organized interests and the mechanisms behind unequal

Organized Interests and the Mechanisms Behind Unequal Representation in Legislatures*

MichaelBecher

IEUniversity

DanielStegmueller

DukeUniversity

Thisversion:December23,2021

Howdoorganizedinterestscontributetounequalsubstantiverepresentationincontemporarydemocracies?Whiletherapidlygrowingliteratureonunequaldemocracieshasturnedtoanalyzingthemechanismsunderlyingthebiasedresponsivenessofelectedrepresentatives,itpaysrelativelylittleattentiontotheroleofinterestgroups.Wediscusstwocentralchannelsthroughwhichinterestgroupsshapeunequalrepresentation:theselectionofpartisanlegislatorsthroughelectionsandpost-electoralinfluencevialobbying.Wearguethatthesechannelsarenotalternativemechanisms,butpotentiallycomplementarystrategiesusedbyrationalactors.Employingagametheoreticmodelandsimulationsofinterestgroupinfluenceonlegislativevoting,weshowthatthislogicmayexplaininterestgroupstrategiesinunequaltimes.Ithasclearimplicationsforempiricalanalysestryingtounbundleelectoralfrompost-electoralinfluence.Ourmodelimpliesthatinterestgroupstrategiesvarywithpartypolarization,andithighlightsachallengeforempiricalresearchonunequalrepresentationandtheliteratureonlobbying:Whatcanbelearnedaboutmechanismsfromthedataalonemightbelimitedbythestrategicactionsofpoliticalactors.Usingstatisticalmodelscommonlyusedintheliteraturetostudybiasesinlegislativevotingorpolicyadoption,researchersarelikelytooverstatetherelevanceofelectionsasachannelthroughwhichgroupsaffectlegislativeresponsivenessandunderstatetheroleinterestgroups’post-electoralinfluence.Ourresultsstresstheimportanceoftheoreticalmodelscapturingthestrategicbehaviorofpoliticalactorsasaguidinglightfortheempiricalstudyofmechanismsofunequalrepresentation.

*WearegratefultoCharlotteCavailé,ThomasChristiano,BenPage,NoamLupu,ImilNurutudinov,JonasPontusson,JanStuckatz,GeorgVanberg,andparticipantsatAPSA2020,IASTworkshop“Knowledge,Power,andtheQuestforPoliticalEquality”,andtheUnequalDemocraciesspeakerseries(VanderbiltUniversityandUniversityofGeneva)forcommentsandsuggestions.

Electronic copy available at: https://ssrn.com/abstract=3946330

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Introduction Whatexplainsunequalrepresentationincontemporarydemocracies?Inthewakeofrisingeconomicinequality,arecentliteraturehascumulatedevidencethatlegislatorsinrepresentativeinstitutions,rangingfromtheU.S.CongresstolegislativeassembliesinEuropeandLatinAmerica,aremoreresponsiveto(ormorecongruentwith)thepreferencestohigh-incomeconstituentsandbusinessintereststhantopreferencesofthosewithaverageincomesandparticularlythepoor(e.g.,Bartels2008;Elsässer,Hense,andSchäfer2017;Gilens2012;GilensandPage2014;LupuandWarner2020;Mathisenetal.inthisvolume).However,thereisnoconsensusonthemainmechanismsdrivingunequalrepresentation.Surprisinglydivergentviewsarecombinedwithonlylimitedevidenceontheimpactoforganizedinterestsonpoliticalinequalityinlegislatures.

Inthischapter,westartbyreviewingthescholarlydebateandidentifyacentralareaofdisagreementabouttherelativeimportanceofinterestgroupsandthemechanismthroughwhichtheyshapesubstantivepoliticalinequality.Then,wepresentasyntheticmodelthatcapturesarepresentativedemocracywithorganizedintereststhatcanseektoinfluencepolicythroughelectoralselectionandpost-electorallobbying.Weusethemodeltoderivepositiveimplicationsonthecontext-varyingnatureofinterestgroupinfluenceandtoclarifythechallengesfacedbyscholarstryingtouncoverinterestgroupinfluenceandtounbundlecompetingmechanismsusingempiricalobservations.

Broadlyspeaking,afundamentaldifferenceamongtheoriesofunequaldemocracyistheirrelativeemphasizeofelectoralselectionorpost-electoralinfluenceasdriversofunequalrepresentation.Prominentexplanationsthattakeanelectoralselectionperspectiveincludepartisandifferencesanddescriptiverepresentation(Bartels2008;Carnes2013;CarnesandLupu2015;Mathisenetal.2021;RhodesandSchaffner2017).Thisanalyticalperspectivefocusesscholars’attentiononexplainingunequalinfluenceoverelectionoutcomes(e.g.,basedoncampaignfinance,electorallaws,organizedlabor,orvoterpsychology).Alternativeexplanationshighlighttheimportanceofpost-electoralchannelsofinfluenceandfocusonlobbying,broadlyconstrued(Flavin2015;HackerandPierson2010;Hertel-Fernandez,Mildenberger,andStokes2019;Kellyetal.2019).

Interestgroupsmayinfluencepoliticalrepresentationthroughbothchannels,electoralselectionandpost-electoralinfluence.Butweknowlittleabouttherelativeimportanceofthesetwochannels.Moreover,thereisnoagreementontheoverallcontributionofinterestgroupstopoliticalinequality.Abetterunderstandingofpossiblemechanismsprovidesfoundationsforstudyingthetotalimpact.

Onetheoneside,thereistheviewthatorganizedgroupsthatrepresentbusinessinterestsandhigh-incomeprofessionalsareanimportantexplanationforwhypolicyoutcomesdeviatesubstantivelyfromthepreferencesofaveragecitizens.ThisperspectiveiscalledBiasedPluralism(GilensandPage2014).Whiledirecttestsarestillrare,thestudyofGilensandPage(2014)coversnearlytwothousandpolicyissuesintheU.S.Itconcludesthatorganizedinterestshaveasubstantialimpactonpublicpolicy,beyondthepreferencesofaveragecitizensandeconomicelites,andthatthisisespeciallypronouncedforbusiness-orientedgroups.Relatedresearchonlegislativevotingratherthanpolicyadoptionusesan


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instrumental-variableapproachandfindsevidencethatlaborunionscandampenthepro-richbiasintheU.S.Congress(BecherandStegmueller2021).TheviewthatorganizedinterestsmatterforpoliticalequalityisofcoursenotrestrictedtoAmericanpolitics.MancurOlson’stheoryofcollectionactionimpliesthatnarrow,concentratedinterestsaremorelikelytoberepresentedintheinterestgroupuniversethanbroad-basedgroupsofcitizens(Olson1965).ItisnothardtofindscholarsofcontemporarydemocracyinEuropewho,afterlookingattheavailabledata,areworriedaboutbiasedpluralism.Forexample,recentcomparativeresearchshowsthatEuropeancampaignfinancesystemsareunequal,benefittingtherichandcorporationsmorethanthepoorthroughtaxexemptionsandotherrules,andthathighercampaignspendingislinkedtoelectoralresults(Cagé2020).

Ontheotherside,thequantitativeempiricalliteratureontheroleofmoneyinpoliticshasgrappledwiththedifficultyofshowingthatinterestgroups’financialcontributionsaffectlegislativevotes.Reviewingdozensofroll-callstudiesonthelinkbetweeninterestgroupcontributionsandlegislativevotingintheU.S.,Ansolabehere,Figueiredo,andSnyder(2003,116)concludethattheevidencethatfinancialcontributionstocandidatesaffectstheirvotes“isratherthin”.Rather,basedontheirownanalysistheyconcludethat“Legislators’votesdependalmostentirelyontheirownbeliefsandthepreferencesoftheirvotersandtheirparty.”Theyaddthemethodologicalrecommendationthatscholarstryingtoassesstheimpactofmoneyonvotesusingobservationaldatashouldincludelegislatorfixedeffectstocontrolforlegislators’ownpreferences,party,andconstituencyinfluence.Bydoingso,scholarsareimplicitlyorexplicitlytryingtoisolateapost-electoralchannelofinfluence.However,thisstrategycanbeproblematicandleadtomisleadinginferenceswhenelectoralselectionandpost-electoralinfluencearecomplements.

Wearguethatelectoralselectionandpost-electoralinfluencearelikelytogohandinhand.Ignoringthiscomplementarity,researchersmaywronglyconcludethatonlyelectoralpoliticsmattersasachannelthroughwhichinterestgroupsaffectpoliticalequalityinlegislatures.Thisissuemattersbothfortestsofpositivetheoriesofunequaldemocracyaswellasnormativeevaluations.Withoutabetterunderstandingofmechanismsitremainsdifficulttodevisestrategiestomitigatesubstantivepoliticalinequalityagainstthebackdropofeconomicinequalityandpopulistchallengestodemocraticinstitutions.

Wesetforthourargumentusingasimpleformalmodelthatisthenusedtogeneratesimulatedlegislatures.Itcapturesatwo-stagepoliticalprocesswithanelectoralandapost-electoralstage.Themodelassumesapoliticalprocesswhereelectoralinfluenceandpost-electoralinfluencecanbecomplements.Thismeansthatanorganizedinterest—whetherpro-poororpro-rich—aimingtoshapepolicyhastofirstensurethattheirpreferredpoliticianiselected.Butthestorydoesnotendonelectionnight.Legislatorshaveaconstrainedagendaandwillcarefullychoosewhichissuestoprioritizeevenamongthosetheyprincipallyagreewith.Thismeansthattheorganizedgroupwillalsohavetolobby(friendly)legislators(Austen-SmithandWright1994;HallandDeardorff2006).

Ourmodelilluminatesthatthestrategiesoforganizedinterestsvaryacrosscontext.Whenpartypolarizationisrelativelylow,theycanfocusonswayinglegislatorsthroughpost-electorallobbying.Increasingpolarizationincentivizesorganizedintereststofocussomeoftheirenergyonhelpingtoselectlike-mindedpoliticians.However,lobbyingwillnotbe


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fullysubstitutedbyelectioneering.Rather,whenpolarizationishigh,andwithpoliticiansfacingcompetingdemands,organizedinterestswillhavetoengageinbothactivities.Thisleadstoanimportantbutlargelyneglectedchallengeforempiricalresearchonunequalrepresentation(andtherelated,butlargelyseparate,literatureonlobbying):whatcanbelearnedaboutmechanismsfromthedataalonemightbelimitedbythestrategicactionsofpoliticalactors.

Theproblemofanalyzingmechanismisnotsimplyduetoconfoundingoromittedvariablebias.Assumethataresearchercanidentifythecausaleffectofthegrouponlegislativebehavior(e.g.,viaanexogenousorinstrumentedmeasureofgroupstrength,oranaturalexperiment).Thekeyquestionthenishowmuchofthetreatmenteffectisduetoelectoralselectionofafriendlylegislatorversuspost-electorallobbying.Toempiricallyillustratethispoint,wesimulatethousandsofpossiblelegislaturesarisingfromaknowndatageneratingprocess(ourtheoreticalmodel)wherewithoutpost-electorallobbyinglegislatorswouldnotsupportaninterestgroup’spreferredpolicy.Wethenapplystatisticalmodelscommonlyusedintheliteratureandshowthatresearchersrisktodrawincorrectconclusionsfromsuchanalyses,overstatingtherelevanceofelectionsasachannelthroughwhichgroupsaffectlegislativeresponsiveness.Furthermore,weillustratetheissueusingroll-callvotesintheU.S.HouseofRepresentatives.1

Empiricalresearchonlobbyingusuallyfacestheproblemthatpost-electoraleffortcannotbeinferredfromobservabledata.However,asweshowinthischapter,ourconclusionstillstandsevenwhenresearcherscanfullyobservepost-electoraleffort(orcorrectfortheknownlackofreliabilityofameasure).Thereasonisthatthegrouplobbiesfriendlylegislators.Inequilibrium,theselectionofafriendlylegislatureandlobbyingarehighly(butnotperfectly)correlated.Empirically,thisleadstoaformofsimultaneitybias.Asaresult,basedonstandardempiricalanalyses,scholarsmayerroneouslyconcludethatallthatmattersforunequalrepresentationiselectoralpolitics.Again,thisempiricalproblemexistseventhoughscholarscancausallyestimatethetotaleffectofgrouppoweronlegislativeresponsiveness.

Income and legislative responsiveness Theideathatallcitizensshouldcountequallyinthepoliticalprocessunderpinsvariousnormativetheoriesofdemocracy.Politicalequalityisconceivedasthe“equaladvancementofinterests”(Christiano2008,95)andisaboutsubstantiveordefactorepresentation,notjustequalpoliticalrights.ThisiswhatDahl(1971)callsequalresponsivenessandthesocialchoiceliteratureoftencallstheanonymityaxiom.Politicalequalityisayardstick,notaprediction.Severalpositivetheoriesofdemocraticpoliticssuggestthatpervasivesocio-economicinequalitiescanlimitequalityinpolicymaking.Forexample,interestgroups’monetarycontributionscaninfluencepost-electoralpolicymaking(GrossmanandHelpman2001)aswellaselectoraloutcomes(Cagé2020).Inthewakeofrisingeconomicinequality

1EvidencefromtheU.S.showsthatelectoraleffort(toinfluenceselection)andpost-electorallobbyingeffortarelinked(Ansolabehere,Snyder,andTripathi2002;Kim,Stuckatz,andWolters2020).


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(Piketty2014;LupuandPontussoninthisvolume),politicalscientistsandothersocialscientistshavepaidincreasingattentiontotheimplicationsofeconomicinequalityforsubstantivepoliticalequality.

BuildingonpioneeringresearchontheU.S.Senate(Bartels2008)andpolicyadoptionintheU.S.(Gilens2012),numerousstudies–morethanenoughtofillasemester-longcourse–havefoundevidencethatelectedpolicymakersinlegislativeassembliesaremoreresponsivetothepreferencesofrelativelyrichconstituentsattheexpenseofmiddle-incomeandpoorconstituents(e.g.,Elsässer,Hense,andSchäfer2017;Gilens2016;Hertel-Fernandez,Mildenberger,andStokes2019;KallaandBroockman2016;PetersandEnsink2015;LupuandWarner2020;Mathisenetal.2021inthisvolume;RigbyandWright2013).Responsivenessherereferstotherelationshipbetweentheopinionsofconstituentsdifferentiatedbyincomeandlegislativeactionsofofficeholders,usuallylegislativevotes2,ortherelationshipbetweennationalpublicopiniondifferentiatedbyincomeandpolicyoutcomes.Whenpolicyquestionsarepolarizedbyincome,manyofthesestudiessuggestthattheviewsoftherichmattermorewhereastheviewsofthepoormatterlittleornotatall(butseeBrunner,Ross,andEbonya2013;ElkjærandIversen2020).Perhapsnotsurprisingly,populistpartiesandpoliticianshavecapitalizedontheperceptionthatdemocracyfavorstheaffluent(Müller2021).

Thedegreeandrelevanceofunequalresponsivenessisamatterofongoingdebate(Erikson2015).Oneviewisthatelectedrepresentativesshouldnotpandertotheviewsofthelargelyuninformedpublic.Rather,goodrepresentativesoughttoleadbymakingchoicesthatareintheenlightenedinterest(howeverdefined)ofcitizens.WeagreewithFederalistPaper71andgametheoreticmodelsofpandering(Canes-Wrone,Herron,andShotts2001)thattherecanbetoomuchresponsiveness.However,thesemodelscannotjustifycomplacencyaboutunequalresponsivenessinthedemocraticprocessthatliesatthecenterofthisvolumeandchapter.Manydisagreementsaboutpolicybetweenrichandpoorcitizensconcerneconomicbreadandbutterissuesarebasedondifferencesinmaterialconditionsorideals.Indeed,anestablishedpoliticaleconomyliteraturepredictsanddocumentsrationalsourcesofdisagreement.Forexample,considerincomeredistributivepolicies,minimumwageincreases,orstimulusspendinginthewakeofaneconomicdepression.Ontheseandsimilareconomicissues,individualsintheU.S.andEuropewithlowerincomesare,onaverage,significantlymoreinfavorofgovernmentaction(Gilens2009;RuedaandStegmueller2019;SorokaandWlezien2008).Basedoncurrenttextbookeconomics,onewouldbehardpressedtoarguethatcitizensupportingthesepoliciesshouldsomehowgetlessweightthancitizensopposingthem.

Assessingthedegreeofunequalresponsivenessrequiresaddressingchallengingmeasurementandestimationissuesthatarediscussedinmoredetailelsewhere(e.g.,seeBartelsinthisvolume).Ourinterpretationoftheliteratureisthatthereissufficientbroad

2Lesswidelystudied,butotheraspectslikebillsponsorship,speeches,orcommitteeworkareclearlyrelevantaswell.


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evidencefortheexistenceofunequalresponsivenesstowarrantaninvestigationofitsmechanisms.

Initialresearchoncongressionalorstate-levelrepresentationintheU.S.waslimitedbysmallsurveysamplesizes,whichposestheriskthatestimatesofunequalresponsivenessaremostlyduetosamplingnoiseinthemeasuresof(correlated)grouppreferences(BhattiandErikson2011).3However,largersurveys,suchastheCooperativeCongressionalElectionStudy(CCES),havereducedthisproblem.Forinstance,Bartels(2016,ch.8)usesthe2010and2012CCESwithmorethan100,000respondentsandfindsdifferentialresponsivenessintheSenate.Senators’roll-callvotingbehaviorispositivelyresponsivetoaverageconstituentopinion,butthisismainlydrivenbyresponsivenesstotheupperthirdoftheincomedistribution.Bartels’estimatesimplythatsenatorsarefivetimesmoreresponsivetohigh-incomethanmiddle-incomeconstituentsandnotatallresponsivetolow-incomeconstituents.SubsequentworkontheU.S.HousedrawsonadditionalCCESwavesandcorrectsforpossibleimbalancesbetweenthesurveysampleanddistrictpopulationsusingmicro-levelcensusdata(BecherandStegmueller2021).Onaverage,thepatternintheHouseisverysimilartotheonefoundfortheSenatebyBartels(2016).

Fieldexperimentalresearchhasaddedimportantinsights,byhelpingtoidentifyinamorecontrolledfashionbiasesthattendtoworkagainstthepoorandinfavoroftheaffluent.KallaandBroockman(2016)findthatlegislatorsaremorelikelytomeetdonorsthannon-donors,whichbolsterstheargumentthatmoneybuysaccess.Anotherstudysendsmessagesfrom(fictional)constituentstopoliticians,randomlyvaryingnameandethnicitybutkeepingthesamecontent(Butler2014).Itrevealsthatpoliticiansexhibitasignificantsocio-economicbiaswhenevaluatingconstituentopinion.FocusingonlegislativestaffersinCongress,Hertel-Fernandez,Mildenberger,andStokes(2019)findthatstafferssystematicallymis-estimatepublicpreferencesintheirdistrict.Thismismatchispartiallyexplainedbypersonalviewsandcontactswithbusinessgroups.Throughanexperiment,thestudyalsodocumentsthatstaffersarelesslikelytoviewcorrespondencefromordinarycitizensasbeingrepresentativeofconstituentpreferencesthancorrespondencefrombusinesses.

Importantly,scholarsextendedthestudyofunequalrepresentationtoassembliesinEurope,LatinAmerica,andelsewhere(e.g.,Bartels2017;ElkjærandIversen2020;Elsässer,Hense,andSchäfer2017;PetersandEnsink2015;LupuandWarner2020;Mathisenetal.2021).Oneapproachinthecomparativeliteratureistomatchdataongovernmentspendingwithdataonpublicspendingpreferencesbyincomegroupsfrommultiplesurveywavesandmultiplecountries.Estimatingtimes-seriescross-sectionmodelsonsuchdata,somestudiesfindthatchangesinpolicyarepositivelyrelatedtochangesinspendingpreferencesoftherichbutnotthepoor(Bartels2017;PetersandEnsink2015).Ontheotherhand,ElkjærandIversen(2020)showthatthesefindingscanbemodel-dependent.Intheirpreferredregressionspecification,policyappearstorespondonlytomiddleincomepreferences.LupuandWarner(2020)combineeliteandmasssurveysin52countriesoverthreedecadestocalculatethedistancebetweentheviewsof

3Onquestionwordingandframingeffects,seeGilens(2012,ch.1);HillandHuber(2019).


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citizensandlegislators.Theyfindthatlegislators’viewsaremorecongruentwiththoseoftherich.

Whilefutureresearchwillsurelyrefineestimatesofthedegreeofunequalrepresentationinalargersetofdemocracies,onecanconcludethatmuchofthispreliminaryevidencerunscountertonormativetheoriesofdemocracystressingsubstantivepoliticalequalityatthepolicymakingstage.

Interest groups and the hunt for mechanisms Itremainsanopenquestionwhythereissomuchpoliticalinequalityinthelegislativearenaandwhatcanbedoneaboutit.Surveyingtheliterature,LarryBartelsnotesthatthere“isclearlyagreatdealmoretobelearnedaboutthemechanismsbywhicheconomicinequalitygetsreproducedinthepoliticalrealm.”(2016,267).Theanalysisofmechanismsinthisbodyofscholarshiphasoftenfocusedontheimportanceofunequalpoliticalparticipation,knowledge,orindividualcampaigncontributions(Bartels2016;Erikson2015;Gilens2012).

Wetakeacomplementaryperspectiveandaskhoworganizedinterestsshapesubstantivepoliticalinequality.Interestgroupsmayfocustheireffortsonshapingelectionoutcomesoronswayingincumbentpolicymakers,whatevertheirpartisanstripes.Towhatextentisunequallegislativeresponsivenessdrivenbyanelectoralselectionchannelratherthanapost-electorallobbyingchannel?Sofar,theexistingevidencedoesnotprovideaclearanswerabouttherelativeimportanceofthesetwomechanisms.Wewilldemonstratethatcommonempiricalstrategiesmayfailtoprovideaclearanswer,andpotentiallyalsounderestimatetheoverallimpactofinterestgroupsonunequalresponsiveness.

OneofthefewstudiesthatdirectlyexaminestherelevanceoforganizedinterestforunequalresponsivenessconcludesthatnationalpolicyintheU.S.issignificantlybiasedtowardeconomicelitesandorganizedgroupsrepresentingbusinessinterests(GilensandPage2014).RelatedresearchatthesubnationallevelfindsthatU.S.stateswithstricterlobbyingregulationsexhibitlesspoliticalinequalityatthepolicymakingstage(Flavin2015).However,theseresultsstandincontrastwithfindingsfromaseparateliteratureonlobbyingandmoneyinpolitics.Itconcludesthatinterestgroups’monetarycontributionhavelittlediscernibleimpactonlegislativevoting(Ansolabehere,Figueiredo,andSnyder2003)andthatgroupswithmoreresourcesdonotnecessarilyhavemuchhighersuccessratesthanothergroups(Baumgartneretal.2009).

Political selection as a pathway to (in)equality

Partisanship

Fromanelectoralselectionperspective,unequalresponsivenessinlawmakingisdrivenbywhattypesofpoliticiansareelectedtooffice.Partisanshipisoftenthestrongestpredictoroflegislativevoting(Bartels2008;Lee,Moretti,andButler2004;McCarty,Poole,and


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Rosenthal2006),andthepartisancompositionofgovernmentsshapeskeypublicpoliciesoverwhichpeoplewithdifferentincomestendtodisagree(Pettersson-Lidbom2008).Inpartisantheoriesofpoliticalcompetitionandpublicpolicy,differentpartiesrepresentdifferentsocio-economicgroupsandpoliticalcompetitiondoesnotleadpartiestoconvergencetothemedianvoter(Hibbs1987).Onceinoffice,politicianstrytoimplementtheirpolicyagendaandarenotverysensitivetolobbyingeffortstodootherwise.Thisaccountimpliesthatreducingpoliticalinequalityinalegislaturerequiresfirstandforemosttobalancetheelectoralarena.

Arelegislatorsfromdifferentpartiesunequallyresponsivetorichandpoorconstituents?ExaminingtheU.S.Congress,Bartels(2016,248–49)findsthatRepublicanHousemembersandsenatorsaremuchmoreresponsivetohigh-incomethantomiddle-incomeconstituentsandlargelyirresponsivetothepoor.WhileDemocraticmembersofCongressaregenerallyalsoresponsivetohigh-incomeconstituents,theydorespondtotheviewsoflow-incomeandmiddle-classconstituents(sometimestotheextentthatthereisnostatisticaldifferenceinratesofresponsiveness).Ananalysisdrawingonrichindividual-levelvoterregistrationdataconfirmsthisbasicpattern(RhodesandSchaffner2017).4AcomparativeanalysisofpolicyadoptioninfourEuropeancountriesfindsthatunequalresponsivenessislesspronouncedwhenleftpartiesareinpowerinthreeoutofthefourcountries(Mathisenetal.inthisvolume).

Descriptive representation

Politicalselectionnotonlyconcernspartisanship.Individualsvaryonmanyattributesandsomeofthemareboundtoshapehowtheybehaveinthepoliticalarena.Inparticular,descriptiverepresentationmattersbecausethecompositionofmanylegislaturesisimbalancedintermsofgenderandtiltedtowardthehighlyeducatedandwell-off.Thus,onemightask,asdidJohnStuartMillinhisConsiderationsonRepresentativeGovernment,if“[p]arliament,oralmostanyofthememberscomposingit,everforaninstantlookatanyquestionwiththeeyesofaworkingman”(Mill1977[1861])?ThereisampleevidencethattheoccupationalclassbackgroundofpoliticiansmattersforlegislativevotingintheUS(Carnes2013)and,comparatively,forthepositionsendorsedbylegislators(CarnesandLupu2015).Politicianswithaworking-classbackgroundaremoreresponsivetotheviewsoftherelativelypoor,evenaftercontrollingforpoliticalparty.Similarly,characteristicslikegenderandraceshapetheresponsivenessofpoliticians(Butler2014,Swers2005).

Thislineofresearchonthelinkbetweendescriptiverepresentationandinequalityinlegislaturesimpliesthatbarrierstoentryinpoliticsforlessadvantagedindividualsarepartoftheprocessdrivingunequalpoliticalresponsiveness.

4Gilens’studyofsystem-levelresponsivenessintheU.S.doesnotfindthesamepartisangap(Gilens2012).Whileinferencesarelimitedbytherelativelysmallnumberofyears,themostresponsiveperiodwasduringthepresidencyofGeorgeW.Bush,driveninpartbysupportfortheIraqwarandthe2001taxcuts.


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What shapes selection?

Economicinequalitymayfavortheselectionofpolicymakersmoreinclinedtoconsidertheopinionsoftheaffluent.Forexample,increasedeconomicinequalitymayincentivizehighercontributionsbythosewhohavemosttolosefromredistributionandthuschangethepartisancompositionofthelegislature(Campante2011).

Itmaybetemptingtothinkthattheelectoralinfluenceofresource-richinterestgroupsispredominantlyaU.S.phenomenonduetoitsoutsizelevelsofcampaignspending.Butwhatmattersinelectoralcontestsistherelativefinancialadvantageofonegroupoveranother.Forexample,Cagé(2020)documentsthatinEuropefundingisnotequallydistributedacrosspoliticalparties;ittendstofavorconservativeoverleftparties.Therichestsectionsofsocietyandcorporationscontributethebulkofprivatepoliticalcontributions,andthatthisspendingisnotelectorallyneutral.Forinstance,whileGermanyhasapubliccampaignfinancesystem,itimposesnolimitsoncorporatedonations(withcarmakersbeingleadingcontributors).IntheUK,electionspendingisstrictlyregulated,butpartiescanreceivelargeamountsofcashinformofdonations.5

Electoralinstitutionsmayalsomatterforselection.Intheabsenceofcrediblecommitmentsbyparties,majoritarianelectoralsystemsexperienceabiasinfavoroflow-taxandlow-redistributionpartiesontheright(IversenandSoskice2006).Thisbiasmayvarywitheconomicinequalitybecauseleftpartieswillhavemoreincentivestosolvetheircommitmentproblemasinequalityincreases(Becher2016).

Organizedlaborcanalsobeaforceformorepoliticalequality.Inourownpreviouswork,wefindthatstrongerlocallaborunionsenhancepoliticalequalityintheU.S.HouseofRepresentatives(BecherandStegmueller2021).Thisisconsistentwithstate-levelevidence(Flavin2018).Whileunionsareendogenoustopolitics,weuseaninstrumentalvariableapproachtoreduceconcernsaboutomittedconfounders.Inlinewiththeevidenceonpartisangapsinresponsivenessjustdiscussedabove,wealsofindevidencethattheimpactofunionsworksatleastinpartthroughtheelectoralselectionchannel.Relatedly,CarnesandLupu(thisvolume)showacrosscountriesthatunionizationispositivelycorrelatedwiththeproportionoflegislatorswithaworking-classbackground.

Post-electoral influence as a pathway to (in)equality

Otheraccountsofunequaldemocracyemphasizetheimportanceofpost-electoralpolitics.Whilecampaigncontributionsshapeelections,theyandothermaterialinducements(e.g.,dinners,vacations,well-paidboardappointments,revolvingdoors)areoftenthoughttomaketheincumbent,wholooksforwardtothenextelection,morepliabletotheviewsof

5ForFranceandtheUK,Cagé(2020)findsevidencethatadditionalmoneyfromindividualsorbusinessisassociatedwithmorevotes.


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well-organizedgroups(GrossmanandHelpman2001).Economicinequalityentailsresourceadvantagesforcorporationsandthewealthyoveraveragecitizensandmassorganizations.Asaresult,evensupposedlypro-poorpoliticiansmayjointhelegislativecoalitioninfavoroftheeconomicallyadvantaged(HackerandPierson2010).

Post-electoralinfluencecantakevariousforms,suchasexchangeorpersuasion.Duetowell-knownmeasurementandcausalidentificationissues,empiricallytestingthepoliticalefficacyoflobbyingisdifficult(Baumgartneretal.2009;FigueiredoandRichter2014).Theliteraturehaspaidparticularattentiononhowtoisolatetheimpactoforganizedgroups'monetarycontributionsonlegislators'behaviorfromthatoflegislators'party,ideology,andconstituency.Toimprovetheveracityofregressionanalysisoflegislativevotesinthisrespect,thereviewofAnsolabehere,Figueiredo,andSnyder(2003)recommendscontrollingforlegislators'partyaffiliationor,ifpossible,toincludelegislatorfixedeffectsthatabsorbapolicymakers’time-invariantattributes.Whileintuitivelyappealing,itisnoteworthythatthisapproachequatesinterestgroupinfluencewithpost-electorallobbying.Thisstrategycanfailtoestimatetherelevanceofthepost-electoralchannelifpre-electoralinfluenceandpost-electoralinfluencearestrategiccomplements.Below,wearguethatthisislikelytobethecaseintimesofpartypolarization.

Nonetheless,fieldexperimentssupporttheideathatmoney(oreventhepromisethereof)providesaccesstolegislators(KallaandBroockman2016;Hertel-Fernandez,Mildenberger,andStokes2019).Alsoconsistentwithapost-electoralinfluenceview,observationalresearchhasfoundthattherevenueoflobbyistsconnectedtolegislatorsdropssubstantivelyoncetheirformeremployerleavesthelegislature(BlanesiVidaletal.2012).Astudyofthecongressionalagendabasedonlegislativespeechesfindsthatcorporatecontributionsareassociatedwithlowerattentionbylegislatorstoissuelikeinequalityandwagesandhigherattentiontoupperclassissues(Kellyetal.2019).Laborcontributionsareassociatedwithhigherattentiontoinequalityandwagesandlowerattentiontoupperclassissues.Theseresultsholdconditionalonpartisanshipandcommitteeassignment.

Theoriesdifferonwhetherorganizedgroupsshouldmainlylobbyopposedlegislators,legislatorsthatareonthefenceontheissue,orlegislatorswhoarefriendlytowardtheirposition(Austen-SmithandWright1994;GrossmanandHelpman2001;HallandDeardorff2006).FollowingtheformalmodelofHallandDeardorff(2006)andanolderinterestgroupliterature,wearguethatorganizedgroupswilloftenconcentratetheirlobbyingeffortsonfriendlylegislators.

Whyshouldorganizedgroupslobbyfriendlylegislators?Oneusefulwaytothinkaboutlobbyingisasprovidingamatchinggrantorlegislativesubsidythatassistslike-mindedlegislatorstoachievetheirownobjectives(HallandDeardorff2006).Forexample,aconservativelegislatormaygenerallybelievethatthecorporatetaxrateshouldbecut,buttherearenumerousissuesonthelegislativeagendathatrequiretheirattention.Givenlimitedtimeandresourcesinalegislaturethatconsidersthousandsofissueseachterm,providingassistance(e.g.,resourcesandinformation)enablesthelegislatortoactivelysupporttheissue:draftingbillsoramendments,convincingconstituents,conveningwithcross-pressuredcolleagues,andfinallycastingacorrespondingvote.Inaddition,lobbying


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friendlylegislatorscounter-actslobbyingofopposinggroups(Austen-SmithandWright1994).

Selection and post-electoral influence as complements

Ratherthanbeingalternativedriversofpolitical(in)equality,electoralselectionandpost-electorallobbyingmaybecomplements.Organizedinterestsmaximizingtheirinfluenceoverthepolicyoutcomepursuetwoobjectives.First,ensuringthatlegislatorsalreadyfriendlytoitsinterestsareelectedand,second,providingtheelectedfriendlylegislatorswithsupporttoachievetheirgoalsinthepost-electoralarena.Undersuchcomplementarity,itwillbeespeciallydifficulttounbundlethemechanismsempiricallyandapplyingstandardstatisticalapproachestostudymechanismsarelikelytoleadtowrongconclusions.

Toclarifythisargument,thesectionbelowintroducesasimpleformalmodelofatwo-stagepoliticalprocesswithanelectoralandapost-electoralstage.Assumingthatbothchannelsarecomplements,themodelhighlightstheresultingbehavioroforganizedinterestsandlegislators.Thepoliticalequilibriumisthenusedasinputforgeneratingsimulatedlegislatures.Themainpointofthemodelistoprovideclearanalyticalfoundationsforthedatageneratingprocessusedinthesimulation,andforthispurposeitprioritizesaccessibilityandtransparencyovertechnicality.Eachofthemodel’skeycomponentsisbasedonarichliteratureandmoreelaborategametheoreticanalysis.Thestrategicinteractionofelectoralselectionandpost-electorallobbyingwepresenthereisrelativelynovelandhasimplicationsforempiricalresearchonunequalresponsivenessinlegislaturesthatarenotasapparentwithouttheguidinglightofthemodel.

A two-stage model Anorganizedgroup,𝐺,caresaboutthepolicyactionofanelectedpolicymaker,𝑃.Thepolicymakermaybeanindividuallegislatororacollectivelegislativebody.Group𝐺mayrepresenttheinterestoftherelativelypoor(e.g.,organizedlabor),orthatoftherelativelyrich(e.g.,corporateinterestgroups).𝑃facesabinarypolicychoice𝑋 ∈ {𝐴, 𝐵}.𝐺’sutilityfromimplementingpolicy𝐴versuspolicy𝐵isgivenby𝑢(𝐴)and𝑢(𝐵),respectively.Tofixideas,weassumethroughoutthat𝑢(𝐴) > 𝑢(𝐵),sothat𝐺strictlypreferspolicy𝐴topolicy𝐵.Themodelcanbeinterpretedintwowayswithoutaffectingtheanalysis.First,thinkof𝐺asalaborunionsupportingapolicy,𝐴,ofmoresocialprotectionforindividualsinthelowerhalfoftheincomedistributionoverpolicy𝐵thatwouldremovesuchprotections.Here,thegroupwillbalancetheproclivityofthepolicymakertosidewitheconomicelitesandbusinessinterestsdocumentedintheliterature.Second,onecanthinkof𝐺ascorporateinterestspushingforlowertaxesoncorporationsortopincomes.Here,𝐺wantslegislatorstosupportapolicythatisnotpreferredbymiddle-incomeandlow-income


12

constituents.Forconcreteness,wewillfocusonthefirstinterpretationinthetext.Butitisimportanttokeepinmindthatthemodelalsoappliestothesecondcase.6

Policyismadeinarepresentativedemocracywhere𝐺caninfluencepolicyintwodistinctstagesofthepoliticalprocess:vialobbyingelectedrepresentativesandbyaffectingwhattypeoflegislatoriselectedinthefirstplace.Toimpactthelatterinanelection,𝐺cantakesomecostlyaction,suchascampaigncontributions,get-out-the-votecampaigns,oradvertisement,tostochasticallyimprovethechancesthatitspreferredtypeofpolicymakeriselected.Toimpacttheformer,𝐺canlobbyelectedrepresentativestoincreasetheprobabilityofthemsupportingagivenpolicy.Policymakersdifferintheirpolicypriorities,beitduetopartymembershiporcategoriessuchasgender,race,orclassbackground.Weassumethattherearetwotypesoflegislators,𝑃 ∈ {𝐿, 𝑅},where𝐿indicatesleftand𝑅right,tocapturethemostimportantaspectofcurrentpartisanpolarization.Thengroup𝐺maychoosetolobbyapolicymakeraftertheelectionand𝑃thenchooseseitherpolicy𝐴or𝐵.Themodeldevelopedbelowconsidersastrategicgroupandagent-basedpolicymakersactingunderpoliticaluncertainty.

The Electoral Stage

Duringtheelection,𝐺choosesalevelofmobilizationeffort,denotedby𝑚,thatmaybelow,(𝑚 = 𝑚!)orhigh(𝑚 = 𝑚").Allthatweneedtoassumeisthatahighermobilizationefforttranslatesintoahigherprobabilitythatthegroup’spreferredtypeofpoliticianwinstheelection.Inatwo-candidateraceinafirst-past-the-postsystem,thisrequireswinningjustmorethan50%ofthevote.Say𝐺’spolicyinterestsaremoreinlinewithleftpolicymakerssothat𝐺prefers𝑃 = 𝐿over𝑃 = 𝑅.Wemodelanelectoratewithalargenumberofvoters(i.e.,therearenoties).Denoteby𝑣#theshareofvotesobtainedbyacandidateoftype𝐿.Themobilizationassumptionmadeabovethentranslatesto𝑃𝑟(𝑃 = 𝐿|𝑚") =𝑃𝑟(𝑣# > 0.5|𝑚") > 𝑃𝑟(𝑃 = 𝑅|𝑚!) = 𝑃𝑟(𝑣# > 0.5|𝑚!).7

Agroup’smobilizationcapacitydependsontwokeyfactors.First,thecostofmobilization,whichisrepresentedbyanon-negativescalar,𝑐$.Second,thegroupsexogenouslydeterminedstrength,e.g.,itsmembershipsizeorcapitalstock.Werepresentthetotalofthelatterbynon-negativescalar𝛽.Groupswithlargermobilizationcapacityhavealargerimpactonelectoralpolitics:

𝑃𝑟(𝑃 = 𝐿|𝑚") = (1 + 𝛽)𝑃𝑟(𝑃 = 𝐿|𝑚!).

6Inthiscase,partylabelsshouldbeswitched.7Differencesinelectoralrulesmaybemodeledusingvariationintheelasticitybetweenvotesandseats(RogowskiandKayser2002).


13

The Post-electoral Stage

Asalreadyarguedabove,weconsiderthesituationwhereelectoralmobilization(andtheresultingselectionof𝑃)andpost-electorallobbyingarecomplements.Managingtogetanumberoftype𝐿politicianselectedisnotnecessarilyenoughfor𝐺toachieveitspolicyobjectives.While𝐿policymakersareapriorimorefavorabletoward𝐴thantype𝑅policymakers,theirsupportforthepolicycannotbetakenforgrantedby𝐺.Policymakersvaryintheirideologicalorpartisanconstraintsandcommitments.Thinkoftype𝐿politiciansashavingalargepolicyagendaandfacingoffersfromothergroupsonotherdimensions,sothattheyhavetomakeadecisionofwhethertoexertcostlyeffort(e.g.,draftingaproposal)tosupport𝐴.Thus,aftertheelection,𝐺considerswhetherandhowmuchtolobbyanygivenelectedpolicymaker.Lobbyingmaytakevaryingformssuchasexertingpressureorprovidinginformationandresources.Werepresentlobbyingeffortbyanon-negativerealnumber,𝑙.Note,thatduetotheaforementionedheterogeneityinprioritiesandconstraintsnotallpoliticiansareequallyresponsivetobeinglobbiedby𝐺.

Ratherthanmodelingthefullcomplexityofpost-electoralpolitics,wecapturethislogicinareducedformbyusingacontestsuccessfunction(Tullock1980;CornesandHartley2005).Theprobabilitythatapolicymakerchooses𝐴over𝐵ischaracterizedbytheeffectivenessofgroup𝐺’slobbyinginfavorof𝐴relativetocountervailinginfluences(suchaslobbyingeffortsofcompetinginterestgroupsortheopportunitycostofnotpursuingotherissues),whicharecapturedbyahurdlefactor𝑧%:

𝑃𝑟(𝑋 = 𝐴|𝑃, 𝑙) =𝛽𝑙

𝛽𝑙 + 𝑧%.

Here𝛽is𝐺’sexogenousstrengthand𝑙istheendogenouslobbyingeffortasdefinedabove.Thehurdlefactor𝑧%isanon-negativerealnumberthatdependsonthetypeofpolitician.Foragivenlobbyingeffort,leftpoliticiansaremorewillingtosupport𝐴thanrightpoliticians:𝑧& > 𝑧# .Aninstructivecaseisthatonly𝐿typesarepositivelyresponsiveto𝐺’slobbying(i.e.,𝑧& issufficientlylargetorenderlobbying𝑅typesprohibitive).Should𝐺decidenottolobby𝐿thenpolicy𝐵isthecertainoutcome.Lobbyingiscostlyand,followingmuchoftheliteratureusingcontestfunctions,weassumealinearcoststructure.

Analysis

Giventhesequentialnatureoftheinteraction,theanalysisstartsinthepost-electoralstage.Foragiventypeofthepolicymaker,𝐺chooseslobbyingeffort𝑙tomaximizethepayoff

?𝛽𝑙

𝛽𝑙 + 𝑧%@ 𝑢(𝐴) + ?1 −

𝛽𝑙𝛽𝑙 + 𝑧%

@𝑢(𝐵) − 𝑙.

Thefirstorderconditionimpliesthat𝐺chooses𝑙untilmarginalexpectedbenefitsoflobbyingequalmarginalcost:


14

𝛽𝑧%(𝛽𝑙 + 𝑧%)'

B𝑢(𝐴) − 𝑢(𝐵)C = 1.

Fornon-negativevaluesof𝑙,group𝐺’soptimalbehavioriswell-definedandhasauniquebestresponse(CornesandHartley2005).Solvingtheequationaboveyieldsoptimallobbyingeffort

𝑙∗ = max D1𝛽 E

F𝛽𝑧%B𝑢(𝐴) − 𝑢(𝐵)C − 𝑧%G , 0H.

Twointuitiveresultsemerge.First,higherpolicystakesfortheinterestgroup,capturedbyalargerutilitydifferentialforpolicies𝐴and𝐵,B𝑢(𝐴) − 𝑢(𝐵)C,inducemorelobbyingeffort.Second,theeffectofthehurdlefactor𝑧%onpost-electorallobbyingisnon-monotonic.Ascountervailingforcesmakealegislatorlessinclinedtosupportthepolicypreferredby𝐺foragivenamountoflobbying,increasing𝐺’slobbyingeffortpaysoffwhentheinitialhurdleisrelativelylow(𝑧% < B𝑢(𝐴) − 𝑢(𝐵)C/4𝛽)butnotwhenthehurdleisalreadyhigh(𝑧% > B𝑢(𝐴) − 𝑢(𝐵)C/4𝛽).

Giventheoptimalpost-electorallobbyingbehavior,wenowshow𝐺’schoiceofcostlymobilizationeffort.Tosimplifynotation,considertheprobabilitiesofthekeyoutcomes.Denoteby𝜋#"theprobabilityofseeingaleftlegislatorelectedgivenhighmobilizationeffort,𝜋#" = 𝑃𝑟(𝑃 = 𝐿|𝑚"),andby𝜋#!givenlowmobilizationeffort,𝜋#! = 𝑃𝑟(𝑃 = 𝐿|𝑚!).Denoteby𝜏#theprobabilityofobtainingthepreferredpolicygivenoptimallobbyingofatype𝐿legislator,𝜏# = 𝑃𝑟(𝑋 = 𝐴|𝑃 = 𝐿, 𝑙∗),andby𝜏& = 𝑃𝑟(𝑋 = 𝐴|𝑃 = 𝑅, 𝑙∗)therespectiveprobabilityforalegislatoroftype𝑅.

Group𝐺exertscostlymobilizationeffortattheelectoralstageifandonlyiftheexpectedvalueofmobilizingislargerthanthecost:

[𝜋#"𝜏# + (1 − 𝜋#")𝜏&]𝑢(𝐴) + [𝜋#"(1 − 𝜏#) + (1 − 𝜋#")(1 − 𝜏&)]𝑢(𝐵) − 𝑐$ >[𝜋#!𝜏# + (1 − 𝜋#!)𝜏&]𝑢(𝐴) + [𝜋#!(1 − 𝜏#) + (1 − 𝜋#!)(1 − 𝜏&)]𝑢(𝐵)

Thissimplifiesto:

𝛽 >𝑐$

𝜋#!(𝜏# − 𝜏&)B𝑢(𝐴) − 𝑢(𝐵)C.

Mobilizationthusrequiresthatthegroupissufficientlystrong(i.e.,𝛽issufficientlylarge),thatthepolicystakes((𝑢(𝐴) − 𝑢(𝐵))aresufficientlyhighrelativetothecostofmobilization(𝑐$),andthatthereispartypolarization,capturedbythepartisangapinresponsivenesstopost-electorallobbyingeffect(𝜏# − 𝜏&).

Partypolarizationislowwhenlegislatorsofeitherpartyhaveasimilarprobabilityofsupportingpolicy𝐴foragivenamountofpost-electorallobbying.Ifpartypolarizationissufficientlylow,thenevenastronggroupwillfocusallitseffortsonpost-electorallobbying.Inthecontextofsufficientlyhighpartypolarization,theinterestgroupwillfirstengageinelectoralmobilizationonbehalfofitspreferredcandidate,andthenengagein


15

post-electorallobbyingifitspreferredcandidatewinstheelection.Thislogicimpliesthatinterestgroupstrategiessystematicallyvaryacrosscontext.

Considertheinteractionofbothstagesinthecaseofhighpolarizationsuchthatonlytype𝐿politiciansareresponsiveto𝐺’slobbying(i.e.,𝑧%issufficientlylargesuchthat𝑃𝑟(𝑋 = 𝐴|𝑃 = 𝑅, 𝑙) = 0forfeasiblevaluesof𝑙).Then,astrong𝐺willexertmobilizationeffortand,if𝐿winstheelection,post-electorallobbyingefforttoachieveitspreferredpolicy,𝐴.Ontheonehand,mobilizationaloneisnotsufficienttoaffectthepolicyoutcome.Ontheotherhand,arationalgroupwillnotsolelyrelyonlobbying.Everythingelseequal,thestrengthof𝐺,asparameterizedby𝛽,improvesboththeelectoralandthepost-electoralchainofinfluence:𝐿ismorelikelytoprevailintheelectionandmorelikelytochoosepolicy𝐴.Inequilibriumtheselectionofthepreferredtypeofpoliticianandtheusepost-electorallobbyingarestronglycorrelated.

Evidence from simulated legislatures Wetracetheimplicationsofourmodelforempiricalanalysisusingasimulationapproach.Wecreate5,000simulatedlegislatures,eachwith435legislators,whosecompositionistheresultofanelectoralprocessincludingstrategicmobilization,andwhosepolicychoiceistheresultofcomplimentarystrategicpost-electorallobbying.Eachlegislatorfacesthechoiceofsupportingoneoftwopolicies,𝐴or𝐵,inaroll-callvote(orprioractionsuchasco-sponsorship).

Thesimulationcapturesasituationwherepolicy𝐴ispreferredoverpolicy𝐵bycitizensinthemiddleandlowerpartoftheincomedistribution,buteconomicelitesandbusinessinterestgroupsgenerallyhaveopposingpreferences.Inthisenvironment,mass-basedorganizationslikelaborunionsmaybeaforceformorepoliticalinequalityinlegislatures(BecherandStegmueller2021;Flavin2018).Continuingwiththisrunningexample,wewouldliketoknowtowhatextenttheeffectoforganizedlaboronlegislativeresponsivenessworksthroughpoliticalselectionratherthanpost-electoralbargaining.Nothingchangeswithrespecttotheidentificationchallengesforunbundlingthemechanismsifonepreferstointerpretunionsasenhancinginequalityorifonethinksoftheorganizedgroup𝐺asabusinessgroupthathaspreferencesaddoddswiththemajorityofvoters(Gilens2012;GilensandPage2014;GrossmanandHelpman2001).

TableIshowstheparametervaluesusedinoursimulation.Togeneratevariationintheabilityofthegrouptoaffectlegislativebehaviorandthussubstantivepoliticalequality,thegroupstrengthparameteracrossthe435districtsisdrawnfromauniformdistributionrangingfrom0.05to0.21.Thisrepresentsdistrictlevelvariationinunionstrength(e.g.,numberofunionmembers).Webasethisrangeondistrict-levelmembershipestimatesfoundinthedataofBecher,Stegmueller,andKaeppner(2018).


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TableI.Parametervalues

Parameter Label Value𝛽 Groupstrength 𝑈(0.05,0.21)

𝑢(𝐴) − 𝑢(𝐵) Policypolarization 5𝑧# Lobbyinghurdle 0.06𝑐$ Mobilizationcosts 0.15𝑣#! Leftvoteshareunder𝑚! U(0.30,0.61)𝑁 Numberoflegislators 435

Intheabsenceofanymobilizationeffortbythegroup,thevoteshareofleftlegislatorscanvaryfrom0.3to0.61;theexpectedvalueofleftvoteshareis0.46.8Thus,leftcandidatesareelectorallydisadvantagedcomparedtotheirrightcompetitorsbutwithanarrowenoughmargintomakeelectoralmobilizationworthwhileinexpectationforawell-organizedgroup.9Realistically,thereissignificantpolicyconflict,asrepresentedbytheutilitydifferencebetweenpolicy𝐴andpolicy𝐵.Organizedinterestsfaceacomplementaritybetweenpartisanselectionandlobbying.Thepositivelobbyinghurdleforleftpoliticians(𝑧#)impliesthatthatwithoutbeinglobbiedby𝐺,evenlike-mindedlegislatorswouldnotsupportpolicy𝐴;rightpoliticiansareneverwillingtosupport𝐴forfeasiblelobbyingeffortsby𝐺.Thisisasituationofpartypolarization.10Thissetupproducespartisanvotingpatternsthatareinlinewithmanykeyvotes.11

Common statistical specifications

Wenowturntoanalysesofthesimulatedlegislaturesusingstandardregressionapproachesusedintheliteratureonlegislativevotingandrepresentation.Akeyparameterofinterestistheregressioncoefficientfor𝛽,whichcapturestheaverageeffectof𝐺’sstrengthinalegislator’sdistrictonrepresentationalinequality.Acommonspecificationwouldregressalegislator’ssupportforpolicy𝐴(i.e.,arecordedrollcallvote)onthegroupstrengthvariableandasetofdistrictcharacteristics.Wehaveconstructedthedatageneratingprocesssuchthatthereisnoendogeneityproblemwithrespecttogroup

8Inthesimulation,weassumethatvotesharesaredrawnfromauniformdistributionthatisshiftedbythegroup’smobilizationeffort.Withoutmobilization(𝑚 = 𝑚!),thevoteobtainedby𝐿,𝑣"!,isdrawnfromauniformdistributionwithsupportontheinterval%𝑣"!#$% , 𝑣"!

&'(&'.Withmobilzation(𝑚 = 𝑚)),thedistributionfor𝑣")isshiftedtotherightwithsupporton[(1 + 𝛽)𝑣"!#$% , (1 + 𝛽)𝑣"!

&'(&].Inthesimulation,theaverageleftvotesharewithmobilizationis0.54;counterfactually,withoutmobilization,itis0.45.9Inoursimulationsofthemodel,thegroupdecidestomobilizeforabout64%ofallcandidates,onaverage.10Thelatterassumptionsimplifiestheanalysisbutisnotneeded.11Inoursimulations,policy𝐴receivesnosupportfromrightlegislators,butissupportedbyabout76%ofleftlegislatorsonaverage.


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strengthandlegislativebehavior.12Thisistofocusonthemechanismproblem.Itillustratesthedifficultiesthatcanariseevenwhenresearchershaveanexogenousmeasureofthegroup’spowerineachdistrict.13Akeydecisionwhendecidingonamodelspecificationisthechoiceofhowtotreatthepartisanidentity(ordescriptivecharacteristics)ofthelegislator,capturedbyanindicatorvariableequalto1if𝑃 = 𝐿.Webeginwithaspecificationthatdoesnotincludethisindicator,followingbyaspecificationwhereitisincluded.Thereasonsforitsinclusionareusuallygivenintermsofeither“controllingforpartisanship”orinaninformalattempttocapturetheselectionchannelanddistinguishitfromaresidual“direct”channel.14Partisanshiphasakeypracticaladvantageforresearchers.Itisdirectlyobservableandmeasuredwithlittleerror.Thiscontrastswithagroup’slobbyingeffort,whichcanusemultipleinstrumentsandonlysomeofthemareobservabletoresearchers(FigueiredoandRichter2014).

TableII.Groupstrength,electoralselection,lobbying,andlegislativeresponsiveness

(1) (2) (3) Est. s.e. Est. s.e. Est. s.e.Groupstrength[𝛽] 1.559 (0.484) 0.327 (0.307) 0.005 (0.143)Leftlegislator[𝑃 = 𝐿] 0.753 (0.031) 0.919 (0.159)Post-electionefforta −0.108 (0.106)Note:Basedon𝑀 = 5000simulatedlegislatureswith435members.Interceptsnotshown.Estimatesfromlinearprobabilitymodelwithheteroscedasticity-consistentstandarderrors.aPost-electioneffortobservedwithoutmeasurementerror(ormeasuredviaproxywithknownandadjustedreliability).Correlationofpost-electioneffortwithelectoralmobilization,Cor(𝑚!, 𝑙∗) =0.023;correlationwithleftelectionwinner,Cor(𝐿, 𝑙∗) =0.962.

TableIIshowstheresultingestimatesobtainedfromlinearprobabilitymodels(accompaniedbytherequiredheteroscedasticity-consistentstandarderrors).Column(1)showsthatgroupstrengthsignificantlyincreasesthesupportforpolicy𝐴.Amarginalincreaseingroupstrengthincreasestheprobabilityofalegislatorsupportingthepolicyby1.6 ± 0.5percentagepoints.Expressedinsubstantiveterms,aonestandarddeviationincreaseingroupstrengthincreasestheprobabilitybyabout7percentagepoints.Thisrepresentsthe“totalimpact”ofanincreaseingroupstrengthonpolicyadoptionbothviachangingthelikelihoodoftheelectionofleftlegislatorsandviachangingtheirsupportforthepolicyvialobbyingonceelected.Aresearcherincludingthepartisanidentityof

12Thus,weignoredistrict-levelcontrolsinwhatfollows.Onemaythinkofthisasasituationwhereanaturalexperiment(e.g.,redistricting)makesthisassumptionplausible.Similarly,withsomemodificationofthestatisticalanalysis,researchersmayhaveaninstrumentalvariable.13Forthesamereason,wealsoabstractfrommeasurementproblemswithrespecttopreferences(BecherandStegmueller2021;HillandHuber2019).14Wewillinvestigateamoresophisticatedempiricaldecompositionofcausalchannelsbelow.


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legislatorsinthespecificationwouldobtaintheresultsdisplayedincolumn(2).Theestimateforthepartisanshipvariableislargeandclearlystatisticallydifferentfromzero(0.75 ± 0.03).Thecoefficientforgroupstrengthisdrasticallyreducedandalmostfivetimessmallercomparedtospecification(1).Giventhesizeofitsstandarderror,onewouldhavetoconcludethatitisstatisticallyindistinguishablefromzero.Facedwiththeseempiricalresultsaresearchermightreachtheconclusionthatonlypartisanselectionmattersforthesupportofpolicy𝐴—whichisclearlyincorrectgiventhemodelthatgeneratedthedata,inwhichtheselectionchannelaloneisnotsufficienttochangesubstantiverepresentationinthelegislature.Recallthatwithoutanylobbyingoffriendlylegislators(somethingthatdoesnotoccurinequilibrium),alllegislatorswouldsupportpolicy𝐵.

Just omitted variable bias?

Arethesestarkresultssimplytheresultofomittedvariablebias,namelyomittedpost-electionlobbyingeffort?Specification(3)ofTableIIincludesameasureoftheintensityoflobbyingaftertheelection.Moreprecisely,weincludethelevelofoptimalpost-electioneffort(parameter𝑙∗inourmodel).Usually,researcherswillnothaveaccesstothisvariable,butworkwithanimperfectproxyoroneorseveralofitscomponents,whichraisesissuesoferrors-in-variablesbias.Here,weshowabest-casescenario,wherearesearchereitherfullyobserves𝑙∗orcorrectsforknownreliabilityofthevariablemeasuredwitherror.Astheestimatefor𝛽signifies,theinclusionoflobbyingeffortdoesnotrecovertheimpactofgroupstrengthwhenthetruedatageneratingprocessexhibitsstrategiccomplementarities.

Can mediation analysis recover the true effect?

Givenadvancesinthestatisticalanalysisofcausalmechanisms,researchersexplicitlyinterestedinmechanismsmaygobeyondtheregressionanalysisaboveandoptforanexpliciteffectdecomposition.Thegoalofthisapproachistodecomposetheeffectofgroupstrengthonpolicychoiceintoanindirectcomponentchanneledviapartisanshipandadirectorremainingcomponent(e.g.,Pearl2001).Imaietal.(2011)definetheformerasanaveragecausallymediatedeffect(ACME)andthelatterastheaveragedirecteffect(ADE).Wefollowtheirdefinitionandtheirguidanceaboutbestempiricalpractice(Imai,Keele,andYamamoto2010).

Panel(A)ofTableIIIshowstheresultingcausaleffectdecompositionestimates.15TheACMEis1.2 ± 0.4indicatingasubstantivelyandstatisticallysignificantimpactofgroupstrengthviatheselectionofaleftlegislator.Incontrast,theADEofgroupstrengthisonly0.3 ± 0.31andnotstatisticallydistinguishablefromzero.Almost80%ofthetotaleffectofgroupstrengthismediatedbytheselectionofaleftlegislator.Again,thesefindingswouldtemptaresearcherintodrawingaconclusioncontratothetruemodel.Namely,heorshemightconcludethatitisthepartisanshipofthelegislator,andthustheselectionmechanism,thatmattersmostforthesupportofapolicyinthelegislatureandthat,as

15Theincludedvariablesarethesameasinspecification(2)before.


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indicatedbytheremainingeffectofgroupstrength,post-electoralinfluenceplaysacomparativelysmall(even“insignificant”)role.

TableIII.Mediationanalysis

Estimate s.e.A:CausaldecompositionestimatesACMEofgroupstrength[𝛽]viaLeftlegislator[𝑃 = 𝐿] 1.232 (0.387)ADE(remainingeffectof𝛽) 0.327 (0.307)Proportionoftotaleffectof𝛽mediatedby𝐿 0.783 B:OmittedM-YconfounderSensitivityanalysis:𝜌Ywhere𝐴𝐶𝑀𝐸 = 0 0.813Truevalueof𝜌[Cor(𝐿, 𝑙∗)] 0.962Test𝜌 > 𝜌Y[𝑝-value] 0.000

Note:Basedon𝑀 = 5000simulatedlegislatureswith435members.CausaldecompositionestimatedfollowingTingleyetal.(2014)withstandarderrorsbasedon500bootstrapdraws.

Acarefuldecompositionanalysiswillalwaysincludeasensitivityanalysisforomittedconfoundingvariables.Aresearcherrealizingthatunobservedvariables(includingpost-electoraleffort)arelikelyconfoundingthemediator-outcomerelationshipwouldconductasensitivityanalysisbysimulatingvariousdegreesofresidualcorrelation,𝜌Ybetweenthemediatorandoutcomeequation(Imai,Keele,andYamamoto2010).InPanel(B)ofTable3wereportacommonquantitythatemergesfromthisexercise:thevalueof𝜌YwheretheestimatedACMEbecomeszero.Inoursimulateddata,thisoccurswhen𝜌Yisabout0.8.Becauseofthelargesizeofthiscorrelation,aresearchermightwellconcludethatonlyanunrealisticallylargecorrelationinducedbyomittedconfounderswouldnegatethestrongestimatedroleofthepartisanselectionchannel.Butagain,underatruedatageneratingprocesswithstrategiccomplementarity,thisempiricalresultprovidesafalsesenseofsecurity:thetrue𝜌valueislargerthan0.8—onaveragethecorrelationbetweenanelectedleftlegislatorandpost-electorallobbyingeffortis0.96.

Roll-call voting in the U.S. Congress Areadermightwonderiftheissuesdiscussedinthispaperdoindeedshowupincommonempiricalapplications.Whileweattemptedtochooserealisticparametervaluesinoursimulations,itispossiblethatempiricalresearchmightnotencountersimilarlystarkpatterns.InTableIVwesummarizetypicalanalysesoffourkeyvotesinthe110thand111thCongress.Wechosevotesonissuesthatenjoyedbroadsupportamonglow-incomeconstituents,suchastheFairMinimumWageActof2007ortheForeclosurePreventionActof2008.Thefirstspecificationregressesrollcallvotesonunionstrength(measuredas


20

district-levelunionmembershipcalculatedfromadministrativedatainBecher,Stegmueller,andKaeppner2018)tocapturetheimpactofgroupstrengthonthebehaviorofelectedrepresentatives.Unionstrengthdoesindeedhaveapositiveimpactonrepresentation:thecoefficientof(logged)unionmembershipisofsizablemagnitudeandstatisticallysignificantforallfourkeyvotes.

TableIV.Estimatesofgroupstrengthonrollcallvotesforsomekeybillswithhighsupportamonglow-incomeconstituents.

Groupstrengthestimates Lowinc. Democratic UnionsizeRollcallvote supporta legisl.votesb Unionsizec +DemocratdLillyLedbetterFairPayAct

0.62 223 (96%) 0.140(0.030)

−0.000(0.006)

FairMinimumWageAct 0.82 233 (100%) 0.097(0.025)

0.011(0.012)

ForeclosurePreventionAct

0.70 227 (96%) 0.109(0.028)

−0.001(0.020)

AffordableCareAct 0.64 219 (87%) 0.156(0.033)

0.046(0.018)

Note:Linearprobabilitymodelswithstatefixedeffects.Robuststandarderrorsclusteredatthestatelevel.a Averageshareoflowincomecitizensin435districtssupportingthepolicy.Constituencypreferencesderived

fromCooperativeCongressionalElectionStudyquestionscorrespondingtoroll-callvote.District-levelsmallareaestimationviamatchingtotheCensuspopulationusingrandomforests.SeeBecherandStegmueller(2021).

b NumberofyeavotesamongDemocrats.PercentageofDemocraticcaucusvotingyeainparentheses.c Coefficientofloggeddistrictunionmembershipnumbers.District-levelunionmembershipcalculatedfrom

administrativedatainBecher,Stegmueller,andKaeppner(2018).d Coefficientofloggeddistrictunionmembershipnumbersafteraddinganindicatorvariableforpartisanshipof

legislator.

ThefinalcolumnofTableIVpresentaspecificationlikelytobeexploredbymanyresearchersatsomepoint(ortobedemandedbyreviewers):ananalysisofrollcallvotesandunionstrengthwhile“controlling”foralegislator’sparty.Wehaveshownabovethatthisstrategyyieldsmisleadinginferencesfortheimpactofgroupstrengthwhenpost-electoralinfluenceandselectionarestrategiccomplements.ThisislikelythecaseinourempiricalexamplegivenhighlevelsofpartypolarizationintheU.S.Congress,wheretheadditionoflegislatorpartisanshipdrasticallychangesthegroupstrengthcoefficient.Formanykeyvotestheimpactofloggedunionmembershipisessentiallynilwithcoefficientsstatisticallyindistinguishablefromzero.Interpretingtheseresultsasevidencefortheoverwhelmingimportanceofpartisanselectionoroftheirrelevanceofunionswouldbemisleading.


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Usingarguablyexogenousvariationinunionstrengthbasedonhistoricalmininglocations,BecherandStegmueller(2021)findinlinewiththeoreticalintuitionthatstrongerunionsmakeitmorelikelythatDemocraticcandidateswincongressionalelections.However,itispossiblethatpost-electorallobbyingisarelevantmechanismatplay.Theoryandevidencesuggestthatelectoralselectionandlobbyingmaygohandinhandwhenpartiesexhibitdivergentideologies.

Usingindividual-leveldatalinkingcontributionsandlobbyingbyfirms,Kim,Stuckatz,andWolters(2020)findthatacampaigndonationtoamemberofCongressbyafirmincreasestheprobabilitythatthesamelegislatorisalsolobbiedby8-10percentagepoints,onaverage.Ourtheoreticalmodelhighlightsthatevenafairlysmallcorrelationbetweenelectoralandpost-electoraleffortcanleadtoaveryhighcorrelationbetweenelectoralselection---havingafriendlylegislatorwintheelection---andlobbying.

Conclusion Interestgroupinfluenceissometimesperceivedasthemainsourcebehindunequalrepresentationinlegislaturesaroundtheworld.Forexample,thepowerofcorporationstoshapepoliciesthatdivergefromtheinterestsofmuchofthepopulationareafrequenttopicofnewsstories.However,academicscholarshipontheissueisfarfromsettled.Tryingtounderstandwhythereappearstobesomuchsubstantivepoliticalinequalityinthepolicymakingprocess,therapidlygrowingunequaldemocraciesliteraturehaspaidonlylimitedattentiontotheroleoforganizedinterests.Thisisinpartduetodataconstraintsbutmayalsoreflectlackoftheoreticalattention.ForEuropeanobservers,itistemptingtothinkthatinterestgroupsandthemoneytheybringtopoliticsismainlyaproblemfordemocracyinAmericaandlessinstitutionalpresidentialsystemsinotherpartsoftheworld.Whilecomforting,thisisadeceivingthought.RecentresearchhasrevealedremarkableinequalitiesincampaignfinancesystemsinEuropeancountriesandpositivetheoryhighlightsthepotentialpowerofspecialinterestgroupsinproportionalelectoralsystemscommonlyfoundincontinentalEurope.

Wehavehighlightedtheoreticallythatorganizedgroupsaimingtoshapepolicyfaceincentivestobringtheirresourcestobearbothintheelectoralandpost-electoralstage.Whenpartiesarepolarized,effortstoshapetheselectionofpartisanpolicymakersinelectionsandpost-electorallobbyinggohandinhandinpoliticalequilibrium.Whenpartypolarizationislow,interestgroupshaveincentivestofocusonlobbyingincumbentpoliticians,regardlessoftheirpartisanaffiliation.Thistestableimplicationfromourmodelmayhelptoexplainvariationininterestgroupstrategiesacrosscountries.Ourargumentandsimulationsalsoshowaneglectedmethodologicalissue.Whenanalyzingdataonlegislativebehaviororpolicyadoption,researchersmaywronglyconcludethatinterestgroupinfluencemainlyworksthroughelectoralselection.Furthermore,ifinterestgroupinfluenceisequatedwithpost-electorallobbying,asissometimesdoneimplicitlyineffortstomitigateconcernsaboutconfounding,thenresearcherscanwronglyconcludethatthereisnointerestgroupinfluenceatall.Thispointisrelevantforresearchonpoliticalinequality,butitalsoappliestothelobbyingliteratureatlarge.


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Admittedly,weoffernoeasyfixforthisproblem.Buttheoreticalawarenesshelpsresearcherstotriangulatedifferenttypesofdataandcomeupwithinnovativeresearchdesigns.Forinstance,findingsoftheimportanceofpoliticalselectionhavetobeinterpretedagainstevidenceonthelinkbetweencontributionsandaccess.

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