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Proportional Representation and Female ParliamentariansAuthor(s): Rob SalmondReviewed work(s):Source: Legislative Studies Quarterly, Vol. 31, No. 2 (May, 2006), pp. 175-204Published by: Comparative Legislative Research CenterStable URL: http://www.jstor.org/stable/40263381 .

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ROB SALMONDUniversityfCalifornia-Los ngelesProportional epresentationand Female Parliamentarians

This article sks, What ffect oes the hoiceof a nation's lectoralystemhaveon thegender ompositionf tsparliamentver ime?" find hathe lectoralsystemas an mportantart oplay, utpreviouswork asoverstated,yfactorsfbetween wo ndthree, owmuch f differencen electoralysteman make.Thisarticle ontributesnupdated onlinearheoryffemale epresentation,n mproveddataset nwomen's epresentationcross pace nd ime,ndmoremoderntatisticaltechniqueshan reviouslysed nresearch n this uestion.This article s about thepolitical representationf women.Successive esearchersave found hateftism,igh evelsoffemale

labor orce articipation,ndproportionalepresentationPR) electoralruleshavea causal mpact n thepercentagefa nation's arliamentwho rewomen. olicymakersnd ctivistsave elied nthis esearchto help guidetheir hinkingboutpossibleelectoral eforms:Ifelectoralystem is betterorwomen han lectoralystem , thensystem should eadopted"s a commoniberal efrain.he iteratureas itstands, owever,s not s useful opolicymakerss itcouldbe,and thassufferedromomepersistentethodologicalhortcomings.Almost llprevioustudies n the uestion f female epresen-tationnparliamentaveasked, What actorsxplain ifferencesnlevels ffemaleepresentationt a given ointntimeTThis uestion,while nteresting,snotperfectlyuited o thepolicymaker'snquiry,whichs,"What ffect ould changenthisndependentactor aveon levelsof women's epresentationver imeT' his article imstoprovide nswers loserto thepolicycommunity'semands nd tocapturehe ynamicshat arlier esearch asmissed. hisgoalrequiresthatmany f themethods fanalysis sed inprevious esearch erethought.nparticular,heprevious ractice fusingpurely ross-sectional atasets eedsupdating.his articlemakesuse of a paneldatasetovering1advanced ndustrializedemocraciesver periodof about50 years,withdata from 81 elections. arlier stimationprocedures,hich elied npurelyinear egression odels, re alsoLEGISLATIVE TUDIESQUARTERLY,XXI, ,May 006 1 5

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176 Rob Salmondupdatedhere.FollowingMatland's 1993) in-depth tudy fthegrowthof femalerepresentationnNorway, propose a logit-esqueS-curvemodel ofthegrowth f women's representationnparliament.The analysis in this article focuses on one known correlateoffemale egislativerepresentation:lectoralrules.Policymakers ftendebateunilaterallyhanging lectoralrules norder oachieve certainpolicyoutcomes, ncluding nhanceddescriptive epresentationfthecommunity. olicymakers o not,however,hold similardebatesoverunilaterally hanging hefemaleproportionf theworkforceormana-gerialworkforce), ltering he level of cultural oleranceforfemaleleaders nthe ountry,rshiftinghenation'sdominant eligion owardone more liberalon gender ssues. Such shifts re beyondthedirectcontrol f the egislature. he electoralrules are almosttheonlywaylegislators an directly engineer" ncreases nthe number f womenin parliament. Thus, this article concentrateson examininghowsuccessful uch electoralengineerings likelyto be.This narrow ocus on the mpact f electoral ulesonrepresenta-tion allows formethodological nnovations n the measurement f,andaccounting or, theroften ultural) auses ofwomen'srepresen-tation. propose a solutionto theproblemof "measuringculture":control or olitical ulturewithoutctuallymeasuringt. n this rticle,I also introducemore-sophisticated ays of quantitativelyapturingthe essence of electoralsystems han have been used in most of theprevious iterature n thistopic.My results howthat he choice of electoral ystemdoes matterforwomen's representationnparliaments ut notas substantivelysmuchofthe arlier esearch as suggested.A shift rom UnitedStates/United Kingdom-style single-member-districtSMD) systemto aNorwegian-style low districtmagnitude) PR systemleads to anincrease nthedescriptive epresentationfwomenbybetween 1.5%and 7%. This increaseis between one-third nd one-half he size ofearlier estimatesof the impactof such a reform. hifts o a Dutch-style high districtmagnitude)PR systemor a mixed systemmayproducea greatermpact,buta shift o an Irish-style ingletransfer-able vote system s less beneficial.The remainder f this article s divided into foursections. InSection I, I review the existing iterature n electoral systemsandwomen'srepresentation,oncentratingnthose studies hathave triedto test heir heories mpirically.n Section I, I outline he nonlineartheory fchanges nwomen'srepresentationndpresent hedata usedto test hetheory.n Section II, I present ndinterpretheresults.Andin Section V, I offer onclusions.


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Proportionalepresentation 177I. ElectoralSystems nd Female Parliamentarians

Therelationshipetween lectoralystemsndtherepresenta-tionof womenhasalready een the ubject fa smallmountain facademic esearch. eforewe reviewhe mpirical indingsnrelationto this uestion,t s useful o setoutthe ausal ogicthroughhichPR ishypothesizedo benefithe lectoral ause of women.WhyMight R Be BetterorWomen?

Thekeydifferenceetweenystemsfproportionalepresenta-tion andmajoritarianlectoral rrangementsies in their districtmagnitude"DM). TheDM measures owmany oliticiansre,onaverage,lected y ach lectoral istrict.nmostmajoritarianystems,each onstituencylects single olitician,ivinghat lectoralystema DM ofone. Thesesystemsre known s single-member-districtsystems.n all PR systems,n theother and, achconstituencysresponsibleor lectingmore han nepolitician.TheDM hasmultipleffectsnelections hat rerelevanto thequestionfwomen's epresentation.eynolds1999, 555)argues hatany MD systemcreatesn ncentiveor artyosses o tand owest-common-denominatorandidatesngeographicalistricts;hese arelyturn ut obe women rminorities."related laim sthat MD elec-tions end oproducemore-adversarialistrict-levelampaigninghanPR elections.ndeed,norder owin a local SMD election, candi-datemust nsurehat ll other andidatesre osers.Not so under Rrules.Men, ome rgue,rebetter orat eastmore ccustomedothis ladiatorialype fpolitical attlehanwomen,makinghemall

elsebeing qual)more ttractiveandidatesor artiesnSMD systems(Duverger 955;Rule1981).Anotherrgumentinkingigh M systemsobetterepresentationforwomen ies nthe ncreasedpportunitiesuch ystemsrovide orsocial ngineeringhroughicketalancingtthedistrictevel. nSMDsystems,localdistrict'slate fcandidatesannot e balanced ygen-der, ace, exual rientation,r ocation.here sonly necandidate,ndeitherhe sa woman rhe sn't.nPRsystemsithowDM,some icketbalancings possible, utaccommodatinghedemands fmultiplegroupss difficult.uchbalancingctsbecome asier s DM increasesfurthernd he emandsor epresentationfwomen,uralommunities,and ethnic roups re less likely o be inoppositiono each other.Thus, icketalancingecomesncreasinglyasy s DM risesDarcy,Welch,ndClark1994, 115;Lakeman 976, 161;Matland 993).


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178 Rob SalmondHigher districtmagnitudes are also associated with highernumbers of parties in the political system Duverger 1954). Thisincrease nthenumber fparties an have two effects. eynolds 1999,555) arguesthat nhighly roportionalystemswithhighDM "smallparties re able togain representationndpartieshave an incentive obroaden their verallelectoralappeal by makingtheir andidate istsas diverse as possible." Second, thepresence n parliament f smallliberal-leftarties,who sometimesmakegender galitarianism pointofdifference etween themselves nd a center-leftarty,s likelytoaidoperation f the contagion rom he eft" heoryfgrowing emalerepresentationutforward yMatland and Studlar 1996).Takentogether,hese mechanismsrepresent small catalog ofreasonswhyPR might e expected operformetter han ther ystemsin terms f genderegalitarianism. herehas, in fact,been very ittledispute n politicalscience thatPR theoreticallyhould prove to bebetter orwomen thanSMD electoral ystems. ut have theneattheo-reticalmodels translatedwell intothemessyworldof realpolitics?

Is PR Better or Women?The StateoftheLiterature n theStateofthe WorldThere have been two strands to the empirical literature: nelooking only at advanced industrialized democracies, the otherincluding lmost ll countriesntheworld.This article peaksdirectlyto the narrower iteraturenly atpresent, anel data goingback 50yearsare not available across the entireworld butnonetheless t isimportanthatwe consider hefindings f both trands f this esearch.StudiesofAdvanced ndustrializedDemocracies. The assertionthatPR is better or herepresentationfwomen dates to thework ofCastles 1981), Rule 1981, 1987),and Norris1985, 1987).BothNorris(1985) and Rule (1987) employed inearordinaryeastsquares OLS)methods to examine cross-sectionaldata frombetween 19 and 24western ountries.Both foundthatthe electoralsystem s the mostsignificantredictor f the evel of female egislativerepresentation.Neither, owever, rovided n estimate f the substantiveevel of thiseffect, eporting nlystandardized oefficients.A latergeneration fresearchers,ncludingMatland 1998) and

Kenworthy nd Malami (1999), exploredthisquestionagain. Theyalso employedOLS methodsand cross-sectional amples (althoughMatland does employ pooled cross-sectional esignfrom ata takenatthree imeperiods).Both the Matland and KenworthyndMalami


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Proportionalepresentation 179studies ound strongndsignificantelationshipetween R andlevelsofrepresentation,stimatinghe mpact f PR atbetween 1%and 16% inthedevelopedworld.These arevery arge ffects henthemean evelofwomen's epresentationcross hedevelopedworldwasonly18%duringheperiod 990-95.Thefourtudies ighlightedere ontrolled,mong therhings,for emale aborforce articipationndaverage ducationevels.AllexceptNorris's tudy lso controlled ordifferentevels ofleftism,anotherurportedource fparliamentaryeatsforwomen. aterdiscusswhetherrnot hese ontrolariables re dequate rreliable.One avenueforresearchnthis reathathas been usedonlysparinglys that f he asestudy. atland1993) looked tthempactofchangesnNorwegian istrict agnitudendpartymagnitudenwomen'srepresentation,nd some scholars ave examined anada(MatlandndStudlar 996;StudlarndMatland 994) ndCostaRica(Jones 004;Matland ndTaylor 997)as testing rounds. ater nthis rticle, use recent lectoral eformsnwestern ountries s"naturalxperiments"o llustratehe omparativeerformancef hemodels eveloped ere gainsthose nthe xistingiterature.Amonghe theractorselievedopartlyxplainevels ffemalerepresentationre cultural ariables, specially hecomparativelystrongrive owardequity"nthe candinavianndNorthernuro-pean ountriesBystydzienski95; nglehartndNorris003;Norris1993); thestrengthf left-wingartiesDuverger 955; Lakeman1970); he resencef multipartyystemLakeman 976)- althoughDuvergers (1954) hypothesisellsus that multipartyystemsprobably caused by the presence of PR; and demographiccharacteristics,uch s highevels feducationnd ow evels fCa-tholicismRule 1981;Welch1978).Somescholars ave advanced hecultural ariable s theonlyfullyndependentariable n thesystem.Not onlyare thepublicattitudestronglyavorable o general oncerns f equityhighlycorrelated ithhigheremale epresentation,ut hey realso corre-latedwith hepresence fa PR systemNorris1987, 120). Someresearchersave uggested,herefore,hat causalarrow oints romculturesaluingfairness"nd he doptionfPR(Norris 004,183).Rokkan1970)followedyBoix 1999),however,howed hat his snot he ase,establishingnsteadhat onservativeartiesnnorthernEurope dopted Ras a protectiongainst eing ompletelyestroyedattheballot oxas the ranchiseasprogressivelyxtended.hus, Rwasadopted or artisanain,notfor easons f nclusiveness.hesefindingshow hat R is not ndogenouslyausedby comparatively


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180 RobSalmondinclusive olitical ultures.Wemaythereforeroceedwith nalysisofthe wovariableseparately.Threeproblems ith heexistingiteratureerve o cast doubtover their indings. irst,many f these tudieshadas few as 19observationsutup to six independentariables.With amples hissmall,thereliabilityf anystatisticalesultsmustbe questioned.DramaticallyncreasingheN wouldmakeformore eliable esults.The secondproblemoncernshevariables sed to control orpoliticalulture,hichs, nmany ays,hemain ompetingxplanationfor ross-nationalifferencesnrepresentationevels. t s doubtfulhatthevariablesctually aptureherelevantlementfpoliticalulture,namely,ttitudesoward avingwomennpositionsf eadershipndpower. woofthemost ommon ontrolariablessed remeasuresfwomen's abor orce articipationndfemale ducationevels.Both fthesemeasuresre luntnstrumentsnd re ubjectovariationor easonsnotrelated o the cceptance f women s leaders.1 elyingn thesemeasures an ead to unstablestimates,speciallyn small-Nwork.The thirdroblem ith he xistingiteraturesthat esearchersalmost xclusivelyely n OLS models. implenspectionfthedataconfirmshat heprocess s not inear ver ime.nNewZealand, ttook60 years fterwomenwerepermittedo runfor arliamentorrepresentationevels o reach %,but tonly ook 0 years fterhatfor epresentationorise loseto 30%.Inthe irst5years fterWorldWar I, the evel ofrepresentationnNorwayncreasednly %,butinthenext 5-year eriod,t ncreasedy25%.These renot solatedexamples.More-sophisticatedodelingsnecessarynordero ccountfor uchpatterns.LS models an also eadto mpossible redictions.Percentagesrebounded t0 and100; inear redictionsre not.

To corrector he hortcomingsn this iterature,nynewstudyon this uestionhould:1) Gatherepeatedbservationsn countriesunder tudy ver lengthyime rame;2) Modelthe mpact f theindependentariables n thepercentagef egislatorsho refemalein uch way s toavoid he ossibilityf mpossibleredictions;nd(3) Developmethods or ontrollingor olitical ulturehat o notrely n the tatisticalmeasurement"f culture.Todate, wopublishedtudies ave xaminedhanges ver imeinwomen'srepresentation,husovercominghe small-Nproblem.McAllisternd Studlarollected ataon 20 countriesver heperiod1950-2000 nd foundhat istPR doesabout10%betterorwomenthan oes SMD (McAllisternd Studlar002;StudlarndMcAllister2002). Unfortunately,owever, heir tudies lso have importantmethodologicallaws.2


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Proportionalepresentation 181The first ethodologicalroblemsthat,ike he ross-sectionalstudies,McAllisterndStudlar'swork elied n OLS analysis. ec-ond, he uthorsrtificiallynflatedheir umber fcases andthere-fore heironfidencen he esults by ountingachyear s a separatecase whetherhere adbeen n election rnot.3 hird,McAllisterndStudlar adenoattempto ontrolorutocorrelationn heiregressionmodel. hisomissions akin osayinghathe evelofrepresentationinelection ttime/ s dependentnlyon the ndependentariablesand notdependentt all on the evel ofrepresentationt t-L Thisassumptions unrealisticfwe consider, or xample,ncumbencyadvantages,nditserves o artificiallynflateheestimatedize ofotheroefficients,ncludinghe lectoralystem. hey urthernflatedthe mpact f the electoral ystem y excludingfordatareasons)another nown orrelatefwomen's epresentation:emale articipa-tion nthe abor orce.Thesemethodologicalroblems astsignificantoubton thereliabilityfMcAllisterndStudlar's indings.onethelesst s worthnotinghat, espitehe ikelynflationf electoralystemffects uetothesemethodologicalroblems,he ncreasedize of their atasetleadsto a smaller stimatedmpact fPR, compared o thecross-sectionaltudies.Studies ith lobal cope.A second treamfresearchddressingthe urportedink etween lectoralystemsndwomen's epresenta-tion asnot onfinedtself o he dvanced ndustrializedemocracies,therebyreatlyxpandinghenumberfcasesundernvestigation.nthis ine fresearch,heres not consensushat he hoice f lectoralsystems importantorwomen's epresentation.either akes and

Almquist's1993) studyf73 nations ornglehartndNorris's2003)62-nationtudyoundny tatisticallyignificantelationshipetweenelectoral ules nd women nparliament. oreover, therarge-Nanalyses including arts fKenworthyndMalami's 1999) andNorris's 2004) work, othof whichreliedon datafrom ver 140nations found ffectsfPR thatwere ignificantutmuch mallerthanhose ypicallyoundntheOECD studies. eynolds1999) alsoconductednanalysis f over160countriesnd found istPR faredsignificantlyetterhan implepluralityule.All ofthese tudiescontrolledor evelsof economic evelopmentn addition o otherculturalndpartisanariables.4Theglobal iteratureshelpfulnthis rticle'sndeavor,espitethedifferentange f cases. First, hese tudies howPR tohaveasmallermpactnfemaleegislativeepresentationhanhatuggested


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182 RobSalmondbyMatland rKenworthynd Malami.Thisdifferenceay rise, sMatland1998, 120)suggests,ecause he oleplayed y nstitutionsin fostering omen'srepresentations dwarfed y the role thateconomic evelopmentas toplay.Alternatively,hesewider tudiesmayhighlighthepoorresults ne can obtainwhen elyingn a verysmall ample. econd, ome f hemethodshese lobal tudiesmployare mprovementsnthose sed nearlier ich-country-onlytudies,andthesebroadernvestigationsuidesome of themethodologicaldecisions describenthefollowingection.

II. Theory ndDataANonlinear heory fFemaleLegislative epresentation

In a 1993 article, ichardMatlanddiscussed hechangingpatternffemale epresentationnNorway.His researchdentifiedfour tages ntheriseofwomen's epresentationrom% to 36% asof1989 Matland 993, 46-50).He titled hese tages GiantsmongMen,"during hich nyfemalemembersfparliamentere electedinspite fbeingwomen"; One Is Enough,"which nvolved singlefemale andidate n eachparty'sicketneachdistrict;Tokenism oMore,"which aw the irst se ofgender uotas; nd Gender qualityJust round heCorner,"nwhichwomenbecame "secondamongequals."A similartoryan be told boutNewZealand, hefirstountrytogrant omen he ighto vote.Throughhemiddle fthe wentiethcentury,epresentationrewvery lowly, eaching% bythemid-1970s.At that ime,heValuesParty, small eft-wingrotest ove-ment,romotedender quityspart f tsplatform.heparty ainedsubstantialoter upport,utNew Zealand's SMD electoralystemensuredhat hegroup ainedno seats.Followinghedemise ftheValuesParty, any f ts ctivistsmoved nto he arger abour artyand, rmedwith hedemonstratedublic upportor heirmessage fequality,ressuredabour nto electingmore emale andidatesorwinnable eats HillandRoberts 990;McLeay2000).Female epre-sentationnLabour's caucus rosequickly. espondingsomeyearslater) o thisdevelopment,hemainright-wingarty olloweduit,andby1999, herewasa female rimeminister,female ppositionleader,nd30% ofthemembersfparliamentMPs) werewomen.Female representationn Denmark, inland,Germany,ndSweden lso seems ofollow hepatternfa period fzerogrowthgiving ise o slowgrowth,ollowed ya secondperiod f dramatic


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Proportionalepresentation 183FIGURE 1AnS-CurveModel of Women'sRepresentation

shiftsnrepresentationevels.Allof hese ountries,ith he xceptionofGermany,lsoexperiencedslowing ate fgrowthnthe1990s.5Itappears,herefore,hat hegeneral elationshipetween imeandthe ercentagefMPs who rewomen s not inear ut -shaped.This ontentionssupportedyMatland'sn-depthesearchnNorway,contextualvidence romNew Zealand, ndquantitativeata fromthese nd other elevantountrieslreadymentioned.Thegeneral -shape fthis urve s sketchednFigure ,whichis divided nto ivebroad stages" hiftingrom orepresentationoequitable epresentation.hese tages re, fcourse,nno senserigidorfixed; heyreustheuristicevices. hefirst ourtages re abeledthe same as thoseMatland oundnNorway,whilethe fifthtage,"True quality,"asnotyet een chievednywhere. athematically,such a modelcan be derived ycalculatinghe"log odds" of thepercentagef seats nparliamenteldbywomen:

/ , , , f [constraint] ] (\)Logodds, , = \n\- M{[percentage] JIn equation 1), constraintepresentsn ex ante researcher-imposedimit nthe evel owhich he redictedalue f he ercentage


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184 RobSalmondcanrise.Note hathis imits differentromny onstraintnLogodds.Forthis rticle,hevalue of the onstraints set t50%,because hislevel ofrepresentationpproximatesender aritynthe egislature,the lmost niversallygreed-upon oal inthis rea ofthefeministproject. heresultsre,however,nnowaydependentn this hoiceof onstraintevel.Details frobustnesshecks n this ssue ppearnthe esultsection. heS-shapedmodel s outlinedbove sonly sefulin cross-nationaltudyf neassumes hat llcountriesnthe amplestartediving omen epresentationtthe ame ime. his ssumptionis clearly alse, o I useda variablendicatinghenumber fyearssince uffrageas firstrantedowomen, variantna variable oundimportantyStudlar ndMcAllister2002),to control or he ime twhichwomen tartedowinpolitical ights.6One consequence f the transformations that tchanges he"natural"igns or achofthe ndependentariablesnthe ystem.fwe expected variable to be associated with n increase n thepercentagef egislators hoarewomen,hen hat ariablewouldbeassociatedwith decrease n the ogodds ofthepercentage.norderto solve thisproblem,performedsimple inear ransformationnthe ogodds.This transformationestoreshe natural"ignfor achofthe ndependentariables' stimatedoefficients.t does not ffectthe oefficientsexcept he onstant)nany ther ay.Thedependentvariable or heregressionsstherefore:

DepVar X-\\J[[cOmtraint]X^\ (2)L {[percentage] \CollectingData to Test heTheory

This ection utlineshe therndependentariables sed nmyanalysis. he literatureeview uggestedhat our roadclasses ofvariablesffecthe ercentagefwomennparliament:oliticalnsti-tutions,atternsfpartisanupport,ocioeconomicactors,nd ulturalfactors. his article ses two measures fpoliticalnstitutions,necapturinghe alientspects f he lectoralystemnd he thermea-suringhe logged) ize of he ssembly.measuredartisanausesofwomen's epresentationnparliamentsing hepercentagefseats nparliamentwarded o eftistarties accordingo Castles nd Mair's(1984) framework].ignore ocioeconomicmeasuresnthis rticle,because he ase selectionnsureshatnlywealthyountriesreunderconsideration.discuss heproblemfquantifyingulturena latersubsection.


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Proportionalepresentation 185This article elies n a dataset overing1 countriesrom 950to2001. The countriesnthe nalysis reamong hewealthiestntheworld, ave ll had numberfdemocraticlectionsuringhe eriod,andhavereliable ataon thevariables reviously entioned.hesetof countries illbe familiaroregulareaders n this ubject, epre-senting list ofthe "usual suspects":Australia, ustria, elgium,Canada,Denmark,inland, rance,West)Germany,reece,reland,Italy, apan,heNetherlands,ewZealand,Norway, ortugal,pain,Sweden,witzerland,heUnited ingdom,nd heUnited tates. achelection s for he ower houseof the egislature,nd democraticelectionswherewomenwerenot llowed ovote only problemnSwitzerland) erenot ncluded. heseobservationsivea totalN of281 separatelections.The rest fthis ection xplainsnsome detailhow this rticledeparts rom raditionalpproachesn twokeydataquestions: owshould nequantify1) electoralystemsnd 2) political ulture?Quantifyinglectoral ystems.reviouswork n this opichas

offered widearray f methods or ategorizinglectoralystems.Most analyseshave reliedon dummy ariables.Matland 1998),McAllisternd Studlar2002),and nglehartndNorris2003) useavariable odedas 0 when heres no element fPR inthe lectoralsystemnd s 1otherwise.nglehartndNorris2003, 141)admithatthis simplemeasure fmajoritarianersusproportionallectoralsystemsmay ail ocapturethermportantariations,uch s districtmagnituderthe evelofdisproportionality."KenworthyndMalami 1 99)propose three-pointcale,whereSMD is coded s 0,anyform fmixed ystemincludinguchdiversesystemssthe ery roportionalerman-styleixedmemberropor-tionalMMP),moderatelyroportionalrish ingle ransferableote,andtokenlyroportionaltalian upplementary-memberystems)s a1, ndparty-listR is a 2. This pproach astwoproblemsnadditiontothe luntnesslreadymentioned.irst,hemixed ategoryontainsa diverse ange f electoral ystems,iving p to its name nmorewaysthanKenworthyndMalami considered. econd,thecodingmechanismmposes heresulthat he stimatedmpact f ist-basedPR willbe exactly wice he ize of theestimatedmpact f mixedsystems,ven houghheres notheoreticaleason oexpecthis esult.Studlarnd McAllister2002) use a series fdummyariablestorepresentour roadfamilies f electoral ystems:istPR, otherPR,first-past-the-postlurality,ndother lurality.he firstndthirdcategoriesreself-explanatory,ut he econd nd fourthategories


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186 RobSalmondappear o act as "remainderins" ntowhich ll forms fnon-pure-typeelectoral ystems re thrown. he category otherPR," forexample, s home for he ow-DM Irish ystemnd thehigh-DMGermanystem. he "other lurality"ategorymayhaveacted s adummyor rench wo-round ajoritylections,r tcouldhave lsoincludedthepost- 994 Italianand post- 996 Japanese ystems,dependingnhow he uthorshose o reatmixedmember ajoritarian(MMM) systems.heproblemf umpingnlikeystemsogethersnot s bad nthis chema s intheMatland/InglehartndNoms tech-niquediscussed arlier,ut t s still bluntnstrument.Reynolds 1999) relies on a ten-categoryoding scheme(operationalized singdummy ariables)thathe and Ben ReillydevelopedReynoldsndReilly 997).This oding ystemscertainlyan mprovement,sthe ategoriesrenarrownoughoensurehatllsystems ithinachcategoryre similarnd there re no researcher-imposed elationshipsetweennyof the ategories.his schemesnotusefulnthepresenttudy,owever,ecause fthe mallnumberof countries nderconsideration ere.Although examine281elections,here reonly21 countriesepresented.f I adopted heReynoldsndReilly pproach,hen hecategoryingle ransferablevote STV) wouldoperates an Ireland ountry-dummy,inglenon-transferableote SNTV) wouldbea Japan ummy,ndMMP wouldalmost e a Germanyummy.hus, ny egressionssing his chemewould uffer romverdetermination,nd t wouldbe impossibleotell whether heresult n STV was an indicationfthat lectoralsystem'smpact r a measurementf the diosyncrasiesf reland.Thechallenge or his rticles topresent coding nstrumentfor lectoral ystemshatuses fewvariables, nsures hat imilarelectoralystemsregrouped ogetherndqualitativelyifferentlec-toral ystemsrenot, ndaccurately easures he ogicbywhich Rishypothesizedoaffect omen's hare f egislativeeats.Ameasurethat ccomplishesll these hingss district agnitude. anyof theeffectshrough hich R is supposed o affect omen's epresenta-tion perate hroughhe ystems'M. Thismeasure lsoallowsus tocapturehe lectoralystemn single ariable.Moreover,his ariableallows stimationf hempacthat hifts ithinhe road Rcategorymightave nwomen's epresentation.singDM toquantifylectoralsystemss nothing ew in political cience,havingbeenused inscholarly orks y Taagepera ndShugart1989), Lijphart1994),and Cox (1997).Matland 1993) considers M as an explanatoryariableforwomen'srepresentationevels before ejectingt in favor fparty


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Proportionalepresentation 187magnitudePM),thenumberf eats partyas n particularistrict.CertainlyM is a superior ariable oDM, because mostof DM'seffectsresupposed o occur t thepartyevel.Nonetheless,M andPM are ikely o be at leastmoderatelyorrelated:fDM is 1,theneachparty'sMcannot e more han ifDM is 100, hent east woPMswillbe large nd almost ll other Mswillbe above1I useDM inplaceofPM inthis tudy ecause f hedifficultyfobtainingM data.Forhis1993studyfNorway,Matland ollecteddataon theperformancef eachpartynevery istrictnNorway or10 elections.This is a very axingdata collection ffort oronecountryindeed,Matlandwent o ive nNorwaywhile ollectingisdata. fcollectingMfor necountryasvery axing,hen ollectingit for 1 countries ouldbe Herculean,nd that s certainly taskbeyondhe copeof this rticle.To ensurehat M isa goodproxy or M, ran simple egres-sionpredictinghe veragePM of all successful artiesnthemostrecent arliamentarylection f the21 countries nder tudy, singtheDM as the olepredictor.7heregressionxplainedver52% ofthevariance faverage M,and theDM variablewas significantntheexpected irectiont a /?-valuef 0.001. This test howsthat,althoughM iscertainlyhebestvariable or apturinghe ppropri-atepart fan electoralystem's peration,M is still verygoodvariable, variablehat apturesmuch fthe nformationontainednthePM variable nd that an be collectedwithoutearningmultiplelanguagesndspendingmanymonths n the oad!A little ine-tuningftheDM measure s requiredeforetcanbe useful.A shiftn DM from to 5 is likely o havea much argerimpactnwomen's epresentationhan shiftrom 6 to 100.For hisreason,heDM is ogged ogeneratehe inal lectoralystemariable.Purely MD andsingle-tierist-basedR electoralystemsreeasy oassign aluesof og(DM).Formore omplicatedystems,iketwo-tierist Rormixedystems,owever,hemeasurementroblemis harder. he mainmechanismhrough hichDM translatesntofemale epresentations thepartyist.All elsebeing qual, systemswith higher M enablewomen o be elected romower lacesonthedistrict'sartyistthanwouldbe elected ndistricts ith owerdistrict agnitudes,nd thereforeheparty's M is higherMatland1993;Noms 1996).Thereforehe uestion or hese therystemss,Howfar own party'sistdoyougo inorder oelectMPs?Forall electoralystems ith wo tiers fdistrictingwhethersimple wo-tieredRor someform fmixedmemberystem),useda weightedverage ftheDMs atthe ower ndhigheriers.8


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188 RobSalmond"Measuring"Political Culture.As notedearlier, vailablestatisticalnformationimits hewaysone can control orpoliticalculture. ncewerecognizehat he tatisticsimplyrenot vailabletodirectlymeasure olitical ulture vera lengthyimeframe, eneedto consider therpproaches.Theapproachsedheres differentndnew.The deabehindhemethods toreliablyundercount"he oleofpolitical ulturenoneregression,hen eliably overcount"t in another egression,husgiving robust onfidencentervalo workwithin.9foneassumesthat ifferentationalultureslay lmost o role ndeterminingevelsof female epresentation,hen he estimates f all other ariables(includinghe lectoralystem) illbe biasedupwards. nthe therhand, foneassumes hatnational olitical ulture lays lmost hesole determinativeole, hen stimates fall other ariableswill bebiaseddownwards. he tricks to know hedirectionfthebiases nthe measures" fculturendtopair control iased nonedirectionwith control iased nthe ther.Inthefirstundercontrol"ethod,ne entersheyear nto he

equation oproxy or ulture. hisstepfollows rom he ssumptionthat heresa singlewesternulturehat evelops toleranceorwomenleaders vertime.The method oes not llowanybetween-countryvariancenthedegree owhich ocietiescceptwomennpositionsfpower. herefore,ny ctual ross-nationalariationnpoliticalulturewill showup intheregressionystems stochastic oise, everelydampeninghe ffect ound n culture nd nflatinghe ffect oundon other ariables orrelated ith ulture. his undercontrolsmiti-gated o a small extent ythe nclusion ftheyears-since-suffragevariable. venwith hismodification,t s a bigstretchosaythatnation's olitical ultureoday s determinedy 1) a single nterna-tional ulturend 2) a legislativeecisionn the1920sor1930s.Theinclusionf he econd ariable egateshe iasveryittle. egressionsusing hese ultural ndercontrolsrewrong, ecausethey uppresstheeffects f culturenfavor f other ariables. heseregressionsoverstatehe mpact f the lectoralystem.The cultural overcontrol" ethod sesthepercentagef seatsheldbywomen fter he reviouslection ocontrol or multitudefsometimes-unidentifiableulturalfactors hatcan influence heprogressf female epresentation.comparedll those lectionsnwhich hepreviousevelofrepresentationas X% and notedwhichmovedmore uickly pwards. also added o the vercontrolegres-sions n interactionerm etweenhe aggeddependentariable ndthenumber fyears hathaveelapsedsince theprevious lection,


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Proportionalepresentation 189because hepassageofdifferentmountsftime etweenlectionsslikely o affect owclosely hedependentariable s related o itslaggedvalue.The presence fthe aggeddependentariable lso serves osignificantlyiasthe egressionesults. sing t, neassumes hathelevelofrepresentationt (t-1) is entirelyueto cultural rocesses;this s the heoreticaleiling f culture'smpact,nda very igh neat that.One assumes hat heassembly ize, electoral ystem,ndpartisanmakeup fparliamentadabsolutelyoimpactt t-1),andthennetestswhetherrnot ffectsf hese therariablesre videntat 0 inspite fthisharsh, estrictivessumption.hismethodeadstoa regressionhere he ulturalariable ends ounfairlyominatetheregression nd artificiallyepresstheeffects f other rulyexplanatoryariablesAchen 000;Griliches961;Maddala ndRao1973).Forcompleteness,heregressionssing he ulturalvercon-trol lso include ll of thecultural ariablesused in the culturalundercontrolegressions.egressionssing his ulturalvercontrolarewrong,ecause hey nfairlyias gainst substantiver tatisticalfindingnallother ariables. heseregressionsnderstatehe mpactofthe lectoralystem.All ofthe ulturalontrol ariables sedhere reunfair,iased,andwrong,ndfor hisreason, nyregressionaken lone givesapoor stimate.akennpairs, owever,therwisedenticalegressionsthat se differentulturalontrols rovide very obust onfidenceinterval ithin hich he ruempact fall other ariablesmustie.

III. Data AnalysisSimplebivariatenalysis rovides ood initial upportor heidea hatheDM mattersorwomen's epresentation.cross hewholesample, he orrelationetweenoggedDM andthefemale ercent-age ofthe egislatures 0.364, significantt/? 0.001. EvenwithSMD casesexcluded romhe nalysis,oggedDM's correlationithwomen's epresentationemainst0.285, gain ignificantt/? 0.001In orderomakemore-concretendreliable laims bout he lectoralsystem'smpact, owever, erequiremore-sophisticatednalysis.

StatisticalMethodsBecausethedata overmultipleountriesver ime, usepanel-correctedtandardrrorsPCSEs). (See BeckandKatz1995 nd1996fora fulldiscussionof thedesirabilityf PCSEs, whichallow


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190 Rob Salmondstatisticallyesirablessumptionso bemadeabout hedata.)10woassumptionsnparticularreuseful ere. hefirst,eteroskedasticityacrosspanels,models he dea that hecombinationfindependentvariablesmay esystematicallyettertpredictingevels fwomen'srepresentationnone countryhan hey re in another. he seconddesirable ropertyfPCSEs is that hey llowfor ontemporaneouscorrelationcross anels, husmodelinghe deathatventshat rossnational oundaries for xample, emporaryop culturemphasisongenderssues, r nternationalventsike heUnited ations' eijingconferencen the tatus f women can affectevelsofrepresenta-tion crossdifferentountriest the same time.11 hese additionalassumptionslso serve oguard gainsthe verconfidencenresultsthat he arlier eneralizedeast quaresGLS) estimationechniquetended oproduceBeckand Katz 1995).Most anel atasetsf hisypelsoemploy statisticalorrectionfor irst-orderutocorrelationAR1),but he egressionsescribednthis rticle onot. nthe vercontrolegressions,nAR1 correctionsnotnecessaryecause f he resencef he agged ependentariable,which erformshe amefunctiononly tronger).nthe ndercontrolregressions,he dditionf nAR1termsundesirableor wo easons.First,heAR1techniquesedwith CSE paneldatamakes seofthelaggeddependentariable. dding heAR1termo theundercontrolregressionsould hereforeesultnboth heunder- nd overcontrolregressionsaving laggeddependentariable ermnthem,whichwoulddefeat heirointpurpose.12econd, he xclusion fanyAR1term rom heundercontrolegressionsnsureshat he stimatesfDM's impact re notdepressed ycultural ontrolshroughnAR1correction,hus rovidingxtra onfidencehathe stimatesfDM'simpactnthese egressionsre, nfact,oohigh.Regression esults

Tables1 and2 reportheregressionesults. he main nalysisthat his rticle elieson is providedn Table 1. Table2 providessubstantiventerpretationf he able1regressions. hennterpretingthe esultst svery mportantorememberhat he egressionshouldbe read npairs: neregressionor vercontrolor ulturend second(with dentical pecification ut forthe exclusion of thelaggeddependentariable) or ultural ndercontrol.The firsthingonotice bout able1 s that he lectoralystemvariablethe oggedDM) is significantnd nthe xpected irectioninbothundercontrolegressionsnd inone of thetwo overcontrol


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ProportionalRepresentation 191TABLE 1Causes of Female Legislative Representation

All Cases PR Cases OnlyUndercontrol Overcontrol Undercontrol Overcontrol(1) (2) (3) (4)

Constant -39.830*** -13.501*** -46.741*** -12.411*(9.414) (4.184) (11.634) (4.922)p-value 0.000 0.001 0.000 0.012ln(DM) 0.300*** 0.050** 0.268*** 0.031(0.023) (0.016) (0.039) (0.025)p-value 0.000 0.002 0.000 0.211Years inceSuffrage 0.027*** 0.006** 0.024*** 0.005*(0.004) (0.002) (0.005) (0.002)p-value 0.000 0.006 0.000 0.038Year 0.019*** 0.007** 0.022*** 0.006*(0.005) (0.002) (0.006) (0.003)p-value 0.000 0.002 0.001 0.013Lagged Dependent ariable 0.886*** 0.866***(0.068) (0.086)p-value 0.000 0.000Lagged Dependent ariable -0.010 0.007Yearsbetween lections (0.017) (0.024)p-value 0.580 0.762ln(Assemblyize) -0.050 -0.018 -0.052** -0.061(0.094) (0.042) (0.114) (0.055)p-value 0.595 0.663 0.648 0.262Left trength 0.011*** 0.001 0.019*** 0.002(0.002) (0.001) (0.004) (0.002)p-value 0.000 0.321 0.000 0.340R2 0.699 0.924 0.626 0.922N 280 272 166 160Note:Panel-correctedtandard rrors re usedthroughoutndappear nparentheses.*p< 0.05; **p< 0.01; ***/? 0.001;all tests re two-tailed.


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192 Rob Salmondregressions.heonly ime he lectoralystemariableosessignifi-cance swhen he ulturalvercontrolsre nplaceandthe ample slimited oPR casesonly.Given his ombinationf constraintsn thesample nd theregression, e shouldnotbe surprised ythisnullfinding,hich oes notrepresentchallengeo the xtantiterature.performed1 robustnesshecks n each of models1) and 2) (whichutilizehe ull ample) overifyhat o onecountry'sbservationseredrivinghe lectoralystemffecto tatisticalignificance.nall of hesechecks,he esulturvivednscathed.13hisdataset hereforeenerallysupportshe onsensusnthe iteraturehathe lectoralystem atters.Other ariablesnTable1 behavegenerallys expected.Morewomen end oget ntoparliaments timegoeson{Year)andwhenthe attle oruffrageightsecedes nto he ast Years ince uffrage).Not urprisingly,heagged ependentariablesanexcellentredictorof women's epresentation.ncreasesn leftismend o increase helevelofrepresentation,lthoughhis ffectisappearsnthe ulturalovercontrol odels. heassemblyizeappears ot omatter.I reran hemainregressions, odels 1) and 2), a number ftimes omake ure hathe hoice fconstraintevelon thedependentvariablewas notdrivingheresults. pecifically,reran hemodelswithhe onstraintet t30%, 40%, 60%, 70%, 80%, 90%,and100%.Thesemodels ested or he mpact f differentonstraintevels ndfor ifferentevels f hedependentariable twhich he ndependentvariables ave maximummpact.n a logit-type odelwith 50%constraint,he oint fmaximummpact or ny ndependentariableis when thedependent ariable s 25% by assumption. hus,therobustnesshecks lso determinef"setting"his oint f maximumflexibilityt15%,20%,and o onmakes differenceo he stimates.14

In bothunder- nd overcontrolmodels,regressionswith aconstraintet ower han 0% have an R2valuesubstantiallyowerthanhe 0%modelR2for he 0%undercontrolodel, or xample,drops o 0.604 from he50% model's0.699). Undercontrolodelswith constraintethigherhan 0%haveverymarginallymprovedR2values,rising y up to0.005. In theovercontrolegressions,he50%modelhas thehighest 2. n allmodels, nder-ndovercontrol,the ignificancef the lectoralystemariable emains emarkablysimilar.he/?-alues nthe ariablenothermodels reusually xactlythe ame s inthe 0%model, ndthemaximumhange n/?-alue s0.004. The50% model hows slightly igherubstantiveffectorelectoralystemshan o modelswith onstraintset bove 50% anda lower ubstantiveffecthan hebelow-50%model.The overallranges fthese ubstantivestimatesrenarrow,rom .252to 0.341


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Proportionalepresentation 193N? N? sO(j

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194 Rob Salmondinthe ndercontrolodels ndfrom,044to 0.069 nthe vercontrolmodels. Takentogether,his evidenceshows that he choice ofconstraintevel nthedependentariable alculationsoes notdrivethe ubstantiveesults.What s notyetclear from able 1 is how much heelectoralsystemmightmatter. able 2 transformshesecoefficientsntoestimatedhiftsnthepercentagef seats heldbywomenundernumberfdifferentcenarios. omparablestimatesromheMatland(1998) andKenworthynd Malami 1999) articles re alsoprovided.Theestimatesregenerally ore onservativehan hose rom ithertheMatland rKenworthyndMalami rticles.Table2 also showsthesensitivitiesf thedifferentodels ochangesnDM, themechanismhroughhichmuch fPR's advan-tage owomen ssupposed ooperate. his rticle's stimatesecomemonotonicallyarger s DM rises.Matland's stimate,n theotherhand,s entirelynsensitiveochangesnDM; all thatmattersnhisestimations that system ses PR. Thispropertys sharedwithMcAllisternd Studlar's2002) estimates. enworthynd Malami'sestimates,longwith hose fStudlarnd McAllister2002),suggesta non-monotonicityntherelationshipetween M andrepresenta-tion evels;both stimatehat shift rom MD to low-DM istPRwouldbe morebeneficialhan shifto a high-DMmixed ystem.These stimatesremore riveny he odingnstrumentshan y hedata ndrun ounterothe upposedmpactfDM onwomen's epre-sentation. ith etter ata ndbettermeasures fthe lectoralystemandculture,his rticleuggestshat reviousstimatesfPR's effecton thenumberffemale arliamentariansere, o some xtent,ver-blown.Note also that hetheory-drivenonfidencentervalCI) inthis rticlesgenerallyo wider han he tatisticallyerived 5%CIsfromhe ther wo rticles. hetwo xtremessumptionsbout ulturedonotproduce CI thatncludesbsolutelyverything.TakingheEstimates n theRoad: SomeNatural xperiments

Itnowremains or s to take hevarious stimatesnto hefieldand ook at the bilityf each estimateopredicthangencases ofelectoral eform ithin single ountry.Table3presentshe hangen evels frepresentationollowingfive ecent ases ofmajor lectoral eformrom ithinhe ample.15France hanged rom double-ballot ajoritarianystemoPR intime or he1 86electionndback gain n ime or 988. talyhiftedfrom listPR systemo a mixed ystemor he1994election,nd n


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Proportionalepresentation 195-S 3 /-s Uo "3 s ~. ^ ^ n ^ ^, as 06 v o - ;oI I -8 " 'I

S ^ JJ C ^ OO |Di vq

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196 Rob Salmond1996bothNew Zealand ndJapanmoved rom majoritarianystemto a mixed R system. oth he awchangenrepresentationndthechange ttributableo theelectoral ystemre listed n Table 3. Icalculated he attributablehangefigures y estimatingn S-curvemodel imilaro the ne nFigure on eachcountry'sevelofrepre-sentationsing hepre-reformata prioro either eformnFrance'scase).Thismethod ives nestimatef what he evelofrepresenta-tion ikelywouldhavebeen sans electoral eform, odeling rowthdue to cultural nd partisan actors. he difference etween hispredictedhange nd the ctual hangenwomen's epresentationstaken o be the hange ttributableo the lectoralystem.16hus, heestimatedevelofrepresentationansreformelies nrepresentationpatternsver hewholepre-reformeriod ingeneral, 0 to 15 elec-tions.While hismethodmaynotprovidehemost recisemeasure-mentnstrument,t s good enough o make hepoint hat ollows.None ofthe modelson offernTable 3 comeaway smellingentirelyf roses.All theconfidencentervalsailto make correctprediction ore han alf he ime. uttheCI advancedn this rticledoesa good ob ofexplaininghe hangeboth herawandattribut-able change, n fact) nNew Zealand,and itcomeswithin % ofpredictinghe hiftnrepresentationevels nJapannd nthe econdFrencheform,ndwithin%of he irstrencheform.neveryasebut ne, heCI generatedy his nalysis oes betterobofpredictingchangesnfemaleepresentationhan itherheMatland rKenworthyandMalamiCIs. Theoneexceptions theNew Zealand ase,forwhichKenworthynd Malami lso correctlyredicthe mount fchange.Further,hemodel dvancednthis rticlemakes rrorsnboth irec-tions, t times verestimatingndatother imes nderestimatingheimpact f the lectoralystem.hisdisparitys to be expected,incethemodels'estimates re of theaverageeffect crossall countrieswhile heyrebeing estedgainstctual hangena particularase.Estimates rom arlier tudiesperformess creditablyn theexperimentalettings.heKenworthyndMalamimodel oesa goodjob ofpredictinghe esultnNewZealand ndcomeswithin .3%ofpredictinghe hangenJapan,ut tdoes notgetwithin .5 standarddeviationsfpredictingheother hanges.Matland's stimate oesnotgetwithin.5 standard eviations fpredictinghe mpact fanyof thewithin-countryhifts. n theeight ccasions hat heearliermodels ail opredicthe evelofchange,heir rrorsverestimateheelectoralystem'smpact very ime. hispatterns furthervidencethathe ower stimatesf he lectoralystem'smpactdvanced ereare more ccurate han arlier stimates.17


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Proportionalepresentation 197IV. Conclusion

Thisarticle as madefour ontributionsothe iteraturen thelink etweenlectoralystemsndgendergalitarianism.irst,thasshownhat he rgumentinkingRandhigherevels ffemale epre-sentations, n broad erms,orrect,ut lso that he onceptualndmethodologicalroblemsresentnearlier tudiesedthose tudies ooverestimatehe mpact f the electoral ystem.Matland's 1998)estimatehat R causes women's epresentationo be 15.6%higherthan totherwise ouldbe bears ittle esemblanceo the xperiencesofanyof thefour ountrieshathave mademajor hanges otheirelectoral ules.Research rom enworthynd Malamifares nlylittle etter.hemodel dvancednthis rticle enerally akesmore-accurate redictionshan ither f the earliermodels nddoes notmake ts rrorsonsistentlynone direction.Second, his rticle asdirectlyddressedhe uestionf hangeover imen women's epresentationnd tsrelationshipo electoralsystems.his s the uestionhepolicy ommunityenerallysks ofthe scientificommunity,ndmostof theprevious esearchnthisareahasnotbeen bleto addresstdirectly.Third, he dataset sed inthis rticle epresents significantadvance nmost arlier fforts.his article's stimatesrebased onten imesmore bservationshanhe esearchyRule,Norris, atland,andKenworthyndMalami.ThetwoMcAllisternd Studlar tudiesthat se similar ata othis tudy'severelyvercountheir ,causingtheir esultso be overstated.Fourth,his rticle asupdatedhe esearch ethodssed o tudythis roblemna numberffronts.ttreatsrowthnwomen's epre-sentations nonlinear,n intuitivelyppealingdea butonethat adnot een ried efore.tuses continuous easureor lectoralystems,anapproachhat itswellwith heoriesbouthow he lectoralystemmightmatter utonerarelyested efore ow.This measure llowsestimatesobe made bout he mpact falmostnykind felectoralreform,omethingreviousmeasures ouldnotdo.The lastof themethodologicalnnovations, hichconcernsstatisticalechniquesor ontrollingor lmost nmeasurableonceptslikeculture, as application utside he iteraturen womenandpolitics. omeaspects fpoliticalulture annot edirectlybservedina reliable ashion.he solution o this roblemsto not ryo mea-surepolitical ulture irectlyt all. Instead fmakingneextremelyunreliablessumptionboutwhat oliticalultures,researchershouldmake woreliablyxtremessumptions,acha counterweighto the


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198 Rob Salmondother. headvantagefthis pproachsthat tprovides very obustCI that an still e narrownoughobe useful. his pproachequireslittle ata ollectioneyondhe ependentariable, hich sespeciallyuseful henookingny istancento istory,owardartsf heworldwhere ata ources reunreliable,r ataspects f culturehat o nothavedirect nd observable ffects.Thearticle,fcourse,s notwithoutmperfectionsf tsown,and some have been raised nthe ext.twouldbe nice fa methodcouldbedevised o et hedatadecidewhat he ndconstraintn thelevel ofrepresentationillbe,ratherhanhavingt mposed ytheresearcher.18t wouldbe especially ice fthedatawere ymmetric,with s many bservationsnthe 0%-50% range s inthe0%-10%range althoughfthis cenario veroccurs, hisresearchuestionwillprobablye moot.Atpresent cannot rovide hese hings,ndthereforehose hallengesre eft or thers.

Rob Salmond s a Ph.D. candidate npolitical cience,4289BuncheHall,UniversityfCalifornia-Los ngeles, osAngeles, A90095nd Pre-Doctoralellow, epartmentofPolitical cience,6634 HavenHall, Universityf Michigan, nnArbor,MI 48109-1045.

NOTESI thank athleen awn,Jeffreyewis,Michael ewis-Beck,tanMarsh, lareSalmond,MikeThies, ana onStein,nd he ditorialtaffnd nonymouseviewers,all of whomprovided eryuseful ommentsndsuggestions uringhis rticle'sdevelopment.also thank he nterparliamentarynion,DuaneSwank, nd Arend

Lijphartor haringhedataon which his rticles based.Aprevious ersion fthisarticlewaspresentedt the2003 annualmeetingftheAmerican olitical cienceAssociationnPhiladelphia, ennsylvania.1 Female aborforce articipationrovides goodexample.Rawparticipa-tion evels ellusonly hatwomen reworking,ot nwhat ectors r at what evels.Countries itharge ervice r tourismndustries ayhavemanywomen mployedinthe ower chelons fthose ectors, hereasn otherwisequivalentountryitha large griculturalectormay ot ountmanyworkingomen s"employed,"ecausethey elp o run familyarm. an wereally onclude rom uchparticipationevelsthat hefirstountrys more ermissiveffemaleeaders han he econd?Recog-nizing his ifficulty,omeresearchersave ncluded measure fwomen's artici-pation nprofessional ccupationsKenworthynd Malami 1999).Althoughhisadjustments certainlynimprovementn thepreviousmeasure,t suffersromhesameproblem. esearchers eedto know o what xtent nation's ulturecceptsthepropositionhatwomen an lead ustas well as mencan,not imply erform


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Proportionalepresentation 199managementraccountancyasks s well. The statisticsnlydealwith he atter.Educational ttainmenttatisticsuffer rom imilar eficiencies.2. It s also unfortunatehatMcAllisternd Studlar's egressionablesdo notallow thereader o construct95% confidencentervalround heir oint stimatesfor nyvariable.3. To understandhy his echniques inappropriate,onsiderheBritishasein 1980and1981.Memberswere lected o theBritish arliamentn1979, nd thesubsequentlectionwas not held until1983.Thus,theevent hat eterminedhedependentariablen 1980 was the 1979election,nd the ame event lso entirelydeterminedhe evelofrepresentationn1981.TheobservationsnBritain or 980and 1981 are twoobservationsf the amecase,not wo eparateases.McAllisterandStudlar, owever,reathese s two eparateand,bythe tandardssumptionsof theOLS model, ndependent)ases. Theaverage arliamentaryermcross heirsample s aboutfour ears. herefore,his ountingtrategyeads to an inflationntheir umberfcasesby factor ffour,eadingnturn oartificiallymall tandarderrors nd substantialverconfidencentheresults.4. In addition,Matland1998) also examined 6 developingountries ndfound hat he lectoralystem asnot mportantorwomen's epresentation.5. Theperiod 988-98 sawrepresentationrow y4.3% inSweden,whereastheprevious 2yearshad seen15.5%growth.nFinland, epresentationarginallydeclinedntheperiod1991-99, fter rowing y13%over heprevious 2years.And nDenmark,heperiod ince1990hasseenrepresentationrow %,whereasthe eriod 977-90 aw 13%growth. epresentationnNorway asremainedlmoststatic ince he ate1980s, fterising y bout 5% intheprevious 0years.Repre-sentationevels nNew Zealandhave imilarlytagnated,lso after 20-year eriodofexplosive rowth.t s interestingo note hat hePRcountries o appear o havestabilized t a higher epresentationevel han ither ew Zealand whichsnowPRbutwaspreviouslyMD) or Canada whichs SMD). Itremains o be seenwhetheror not ther MD countries ill stabilize t ower evels han R countries.6. For hose ountrieshat xperiencedn authoritariannterludefter omenfirst onsuffrageGreece,Portugal, pain), use thedatewhen uffrage asfirstgranted.imply ecausebothwomen nd men ostpolitical ightsor period oesnotmean hat,pon edemocratization,omen tartedgain rompositionfpoliticalpowerlessnessomparedomen.7. I calculatedhedependentariable y takinghenumber f seatswonbyeachpartynddividinghat aluebythenumberfelectoral istrictsnthe ountry.I didnot nclude constantermn theregression,ecausethere s goodreason obelieve hat party'sM equals0 when herereno seats noffer,nd usedrobuststandardrrorso combat eteroskedasticitynthedata,but heresult s notdepen-dent n eitherf thesemethodologicalecisions. ome of theresidual ariancenPM is likely ue to legalthresholdsor epresentationnsomehigh-DM R coun-tries. heN in theregressions 127.

8.Thus, f75%ofthe arliaments elected ta lower ierwith DM of6,andthe ther 5% areelected t a higher,ational ierwith DM of100, hen he verallDM of the ystems coded s 29.5. This methodaptureshe dea that t spossibleto be lower na party'sist nd stillget lectednthis ormf mixed ystemhantisina simple Rsystem ith DM of ix,but rospectiveandidatesenerally ust


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200 Rob Salmondbeplaced higherhan nsystems ith 100-seat ational istrict.nemight rguethathis ountingtrategys unfairoMMsystemsndtoMMP inparticular.eopleelectednSMDs in MMPsystemsike hosenGermanyndNew Zealand reoftenon their arty'sist or hePRtier nd comeoff hepartyistbefore hePR seats reallocated. f theSMD winners re all menbut he ist s gender alanced,hen nceall themen omeoff hepartyist t ooksvery emalewhen he ist llocationsredone, esultingna gender-balancedarliament.hereforehe PR tier) ist ompo-sition s thekeydeterminantfgender alance ntheparliament,nd theDM as itrelates o thenational istmight e the ppropriate easure f DM in the ontextfthis esearchuestion. o test his heory,reranheregressions ith hisdifferentcoding or heMM systems' M. Therewas nochangenthe tatisticalignificanceor substantivemportancef thevariable.9.Anotheroodway oproxy or oliticalultures toemploy fixed-effectsmodel,whichmeasures achcountry'solitical ulturentirelyndependentlysingcountryummies. hatmethod s notappropriateor hisresearchuestion, ow-ever, ecause heresvirtuallyowithin-countryariationnthendependentariableof nterestthe lectoralystem). hisapproachwouldresultnestimatesf the f-fect f electoralystems eingdriven ysix main ases,three fthem romrance,and one each fromtaly,Japan, nd New Zealand.Thus,the estimates ould behighly nstable nd notgeneralizable.10.Theregressionssepanel-correctedtandardrrorsncombinationithcorrectionor ommon-poolirst-orderutocorrelationAR1), as recommendedyBeck and Katz 1995). Beck andKatz 1996) do express ome caution boutusingPCSEs and AR1 when laggeddependentariable s presentntheregressions.retestedhe ffected odelswithoutheAR1correctionnd found egligible iffer-ence in the substantiver statisticalignificancefanyvariable.KristensenndWawro2003)point o furthermprovementshat an be madeover hePCSE meth-odologynpaneldatawithaggeddependentariables. hese mprovementsely na fixed-effectsodel.Becausethedatahere renotwell suited ousing ixed ffects(as Kristensennd Wawro hemselvesote), retained CSEs in this nalysis.11 AlthoughhePCSE techniqueoes control or ontemporaneousorrela-tion cross anels, estimated version f hemodelwith wodummyariables,neindicatingears fter heBeijing eclaration adbeenmade nd notheronly odedas a 1 for uropeanUnionmembertates)ndicatingheyears fterhe tart f theEuropeanUnion's nitiativesogetmorewomen ntoparliaments.either fthesedummyariables roved significantredictorfthedependentariable,ndtheinclusion f these ariables id notmateriallylter nyof the ther stimates.12. I amverygratefulo an anonymouseviewer or uggestionsegardingAR1 corrections.13. Forfurtherobustnesshecks, reestimatedodels1) and 2) ofTable1,first sing he untransformedlinear)dependentariable ndthenusing simpledummy ariablefor lectoral ystems,he sameas the variableusedbyMatland(1998) andothers,nplaceofthe oggedDM variable. ran hese egressionsimplyto show hat hegeneral esultsnthis rticlerenotdriven y anyform f method-ological kullduggery.heresults emainroadlyhe ame n hese egressions,hichmixaspectsof the new modelwith spectsof oldermodelson this opic.Theseregressionslso ndicate hat he lectoralystemmatters,utnot s much sprevious


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ProportionalRepresentation 201research assuggested.ullresults f hese egressionsre vailable rom he uthoruponrequest.14. The robustnesshecksperformedere hould nspire onfidencentheresults,ut hevery estwaytomodel his atawithoutny onstraintstall,eitherintermsfmaximumevels r nterms fpoints f ymmetry,ouldbetoadapt hescobitmodelforbinary ependentariables sedby Nagler 1994) to work nthecontext fpaneldataandpercentages.uch a methodologicaldvance s,however,wellbeyond he copeof this rticle.15. I do not nclude nalysis f France's 1958 electoral eformnthis estbecause neitherhe MatlandnorKenworthynd Malami articles ven claimed oexplain atternsfchangenrepresentationevels nthe 1950s.16.Onemight rgue hat hemeasurementmployed ere nderstateshe rueimpact f the lectoralystem,ecausepast ncreasesnrepresentationre assumedto continue.n NewZealand,for xample, epresentationevels n 1993 hadgonehigherhannanyother MD systemt that ime.Why ssume hat hese ncreaseswouldhavecontinued, henCanada's representationf women tagnatedt ustabove20% inan SMD systemnthe1990s?There re wo nswers. irst,he ropor-tion fwomen lected o New Zealandmayoraltiesose nparallelwith arliamen-tary epresentationnthe1980s andearly1990s and continuedorise,withoutnyshiftothe lectoralystem,hroughhe est f he1990s.Second,f heresanybiasin this ase,thentamountso ess than1% in most f thesenaturalxperimentsnotenough o make nysubstantiveifferenceotheconclusions rawn rom heanalysis.17. Somereadersmightrgue hat his est s unfair o earlier esearchers.Afterll,this rticle tartedynotinghattwanted o answer differentuestionfromhat sked nearlierwork nthe ubject: thercholars ave tudiedwomen'srepresentationylooking t thestatic ifferencesetween lectoral nvironmentsacross pace,but his rticle's im s to ook tdynamicifferencescross paceandtime.tprobablys a bitunfairo take he arlier esearch utof ts tatic rena ndapplyhe stimateso hangesver ime. his s,however,recisely hat olicymakersdo with hisresearch. olicymakersn a givenplaceare interestedxactlynhowchanges o electoral ulesmight hangerepresentationver time and untilnowthey avehadno choicebut o use researchhat idnotdirectlynswer hat uestionas their uide.Thepurpose fTable 3 is to show hat here owexists n alternativeestimatef the electoral ystem'sffect,nd this stimateutperformshe earlierresearchnthe ontexthat oncerns olicymakers.18.There re, nfact, omemethods hat llowsuchestimation,ut hey onotworkn the ontextfthis esearchroject. sing he ogof theratio fwomento men s thedependentariable llows regressionn which hedependentariableapproaches egativenfinitys time oestozero andapproaches constants timeapproachesnfinity.hatconstant, hichwouldbe impliedn the nterceptf aregressionsing hisdependentariable, aking over ll time-basedndependentvariables ndleaving therndependentariables ntransformed,s theconstraintthat have mposednmyformulationsf this egression.woproblems,owever,arise nusing his egressionn this tudy. irst,ime s nowhere ear approachinginfinity,"eaninghat stimatesf he onstanterm revery mprecise.econd, heunbiased stimationf the onstant elies n unbiasedmeasures f all independent


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202 Rob Salmondvariables and that ondition s not met nthe researchdesignused here. reran heseestimationsnyway, ndpredictably,he pecificationshat ndercontrolled or ulturegave estimatesof the constant of 70-71%, withstandard errorsof about 8, whilethose specificationsovercontrolling or culturegave estimates n the mid-3 s, withstandard rrors f about6. The fact hat he ikely ceilingforwomen's representationlies somewherebetween30% and70% willnotcome as news toanybody.Thepatternsof substantive nd statistical ignificanceon the electoralsystemvariablesremainedunchanged ntheseregression pecifications. t should be reiteratedhat performedrobustness hecks on theregressionsreportedn this articleusingdifferentevels oftheconstraint,nd I foundno significant hanges nthecoefficients. amverygratefulto Kathleen Bawn and an anonymousreviewerforsuggestions regarding echniquein thisarea.

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