Clark, Golder / Rehabilitating Duverger - PDF document

Clark, Golder / Rehabilitating Duverger’s TheoryDuverger’s TheoryTesting the Mechanical andWilliam Roberts ClarkUniversity of Michigan, Ann ArborFlorida State University, TallahasseeAlthoughDuvergeristraditionallyseenassynonymouswiththeinstitution-alistapproachtopartysystems,thisarticleshowsthathebelievedsocialpres-sureswerethedrivingforcebehindthemultiplicationofparties.Electoralinstitutionsareimportant,butonlybecausetheydeterminetheextenttowhichsocialforcesaretranslatedintopoliticalparties.Althoughtheliteraturehasfinallycometorealizethatsocialandinstitutionalforcesinteracttoshapepartysystems,scholarsstilldonotseemtofullyunderstoodtheimplicationsofDuverger’stheory.Thisarticleshowsthatexistingresearchemploysflawedstatisticalspecifications,makesinferentialerrors,anddoesnotcalculatede-siredquantitiesofinterest.Usinganewdatasetthatincludeselectionssince1946,theauthorsreexamineDuverger’stheoryandfindthatmoderntestslargelybearouthisexpectationswhenproperlyspecifiedandinterpreted.Thisanalysisalsoextendscurrentresearchbyspecificallyestimatingthemechanical and strategic modifying effects of electoral institutions.Keywords:Duverger;socialheterogeneity;partysystems;electoralheliteratureaddressingthenumberofpoliticalpartiesinapolityisoneoftherichestincomparativepolitics(Cox,1997;Duverger,1954/1963;Lijphart,1994;Lipset&Rokkan,1967;Riker,1982).Bothinstitutionalandsociologicalbranchesofthisliteraturehaveapedigreedhistory.Recently,scholarshaveattemptedtocombinetheseapproachesintoacoherentexplanationofpartysystemdevelopmentbyarguingthatsociologicalandinstitutionalfactorshavesomesortofinteractiveeffectonthenumberofparties Comparative Political StudiesVolume 39 Number 6August 2006679-708http://cps.sagepub.comhttp://online.sagepub.com theinfluenceofballotsystemscouldbecomparedtothatofabrakeoranaccelerator.Themultiplicationofparties,whicharisesasaresultofotherfactors,isfacilitatedbyonetypeofelectoralsystemandhinderedbyanother.Ballotprocedure,however,hasnorealdrivingpower.ThemostdecisiveinfluencesinthisrespectareaspectsofthelifeofthenationsuchasideologiesandparticuThusfarfromtakingsocialstructureas“moreorlessaresidualerror,somethingthatmightperturbapartysystemawayfromitscentraltendencydefinedbytheelectorallaw,”asAmorimNetoandCox(1997,p.151)claimintheirmuch-citedanalysisofpartysystems,Duvergerclearlybelievesthatsocialforceswerethedrivingforcebehindthemultiplicationofparties.Duvergerseespoliticalpartiesasareflectionofsocialforcesorwhathecalls“spiritualfamilies.”Inhisview,thesefamiliesaremadeupofindividualswithasetofsociallydeterminedcommoninterests.Associaldevelopments(primarilyindustrializationandtheexpansionofthefranchise)increasethenumberofpoliticallymobilizedspiritualfamilies,Duvergerclaimsthatthenumberofpartiesincreaseaswell.WedonotmeantosuggestthatelectorallawsdonotplayanimportantroleforDuverger;theyobviouslydo,butonlybecausetheydetermine“thepresenceorabsenceof‘brakes’upontheten-dency[forparties]tomultiply”(Duverger,1952,p.1071).Inotherwords,electoralinstitutionsmodifytheeffectofsocialforcesonthecreationofpoliticalparties.Socialforcescreatemoreorlesspressureforthemultiplica-tionofpoliticalpartiesandelectorallawseitherpermitthesepressurestoberealizedortheyconstrainthembydiscouragingtheformationofnewparties.Duvergerarguesthatsingle-memberdistrictpluralityruleelectionsdis-couragetheformationofmorethantwoparties,nomatterwhethersocialforcesencouragealargenumberofpartiesornot.Incontrast,heobservesthatsuchabrakeontheformationofpartiesisabsent(orweaker)inmorepermissiveelectoralsystems.Asaresult,multipartysystemsarefreetoforminpermissivesystemssolongassocialfactorswarrantthem.ItfollowsthatDuverger’s(1954/1963)famousobservationthat“thesimplemajority[bywhichhemeansplurality]singleballotencouragesthetwo-partysystem;onthecontraryboththesimple-majoritysystemwithsecondballotandproportionalrepresentationfavourmultipartism”(p.239)ishisexplanationforthenumberofpartiesbutinstead,asetofempiricalimplicationsthatarededuciblefromhistheory.ItispreciselythefailuretorecognizethispointthatledDuvergertobelabeledasapureinstitutionalistandthatencouragedalmost40yearsofinstitutionalanalysesofpartysystemsthatlargelyignoresociologicalfactors.AlthoughDuverger’stheorygeneratesaclearexpectationthatthenumberofpartieswillbesmallwhentheelectoralsystemisnotpermissive,theClark, Golder / Rehabilitating Duverger’s Theory681 Electoralinstitutionsdeterminehowaccuratelypartysystemsreflectexistingsocialcleavagesthroughthestrategicincentivesthattheycreateforbothelitesandvoters.Forexample,itiswellknownthatsmalldistrictmagnitudesgrantconsiderableelectoraladvantagestolargeparties.ThisisillustratedquiteclearlyinBritainwheretheLaborandConservativepartiesaretypicallyawardedamuchlargershareofseatsthantheshareofvotestheyreceive.Itistheexistenceofthis“mechanicaleffect”thatcreatesincentivesforstrategicvotingonthepartofvotersandforstrategicentryorwithdrawalonthepartofpoliticalentrepreneurs(Cox,1997;Duverger,1954/1963).Membersofsocioeconomicgroupsrepresentedbysmallpartiesaremorelikelytovotestrategicallyiftheyfindthemselvesinsingle-memberdistrictelectoralsystemsthaniftheyvoteinmultimemberdistricts.Incontrast,thebenefitsofstrategicvotingareunlikelytoloomaslargeinhighlyproportionalsystems,suchasthoseinIsraelortheNetherlands.Inasimilarmanner,politicalentrepreneurswillbemorewillingtoformnewpartiestotakeadvantageofunrepresentedconstituenciesinpermissiveelectoralsystems.Inlesspermissivesystems,theseentrepreneursaremorelikelytopreferseekingelectedpositionbyrunningwithinanexistingparty.Thesestrategicconsiderationsindicatethatelectoralinstitutionsmodifytherelationshipbetweensocioeconomiccleavagesandthenumberofparties.Inparticular,thisframeworkindicatesthattherearetworeasonswhyacoun-trymighthaveasmallnumberofparties.First,itcouldbethecasethatthedemandforpartiesislowbecausetherearefewsocialcleavages.Inthissitua-tion,therewouldbefewpartieswhethertheelectoralinstitutionswereper-missiveornot.Second,itcouldbethecasethattheelectoralsystemisnotpermissive.Inthissituation,therewouldbeasmallnumberofpartiesevenifthedemandforpoliticalpartieswerehigh.Onlyapolitycharacterizedbybothahighdegreeofsocialheterogeneityandahighlypermissiveelectoralsystemisexpectedtoproducealargenumberofparties.Thislineofreasoning generates the following hypothesis:Hypothesis1:Socialheterogeneityincreasesthenumberofparties,butonlywhenelectoral institutions are sufficiently permissive.Clark, Golder / Rehabilitating Duverger’s Theory683problembecausesocialheterogeneityandelectoralinstitutionsarebothpredictorvariablesinthistheoreticalframework.Werecognizethatanendogeneityissuemaystillexistifonebelievesthatthenumberofpartiesdeterminesthechoiceofelectorallawsorthedegreeofsocialheterogeneity.Ourresponsetothisisthatelectoralinstitutionsandsocialheterogeneityarebothtypicallyquitesticky(atleastintheshortrun)andthattheycanthereforebetreatedasexogenously4.Onemightrestatethishypothesistoclaimthatelectoralinstitutionsinfluencethenumberofpartiesonlywhenthereisahighlevelofsocialheterogeneity.However,thisrestatementis whethertheinteractivemodelhasahigher(adjusted)thaneitherofthepuremodels.However,Duverger’stheoryisnotjustthatthereissomeinteractionbetweeninstitutionalandsociologicalfactors.Itismuchmoreconcretethanthat—socialheterogeneityshouldincreasethenumberofpartiesonlywhentheelectoralsystemissufficientlypermissive.Althoughitwillcomeasasurprisetomany,noneoftheexistingstudiesweciteaboveshowwhethersocialheterogeneitysignificantlyincreasesthenumberofpartieswhentheelectoralsystemispermissive.Althoughitispossibleforthereadertocalculatethemarginaleffectofsocialheterogeneityinpermissivesystems()withalittlealgebraicmanipulationusingthetableofresultsinthesearticles,itisnotpossibletodeterminewhethertheseeffectsaresignificantwithoutaccesstothevariance-covariancematrix.Thisisbecausethestandarderrorforthemarginaleffect var()var(

PartialInstitution=++× Institutioncov(Thereadercannotcalculatethisstandarderrorwhenisgreaterthan0withoutthecovarianceterm.Noneoftheexistingstudiesprovidethereaderwiththisterm.Asaresult,itisimpossibletoevaluateDuverger’sclaimthatsocialheterogeneityleadstosignificantlymorepartieswhenelec-toralinstitutionsarepermissivebasedontheevidencepresentedinthelitera-ture.Therecentstudiesalsofailtoprovideotherquantitiesofsubstantiveinterest,suchasthemagnitudeoftheeffectofsocialheterogeneityunderdif-ferentelectoralrulesorestimatesofthemechanicalandstrategiceffectsofAnotherproblemwithexistingstudiesisthattheyemployinteractionmodelsthataremisspecified.Forexample,allconstitutivetermsshouldbeincludedinmultiplicativeinteractionmodelsexceptinextremelyrarecircumstances(Bramboretal.,inpress).Thisisbecausealloftheparametersofinterestwillbeestimatedwithbiasifthecoefficientonanyomittedtermisnotprecisely0.Despitethesepotentiallydireconsequences,allofthearticlesweciteabovepresentresultsfrommodelswhereatleastoneconstitutivetermisomitted;manyshowresultswheremultipletermsareomitted.Forexample,thepreferredinteractionmodelsofOrdeshookandShvetsova(1994,p.114)andAmorimNetoandCox(1997,p.165)bothomittheconClark, Golder / Rehabilitating Duverger’s Theory6855.Constitutivetermsarethoseelementsthatconstitutetheinteractionterm.Thustheconstitutive terms in Equation 1 are6.Technically,biaswillresultunlessthecoefficientontheomittedtermis0orifthecoefficients from a regression of the omitted variable on the other variables are all 0. stitutiveterms.Wearecertainlynotsuggestingthatalloftheresultspresentedintheseanalysesarenecessarilywrong.However,wedobelievethatthereisapotentialforbiasandthatasaresult,incorrectinferencesmayhavebeendrawn.Finally,severalscholarsincorrectlyinterprettheresultsfromtheirinteractionmodels.Inparticular,itiscommonforauthorstointerpretthecoefficientsonconstitutivetermsasunconditionalmarginaleffectsjustastheywouldifthecoefficientscamefromalinear-additivemodel.Thisisclearlywrong.Forexample,Mozaffaretal.(2003,p.387)claimthatelectoralinstitutionssuchasdistrictmagnitudereducethenumberofpartiesbecausetheircoefficienton)isnegativeandsignificant.Likemanyothers,theyforgetthatthiscoefficientindicatesthemarginaleffectofelectoralsystempermissivenessonlywhensocialheterogeneityis0.Thisiseasytoseeonceoneremembersthatthemarginaleffectofelectoralsystempermissivenessis PartiesInstitutionSocialNotethatnotonlyistheirinterpretationincorrectbutalsothisparticularcoef-ficient()issubstantivelymeaninglessbecausesocialheterogeneityisnever 0 in the real world.Itshouldbepointedoutthatourcriticismsoftheexistingliteraturearenotminoreconometricquibbleswithlittlesubstantiveimport.Forexample,areanalysisoftheexaminationofAfricanpartysystemsbyMozaffaretal.(2003)illustratesthatalmostnoneoftheirsubstantiveconclusionsregardingtheeffectofelectoralinstitutions,presidentialelections,andethnicheterogeneityaresupportedbythedataoncetheirmodelisfullyspecifiedandcorrectlyinterpreted(Bramboretal.,inpress).GiventheeconometricproblemswiththeexistingliteratureandtheabsenceoftherequiredquantitiesofinterestnecessarytoevaluateDuverger’stheory,itisworthwhilereexaminingthesociologicalandinstitutionaldeterminantsofpartysystemsize.WebuildontheexistingliteraturebyusingareanalysisofAmorimNetoandCox(1997)asabenchmarkagainstwhichtocomparetheadditionalinformationsuppliedbyourinvestigation.686Comparative Political Studies receiveasizeableshareofvotesineverydistrictinthecountrybutnotwinapluralityofvotesinanyoneconstituency.Inthisextremecase,thenumberofpartiesreceivingvoteswouldclearlybelargerthanthenumberofpartiesawardedseats.However,anidenticaldistributionofvotesacrossmultimemberdistrictsemployingaproportionalrepresentationformulacanbeexpectedtoyieldaconsiderablenumberofseatsforpartiesthatwouldnotwinapluralityinanysingle-memberdistrict.Thismeansthatmoreelectoralpartiescanactuallywinseatsandobtainrepresentationinthelegislatureasthedistrictmagnitudeincreases,holdingthedistributionofvotesconstant.UsingDuverger’smetaphorofelectoralinstitutionsasabrake,thismeansthatthenumberofelectoralpartiesshouldbetranslatedintolegislativepartieswithlessfrictionasdistrictmagnitudebecomeslarger.Thenumberofelectoralpartiesshouldalsobetranslatedintolegislativepartieswithlessfrictionwhenthereareuppertierseats(AmorimNeto&Cox,1997).Thisisbecausetheseseatsaretypicallycompensatoryinnature.Forexample,39seatsaredistributedinasecondtieramongthepartiesinSwedenwhoseshareoftheseatsislessthantheirshareofthevotes.Thusonewouldexpectthenumberoflegislativepartiestoincreaseasthenumberofelectoralpartiesgrows.Moreover,theextenttowhichthisoccursshoulddependontheproportionalityoftheelectoralsystem’smechanicaleffects. More specific, the following can be hypothesized:Hypothesis2:Thenumberofelectoralpartiesshouldhaveagreaterpositiveeffecton the number of legislative parties when district magnitude is large.Hypothesis3:Thenumberofelectoralpartiesshouldhaveagreaterpositiveeffectonthenumberoflegislativepartieswhenthepercentageofseatsallocatedinupper tiers is large.A Test for the MechanicalLegislativePartiesElectoralPartiesMagnitudeElectoralPartiesMagnitudeElectoralPartiesLegislativePartiesmeasurestheeffectivenumberoflegislativeparties,ElectoralPartiesmeasurestheeffectivenumberofelectoralparties.688Comparative Political Studies9.Typically,theeffectivenumberofpartiesiscalculatedas1/,whereisthepercentageofseatsorvoteswonbytheparty.However,measurementproblemsarisewhenofficialelectoral becauseitwasnotpossibletoidentifyformalpartiesinthesecountries.WealsodroppedColombianelectionsbetween1958and1970becausetherewasaconstitutionalagreementduringthisperiodthattheConservativePartyandtheLiberalPartywouldalternateinpowerandsharethelegislativeseatsirrespectiveoftheelectoralresults.ElectionsinPapuaNewGuineaandMauritius,aswellasMaltasince1987andSouthKoreabetween1988and1995,werealsoomittedbecausetheuppertierseatsinthesecountriescannotbeconsideredcompensatory.Althoughtheseelectionsareomittedfortheoreticalreasons,severalothersaredroppedbecauseofmissingdataononeormoreoftheexplanatoryvariables.Together,theseomissionsleaveatotalof680legislativeelections.WetestHypotheses2and3usingbothcross-sectionalandpooledanalyses.Inthepooledanalyses,theestimationissuesthattypicallyarisewithlongitudinaldatawerecomplicatedbythestructureofourparticulardata.ThecrucialthingtorememberisthatalthoughOLSisconsistentwithlongitudinaldata,thestandarderrorsmaybeincorrect.Feasiblegeneralizedleastsquaresoffersonesolutiontothisproblem.However,feasiblegeneralizedleastsquaresisinappropriateherebecauseitwouldsignificantlyunderesti-matethestandarderrorsgiventhatthenumberoftimeperiods(orelections)isnotverylargecomparedtothenumberofcountriesinourdataset(Beck&Katz,1995).Panel-correctedstandarderrors(PCSEs)mightbeanothersolu-tion.However,becausetheaccuracyofPCSEsincreaseswiththenumberofelectionspercountryandmanycountriesinourdatasethavehadfewelec-tions,itisreasonabletoquestiontheusefulnessofPCSEsinthisparticularapplication.Asaresult,weuseathirdoptionandemployOLSwithrobuststandarderrorsclusteredbycountry.Althoughitiscommontoincludealaggeddependentvariablewithlongitudinaldatatotakeaccountofserialcorrelation,thestructureofourdatasuggeststhatthiswouldbeinadvisablehere.Oneproblemisthatourobservationsdonotcomeinregularintervalseitherwithincountriesoracrosscountries.Inthesecircumstances,itishardtoknowhowonewouldinterprettheestimatedcoefficientonanylaggeddependentvariablewereonetobeincluded.Thesecondproblemisthatthepanelnatureofourdataset(smalllarge)meansthattheinclusionofalaggeddependentvariablewouldsignificantlyreducethesamplesizeanddropallcountriesthatonlyeverexperiencedoneelectioninanygivendemocraticperiod.Thusforboththeoreticalandpracticalreasons,wepresentresultsfrommodelswherethereisnolaggeddependentvariable.AnyanxiousreadersatthispointshouldbecomfortedbythefactthatemployingPCSEswithorwithoutalaggeddependentvariabledoesnotqualitativelychangeourinferences.690Comparative Political Studies Table 1 Dependent Variable: Effective Number of Legislative PartiesCross-Sectional AnalysisPooled Analysis 1980s1980s1990s1946 to 2000AmorimAmorim1990sEstablished1946 to 2000EstablishedRegressorNeto & Cox DataWhole SampleDemocraciesWhole SampleDemocraciesElectoralParties0.51***(0.05)0.38***(0.06)0.39***(0.07)0.46***(0.07)0.61***(0.06)0.63***(0.06)ln(Magnitude)–0.31***(0.10)–0.14(0.15)–0.26(0.19)–0.02(0.06)–0.04(0.06)UppertierSeats0.01(0.01)0.019(0.014)–0.01(0.02)0.02**(0.01)0.01(0.01)ElectoralPartiesln(Magnitude)0.08***(0.01)0.16***(0.03)0.09***(0.04)0.13***(0.04)0.05**(0.02)0.06**(0.02)ElectoralPartiesUppertierSeats0.004***(0.001)0.002(0.002)–0.003(0.002)0.007(0.005)–0.004(0.003)0.001(0.003)Constant0.58***(0.13)0.99***(0.20)1.20***(0.29)0.90***(0.29)0.52**(0.17)0.46**(0.16)Observations54548154680604.93.94.76.85.85.88 Note:Standarderrorsaregiveninparenthesesforcross-sectionalmodels;robuststandarderrorsclusteredbycountryareusedforthepooledmodelb. Established Democracies omits elections from countries that transitioned to democracy after 1989. Intheprevioussection,weexaminedhowelectoralinstitutionshaveamechanicalreductiveeffectonthenumberoflegislativepartiesevenwhenvoterbehaviorisexogenouslydetermined.Inthissection,weaddressthewaysinwhichelectorallawsmayhaveasecondreductiveeffectbyinfluencingthebehaviorofvotersandcandidates.Duverger(1954/1963)referstothebehavioraleffectofnonpermissiveelectorallawsonvotersandcandidatesasthe“psychologicaleffect.”Inasimilarmanner,Riker(1982)alertsustothewayinwhichelectorallawsencouragestrategicvotingandthestrategicentryofcandidates.Inthissection,wealsoreexaminethequestionastowhetherpresidentialelectionsinfluencethenumberofparties.AccordingtoDuverger,themechanicaleffectofelectoralinstitutionsfavoringlargepartiescreatesincentivesforstrategicentryandstrategicvoting.Partiesthathavenochanceofwinningareencouragedtowithdraw.Ifthesepartiesfailtowithdraw,thenvoterswillhaveanincentivetovotestrate-gicallyinfavorofbetterplacedparties.Thusdisproportionalsystemswithlowdistrictmagnitudesarelikelytoreducethedemandforpoliticalpartiescreatedbysocialheterogeneity.Incontrast,onemightexpectsocialhetero-geneitytohaveagreaterimpactinthosecountriesthathaveuppertierseats(AmorimNeto&Cox,1997).Thereasonforthisisthatthecompensatorynatureoftheseseatsencouragespoliticalpartiestoremaininelectoralcon-testsbecauseoftheirincreasedlikelihoodofactuallywinningaseat.Votersmayalsobemorewillingtosupportminorpartiesinthesecountriesbecausetheirvotesarelesslikelytobewasted.However,notethattheevidencewepresentinthelastsectionsuggeststhatuppertierseatsmaynothavethispredictedeffect.Becauseuppertierseatsarenotfoundtohaveamechanicaleffectonthetranslationofvotesintoseats,itisunlikelythattheywouldgenerateastrategiceffectonthepartofvotersandpartyelites.Thisisanempiricalissue,ofcourse,andcaneasilybetested.Theargumentwepresentabove,Hypothesis4:Socialheterogeneityincreasesthenumberofelectoralpartiesonlywhen the district magnitude is sufficiently large.Hypothesis5:SocialheterogeneitywillincreasethenumberofelectoralpartiestoRecentresearchsuggeststhatpresidentialelectionsalsohaveanimportantimpactonlegislativeelections(Jones,1994).Thusfar,theresultsaresomewhatcontradictory.Someresearchfindsthatpresidentialelectionsincrease694Comparative Political Studies ElectoralPartiesPresidentCandidatesmeasuretheeffectivenumberofelectoralpartiesandpresidentialcandidates,respectively.theeffectivenumberofethnicgroupsandisourproxyforsocialheterogeneity.Althoughthenumberofethnicgroupsrepresentsjustoneelementofsocialheterogeneity,itisaproxythatallpreviousanalysesuseand,therefore,providesthebestmeansforcomparingourresultswithexistingfindings.Onceagain,Magnitudeistheaveragedistrictmagnitudeandisthepercentageofassemblyseatsallocatedinuppertiers.Finally,Proximitymeasuresthetemporalproximityofpresidentialandlegislativeelections. 212istheyearofthelegislativeelection,istheyearofthepreviouspresidentialelection,andistheyearofthenextpresidentialelection(AmorimNeto&Cox,1997).Thisequals1wheneverpresidentialandlegis-lativeelectionsareheldconcurrentlyand0whenevertherearemidtermleg-islativeelectionsornodirectpresidentialelections.ThevariousinteractionThemarginaleffectofethnicheterogeneityonthenumberofelectoralpartiesis


ElectoralPartiesEthnicMagnitudeUppe=++167ln()rtierSeatsFollowingDuverger’stheory,ethnicheterogeneityshouldnotinfluencethenumberofelectoralpartiesinnonpermissiveelectoralsystems.Thusshouldbe0.However,themarginaleffectofethnicheterogeneityshouldbecomepositiveandsignificantoncetheelectoralsystemissufficientlypermissive.Becausedistrictmagnitudeanduppertierseatsarebothexpectedtoincreasethepermissivenessofelectoralinstitutions,shouldbepositive. The marginal effect of temporally proximate presidential elections is ElectoralPartiesoximityesidentialCandidates696Comparative Political Studies12.Unliketheexistingliterature,whichtypicallymeasuresthenumberofethnicgroupsusingtheindexofethnolinguisticfractionalization,weemployanewer,andarguablybetter,measure of ethnic fragmentation drawn from Fearon (2003). Table 2 Dependent Variable: Effective Number of Electoral PartiesCross-Sectional AnalysisPooled Analysis 1980s1980s1990s1946 to 2000AmorimAmorim1990sEstablished1946 to 2000EstablishedRegressorNeto & Cox DataWhole SampleDemocraciesWhole SampleDemocraciesEthnic–0.05(0.28)0.06(0.37)–0.70(0.68)0.19(0.13)0.11(0.14)ln(Magnitude)–0.08(0.30)0.51(0.44)–0.61(0.59)0.33*(0.20)0.08(0.23)UppertierSeats0.04**(0.01)–0.07(0.04)0.01(0.02)–0.02(0.06)0.05***(0.02)–0.06*(0.03)PresidentCandidates0.22(0.27)0.36(0.26)0.07(0.22)0.35**(0.16)0.26*(0.15)Proximity–6.05***(0.88)–5.88***(0.84)–4.19***(1.26)–4.95***(1.24)–3.42***(0.55)–3.10***(0.46)ln(Magnitude)0.39***(0.07)0.37*(0.20)–0.09(0.17)0.63*(0.34)0.08(0.12)0.26(0.17)UppertierSeats0.07***(0.02)–0.005(0.01)0.01(0.04)–0.02**(0.01)0.06***(0.02)Proximity2.09***(0.26)1.84***(0.43)0.99**(0.46)1.42***(0.44)0.80***(0.23)0.68***(0.23)Constant2.40***(0.21)2.60***(0.51)4.08***(0.95)5.15***(1.32)2.81***(0.34)2.92***(0.35)Observations51516239555487.71.77.29.48.30.40 Note:Standarderrorsaregiveninparenthesesforcross-sectionalmodels;robuststandarderrorsclusteredbycountryareusedforthepooledmodelb. Established Democracies omits elections from countries that transitioned to democracy after 1989. Theevidencetosupporttheclaimthatethnicheterogeneityincreasesthenumberofpartiesonlywhendistrictmagnitudeissufficientlylargealsoappearstobemixedatfirstsight.Ononehand,ethnicheterogeneityfailstoaffectthenumberofpartieswhendistrictmagnitudeis1,asallofthemodelspredict(isalwaysinsignificant).Ontheotherhand,thecoefficientonMagnitude)ispositiveandsignificantinonlyhalfofthemodels.However,itisimportanttorememberthatwearenotprimarilyinterestedinwhetherthecoefficientonthisinteractiontermissignificant.Instead,whatwereallywanttoknowiswhetherthemarginaleffectofethnicheterogeneityispositiveandsignificantoncetheelectoralsystembecomessufficientlypermissive.Figure1plotsthismarginaleffectacrosstheobservedrangeofdistrictmagnitudeforthecasewhentherearenouppertierseats.Itdoesthisforallthreemodelsthatomitdemocraciesthatemergedafter1989.Atthetop,Figure1apresentstheresultsfromthepooledmodelwithestablisheddemocracies.Belowthisaretheequivalentfiguresforthe1980scross-section(Figure1b)andthe1990scross-sectionwithestablisheddemocra-cies(Figure1c).Thesolidslopinglinesindicatehowthemarginaleffectofethnicheterogeneitychangesastheaveragedistrictmagnitudeincreases.Onecanseetheconditionsunderwhichethnicheterogeneityhasasignifi-canteffectonthenumberofpartiesbyconsideringthetwo-tailed90%confi-denceintervals(dashedlines)thatareshown.Theeffectofethnicheteroge-neityissignificantwhenevertheupperandlowerboundsoftheconfidenceintervalarebotheitheraboveorbelowthe0line.Allthreefiguresclearlyillustratethatinestablisheddemocracies,ethnicheterogeneitysignificantlyincreasesthenumberofpartiesoncetheelectoralsystemissufficientlypermissive.ThisisexactlywhatDuverger’stheorypredicts.Tobemorespecific,Figure1a,basedonthepooledmodelwithestablisheddemocracies,indicatesthatethnicheterogeneitywillincreasethenumberofelectoralpartiesoncewemovebeyondnonpermissiveelectoralsystemswithsingle-memberdistricts—whenln(Magnitude)=0.Althoughnotshownhere,theequivalentfiguresfromthetwomodelsthatincludecountriesthattransitionedtodemocracyafter1989providemuchweakerevidenceinsupportofDuverger’stheory.Infact,the1990scross-sectionisparticularlyanomalousgiventhatthecoefficientonMagnitude)isnegative(althoughinsignificant).Theseweakerresultsareperhapsnottoosurprisinggiventhatthehypothesislinkingelectoralsystempermissivenessandethnicheterogeneitytothenumberofpartieslargely700Comparative Political Studies14.Wecouldexaminethemodifyingeffectofuppertierseatsbydrawingadditionalslopinglinescorrespondingtovariousuppertierseatallocations.However,wedonotdothisbecausethere is no robust evidence that upper tier seats ever have the predicted modifying effect. assumesthatpartysystemsareinsomesortof“equilibrium.”Manyofthenewlydemocraticcountriesthatwereincludedinthesetwomodelsmaysim-plynothavereachedtheirequilibriumyet,therebyweakeningtheresults.Thistentativeexplanationreceivessomesupportfromthefactthatdistrictmagnitudedoeshavethepredictedmodifyingeffectinthe1990scrosssectiononcewefocusonestablisheddemocraciesonly.Whatabouttheeffectofpresidentialelections?TheevidencepresentedinTable2providesconsiderablesupportfortheclaimthattemporallyproximatepresidentialelectionsreducethenumberofpartieswhentherearefewpresidentialcandidates(isnegativeandsignificantinallmodels)butthatthisreductiveeffectbecomesweakerasthenumberofpresidentialcandidatesincreases(ispositiveandsignificantinallmodels).Figure2plotsthemarginaleffectoftemporallyproximatepresidentialelections.Thesolidslopinglineindicateshowthismarginaleffectismodifiedbythenumberofpresidentialcandidates.Onceagain,onecandiscernwhetherthiseffectissignificantbyexaminingthetwo-tailed90%confidenceintervalsthataredrawnaroundit.Itshouldbeclearthattemporallyproximatepresidentialelectionshaveastrongreductiveeffectonthenumberofpartieswhentherearefewpresidentialcandidates.Aspredicted,thisreductiveeffectdeclinesasthenumberofcandidatesincreases.Oncethenumberofpresidentialcandidatesbecomessufficientlylarge,presidentialelectionsstophavingasignificanteffectonthenumberofparties.AlthoughFigure2isbasedonthepooled702Comparative Political Studies TheMarginalEffectofTemporallyProximatePresidentialElectionsontheEffectiveNumberofElectoralParties modelwithestablisheddemocracies,alloftheotherspecificationsproducealmostidenticalfiguresirrespectiveofwhethertheyincludeorexcludethosenewdemocraciesthatemergedafter1989.Manypreviousstudiesfindthatpresidentialelectionseitherreducethenumberofelectoralparties(Cox,1997;Mozaffaretal.,2003;Shugart&Carey,1992)orhavenoeffect(Coppedge,2002;Samuels,2000).Oneexplanationfortheseconflictingresultsmightliewiththedifferentgeographicsamplesemployedintheseanalyses.However,itisinterestingtonotethatFigure2offersanotherpotentialexplanation.Thefigureindicatesthatpresidentialelectionswillreducethenumberofpartiesinsomecountriesbuthavenoeffectinothersbecausetheeffectoftemporallyproximatepresidentialelectionsdependsonthenumberofpresidentialcandidates.Tosummarize,ourbriefinvestigationofthestrategicmodifyingeffectofelectoralrulesandtheimpactofpresidentialelectionsgeneratesseveralimportantresults.Mostsignificant,thereisstrongevidencetosupportDuverger’stheorythatsocialheterogeneity,asmeasuredbyethnicheteroge-neity,significantlyincreasesthenumberofelectoralpartiesoncetheelec-toralsystembecomessufficientlypermissive.Second,wefindthatthecon-clusionreachedbyAmorimNetoandCox(1997)regardingtheimpactofuppertierseatsonthenumberofelectoralpartiesisbasedonasingleextremeoutlierintheirdataset(Belgium).Ourownresultssuggestthatuppertierseatshavelittlestrategicimpactonvotersandpoliticalelitesbecausethereisnoconsistentandcompellingevidencethattheyeverhavethepredictedmodifyingeffectonethnicheterogeneity.Finally,ouranalysisindicatestheimportanceofconsideringthenumberofpresidentialcandidateswhenad-dressingtheimpactofpresidentialelectionsonpartysystemsize.Bydoingso,wecanfindapotentialexplanationforsomeofthecontradictoryresultsintheliterature.Whatdeterminesthenumberofpartiesinapolity?Ouranalysisprovidesseveralcontributionstotheexistingliteraturethatseekstoanswerthisquestion.OneistorehabilitateDuverger’stheoryofpartysystems.Bydoingso,weobtainaclearerexpositionoftheunderlyingcausalprocessbywhichsociologicalandinstitutionalfactorsinteracttoshapepartysystemsthanisprovidedbythecontemporarypartysystemliterature.WeshowthatalthoughDuvergeristraditionallyseenassynonymouswiththeinstitutionalcamp,heinfactrecognized50yearsagothatelectoralinstitutionsaffectthenumberofpartiesonlybymodifyingtheeffectofmorefundamentalsocialClark, Golder / Rehabilitating Duverger’s Theory703 Table3isthattheyprovideanempiricalmeasureofthemechanicalandstrategicmodifyingeffectsofdistrictmagnitude.Althoughourresultsconsistentlyprovidestrongevidencethatdistrictmagnitudehasastrongmodifyingeffectonthenumberofelectoralandlegislativeparties,thesameisnottrueforuppertierseats.Tosome,thismightseemsurprising.Onepossibleexplanationfortheseanomalousresultsmightbeourfailuretodistinguishbetweendifferenttypesofuppertierseats.Forexample,itmaybethecasethatuppertierseatshaveamodifyingeffectonlywhentheelectoralformulaemployedinthelowertierismajoritarian.Theanalysispresentedhere(andinallpreviousstudies)doesnottakethisintoaccountandsimplymixesthosecasesinwhichthelowertierismajoritarianwithcasesinwhichitisproportional.Thismakesithardertofindanyeffectforuppertierseatsbecausetheabilityoftheseseatstoincreaseproportionalityislikelytobelimitedifthelowertieralreadyemploysaproportionalformula.Moreover,thelikelihoodthatuppertierseatswillhaveamodifyingeffectshouldbestrongerwhenthedistrictmagnitudeintheuppertierislargerandincountrieswheretheelectoraltiersarelinked(i.e.,wheretheunusedvotesorseatsinthelowertiersareusedtoallocateseatsintheupperClark, Golder / Rehabilitating Duverger’s Theory705Table 3 The Marginal Effect of an Additional Ethnic Group on theEffective Number of Electoral and Legislative PartiesStrategic EffectMechanical Effect District Magnitude(Example)Electoral PartyLegislative Party1Australia0.110.072 to 5Chile0.29 to 0.540.20 to 0.395 to 10Greece0.54 to 0.720.39 to 0.55Argentina10 to 20Portugal0.72 to 0.900.55 to 0.72lLuxembourg120 to 150Israel1.37 to 1.431.24 to 1.31 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