Duverger’s Law in Mixed Legislative Systems: The Impact of National Electoral Rules on District...

Duverger’s Law in mixed legislative systems: The impact of national electoralrules on district competition

TIMOTHY S. RICHWestern Kentucky University, USA

Abstract. How do institutional factors shape district competition in mixed legislative systems? Preliminaryevidence suggests the distinction between sub-types of mixed systems alone poorly explains variation indistrict results. Consistent with the contamination thesis, this analysis suggests three additional national-level factors at play: fused ballots, the electoral threshold for proportional representation seats, and theexistence of compulsory voting laws. Regression analysis on an original dataset covering 90 mixed systemelections in 23 countries (1990–2012) finds that while mixed member majoritarian systems correlate withfewer district candidates, these three often overlooked factors are also statistically significant. This analysishighlights the complexity of mixed systems and suggests why many of them diverge from Duverger’s Law.

Keywords: district competition; mixed legislative systems; Duverger’s Law; contamination thesis

Introduction

How do institutional factors shape election outcomes? A large literature tackles this ques-tion in majoritarian and proportional systems (e.g., Rokkan 1970; Lijphart 1977; Taagepera& Shugart 1989; Norris 2004) and provides clear expectations on the number of parties.While a growing literature similarly addresses institutional effects in mixed legislativesystems that combine single member districts (SMDs) with seats filled by proportionalrepresentation (PR), few cross-national studies tackle district competition. This level is amore direct means to address Duverger’s Law, which expects two-party competition underSMDs and multiparty competition under PR. Duverger’s Law inherently remains a district-level theory (Sartori 1986; Cox 1997) and where aggregation to the country level potentiallymasks underlying trends.

Considering the popularity of the mixed system electoral design among a diverse rangeof countries and historical experiences, a greater understanding of the correlates of districtcompetition offers insight as to why these systems often fail to meet initial expectations.Such disconnect between expectations and reality has broad ramifications – for example,failure to conform to Duverger’s Law may produce non-Condorcet winners (Colomer2001) and further alienate supporters of parties who fail to achieve representation (Duch &Palmer 2002; Tavits & Annus 2006).

Cross-national studies often compare mixed systems directly to pure majoritarian orproportional systems, where outputs such as the number of parties are found to diverge(e.g., Herron & Nishikawa 2001; Kostadinova 2002). A common distinction is madebetween mixed member proportional (MMP) versus mixed member majoritarian (MMM),with some scholars often characterising the former as a subcategory of traditional PR

182 European Journal of Political Research 54: 182–196, 2015doi: 10.1111/1475-6765.12067

© 2014 European Consortium for Political ResearchPublished by John Wiley & Sons Ltd

systems (Lijphart 1994; Reynolds & Reilly 1997; Doorenspleet 2005). However, if, asHerron and Nishikawa (2001) and Ferrara (2004a) suggest, mixed systems are theoreticallyand empirically distinct in terms of competing electoral incentives, a focused analysis ofmixed systems appears warranted. Single country studies risk focusing on idiosyncraticfactors, while an analysis of only one election per country complicates identifying theevolution of party and voter adaptation to the institutional environment over time (Reed2001; Duch & Palmer 2002). While laying out potential mechanical and behavioural differ-ences between MMM and MMP systems, the limited number of district-level analysesrarely capture the range of other institutional influences such as the electoral threshold forparty list representation or the use of a fused ballot.

This study moves beyond the existing district-level analyses, with a dataset of 90 mixedsystem elections covering 16,298 district results in 23 countries labeled ‘Free’ or ‘PartiallyFree’ by Freedom House from 1990 (when their proliferation started) to 2012 (see Appen-dix Table 1).1 Previous district analyses (e.g., Moser & Scheiner 2004, 2009; Ferrara &Herron 2005) often cover only about a dozen elections, and usually only one or twoelections per country, potentially incurring a selection bias. Riera (2012), the largest districtanalysis to date, includes 15 countries and 57 elections, 11,038 districts in total. However,this still potentially creates a selection bias with its omission of several Asian and Africancases. In addition, while a large literature suggests several institutional factors in mixedsystems, consistency is lacking in the variables included in analyses. In contrast, this analysisincludes all of the commonly proposed institutional variables within mixed systems, as wellas co-existing electoral institutions, and thus provides for a more rigorous analysis of districtcompetition.

The article begins by briefly reviewing the literature on electoral competition and mixedsystems. This review is followed by an unpacking of the moving parts within mixed systemsand the broader competitive environment, generating several hypotheses. Regressionanalysis suggests the use of a fused ballot and compulsory voting laws increase the numberof district competitors, while the electoral threshold for party list representation reducesthis number. The conclusion highlights how this research aids in interpreting existingresearch on mixed systems and Duverger’s Law, and the importance of moving beyondnational-level analyses and areas for future work.

Duverger’s Law and mixed member systems

One of the most consistent findings in the electoral politics literature is Duverger’s Law: themechanical and psychological effects of SMDs lead to two-party competition,whereas largerdistrict magnitude produces a multiparty system (Duverger 1954; Downs 1957; Riker 1982;Cox & Shugart 1991).As there can only be one winner in SMDs, smaller parties are expectedto disappear or align with larger parties with greater chances of victory. Similarly, voters areunlikely to vote for candidates with little chance of winning (Cox 1997; Golder 2006).Whileoutliers exist (see Chhibber & Kollman 2004; Singer & Stephenson 2005), evidence from abroad selection of majoritarian and proportional systems is consistent with Duverger’s Law.

Duverger’s Law faces greater challenges among mixed legislative systems. Initial pro-ponents view these systems as a form of natural laboratory where both tiers behave

DUVERGER’S LAW IN MIXED LEGISLATIVE SYSTEMS 183

© 2014 European Consortium for Political Research

independently holding all else constant (Lancaster & Patterson 1990; Moser 1997;Stratmann & Baur 2002; Moser & Scheiner 2004). Increasing evidence suggests additionalincentives for more parties to run candidates in SMDs beyond that expected byDuverger. Duverger (1986) himself suggested that district competition could spill overinto the PR tier, yet most scholars supportive of a contamination thesis focus on addi-tional factors that cross tiers, such as party interests or qualifying for public funds, thatmay increase the number of district candidates (Herron & Nishikawa 2001; Ferrara et al.2005). For example, district competition produced more victories for smaller parties inLithuania’s 1992 election than the proportional tier (Martinaitis 2012: 394). According tothe contamination thesis, we should expect a deviation from ‘Duvergerian gravity’ andgreater dispersion of votes from the top two competitors (Cox & Schoppa 2002; Ferraraet al. 2005), with district outcomes conforming to Duverger being the exception ratherthan the norm.

The main institutional difference between classes of mixed legislative system addresseshow the tiers (seat types) are linked. Under a MMP, the overall distribution of seats isdictated by the party list vote, which compensates for the inherent disproportionality ofSMDs and creates an explicit contamination. In contrast, under a MMM, no explicit linkagebetween the seat types exist, with the allocation of SMDs and PR conducted separately,allowing for very disproportional outcomes. Previous research at both the national anddistrict levels consistently finds differences based on tier linkage (MMM versus MMP) interms of party fragmentation, fiscal policies, accountability and turnout (e.g., Doorenspleet2005; Ferrara & Herron 2005; Thames & Edwards 2006; Riera 2012). In terms of districtcompetition, non-viable district candidates are expected to have less incentive to run andvoters less incentive to vote sincerely under MMM, while there are minimal disincentivesfor non-viable district candidates under MMP.

Despite these expectations, a clear tier distinction is not patently evident in descriptivedata from 90 mixed elections. The vote concentration for the top two district candidatesdiffers marginally by tier type and not in the expected direction, with MMM averaging 76.97per cent of the vote compared to 78.46 per cent under MMP. Nagayama triangles provideadditional evidence suggesting that tier linkage alone does not adequately explain districtcompetition. Nagayama (1997) noticed that graphing the vote percentage for winningcandidates in SMDs on the x axis by the percentage received by the runner-up on the y axis(which cannot exceed 50 per cent) created a triangle-shaped distribution. Regions within aNagayama triangle correspond with trends in party competition (Reed 2001, 2007;Likhtenchtein & Yargomskaya 2005; Taagepera & Allik 2006; Diwakar 2007). In particular,the left side of the triangle corresponds with multiparty competition, while the top angleand right side of the triangle correspond with competitive and non-competitive two-partycompetition, respectively. Based on Duverger’s Law and the ‘best of both worlds’ thesis, theexpectation would be that district results in both MMM and MMP systems will concentrateat the top and right side of the triangle, whereas the contamination thesis would expect agreater percentage of districts to be located on the left side of the triangle consistent withmultiparty competition in districts. In addition, if MMM systems discourage additionalcandidates while minimal disincentives exist under MMP, the expectation would be forMMM districts to concentrate largely at the top and right side, with MMP concentrating onthe left side.

184 TIMOTHY S. RICH


When district-level data is aggregated into two triangles – MMM and MMP systems(Figure 1) – the majority of districts in MMP systems reside along the left side of thetriangle, consistent with fragmented multiparty systems and the contamination thesis.However, MMM districts cover much of the area of the entire triangle, showing no con-vergence to competing theoretical expectations. This pattern is partially a result of theresimply being more districts in MMM than MMP (13,124 versus 3,174), although the averagevote captured by the top two candidates differs marginally between MMM and MMP (76.9versus 78.5 per cent). A cursory view of Nagayama triangles suggests that while a contami-nation effect appears present in both types of mixed systems, the effects appear lessconsistent in MMM systems. Thus the MMM-MMP distinction alone provides limitedexplanatory leverage in explaining patterns in district competition and may mask theeffects of other factors within mixed systems.

Three factors may help explain this deviation from expectations. First is whether thesystem employs a one- or two-vote system. Most mixed systems provide voters with twophysical ballots – one for an SMD election and one for a party list (either at the national orregional level). However, a few use only one fused ballot (e.g., Albania in 1992, Mexico,Seychelles, South Korea in 1996–2000), where voters directly choose candidates in an SMDelection with the votes aggregated to allocate party seats.As such, one-vote systems encour-age voting for non-viable district candidates as a means to ensure marginal representationon the party list, in contrast to strategic voting for viable district candidates.Therefore, moredistricts would be found on the left side of the Nagayama triangle. As one of the fewcountries to switch between a one- and two-vote system, South Korea shows a decline in thenumber of district candidates after moving to a two-vote system in 2004 (Rich 2011).Similarly, in cross-national district analysis, Ferrara and Herron (2005) find a fused ballotcorrelates with a greater number of district candidates. Despite this explicit form of con-tamination, controls for fused ballots often are omitted from mixed system analyses.Descriptive statistics find a marginal difference between MMM systems with and withoutfused ballots (76.7 and 77 per cent, respectively), with a noticeably larger divergence underMMP (70.2 and 79.3 per cent, respectively).

MMM MMP

01

02

03

04

05

0R

unne

r U

p

0 10 20 30 40 50 60 70 80 90 100Winner

01

02

03

04

05

0R

unne

r U

p

0 10 20 30 40 50 60 70 80 90 100Winner

Figure 1. Nagayama triangles For MMM and MMP systems.



Second, if the party list creates a contamination effect on district competition, a closeranalysis of how party list seats are allocated is also warranted. Among formulas for allo-cating seats in PR systems, the literature identifies the d’Hondt formula as producing moredisproportional outcomes than other quota or divisor formulas as it rounds remainders tofavour larger parties (Lijphart 1990; Cox 1991; Schuster et al. 2003; Bochsler 2010). Yet itscontaminating influence on district competition remains unclear. In contrast, the electoralthreshold may have a more explicit contaminating effect. The electoral threshold sets thepercentage of the vote a party must receive to gain any PR seats. In pure PR, a lowthreshold encourages small parties to compete, whereas a higher threshold benefits largerparties and can encourage outcomes resembling two-party competition seen in pluralitysystems. Kostadinova (2002) finds that the threshold negatively correlates with the numberof national parties. Additionally, if running district candidates is a means to boost PR seats(e.g., Cox & Schoppa 2002), under a higher threshold this boost of PR votes is unlikely totranslate into additional party seats. If a contamination effect occurs, the electoral thresholdfor PR seats would be expected to similarly influence district competition by discouragingsmaller parties from contesting elections and disincentivising public support for remainingnon-viable entrants (e.g., Ferrara & Herron 2005). Similarly, a lower threshold whichencourages entrants for PR seats may also increase entrants in district competition, result-ing again with a greater concentration of districts on the left side of the Nagayama trianglethan previously expected.

Third, compulsory voting laws remain largely neglected in the mixed systems literature.Such laws have varying effects on voting behaviour, with most evidence suggesting anincrease in turnout (e.g., Lijphart 1999; Blais 2006; Baek 2009). Compulsory laws potentiallydistort Duvergerian expectations in district competition, in part by pushing those disinter-ested in the electoral process to vote.Thus, support for non-viable district candidates undercompulsory voting laws, either out of ignorance of the institutional effects or as a protestvote, may mirror the effects of a fused ballot and result in a greater number of candidatesat the district level and thus more districts on the left side of the Nagayama triangle.

Based on the existing literature, this analysis tests the following hypotheses:

H1: Mixed systems using a fused ballot will positively correlate with votefragmentation.

H2: The electoral threshold for party list seats will negatively correlate with votefragmentation.

H3: The existence of compulsory voting laws will positively correlate with votefragmentation.

Measuring district competition

While previous works address national-level outcomes, these may tell us very little aboutdistrict competition. After all, the constraining effect of SMDs on national party systems isultimately a product of district mechanics, and yet Duverger’s Law is seldom tested at the

186 TIMOTHY S. RICH


district level (e.g., Singer & Stephenson 2009). To analyse district competition in mixedsystems, I focus on the number of parties, which has proven crucial in explaining competi-tion and the electoral process more broadly (Lipset & Rokkan 1967; Powell 1982;Taagepera & Shugart 1989). The effective number of parties (ENP) provides a simpleweighted measure of the relevant parties (Laakso & Taagepera 1979) and remains thestandard measure of the number of parties in the literature. If Duverger’s Law holds,the expectation would be for a district-level ENP near 2. I apply the concept of ENP to thedistrict level, henceforth referred to the effective number of candidates (ENCs).2 Districtsin the dataset average 2.4 ENCs, which is suggestive of tier contamination.

Not only do factors within mixed systems vary considerably – for example, in terms oftier linkage or the electoral threshold – but these also do not operate in a vacuum and thusthe larger institutional environment requires consideration. For example, presidential,federal and bicameral systems potentially produce another form of contamination separatefrom that suggested in the mixed systems literature. Presidential systems encourage theformation of parties in general (Shugart & Carey 1992; Jones 1999); however, their influ-ence in mixed systems is unclear. For example, the presence of a directly elected presidentmay polarise competition, conducive to the reduction of parties (Linz 1994; Ackerman2000) or encourage coattail voting like that in the United States (Mondak 1990). Similarlyfederal systems and bicameralism may provide alternative means for party entry and thusdistort competition in mixed systems (see Lago & Martinez 2007). Despite these co-existinginstitutions potentially influencing outcomes in mixed systems, most mixed system researchonly controls for the influence of a directly elected president (e.g., Kostadinova2002; Herron & Nishikawa 2001; Thames & Edwards 2006; Riera 2012). In contrast, thisanalysis attempts to include both the internal and co-existing institutional factors influenc-ing competition.

For independent variables, I first include dummy variables for mixed membermajoritarian systems (MMM), the use of a one-vote fused systems (Fused Ballot) and thepresence of compulsory voting laws (Compulsory), as well as the formal threshold for seatsin the proportional list tier (Threshold). For additional institutional controls, I start withHerron and Nishikawa (2001), which included a dummy variable for the use of the d’Hondtformula for party list allocation (DhondtPR), the size of the legislative chamber (ChamberSize), the ethnic fractionalisation of the country (Ethnic Fractionalization),3 and dummyvariables for the presence of a directly elected president (President) and for post-communist countries (Post-communist).4 Next, I include combined Freedom House scoresof political rights and civil liberties recoded so that higher numbers equate to greaterfreedom (FreedomHouse);5 the number of elections under a mixed system (Number ofElections);6 and dummies for partially compensatory systems (Partially Compensatory),7

the presence of an additional legislative chamber (Bicameral), federal systems (Federal)and the use of regional PR lists rather than a national list (Regional PR).8 Of the includedindependent variables, only two correlate beyond 0.6: fused ballots and compulsory voting(0.63).

To test for robustness, as well as address potential temporal and spatial correlationspresuming that elections in the same country are correlated, I test four models. First, Ifollow Nishikawa and Herron (2004) and Kostadinova (2002) and employ an ordinary leastsquares (OLS) with robust standard errors clustered by country-election and a random



effects generalised least squares (RE GLS) regression.9 Next, following Riera’s (2012)analysis on the effective number of parties at the district level, I employ a poisson model.Finally, Following Taagepera et al. (2014), I also employ a mixed effects hierarchical modelthat includes random effects at both the country and the election levels.Table 1 provides theregression results.

Using OLS (model 1), MMM systems, along with our three main variables of interest,reach statistical significance in the expected direction. MMM systems correlate with adecline of fraction of an effective candidate (–0.154), consistent with conventionalwisdom on the salience of tier linkages and the fact that MMM systems encourage stra-tegic voting in district elections among those initially supportive of smaller parties. Whilethe contamination thesis largely focuses on the simple presence of PR seats increasingthe number of district candidates, the results here suggest an opposite contaminationexists where reducing the proportionality of the PR list discourages district entrants.Although substantively the effect of increasing the electoral threshold by 1 per cent isminor (less than a tenth of a candidate), this does suggest an unintended consequence ofan electoral rule often overlooked. In contrast, both fused ballots and compulsory votinglaws produce a boost of roughly a third of a candidate, distorting Duvergerian expecta-tions by creating additional powerful incentives for voters. In terms of additional controls,chamber size correlates with a substantively negligible boost in the number of candidates,while the presidential dummy correlated with roughly a decline in a third of candidate.Both the dummy variable for post-communist countries and the Freedom House measurepositively correlate with the number of candidates at 0.001. Finally, the use of a regionalPR list produces a larger substantive effect than the MMM variable, with a decline ofnearly a third of a candidate, suggesting that the structure of the PR list influences itscontaminative effects.

Model 2 employs a random effects GLS model, with results largely comparable to theoriginal model. Again, the effect of a fused ballot more than cancels out the reductiveeffects of MMM (the later which fails to reach significance), while the presence of com-pulsory voting laws increases the number of district candidates by a third. Of particularnote, the use of d’Hondt formula for allocating party list seats, known for advantaginglarger parties, surprisingly correlates with a boost of over a tenth of a candidate, butonly at the 0.05 level. The number of elections also correlates with a negligible declinein candidates, consistent with assumptions of a learning effect among voters, significantat 0.05.

Moving to model 3, a poisson model produced similar patterns, although the coefficientswere consistently roughly half of that of the previous models.

Finally, moving to a hierarchical model (model 4) again produces results similar to theoriginal two models, both in statistical and substantive significance. MMM systems nega-tively correlate with roughly a tenth of a candidate, while the presence of a fused ballot andcompulsory voting laws both exhibit a larger coefficient, encouraging additional entrantsbeyond what Duverger would expect.

In sum, across four model specifications, regression analysis provides consistent evi-dence not only that MMM correlates with fewer district candidates, but that the presenceof a fused ballot and compulsory voting laws have larger substantive influence in theopposite direction. The negative correlation between the electoral threshold and the

188 TIMOTHY S. RICH


Tabl

e1.

Cor

rela

tes

ofdi

stri

ctco

mpe

titi

on

Mod

el1

Mod

el2

Mod

el3

Mod

el4

Spec

ifica

tion

Clu

ster

edO

LS

Ran

dom

effe

cts

GL

SPo

isso

nM

ixed

HL

M

MM

M–0

.154

*(0

.068

)–0

.137

(0.0

71)

–0.0

66**

*(0

.020

)–0

.136

(0.0

77)

Fus

edba

llot

0.34

8***

(0.0

79)

0.34

9**

(0.1

13)

0.14

5***

(0.0

31)

0.33

6**

(0.1

16)

Thr

esho

ld–0

.061

***

(0.0

12)

–0.0

56**

*(0

.012

)–0

.027

***

(0.0

04)

–0.0

55**

*(0

.013

)

Com

puls

ory

0.32

9**

(0.1

20)

0.38

7***

(0.1

16)

0.14

5***

(0.0

33)

0.37

5**

(0.1

29)

Dho

ndt

PR

0.08

7(0

.070

)0.

133*

(0.0

62)

0.03

5(0

.025

)0.

138*

(0.0

64)

Cha

mbe

rsi

ze0.

001*

**(0

.000

)0.

001*

*(0

.000

)0.

000*

**(0

.000

)0.

001*

*(0

.000

)

Eth

nic

frac

tion

alis

atio

n–0

.020

(0.0

19)

–0.0

23(0

.022

)–0

.009

(0.0

06)

–0.0

20(0

.024

)

Pre

side

nt–0

.283

**(0

.103

)–0

.294

**(0

.114

)–0

.120

***

(0.0

34)

–0.2

86*

(0.1

22)

Post

-com

mun

ist

0.40

3***

(0.0

59)

0.42

2***

(0.0

85)

0.17

5***

(0.0

27)

0.41

1***

(0.0

90)

Free

dom

Hou

se0.

063*

**(0

.013

)0.

070*

**(0

.013

)0.

027*

**(0

.004

)0.

068*

**(0

.014

)

Num

ber

ofel

ecti

ons

0.00

1(0

.014

)–0

.027

*(0

.013

)0.

000

(0.0

03)

–0.0

26*

(0.0

13)

Par

tial

lyco

mpe

nsat

ory

–0.0

95(0

.078

)–0

.105

(0.0

89)

–0.0

42*

(0.0

20)

–0.0

96(0

.096

)

Fede

ral

0.25

8**

(0.0

95)

0.31

2***

(0.0

98)

0.10

7***

(0.0

30)

0.30

6**

(0.1

05)

Bic

amer

al–0

.204

(0.0

68)

–0.2

07**

(0.0

77)

–0.0

85**

*(0

.021

)–0

.205

*(0

.082

)

Reg

iona

lPR

–0.3

50**

*(0

.105

)–0

.359

***

(0.1

09)

–0.1

50**

*(0

.032

)–0

.354

**(0

.117

)

Con

stan

t2.

222*

**(0

.232

)2.

229*

**(0

.217

)0.

795*

**(0

.070

)2.

234*

**(0

.229

)

Cou

ntry

-lev

elin

terc

ept

0.04

8(0

.069

)

Ele

ctio

n-le

veli

nter

cept

0.18

0(0

.017

)

N16

,298

16,2

9816

,298

16,2

98

R2

0.19

40.

176

0.00

5

LR

Chi

221

1.18

Wal

dC

hi2

94.7

6

Not

es:

Coe

ffici

ents

,wit

hst

anda

rder

rors

inpa

rent

hese

s.**

*p

<0.

001;

**p

<0.

01;*

p<

0.05

.



number of candidates, while substantively minor, suggests an overlooked form of contami-nation. Consistent with findings elsewhere, districts in post-communist countries exhibitadditional competitors – the largest coefficients across all four models – while FreedomHouse scores exhibit a positive, though substantively minor, boost as well. Finally, regionalPR lists, perhaps in part due to providing less proportionality than national lists, correlatewith roughly a quarter of a candidate drop in three models.

Additional model specifications were tested both for robustness and as preliminary testsof additional claims regarding mixed systems. First, to identify whether the results weremotivated by non-competitive district elections, a dummy control was included for the mostcompetitive districts (defined as a winner’s margin of less than 10 per cent and alternativelytested at less than 5 per cent). While this inclusion positively correlated with ENCs in eachmodel at 0.001, neither specification of competitive districts changed the findings of theoriginal models. Second, restricting the dataset to countries labeled ‘Free’ by FreedomHouse produces consistent findings with the original OLS and poisson models, with lessconsistency on the four main variables of interest in the GLS and hierarchical models.Third, models were tested replacing Freedom House scores with Polity scores. Initialmodels on the whole dataset produced somewhat divergent results, with only the fusedballot variable consistent with the Freedom House models in all four models. However,when restricted to countries with a Polity score of six or higher (the common cut-off to beconsidered democratic in the literature), the results across all four models are remarkablyconsistent with those presented in Table 1. Fourth, due to the high correlation between thefused ballot and compulsory voting variables, models were tested with an interaction term.These models produced largely consistent results except that the compulsory voting vari-able failed to reach significance across models, while the interaction term produced a minorboost significant at 0.05 or greater in each model.

Finally, each original model was rerun first with the inclusion of an East Asian dummyvariable (Japan, South Korea, Taiwan) and second with a broader Asian dummy variable(also including Thailand and the Philippines) as a means to address debates regardingsystematic deviation of Asian democracies, usually couched in cultural terms (e.g., Zakaria1994; Inoguchi & Newman 1997; Sen 1999; Hicken 2006; Reilly 2007; Shin 2008). The EastAsian variable did not reach significance in any model, nor did the inclusion change thecore findings. In contrast, models that included the Asian variable found it significant at 0.01or stronger in every model, with a decline of roughly a quarter effective candidate, with theMMM significant in only two models. Although short of a fuller explanation of an Asiandivergence and what commonalities these countries may share,10 these findings suggest thepossibility of a divergence separate from just the institutional components of their mixedsystems.

Overall, these findings suggest factors within mixed systems and the broader electoralenvironment that influence outcomes. Evidence regarding fused ballots, electoral thresh-olds for PR seats and compulsory voting laws all are consistent with the proposed hypoth-eses, while the evidence regarding MMM systems is largely consistent with conventionalwisdom. Since the variables are national-level factors, elaborating on a microcausal mecha-nism at the district level admittedly remains nebulous – not unlike previous research.Unfortunately, the lack of comparative data for district-level elections prevents a moremicrolevel approach. However, the findings justify the further unpacking of institutional

190 TIMOTHY S. RICH


variations within the family of mixed systems and provide additional evidence of a con-tamination effect distorting Duvergerian expectations.

Conclusion

As mixed systems proliferate, anticipating their institutional effects is critical in limitingthe discrepancy between what the public and elected officials expect and the actualoutcome of the electoral process. Moving beyond national-level analyses, this study findsthat in addition to MMM three factors largely absent in previous research (i.e., fusedballots, the electoral thresholds for PR seats and the presence of compulsory voting laws)appear to influence district competition, highlighting the importance of analysing themany moving parties within mixed systems and the broader electoral environment. Thisanalysis moves us closer to identifying the conditions in which Duverger’s Law may nothold in mixed systems, rather than assuming an inherent yet unmeasured contamination.If promoting two-candidate-dominated competition in districts is desirable, this analysissuggests that would be reformers consider factors beyond the MMM-MMP distinction. Inparticular, such reforms should avoid both fused ballots and compulsory voting laws,which, despite the latter encouraging broader citizen participation, create incentives inconflict with Duverger’s Law. Furthermore, the findings here suggest how the PR tierpotentially contaminates district competition as the electoral threshold negatively corre-lates with the number of candidates. Increasing the electoral threshold, while potentiallydecried by the public and smaller parties as a mean to restrict competition, appears toprovide a relatively simplistic means to encourage two-party competition without whole-sale electoral change.

How voters interpret mixed system institutions remains poorly understood. Thisanalysis does not suggest that voters necessarily are aware of the myriad of institutionaleffects on district competition, but that seemingly minor national-level variations appearto have substantive effects at the district level. While this cross-national analysis providesinsight on national-level correlates to district competition, future analyses should expandupon our limited comparative data of district-level dynamics, such as to the extent incum-bency advantages assist Duvergerian pressures. In addition, the stability of partiesover multiple elections, as well levels of competition and funding laws should shed addi-tional light on district competition. Similarly, tracking individual districts over time maymore accurately capture the learning effects in mixed systems over time. Despite suchlimitations, this analysis problematises often overlooked aspects of mixed systems whileempirically testing on a more representative sample of district elections than previousresearch.

Mixed legislative systems arise in diverse contexts, but without cross-national analysisfrom a similarly representative set of cases our knowledge of general patterns will remainlimited. Moving beyond case-specific explanations gives new adopters a more accuratebaseline in which to evaluate their particular mixed system and prevents labeling examplesas divergent based on expectations from frequently analysed cases such as Germany, NewZealand and Japan. Mixed systems may confound Duvergerian expectations, but broadercross-national studies aid in identifying the limits of this divergence.



Supporting Information

Additional Supporting Information may be found in the online version of this article at thepublisher’s web-site:

Table 1A: Inclusion of Control for Competitive (10) DistrictsTable 1B: Inclusion of Control for Competitive (5) DistrictsTable 1C: Only Districts in Countries Labeled ‘Free’Table 1D: Replacing Freedom House Scores With PolityTable 1E: Only Districts With Polity Scores of 6 or BetterTable 1F: Inclusion of an Interaction Between Fused Ballots and Compulsory VotingTable 1G: Inclusion of Control for East Asian CountriesTable 1H: Inclusion of Control for Asian Countries

Notes

1. I include only cases which at minimum have (a) multiple single member one-vote districts besides thoseinstituted to represent minority groups and (b) proportional list seats consistently allocated at thenational and/or regional level that overlap with the nominal tier. These criteria closely match those ofShugart and Wattenberg (2001), and comprise the vast majority of mixed systems mentioned in theliterature. I exclude countries labeled ‘Not Free’ by Freedom House due to the inability to separateelectoral institutional effects from the regime’s broader coercive effects (e.g., Guinea, Kazakhstan,Pakistan and Tajikistan).

2. Due to data constraints (many of the countries included in this study only identified the top twocandidates by name/party), I lump all votes beyond the top two candidates as one ‘effective’ party.Admittedly this under-represents fractionalisation, but allows for a much larger number of districtelections to be used for analysis.

3. This measure attempts to tap into the number of social cleavages, which should also influence thenumber of contestants (Ordeshook & Shvetsova 1994; Cox 1997; Clark & Golder 2006; Brambor et al.2007). Ethnic heterogeneity is measured as the effective number of ethnic groups within the country.All

Appendix Table 1. Countries and elections included in district analysis

Albania 1997, 2001, 2005 Mexico 1991, 1994, 1997, 2000, 2003,2006, 2009, 2012

Armenia 1999, 2007, 2012 Nepal 2008

Bolivia 1997, 2002, 2005, 2009 New Zealand 1996, 1999, 2000, 2005, 2008,2011

Bulgaria 2009 Philippines 1998, 2001, 2004, 2007, 2010

Croatia 1992, 1995 Russia 1993, 1995, 1999, 2003

Georgia 1995, 1999, 2004, 2008, 2012 Seychelles 1998, 2002, 2007, 2011

Germany 1990, 1994, 1998, 2002, 2005, 2009 South Korea 1996, 2000, 2004, 2008, 2012

Hungary 1990, 1994, 1998, 2002, 2006, 2010 Taiwan 2008, 2012

Italy 1994, 1996, 2001 Thailand 2001, 2005, 2011

Japan 1996, 2000, 2003, 2005, 2009, 2012 Ukraine 1998, 2002

Lesotho 2002, 2007, 2012 Venezuela 1998, 2000

Lithuania 1992, 1996, 2000, 2004, 2008, 2012

192 TIMOTHY S. RICH


data comes from the CIA Factbook, except for two countries where this source did not provide anethnic breakdown (i.e., Seychelles and Venezuela). Estimates of the ethnic heterogeneity were pro-duced from government sources.

4. Mixed systems have been particularly popular in post-communist countries where democratisation,party institutionalisation and electoral reforms coincided (Bielasiak 2002).

5. As well as a measure of the openness of competition, Freedom House scores attempt to approximatethe availability of information regarding the electoral system.

6. A system was considered different if the compensatory system changed or if the number of ballotschanged as these two factors would likely have an influence on party strategy as well as voter compre-hension of the system. While Germany has used MMP since 1957, the 1990 election was the first afterunification. Because of this, I coded this election as the first under the system. Also see Moser andScheiner (2004).

7. While technically MMM, partially compensatory systems (Hungary, Italy and Mexico) provide addi-tional rules that limit the disproportionality of outcomes. For example, in Mexico, an extra provisionprevents a single party from winning more than 315 seats, limited further to 300 seats if the partyreceives less than 60% of the national vote. In Italy, negative voter transfers under the scoparo systemsubtracted PR votes for every SMD a party won. Some scholars view these as essentially a thirdcategory (see, e.g., Ferrara 2004b). Removing this variable produces results largely consistent with themodels presented here.

8. Of these independent variables, only two are correlated above 0.6: fused ballots and compulsory voting.9. Nishikawa and Herron (2004) use clustered errors by country, but focus on national-level election

results. Unlike them, I do not employ a standard OLS based on the assumption that errors correlateover time within individual countries. A feasible generalised least squares model (FGLS) is also notappropriate in that it potentially significantly under-estimates the standard errors given that the numberof time periods (elections) is small in relation to the number of countries. Similarly, OLS with panelcorrected standard errors (PCSE) requires all cases (i.e., countries in this analysis) to have some timeperiods (i.e., years) in common (see Beck & Katz 1995).

10. Asia, after all, is not homogenous, nor is there a single idea of Asia (Acharya 2010: 1001).

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Address for correspondence: Timothy S. Rich, Western Kentucky University, Grise Hall – 311, 1906 CollegeHeights Boulevard, Bowling Green, KY 42101, USA. E-mail: [email protected]

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