quantifyingrepresentativity.docx
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quantifyingrepresentativity
quantifyingrepresentativity
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Paper5Votingmatters-Issue10,March1999
QuantifyingRepresentativity
PKestelman
PhilipKestelmaniskeenonmeasuringelectoralrepresentativity,andworksinfamilyplanning.
WhatisaProportionalRepresentation(PR)electoralsystem?
Seriouslybeggingthatquestion,Gallagher(1991:
49)arguedthat"EachmethodofPRminimizesdisproportionalityaccordingtothewayitdefinesdisproportionality,andthuseachineffectgeneratesitsownmeasureofdisproportionality".
However,GallagheroverlookedSingleTransferableVoting(STV);anomissionrepairedbyHill(1997),invokinga'Droopproportionalitycriterion'(DPC:
Woodall,1994:
10):
"If,forsomewholenumberskandm(wherekisgreaterthan0andmisgreaterthanorequaltok),morethankDroopquotasofvotersputthesamemcandidates(notnecessarilyinthesameorder)astheirtopmpreferences,thenatleastkofthosemcandidateswillbeelected.Inparticularthismustleadtoproportionalitybyparty(exceptforoneDroopquotanecessarilyunrepresented)ifvotersdecidetovotesolelybyparty".
Thusdefined,PRsystemsincludeAlternativeVoting(AV:
k=1);thoughoverhalfthevotersmaybeunrepresented!
Accordingtothe1937IrishConstitution,notonlyparliamentarydeputies(multi-memberSTV),butalsothePresident(AV),shallbeelected"onthesystemofproportionalrepresentationbymeansofthesingletransferablevote".
YetnobodyregardsAVasaPRelectoralsystem.InfairnesstoWoodall(1994:
10),"AnysystemthatsatisfiesDPCdeserves...toberegardedasasystemofproportionalrepresentation(withineachconstituency)".Atthatlevel,Hill's"exaggeratedcase"(three-memberSTV)ispersuasive;howeverdisproportionaltoPartyFirstPreferences.Nonetheless,constituencylevel'PR'(includingAV)isnotenoughforPRasnormallyconstrued.
(Hill(1992)reasonedthat,ifvotersvotesolelybyparty,eachnominatingsufficientcandidates,"thenSTVwillproducesplendidproportionality,...,whileanydiscrepancyduetofractionsofquotascanbeexpectedtoevenoutoveranumberofmulti-memberconstituencies".Indeed,themainpoliticalquestionishowfaithfullytotalseatsreflectPartyFirstPreferencesoverall(regionallyand/ornationally).
PartyTotalRepresentativity
Inparliamentaryelections,thesimplestmeasureoftotaldisproportionalityistheoveralldeviationbetweenover-representedPartySeat-fractionsandVote-fractions:
theLoosemore-HanbyIndex(LHI),
LHIcomplementstheRoseIndexofProportionality(RIP);forwhichIpreferthemoreexplicitterm,PartyTotalRepresentativity(PTR).
Table1belowdemonstratesthecalculationofPTR=100%-LHIforthe1997IrishGeneralElection,whichprovedunprecedentedlydisproportionaltoPartyFirstPreferences.
Table1:
STVParty(FirstPreference)VotesandSeats:
Numbers,FractionsandDeviations:
GeneralElection,IrishRepublic,1997
*Loosemore-HanbyIndex(LHI)=12.9percent=Overalldeviationbetweenover-representedPartySeat-fractionsandVote-fractions:
complementingPartyTotalRepresentativity(PTR)=87.1percent.Source:
Dáiléireann(1998).
TheIndependentCommissionontheVotingSystem(Jenkins,1998:
47)gavea1997IrishGeneralElectionLHIofonly9.8percent(theirDVor'deviationfrompro-portionality':
Dunleavyetal,1997:
10).However,thetwomainparties(FiannaFáilandFineGael)alonereceived11.6percentmoreSeatsthanVotes(FirstPreferences);andexactLHI=12.9percent(Table1).LHI(andhencePTR)areoftenmiscalculated.
OtherMeasures
McBride(1997:
9)invoked"O'Leary'sindexofproportionality":
theratioofeachparty'sSeat-fractiontoitsFirstPreferenceVote-fraction(S%/V%).However,theproblemishowtocombinesuchparty-specificratios(ordeviations,S%-V%:
seeTable1above)intosomemeasureofoveralldisproportionality.O'Leary(1979:
100)favouredtheRaeIndexofDisproportionality(RID),measuringpartyaveragedisproportionality(contrastLHIabove):
whereN=Numberofpartiesexceeding0.5percentofvotes.
Thepalpablearbitrarinessofthisaveragedisproportionalityperparty(whynotacutoff-pointof0.1percent,or5.0per-centofvotes,forthatmatter?
)mayberedeemedsomewhatbydefiningNasthe'effectivenumberofparties'(LaaksoandTaagepera,1979):
TaageperaandShugart(1989:
260)preferredN2onpracticalgrounds;though(entropy-based)N1enjoyed"equallygoodconceptualcredentials".
Gallagher(1991)arguedthatRIDwas"toosensitivetothenumberofparties";towhichLHIwas"muchtooinsensitive".Accordingly,heproposeda"leastsquaresindex":
theGallagherIndexofDisproportionality,
Nevertheless,Gallagher(1991:
47)considered"probablythesoundestofallthemeasures"theSainte-Lagu?
Index,
Unfortunately,SLIrangestheoreticallyfromzerotoinfinity;whichGallagheracknowledgedwas"lesseasilyinterpreted"thanLHIorGID(ranging0-100percent).Thusinthe1997IrishPresidentialElection,AVFirstCountLHI=55percent(complementingPTR=45percent:
PresidentMcAleese'sFirstPreferenceVote-fraction:
Table2below);whereasSLI=121percent!
Table2:
AVPartyVote-fractions,Seat-fractionsandDeviations,byCount:
PresidentialElection,IrishRepublic,1997
*FirstCountLHI=54.8percent:
PTR=45.2percent.
**FinalCountLHI=44.4percent:
PTR=55.6percent.
Source:
IrishTimes,1November1997.
Lijphart(1994:
60)preferredGIDassteering"AmiddlecoursebetweentheRaeandLoosemore-Hanbyindices.Itskeyfeatureisthatitregistersafewlargedeviationsmuchmorestronglythanalotofsmallones";andcontrastedtwohypotheticalelections(abstractedinTable3below).
Withoutdefiningany'LijphartProportionalityCriterion',hemaintainedthatElection1was"highlydisproportional"(GID=LHI=5.0percent);whereasElection2was"highlyproportional"(GID=2.2percent;butLHI=5.0percent).Ironically,hisintuitively"muchmoreproportional"Election2yieldedthehigherSLI,consideredbyGallagher(1991:
49)"thestandardmeasureofdisproportionality"!
Woodall(1986:
45)preferredtheFarinaIndex,
FIistheanglebetweentwomulti-dimensionalvectors,whosecoordinatesarePartySeat-fractionsandVote-fractions:
theoreticallyrangingbetween90°(cosFI=0)andzerodegrees(parallelvectors:
exactPR).Asafractionofarightangle,FID=FI/90°;soranging0-100percent(insteadof0-90°).
InTable3,FID(likeRIDandGID)evaluatesElection1asmoredisproportionalthanElection2.However,asHill(1997)recognised,FIDalsoposesproblemsofinterpretation;remainingafarcryfromthepristinesimplicityofLHI.
Hill(1997)reproachedPTRandothermeasures(their"fatalflaw")asconfinedtoPartyFirstPreferences.Nonetheless,heacknowledgedthattheconceptofTotalRepresentativitymaybegeneralised(e.g.fromPartyto'Cumbency',GenderandName:
Kestelman,1996);andextendedbeyondtheSTVFirstCount.YetheregardedFinalCountPTRasmerelycomparingSTVwithitself!
Table3:
FiveMeasuresofOverallDisproportionality:
TwoHypotheticalElections
*Asdefinedinthetextabove.
Minor/Micro-Parties
AsHill(1997)implied,minorpartiesandindependents('microparties'-representingnobodybutthemselves)mayneeddisaggregatingbeforecalculatingoverallmeasuresofdisproportionality.ExactLHInecessitatesdisaggregatingthevotesforeveryrepresentedparty(andelectedindependent)fromunrepresentedparties;asinTable1above.SLImayalsobecalculatedwithoutdisaggregatingunrepresentedparties.
Ontheotherhand,exactGIDrequiresdisaggregatingevenunrepresentedpartyvotes.Moreover,inevaluatingafewlargedeviations(S%-V%)asmoredisproportionalthanmanysmalldeviations,withthesametotaldeviation(andhenceLHI),GIDimpliesthat,themorefissiparouslypeoplevote,themoretheydeservetobeunder-represented.Incontrast,LHIconsistentlymeasuresthetotalunder-representationofallunder-representedvoters.
Conclusions
Gallagher(1991:
33-34)lamentedthat"Thereisremarkablylittlediscussionofwhatexactlywemeanbyproportionalityandhowweshouldmeasureit...howdowedecidewhichisclosertoperfectproportionality?
"-whencomparingdifferentelections.Noticealreadytwodifferentsensesoftheterm'proportionality'here!
Hencemypreferencefortheterm'representativity'formeasuresadmittingmattersofdegreetotherelationshipbetweenvotesandseats.
Gallagher(1991:
46)reportedthat,at82nationalelectionsin23countries(1979-89),LHI,GIDandSLI(butnotRID)provedimpressivelycorrelatedwitheachother:
sowhycomplicatematters?
Besides,measuringaveragedisproportionality(RID)necessitatescountingparties-arathermoveablefeast-andthereseemslittlevirtueinquantifyingsomehybridbetweenthedistinctconceptsoftotalandaveragedisproportionality
ThereremainslegitimatescopefordebatingtherelativemeritsofSTVfirstorfinalpreferencerepresentativity,innationalaggregateorconstituencyaverage,respectingpartyorotherconsiderations.Inevaluatingtherepresentativitymediatedbydifferentelectoralsystems,nomeasureisperfect.
Agenerationafteritsintroduction(LoosemoreandHanby,1971),LHIsurvivesrelativelyunscathed.Iremainpeculiarlysusceptibletothecomplement(PTR)ofthatsimplestLHI;doubtingwhethermorecomplexmeasuresofoveralldisproportionalitywouldmateriallyaffectelectoralcomparisons(forexample,STVrepresentativitybyDistrictMagnitude:
Kestelman,1996).
References
Dáiléireann(1998):
28thDáilGeneralelection,June1997.ElectionResultsandTransferofVotes.TheStationeryOffice,Dublin.
Dunleavy,Petal(199
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