premium). Thus we also use the term plurality premium in order to stress the fact that the simple plurality winner will always be entitled to the premium. Greece applies this electoral rule since 2007. Another example of how this mechanism is applied are the 2006, 2008 and 2013 Italian legislative elections.

By minor electoral reforms we mean small changes in the magnitude or in the boundaries of certain districts.

Practically, our model can be viewed as a multi-party model if one interprets \({v_{3}}\) as the sum of the vote shares of all other parties. As long as \({v_{3}} <\min \{{v_{1}},{v_{2}}\}\) our third party stands for the collection of all other small parties.

The main results of this paper also hold true when one considers a more general class of distributions \(\Phi (\cdot )\), as we show in the proof of Lemma 1 (Appendix A).

Note that in our model (with three parties) the threshold for awarding the bonus to the winner is \((1-{v_{3}})/2\) simply because this is the threshold for plurality.

To see this, consider the case of \(l=0\). Then our electoral rule is purely proportional, whereas in the case of \(l=1\), it becomes a FPTP system with only one nation-wide district.

All appendices containing additional results, supporting material and the formal proofs can be found by following the link at the end of the paper in the section titled Electronic supplementary material.

The formal proofs (Appendix A) and the analysis of the general case (Appendix B) will demonstrate that it is not the constant nature of \({u_{i}}(\cdot )\) for \(s_{i}^{l}({v_{i}})>1/2\) that drives our results but the assumption that the gain from an extra seat should be less, for a party that already controls the majority in the parliament, compared to the gain when this party participates in a coalition government or is in opposition.

All proofs can be found in Appendix A.

Notice that \(f_{i}(\cdot )\) is strictly increasing in \(a_{i}\) and replace \(a_{i}\) with \(v_{3}\) in the equation (since by assumption we have \(v_{3}<a_{i}\)). Then observe that for every \(v_{3}>0\) it is always true that \(f_{i}(\cdot )>0\).

By analogy, when \(f_{i}(\cdot )<0\), it measures the expected loss from running second and \(l=\frac{v_{3}}{1+v_{3}}\) instead of \(l=0\) was applied.

This model can be used to study transitions from less (\(l=\frac{v_{3}}{ 1+v_{3}}\)) to more proportional (\(l=0\)) rules too. Since, in equilibrium, there are only two candidate values of l for an optimum, it must be that either \(l=0\) or \(l=\frac{v_{3}}{1+v_{3}}\). If the proposer has enough seats to implement the reform single-handedly - which usually is the case when a majoritarian rule is the status quo rule - the proposer will chooses the PR rule (\(l=0\)) if it expects to lose the election with sufficiently high probability. Otherwise, it picks \(l=\frac{v_{3}}{1+v_{3}}\), which allows it to form a single-party government in the event of an electoral victory.

That is, we have \(\frac{\partial l(v_{3})}{\partial v_{3}}=\frac{\partial l(v_{3})}{\partial ENP}\times \frac{\partial ENP}{\partial v_{3}}>0\) implying \(\frac{\partial l(v_{3})}{\partial ENP}>0\).

Detailed variable definitions can be found in Appendix C.

The squaring of deviations in the Gallagher index is intended to make it different when the “third party” is a single party, as opposed to the situation (as in our model) where it is the aggregate of small parties. As a result, the Gallagher index introduces a difference where the model (and the Losemore-Hanby index) prefer to see equivalent situations. Nevertheless, our findings are robust to using the Gallagher index and additional results are available by the authors upon request.

Assuming symmetry, if one replaces the vote shares of dominant parties with their expected ones (\(E[v_{i}]=\frac{1-v_{3}}{2}\)) and computes their seat shares \(s_{i}^{l}(v_{i})\) as a function of the applied rule l (by Lemma 3 in the symmetric case we have \(l=\frac{v_{3}}{1+v_{3}}\)), after some algebra, one can get the predicted Losemore-Hanby index for country n at election t which becomes: \(\widehat{LH}_{n,t}\big( \frac{ v_{3}}{1+v_{3}}\big) =\frac{( v_{3}) _{n,t}}{2}\). Since in our sample the average vote share of third parties (other than the two major ones) is 0.19, one can calculate the LH index for the symmetric case and obtain a value of 0.095.

While most of the literature uses the ENP index our theoretical prediction is stated in terms of \(v_{3}\). One problem with the ENP index is that it is not invariant to how \(v_{3}\) is distributed across different small parties. In order to address this issue and increase the fit between our theoretical and empirical predictions, we estimate again Model 1 by replacing ENP with \(v_{3}\). This is done when we estimate Model 3 (Appendix B). We obtain very similar results.

The rationale for using those additional controls is similar to that of using the margin of victory and the high institutional constraints dummy in order to control for electoral uncertainty, the size and the allocation of office perks among different parties and branches of the executive (which implicitly determines the value of a single-party government). Similarly, the age of the democratic regime is a proxy for a more established (and perhaps more inclusive) democracy.

The expectation that \(\beta _{2}<0\) is a direct implication of our theoretical model. Recall that we have shown \(\partial ENP/\partial v_{3}>0\) which implies that \(\beta _{2}=\frac{\partial ^{2}LH}{(\partial ENP)(\partial v_{3})}\) should have the same sign with \(\frac{\partial ^{2}l(v_{3})}{(\partial v_{3})^{2}}=-\frac{2(1+v_{3})}{(1+v_{3})^{4}}<0\). Moreover, since ENP and \(v_{3}\) are monotonically related, we also estimate Model 2.b where we replace ENP with \(v_{3}\). In this case, it is straightforward to check that \(\beta _{2}=\frac{\partial ^{2}LH}{ (\partial v_{3})^{2}}\) should have the exact same sign with \(\frac{\partial ^{2}l(v_{3})}{\left( \partial v_{3}\right) ^{2}}<0\). We present those estimation results in columns 6 and 7 (Table 3).

Note that the statement regarding the threshold is not biconditional. That is, while \(v_{3}<1/3\) always implies that the two dominant parties are never threatened by any of the other parties the converse statement is not necessarily true as this depends on how \(v_{3}\) is distributed among the other parties. That is why we get a clear positive (and decreasing) effect when \(v_{3}<1/3\), but we do not get a clear prediction when \(v_{3}>1/3\).

The effect of electoral rules on ideological divergence (polarization) has been thoroughly examined both theoretically (e.g., Cox 1990) and empirically (e.g., Bertelli and Richardson 2008; Calvo and Hellwig 2011). Our approach is different in the following sense: we are interested in the reverse direction of the relationship between ideological divergence and electoral rule disproportionality.

Cox (1990) finds that centripetal incentives are stronger in majoritarian systems while proportional systems are dominated by centrifugal incentives.

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Titel: Strategic electoral rule choice under uncertainty
verfasst von: Konstantinos Matakos
Dimitrios Xefteris
Publikationsdatum: 01.03.2015
Verlag: Springer US
Erschienen in: Public Choice / Ausgabe 3-4/2015
Print ISSN: 0048-5829
Elektronische ISSN: 1573-7101
DOI: https://doi.org/10.1007/s11127-014-0228-5

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