How Do Voters Respond to InformationEvidence from a Randomized CampaignIZA DP No 7340Chad KendallTommaso NanniciniFrancesco Trebbi How Do Voters Respond to Information Evidence from a Randomized Ca ID: 416405
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Forschungsinstitut zur Zukunft der ArbeitInstitute for the Study of Labor How Do Voters Respond to Information?Evidence from a Randomized CampaignIZA DP No. 7340Chad KendallTommaso NanniciniFrancesco Trebbi How Do Voters Respond to Information? Evidence from a Randomized CampaignChad KendallUniversity of British ColumbiaTommaso Nannicini IZA Discussion Paper No. April BSTRACTHow DoVoters Respond to Information?Evidence from a Randomized CampaigRational voters update their subjective beliefs about candidates’ attributes with the arrival of information, and subsequently base their votes on these beliefs. Information accrual is, however, endogenous to voters’ types and difficult to identify in observational studies. In a large scale randomized trial conducted during an actual mayoral campaign in Italy, we expose different areas of the polity to controlled informational treatments about the valence and ideology of the incumbent through verifiableinformative messages sent by the incumbent reelection campaign. Our treatments affect both actual vote shares at the precinct level and vote declarations at the individual level. We explicitly investigate the process of belief updating by comparing the elicited priors and posteriors of voters, finding heterogeneous responses to information. Based on the elicited beliefs, we are able to structurally assess the relative weights voters place upon a candidate’s valence and ideology. We find that both valence and ideological messages affect the first and second moments of the belief distribution, but only campaigning on valence brings more votes to the incumbent. With respect to ideology, crosslearning occurs, as voters who receive information about the incumbent also update their beliefs about the opponent. Finally, we illustrate how to perform counterfactual campaigns based upon the structural model.JEL Classification:D72, D83Keywordsvoting, information, beliefs elicitation, randomized controlled trialCorresponding author:Tommaso NanniciniDepartment of EconomicsBocconi UniversityVia Roentgen 120136 MilanItalymail: tommaso.nannicini@unibocconi.it We would like to thank Matilde Bombardini, David Green, Andrea Mattozzi, Jim Snyder, and seminar participants at Alicante, Bank of Italy, Bocconi, Carlo Alberto Turin, EIEF Rome, Harvard, LSE, MILLS workshop, MIT, Petralia workshop, Rotterdam, SciencesPo Paris, UBC, UK Leuven, and Warwick for useful comments. Federico Cilauro, Francesco Maria Esposito, Jonathan Graves, Nicola Pierri, and Teresa Talò provided outstanding research assistance. A large number of people were instrumental in implementing our experimental design: the mayor of Arezzo, Giuseppe Fanfani, and his 2011 reelection campaign, in particular Claudio Repek, were extremely cooperative throughout the entire process; Massimo Di Filippo, Fabrizio Monaci, and the team of “IPR Feedback” showed tremendous expertise in conducting the surveys. Nannicini acknowledges financial support from the European Research Council (under grant No. 230088). Remaining errors are ours and follow a random walk. alsoshowthat,althoughonlyvalencetreatmentsweree ectiveinchangingvotes,ourinformationaltreatmentsalongboththevalenceandideologicaldimensionhadlargee ectsonvoters'beliefs,mov-ingbothrstandsecondmomentsofthebeliefdistributionsforthetwomaincandidates.Indeed,campaigninformationa ectednotonlyvoters'beliefsaboutthecandidateoriginatingthemessage,butalsotheirbeliefsabouttheopponent.Intuitively,inBayesiansignalinggames,receivingnomessageisvaluableinformationandourevidenceoncross-learningappearsfullyconsistentwithupdatinginthecontextofaBayesianpoliticalsignalinggame.Thefullcharacterizationoftheindividualbeliefdistributionsweproposeisthecombinationofacarefuldesignofoursurveysandstructuralestimationofarandomutilityvotingmodel.Thelattercomponentofourmethodologydeliverspreciseestimatesofutilityweightsinvoters'preferencesforacandidate'svalenceandideology.Wereportautilityweightonvalenceroughlyequaltothatonideologicallossesawayfromavoter'sblisspoint.Interestingly,wealsoshowthatthepreferenceweightsareheterogeneousinthepopulationanddependonthepoliticalstanceofthevoter,withvotersontherightplacinglessemphasisonthevalencedimension.Finally,weshowthattheideologicallossfunctionawayfromthevoter'sblisspointisconcaveindistance,notconvex(e.g.,quadraticlosses)ascommonlyassumedintheliterature.TherandomutilitymodelweusefollowsthemethodoutlinedinthetheoreticalpaperofRamalhoandSmith(2012)toaccountfornon-randomnessinvoters'willingnesstodisclosetheirvotes.Whilenon-responseinsurveydataisoftenassumedtoberandom,wedemonstratetheimportanceofaccountingforitsendogeneityandsuggestthatthismethodshouldbemoreoftenutilizedinempiricalstudiesinwhichsurveyresponsesarereliedupon.Weconcludeouranalysisbysimulatingcounterfactualelectoralcampaignstoassessthee ectsofspecicblanketortargetedelectoralcampaignsonvoteoutcomes.Wendablanketcampaignofvalencemessagestobethemostvaluableinpersuadingvoters,whichisconsistentwithvoterslackingpriorinformationonthequalityofcandidates.Thispaperisrelatedtoseveralstrandsoftheliterature.Thee ectivenessofelectoralcampaignsinmaturedemocraciesisthesubjectofalargeliterature,includingAnsolabehereetal.(1994),AnsolabehereandIyengar(1995),GerberandGreen(2000),GreenandGerber(2004),Gerber,Green,andShachar(2003),Nickerson(2008),andDewan,Humphreys,andRubenson(2010).Typicallythefocusofthesepapersiseitheronself-declaredoutcomesforvotechoicesoronactualoutcomesforturnout.Methodologically,thesepapersrelyoneithersmall-scaleexperimentsforpartisanadsoronrandomizednon-partisancampaignsforturnout.Ourpapercomplementsthisliteraturebyfocusingonactualelectoraloutcomesinalargescaleeldexperiment.Wemustclarify2 thatourpaperisnottherstinstanceofalargescalerandomizedpartisancampaign.Gerberetal.(2011)lookatrandomizationoverintensityofTVads(withnocontroloverthemessagecontent)onself-declaredchoicesduringthe2006RepublicanprimaryfortheTexasgubernatorialelection.Theyndlarge,butshort-lived,e ectsofsuchTVads,inconsistentwithBayesianupdating.Unliketheirapproach,werandomizethecontentofpartisanadsandalsoevaluatetheirimpactonactualvoteshares.Ourpaperalsocomplementsthisliteraturefromamethodologicalstandpointbyaugmentingthereducedformapproachwithstructuralestimation.Albeitinthecontextoflessmaturedemocracies,theliteratureindevelopmenteconomicshasalsoexperimentedwithinformationalcampaigning.RelevantcontributionsincludeWantchekon(2003)andFujiwaraandWantchekon(2013),exploringpoliticalclientelisminBenin,Vicente(2013),andBanerjee,Green,andPande(2012).Banerjeeetal.(2011)focusonnon-partisaninformationalcampaignsinIndiaandshowthatinformationaboutthequalicationsofcandidatesmattersforturnout,voteshares,andtheincidenceofvotebuying.Thispaperisrelatedtoavastliteratureoncandidate'svalence,initiatedbyStokes(1963)andincludingEnelowandHinich(1982),AnsolabehereandSnyder(2000),Groseclose(2001),Schoeld(2003),AragonesandPalfrey(2002)amongothers.Morerecently,AshworthandBuenodeMesquita(2009),KartikandMcAfee(2007),andBernhardt,Camara,andSquintani(2011)provideinter-estingtheoreticalstudiesofstrategicelectoralcompetitionwithcandidatesdi erentiatedalongboth(ideological)policyplatformandvalencedimensions.GalassoandNannicini(2011)studytheinterplaybetweencandidates'valenceandthecontestabilityofelectoraldistricts.Finally,thispapercontributestothegrowingliteraturefocusedontheelicitationandquan-ticationofsubjectivebeliefs.ElicitationofpriorsisthesubjectofDominitzandManski(1996),Manski(2004),Blass,Lach,andManski(2010),GillandWalker(2005),andDu yandTavits(2008)amongothers.Tothesecontributions,whichmostlyfocusontheelicitationofexpectationsofeconomicoutcomes,ourworkprovidesausefuladditioninthecontextoftheelicitationofmul-tivariatebeliefs.Inparticular,weshowhowtodecoupleinformationaboutmarginalbeliefsandtheirdependenceusingacopulafunctionapproach.Webelievethisapproachmaybeofuseoutsidethepolitico-economicapplicationinourstudy.Therestofthepaperisorganizedasfollows.Section2presentstheempiricalmodel.Section3describestheexperimentalsetting.Section4discussesthereducedformresultsonvotechoices.Section5focusesonthestructuralestimatesofthemodelandSection6ontheexperimentale ectsonvoters'beliefs.Section7presentsourcounterfactualsanddiscussestheimplicationsoftheheterogeneousresponsetoinformationonthepartofvoters.Section8concludes.3 2EmpiricalModel2.1VotersandCandidatesConsideranelectoralracebetweentwocandidates,A,theincumbent,andB,thechallenger.LetthesetofvotersbeN,withjNj=N.Avoteriischaracterizedbyanidealpolicypointdistributedoveraniteanddiscretepolicyspace,,whichiscommonacrossallvoters,withpoliciesP2.Thediscretenessassumptionismeanttocaptureanempiricalfeatureofthesurveydataemployedinthesubsequentanalysis.Votersareheterogeneous,withblisspointsq2,andreceivedisutilityfromapolicychoiceawayfromtheirblisspoint.TheyalsoreceiveutilityfromthelevelofvalenceoftheelectedcandidateV2,wherethesetisniteanddiscrete.Whenpolicypisimplementedbycandidatejofvalencev,theutilityforvoterioftypeqisassumedtobe:U(v;p;q)= v�u(q�p)� u(q�p)v+"i;jwheretheutilityfunctionincludesadeterministicportionandacandidate-specicrandomutilitycomponent"i;j,independentofVandP.Theparameter indicatestherelativepreferenceweightofvalenceversusthepolicystance.Weassumeu(0)=0,u0(x)0forx�0,andu0(x)0forx0.Forexample,aquadraticlossawayfromvoteri'sblisspoint,(qi�p)2,tsthissetofassumptions.1However,weassumethemoregeneralformu(x)=jxjwith0.Thepolicystanceofthepolitician,p;a ectsvotersheterogeneouslydependingupontheirownidealposition,q,butcandidatesofhigherqualityvarefavoredbyallvoters.Wealsoallowforinteractionsbetweenvalenceandpolicypositionsthataregovernedby .Therandomutilitycomponent"i;jofvoteri'spreferencesforcandidatejcapturesthepersonalappealofjtoi.ItisnotimportantforourpurposestospecifywhetherthetwocandidatesAandBimplementtheirrespectiveidealpolicypositionPonceinoce(seeAnsolabehere,Snyder,andStewart,2001;Lee,Moretti,andButler,2004)orstrategicallycatertheirpolicytovoters(e.g.,asinastandardDownsiansetting).Weareinterestedinthevoters'utilitiesatthetimetheyplacetheirvote,whichonlydependupontheirbeliefsabouteachcandidate'sposition,andnotonhowthepolicypositioncameaboutorwhetherornotitisactuallyimplemented.Ingeneral,ourapproachisrobusttothedetailsoftheelectoralcompetitionstructure.Allvotersparticipateintheelection(votingiscompulsoryinourempiricalsetting).VoteriisassumedtohaveajointpriordistributionfunctionoverVandP,fi;jV;P(v;p),forj=A;B,evaluatedatpoint(v;p)anddenedoverthesupport.WedonotprecludeVfrombeingpotentiallycorrelatedwithPandweallowpriorstodi erbaseduponi'scharacteristicsoridealpointq. 1Quadraticlossfunctionsarestandardintheliterature(e.g.,seeAnsolabehereandSnyder,2000).4 Ourexperimentaltreatmentsinducearandomizedchangeintheinformationsetsofvoters,whichwedescribeindetailinSection3.Thediscretenessoftheexperimentalstrategyinducesanitesetofinformationaltypesofvoters.Type1:ReceivingamessageaboutV;butnotP;ofA:Type2:ReceivingamessageaboutP;butnotofV;ofA:Type3:ReceivingamessageaboutbothVandPofA:Type4:ReceivingnomessageaboutVorPofA:Forsimplicity,a\message"indicateshaving(randomly)receivedacampaigninformationtreat-ment,H2f1;:::;4g.LetusindicateasT(h)thesetofvoterstreatedwithinformationtypeH=handletfi;AV;P(v;pjH=h)indicatesthesubjectiveposteriorprobabilitythatvoteri,treatedbymessageh,assignstotheeventthatcandidateAhasvalenceV=vandpositionP=p.Theprocessofupdatingbeliefstypicallyre ectsthecharacteristicsofthegameplayedbetweenvotersandpoliticalcandidates(e.g.,asignalinggame).Ourapproachallowstoleavethenatureofsuchstrategicinteractionunspecied.TheexpectedutilityfromtheelectionofAforvoteri,treatedbyhandwithidealpointq,is:EUiA(h;qi)=XpXvfi;AV;P(v;pjH=h)U(v;p;qi)+"i;A.If,instead,Biselected,theexpectedutilityforvoteroftype(h;qi)is:EUiB(h;qi)=XpXvfi;BV;P(v;pjH=h)U(v;p;qi)+"i;B.Theprobabilitythatioftype(h;q)supportscandidateAisgivenby:PrEUiA(h;qi)EUiB(h;qi).(1)GiventheprobabilitythatavotersupportscandidateA,wecanconsiderastandard,conditionallogitmodel,assuming"ijtobei.i.d.acrossvotersanddistributedwithaTypeIextreme-valuedistributionwithcumulativedistributionfunctionF("ij)=exp(�e�"ij).Providedinformationonthechoiceofitovoteforj,Yi=j,weobtaintheloglikelihood:lnL()=NXi=1XjdijlnPr(Yi=j)=NXi=1XjdijlneEUij(h;qi) PleEUil(h;qi)wheredijis1ifivotesforj,and0otherwise.Notethatthevectorofparametersofinterest,,includesbothpreferenceparameters[ ;; ]andtheparametersofthejointbeliefsfi;jV;P(:),whichwedeneinthefollowingsubsection.5 Onepotentialproblemwiththestandardlogitmodelinasettingemployingvotedeclarationsasopposedtoactualvotesisthatvoters,whensurveyed,mayprefernottodisclosetheirvote.Ifthesampleofvoterswhodonotdisclosetheirvoteiscompletelyrandom,onecanapplythelogitmodeltothesubsampleofresponders.Thisistheapproachtypicallyfollowedintheliterature,oftenwithoutdiagnosticsinsupportofthecrucial\missingcompletelyatrandom"assumption,requiredforanunbiasedestimate.WeprovideevidenceinSection5thatindicatesthatthesubsampleofvotersthatchoosenottodisclosetheirvotesispredictable,soestimationofthestandardlogitmodelwouldleadtobiasedestimatesinoursetting.Wethereforeapplyanovelchoice-basedapproachsuggestedbyRamalhoandSmith(2012)thatallowsfornon-randomnon-responseunderweakassumptions.Themodelassumesthat,conditionalonthevoter'sactualvote,theprobabilitywithwhichavoterchoosestorespondtothesurveyisconstant,butthatthisprobabilitycandependontheirvote.Underthisassumption,wecandenetheloglikelihoodas:lnL()=NXi=10@oiXjdijlnjeEUij(h;qi) PleEUil(h;qi)+(1�oi)ln0@1�XjjeEUij(h;qi) PleEUil(h;qi)1A1Awhereoiis1ifidisclosesthevote,and0otherwise.Theadditionaljparametersaretheprobabil-itieswithwhichavoterdisclosesthevoteforj.Thersttermoftheloglikelihoodistheprobabilitythatavotervotesforjanddisclosesthevote.Thesecondtermre ectstheprobabilitythatthevotervotesforoneofthecandidates,butchoosesnottodisclosethevote.Notethatwhenj=1forallj,suchthatthevoteisalwaysobserved,weobtainthestandardlogitmodelasaspecialcase.OurresultsinSection5rejectj=1forallj,meaningthatwearejustiedinaccountingforthepossibilityofnon-randomnon-response.2.2Voters'SubjectiveUpdatingHere,wespecifytheprocessbywhichvoters'subjectivebeliefsareupdatedinthepresenceofcampaignadvertising.Forillustrativepurposes,considerthefollowingtimeline. 6 Ourrstassumptionisthatvotersconsiderthecampaigninformationtobetruthful.SucientfreedomofthepressintheItalianelectoralcontextguaranteesthatsuchanassumptionmaybevalidinthecaseoffactualadvertising,asweemployinourexperimentalsetup.Allmessagesarefactualandcanbeindependentlyvalidated.Secondly,weassumerationalBayesianvoters.2Werefrainfromimposingdistributionalas-sumptionsonpriors,posteriors,andonthedistributionofsignals.Instead,weadopttheoptionofelicitingsubjectivepriorsandposteriorsfromspecicallydesignedsurveys.Thisisanimportantstepfortwomainreasons.First,elicitationallowsustoassessquantitativelyhowthemessagingstrategyweemployedexperimentallyoperatesintheeld.Indeed,votersarenotawareoftheran-domizationprocessandupdatetheirbeliefs\asif"themessagesweredirectlysentbythecandidate.Thisisnotanassumption,butpartoftheexperimentaldesign.UndertheassumptionofBayesianvoters,beliefupdatingaboutcandidateAimplies:fi;AV;P(v;pjH=h)=Pri;A(H=hjV=v;P=p) Pri;A(H=h)fi;AV;P(v;p)forh=1;2;3,wherethesubjectiveupdatingtermPri;A(H=hjV=v;P=p) Pri;A(H=h)canberecovereddirectlyfromthedataafterelicitationoffi;AV;P(v;pjH=h)andfi;AV;P(v;p).Second,ourapproachallowsforgeneralstrategicelectoralcommunicationbetweencandidatesandvotersinthebackground.WearenotrequiredtomodelorrestrictthevotinggameplayedamongN,A,andB.AnystrategicsignalingiscapturedbytheupdatingtermPri;A(H=hjV=v;P=p) Pri;A(H=h),whichweestimate,notmodel.3Bayesianupdatingincasethevoterreceivesnomessagefromthecandidaterequiresfurtherdiscussion.ConsiderthecaseofafullyrationalBayesianvoterthatreceivesnocampaignadvertisingfromacandidate,butknowsthatsuchactionwasavailable.Insuchacase,asChappell(1994)states,\absenceofamessageprovidesinformationwhichshouldbeusedinBayesianupdating"withtheresultthatsubjectiveposteriorsprobabilitiesaredi erentfrompriorsevenabsentanymessagehavingreachedthevoter.InthecaseofposteriorsaboutcandidateB,forinstance,thisrequiresthatvoteriupdatespriorsbasedonabsenceofanHmessagefromB.Formally:fi;BV;P(v;pjH=h)6=fi;BV;P(v;p)forh=1;2;3,(2)whichisjustiedfromvoterihavingobservedatleastoneextracampaignmessagefromAwithoutanycorrespondingcounter-messagefromB. 2Notethat,whileweneedvoterstoberationalandvotesincerely,theassumptionofBayesianupdatingissimplyconvenientfortheexposition,asourempiricalframeworkallowsustoidentifybeliefupdatinginmoregeneralterms.3Adynamicrepeatedelectionmodelwithbothideologicalandvalenceconsiderationsthatwouldtourproblemis,forinstance,proposedinBernhardt,Camara,andSquintani(2011).7 Thedegreeofrationalityembeddedincondition(2)cannotbeextended,however,totheexper-imentalcontrolgroupH=4,whichdoesnotreceiveanytypeofinformationaltreatmentbyeitherAorBandhencehasnopossibilityofknowingthatsuchspecicmessageswouldbeavailablebutwerenotemployed.ThefundamentalassumptionofourexperimentaldesignmirrorsaStableUnitTreatmentValueAssumption(SUTVA,seeCox,1958;Rubin,1978),asitrequiresthepotentialoutcomeofacontrolunittobeuna ectedbythetreatmentassignmentoftheotherunits.Absentcommonshocks,weshouldassumeforH=4thattheposteriordistributionisidenticaltothepriordistribution,thatis,foreveryi2T(4),fi;jV;P(v;pjH=4)=fi;jV;P(v;p)forj=A;B.Moregenerally,weconsideraprocessofBayesianupdatingwhichaccommodatescommonshocksacrossvoters,underthe(testable)assumptionthatthesubjectiveprobabilitiesonsuchshocksareidenticalacrossalli2NandindependentofH.Consider,forinstance,thecaseofposteriorselicitedafteracommoninformationalshock,W,whichcanbethoughtofasthegeneralcampaigncarriedoutbythecandidatesbesidestheinformationalmessagesfromAthatwerandomizeatthemargin.Withrespecttocandidatej,voteriwillbecharacterizedbythefollowingposteriors.Assumption1(SUTVA):fi;jV;P(v;pjH=h;W)=Pri;j(H=hjV=v;P=p) Pri;j(H=h)Prj(WjV=v;P=p) Prj(W)fi;jV;P(v;p)forh=1;2;3;j=A;Bandfi;jV;P(v;pjH=4;W)=Prj(WjV=v;P=p) Prj(W)fi;jV;P(v;p)forj=A;B.ThecredibilityofAssumption1cruciallyrestsontheexperimentaldesigndescribedinSection3andisempiricallyvalidatedinSection4.Finally,theelicitationofmultivariatebeliefs,evenonexpertsubjects,isnotanobviousexercise(KadaneandWolfson,1998;Garthwaiteetal.,2005)andistheobjectofavastliteratureborderingstatisticsandpsychology(datingatleastasbackasSavage,1971).Weoutlineourapproachnext.2.3ElicitationofMultivariateBeliefsElicitationofbeliefsandpriorsisincreasinglycommonineconomicsandpoliticalscience,andisstandardinpsychologyandstatistics.4Wedescribeatransparentprotocolofelicitationwedesignedtoberobusttothebehavioralandtechnologicalconstraintsweface.Specically,wesampledalargenumberofvotersandneedtoelicitmultivariatebeliefsfromeach. 4Forrecentexamplesineconomics,seeDominitzandManski(1996);Manski(2004);Blassetal.(2010);andZafar(2009).SeeGillandWalker(2005)andDu yandTavits(2008)forapplicationsinpoliticalscience.8 Foreachmaincandidatej=A;Bandeachvoteri,jointvalenceandideologysubjectivepriorsfi;jV;P(v;p)andposteriorsfi;jV;P(v;pjH=h)aredenedover.Intheremainderofthissubsection,letusfocusforbrevityontheelicitationofsubjectivepriors,withtheunderstandingthatthesameprocessappliestoposteriors.Intheempiricalanalysiswewillxthecardinalityofbothandtosmallintegergures,basedonMiller(1956),andalargebodyofcognitivepsychologysuggestingthatindividualscanbequitepreciseinevaluatingchoicesonrelativelycoarseunidimensionalsupports,butdisplayhardlyanyprecisiononnersupports.Specically,forreasonsexplainedbelow,weassumethecardinalityoftobeequalto5andthecardinalityoftobeequalto10.Itisevident,however,thatevenforjj=5andjj=10,\bruteforce"elicitationforbothcandidateswouldrequireeachrespondertoanswer5102=100di erentquestionsonthesubjectivelikelihoodofeachspecic(v;p)realization,ane ortwhichwouldlikelyfrustratepoliticalexperts,letaloneregularvoters.Garthwaite,Kadane,andO'Hagan(2005)presentaninsightfuldiscussiononthedicultyofelicitationformultivariatepriors.Tothisissue,thereaderversedinelicitationmayaddtheproblemofe ectivelytrainingtelephoneinterviewersintheconsistentelicitationofjointprobabilities.5Therefore,wefollowanalternativeroute.2.3.1MarginalBeliefDistributionsWerstfocusoninformationmoreeasilyelicitablefromvoters:theunivariatemarginalsfi;jV(v)andfi;jP(p).Eveninthiscase,fullelicitationofmarginalswouldrequirealargesetof(jj+jj)2=30questions.Westreamlinetheprocessinordertomaintainfeasibilitywithoutexcessivesacriceofaccuracy.Westartbyimposingasimpleregularityassumptiononthedistributionofbeliefs.Assumption2:Subjectivebeliefdistributionsareunimodal.Althoughrestrictive,thisassumptionmakestheinterpretationoftheelicitedprobabilitiesmoredirect.Allofourremainingdistributionalassumptionscanbeillustratedusingthequestionsinoursurveysbywayofexample.WefocusonlyonAforbrevityandconsiderrsthisideologicalpositionP.Weenquireaboutthecentraltendencyofthemarginalprioronideologyasfollows.Q1:HowwouldyoumostlikelydenecandidateA'spoliticalposition?Left(1);Center-Left(2);Center(3);Center-Right(4);Right(5);Don'tKnow(�999). 5Whiletheuseoftelephoneinterviewsisnotgenerallynecessary,inourcontextitiswasrequiredtoensuretimelyelicitationofalargesampleofthevotingpopulationascloseaspossibletoelectionday.9 Areasonableinterpretationoftheanswer,withminimalconfusionfortherespondent,isthatthemodeiselicited.Inparticular,weallowthemode,^p;tobeonlyoneofthesevecategories.Assumption3:=f1;:::;5g:Ananswerof\Don'tKnow/Don'tKnowA"implies atpriors,orfi;AP(p)=1=jj=0:2foreveryp.Ourchoiceofthesetfollowstheestablishedresultincognitivepsychologythatindividualsarewellversedinchoicesoverdiscretesetsoflimiteddimensionality(jj10),butthatthiscapacitydeterioratessharplywhenthenumberofoptionsrisesabovesmallintegers(Miller,1956).Suchanassumption,however,hascosts,asemphasizedinManskiandMolinari(2010).Conditionalonnon- atpriors,wefurtherenquireaboutthedispersionaroundthemode.6Q2:HowlargeisyourmarginofuncertaintyaroundcandidateA'spoliticalposition?Certain(1);Ratheruncertain,leaningleft(2);Veryuncertain,leaningleft(3);Ratheruncertain,leaningright(4);Veryuncertain,leaningright(5).Weindicatethelevelofincreasingtightnessofthepriorswiths2=f1;:::;4g,wheres=1ismaximaldispersion,i.e.,thecaseof atpriors;s=2indicatessubstantialuncertainty(answers3or5toQ2);s=3indicatesintermediateuncertainty(answers2or4toQ2);ands=4ismaximaltightness,whichcoincideswithadegeneratepriorspikingat^p(answer1toQ2).Q2alsoelicitsinformationabouttheskewofthebeliefs.Whilewedonotallowexplicitlyforananswerofsymmetricdispersionfors=2;3,nottooverloadtheresponder,theestimationbelowallowsforsymmetricbeliefdistributions.7Letusindicatewithz2f�1;1ganegative(i.e.,totheleft/lowervalues)orpositive(i.e.,totheright/highervalues)asymmetryinQ2.Letusdenethemodalprobabilitymasswith P=fi;AP(p=^p).Intuitively,weassumetheprobabilitymassatthemodefi;AP(p=^p)islowerthehigherthelevelofuncertainty.Weallow Ptovarywithsandestimate P;s,fromthedatafors=2;3,imposingthebounds:Assumption4:1=jj P;2 P;31:Wefurtherassumetheo -modemass,1� P;s,tobeallocatedasymmetricallyaroundthemodedependingontheindicatedasymmetry,z.Weassumetheo -modemassdecaysproportionally 6Interviewersweretrainedduringpilotinterviewstoexplaintovotersthatthisquestionentaileduncertaintyaboutsubjectiveevaluationsonthecandidates,andshouldnotbeinterpretedasaright-or-wrongquestion.7Inoursurveys,weactuallyincludedapossibleanswer\uncertain"toassesstheshareofrespondentsindicatingsymmetricdispersionaroundthemode.Theshareofrespondentsinthatcategorywassolowforideology(andactuallynoneforvalence)thatweomititfromexposition.10 tothedistancejp�^pjfromthemodeataconstantrate,asdictatedbyafunctiong(x1;x2):f1;:::;jj�1g[0;1]![0;1]withgx1(x1;x2)0andgx2(x1;x2)0.Insynthesis,weimpose:Assumption4':fi;AP(p6=^p)=8:1=jjg( P;s;z(p�^p))0fors=1fors=2;3fors=4:Concerningg(:),weallocate P(1� P;s)massinthedirectionoftheasymmetryimposingthat P2[1=2;1],andallocate(1� P)(1� P;s)intheoppositedirection,assumingalineardecayoftheo -modemassinbothdirections.Thisspecicationofgallowsforavery exible,butparametricallyparsimoniousmarginaldistribution.ConcerningthevalencedimensionV,weagainenquireaboutthemodalbelief.Q3:Settingasidehis/herpoliticalposition,howwouldyoumostlikelygradecandidateA?From1(minimumcompetence)to10(maximumcompetence)orDon'tKnow(�999).Thesetisthenassumedtobeasfollows:Assumption5:=f1;:::;10g.ThisparticularformatofQ3wasdrivenbythefamiliarityofItalianvoterswithprimaryandsecondaryeducationgradescoringrules,with10indicatingthebestpossiblemarkinaschoolassignmentandfailinggradesbeingbelow6.ThedispersionaroundthevalencemodeandtheskewnessofvalencebeliefsaremodeledsimilarlytoAssumptions4and4'withreplacingintheconstructionoffi;AV(v).Weomittheirdescriptionforbrevity.Forillustrativepurposes,Figure1providesanexampleofthemodeledpriorbeliefsaboutthevalenceofAforoneparticularvoter.Thedistributioninthegureisbaseduponthevoter'sreportedmode(^p=7)anduncertainty(s=2)andtheestimatesweobtainfortheparametersgoverningthedistribution.Finally,wemustemphasizethatweonlyelicitthebeliefsaboutvalenceandideologyfortheincumbentcandidate,A,andhismainchallenger,B,duetotheinfeasibilityofelicitingbeliefsaboutallminor,third-partycandidatesparticipatingintheelection.InourestimationinSection5,weassumethatthebeliefsofallnon-incumbentcandidatesarethesameasthoseelicitedforthemainchallenger,B.Whilethisisastarkassumption,wejustifyitbythefactthatthemainnon-incumbentcandidateswereideologicallysimilarandtheirqualitieswererelativelyunknown( atbeliefsalongthevalencedimensionarequitecommonfornon-incumbentcandidates).8 8Themainthird-partychallengerwasalsoaright-wingcandidate,likeB,butwassidelinedbytheirpartyduetopendinglegallitigationrelatedtohispreviousstintinoce.SeeSection3formoreinstitutionaldetails.11 2.3.2JointBeliefDistributions:ACopula-BasedApproachHavingderivedtheunivariatemarginals,wenowderivethejointdistributionsforallvoters.Givenanytwo(univariate)marginals,itispossibletoconstructajoint(bivariate)distributionininniteways.Copulas,introducedbySklar(1959),areusefuldevicesforprovidingarepresentationofamultivariatedistributionfunctionintermsofitsunivariatemarginaldistributions.Droppingthesuperscripts,givencumulativemarginals,FV(v)=Pr(Vv)andFP(p)=Pr(Pp),acopulafunctionCsatisesFV;P(v;p)=C(FV(v);FP(p))whereFV;P(v;p)=Pr(Vv;Pp)isthejointcumulativedistributionfunction.Cisuniqueforcontinuousdensities.Fordis-cretedensities,asinoursetting,typicallythesamejointdistributioncanberepresentedbydi erentcopulas,butaspeciccopulauniquelyidentiesajointdistribution.Themarginaldistributionscarryalloftheinformationrelatedtothescalingandshapeofthejointdistributionfunction,whilethecopulafunctionincorporatestheinformationconcerningthedependencerelationshipamongtherandomvariables.Forparsimony,wewillfocusoncopulafamiliescharacterizedbyonedepen-denceparameter.Notice,however,thatthedependenceparameterdoesnotcoincidewithalinearcorrelationparameter;nonlineardependenceisaccommodatedaswell.Weinvestigatethreepopulartypesofcopulas,allowingfordi erentdegreesofassociationbetweenVandP.First,independencebetweenVandPproducestheintuitivecopulaFV;P(v;p)=FV(v)FP(p).Second,weallowforcommondependenceacrosssurveyedvoters,givenbyassociationparameter�11,employingtheFarlie-Gumbel-Morgensen(1960)familycopula,FV;P(v;p)=FP(p)FV(v)(1+(1�FP(p))(1�FV(v))),where�0impliespositivedependenceand0negativedependence.Potentially,couldbemadevoter-typedependent(e.g.,allowingforadi erentforleftandright-wingvoters),butnotvoter-specic.TheFGMfamilyis exible,butallowsonlysmalldeparturesfromindependence.ThethirdtypeofcopulafamilyweconsideristheFrankfamily,FV;P(v;p)=1=log(1+D()),withD()=(eFP(p)�1)(eFV(v)�1)=(e�1)and=�.TheFrankfamilyallowslargerdeparturesfromindependenceandrequires6=0.Indeed,theFrankcopulaiswellsuitedtomodeloutcomeswithstrongpositiveornegativedependence.Thedependenceparameterisnotelicitedfromthesurvey,butcanbeestimatedfromthedata.Recallthatweobservevotedecisionsandsuchdecisionsarefunctionofthevoters'posteriors.Givenacopulafamily,wecanestimateadependenceparameteraspartofthevectorofparameters,,bymaximizingthelikelihoodofobservingthosevotesasinequation(1).Onecanfurtheremploystandardgeneralizedlikelihoodratioteststoassesstherelativequalityoftheassumptionsonthecopulafamilyandselectthepreferredfamily.Wefollowthisapproach.12 Tosummarize,oursetofparametersofinterestis=[A;B; ;; ;0]withbeliefparameters0=[ P;2; V;2; P;3; V;3; P; V;A;B],whereweallowtheassociationparametertobedi erentforAandB.Estimating0fromvotedecisionsisonlyfeasiblefortheposteriorjointdistribution.Thepriorjointdistributioncanbefullycharacterizedunderanadditionalassumption.Assumption6:Subjectivebeliefdistributionshaveconstant0.Inparticular,whileweallowmarginalstobea ectedbyourinformationaltreatment,weassumethatthedependencebetweenideologyandvalenceofthecandidateisconstant.Forexample,assumingthatamoderatepolicystanceispositivelycorrelatedwithsmartercandidates,informationthatmovessubjectivepriorstowardhigherlevelsofvalenceVisallowedtohaveanimpactonthepolicystanceP,pushingittowardamoremoderatestance,butitisnotallowedtochangetheassociationbetweenPandV.9Figure2andFigure3provideanexampleofthejointdistributionsforaparticularvoter'sbeliefsaboutcandidateApriortotheelectioncampaignandafterreceivingthevalencemessagetreatment.Eachjointdistributionisdeterminedassumingindependenceofthemarginalsandbasedontheestimatesoftheparametersgoverningthemarginaldistributions.Forthisparticularvoter,receivingthevalencemessageincreasedhisbeliefaboutthevalenceofAandalsoreducedtheuncertaintyalongbothdimensions.InSection6,wewillseethatsuchchangesinbeliefsarerepresentativeofvotersreceivingthevalencemessagetreatment.3ExperimentalDesignInMay2011,incollaborationwiththereelectioncampaignoftheincumbentmayorintheItaliancityofArezzo,weimplementedtheexperimentalstrategyembeddedintheaboveempiricalmodelduringthemayor'sactualelectoralcampaign.Specically,wedividedthecityintofourareas,randomizingattheprecinctlevel,andtheincumbentsentdi erentcampaignmessagesbothbymailandbyphonecalltovotersintheseareas.Inthissection,wedescribetheinstitutionalsetting,aswellasthenatureofthe(randomized)campaignmessagesandtools.3.1InstitutionalSettingInItaly,mayorsofcitieswithmorethan15,000inhabitantsaredirectlyelectedunderapluralitysystemwithruno ,thatis,intherstroundthecandidatewhoobtainsmorethan50percentofthe 9AsanalternativetoAssumption6,onecouldcalibratejforthepriordistributionatspecicvaluesandobservethesensitivityoftheresults.Anaturalrangeofvaluescouldbethecondenceintervalofthedependenceparameterfortheposteriors.Wedonotpursuethisavenuehere.13 votesiselected,otherwisethetwocandidatesreceivingthemostvotescompeteinasecondroundwhichtakesplacetwoweekslater.Mayoralcandidatesaresupportedbyoneormorepartylists,butvoterscancastseparatevotesforacandidateandapartylistsupportinganothercandidate.Theycanalsovoteonlyforamayoralcandidate,withoutexpressinganypreferenceforpartylists,buttheoppositeisnotallowed,becausevalidvotesforapartylistareautomaticallyattributedtothecandidateformayorsupportedbythatparty.Electedmayorsserveave-yeartermandaresubjecttoatwo-termlimit.Italianmunicipalitiesareinchargeofawiderangeofservices,fromwatersupplytowastemanagement,frommunicipalpolicetocertaininfrastructures,andfromhousingtowelfarepolicies.Mayorsarethekeypoliticalplayersatthelocallevel,astheycanalsoappointtheexecutiveocersanddismissthematwill.Thecitycouncil,whichactsasthelegislativebody,canforcethemayortoresignwithanocondencevote,butinthiscasethecouncilisalsodissolved.Becauseofthisinstitutionalsetting,municipalelectionshavehighsalienceandturnoutisusuallyveryhigh.ArezzoisaprovincialcapitalcityinthecenterofItaly,locatedintheprovinceofthesamename.In2011,ithad100,455inhabitantsand77,386eligiblevoters.Forelectoralpurposes,thecityisdividedinto95precincts(thesmallestelectoralunitwhichusuallycoincideswithaclusterofstreets),whichvotein42pollingplaces(e.g.,schools,publicbuildings).Fromapoliticalpointofview,thecitywascontestable.GiuseppeFanfani,theincumbentmayorelectedin2006whoacceptedrandomizationofapartofhisreelectioncampaign,belongedtothecenter-leftcoalition,butbeforehisrstelectionthecenter-rightcoalitionwonfortwotermsinarow.In2011,hismainchallengerwastheocialcandidateofthecenter-rightcoalition,GraziaSestini,aformerviceministeratthenationallevel.Sixother(minor)third-partycandidateswerealsopresentintheballot.Themainthird-partycandidatewasaformermayorofthecenter-rightcoalition,LuigiLucherini,sidelinedbyhispartyduetopendinglegaltrouble.10LocalpoliticalcampaignsarenotverysophisticatedinItaly,andtheymostlyrelyonpublicrallies,directmailing,andTVappearances(butnoads).Phonebanksarerarelyused,anddoor-to-doorcanvassingalmostneveroccurs. 10Themayoracceptedourproposaltorandomizehiscampaignbecauseofthepossibilityofreceivingpotentiallyusefulinformation.Asthecenter-rightcoalitionwassplitbetweenamainchallenger(Sestini)andalesscompetitiveone(Lucherini),heexpectedeithertowinintherstroundortogototheruno .Therefore,ourrandomizedtrialcouldprovidehimwithane ectivestrategyforcampaigninginthetwoweeksbetweentherstandsecondround.14 3.2RandomizedCampaignTooperationalizeourinformationaltreatments,westudiedthecampaignmaterialsoftheincumbentandassembledrelevantinformationsoastoisolateslogansbasedoneitherhiscompetenceascitymanager(valencemessage)orhispoliticalstance(ideologymessage).Becausewewantedtostayawayfromthestrategicgamebetweenhim,theothercandidates,andthevoters(thatis,wewantedtorandomizehisactualcampaign),weactuallydevisedtwodi erentideologicalmessages:oneleaningtowardtheleftandoneleaningtowardthecenterofthepoliticalspectrum.Wethenallowedhimtochoosebetweenthetwoandheselectedtheleftistmessage.Furthermore,althoughourtreatmentofinterestcoincideswithpartisancampaignmessagesdeliveredbyoneofthecandidates,asopposedtonon-partisaninformation,wewantedourinforma-tionaltreatmentstobefactualandnon-emotional,astypicalforcheaporcostlysignalinggames.11Forthisreason,wematchedthemainsloganswithbulletpointsbasedonveriableinformationabouttheincumbent'sperformanceandpolicychoicesduringhisrstterminoce.Futureresearchshouldextendtoemotionalmessagesaswell,butwedidnotexplorethisavenuehere.AppendixFiguresA1andA2showthemail yerscontainingthetwomessages.12Thevalence yerisbuiltaroundtwokeywords:competenceande ort.Theimplicitmessageisthatvotersshouldreelecttheincumbentbecausehewascompetentande ectiveascitymanager.ThefactualinformationprovidedreferstothefactthatArezzodevelopedanurbandevelopmentplanthatwasrankedrstbytheregionalgovernmentandreceivedextrafundingbecauseofitsquality.Theextrafundingwasusedtorebuildmonuments,roads,andparkingslotsinthecitycenter.Theideology yerisbuiltaroundtwokeywords:awarenessandsolidarity.TheimplicitmessageisthatvotersshouldreelecttheincumbentbecausehesharesvaluesthatarecommonlyassociatedwiththeItalianleft.Thebulletpointsfurtherreinforcetheleftisttoneastheypointto\public"services,suchaschildcareandfoodfacilitiesforthepoor,thatwereexpandedduringhisrstterminoce.13Noticethatthetwomail yersareidenticalinsize,layout,colors,fonts,numberofwords,andphotoofthecandidate;onlythecontentofthecampaignmessagedi ers. 11Themarketingandadvertisingliterature(seeLiuandStout,1987)hasexploredsubjectiveresponsestofactualversusemotionalornonfactualmessages,indicatingsystematicdi erences.Asaninterestingcounter,Gerberetal.(2011)presentarandomizedtrialinvolvingnonfactualcampaignmessages.12IntheAppendix,wealsoreporttheEnglishtranslationofthetextofthetwo yers.Additionalmaterialsrelatedtoourrandomizedcampaigncanbefoundonthewebsite:www.igier.unibocconi.it/randomized-campaign.13Tovalidateouroperationalizationofthetwoinformationaltreatmentsexante,werandomlyassignedthetwo yersto50universitystudentsatBocconiUniversity(inMilan)whodidnotknowthemayorofArezzo.Wethenaskedthemtogivetheirsubjectiveassessmentofthepolitician'svalenceandideologyusingthesamequestionsdescribedinSection2.Forthe25studentswhoreceivedtherstmessage,theaveragevalenceevaluationwas6.650(s.d.0.963)andtheaverageideologyevaluationwas3.100(s.d.0.700).Forthe25studentswhoreceivedthesecondmessage,thesevalueswere5.450(s.d.0.973)and2.050(s.d.0.669),respectively.15 Thetwocampaignmessages|valenceandideology|weresuppliedtovotersintwoways,throughdirectmailingandphonecalls.Therandomizationdesignwasimplementedasfollows.Weran-domlydividedthe95precinctsintofourgroups:(i)24precinctsreceivedthevalencemessage;(ii)24precinctsreceivedtheideologymessage;(iii)24precinctsreceivedbothmessages;(iv)23precinctsreceivednomessage(controlgroup).Furthermore,werandomlysplittherstthreegroupsintotwosubgroups:intherst,thetreatmentwasadministeredbybothdirectmailandphonecalls(12precincts);inthesecond,bydirectmailonly(12precincts).14AppendixTableA1reportstheex-antebalancetestsofpredeterminedvariablesattheprecinctlevel.Theavailablevariablesincludethenumberofeligiblevotersenlistedineachprecinct,thecity-wideneighborhoodeachprecinctbelongsto,andpastelectoraloutcomesofnational,regional,European,andmunicipalelections.Asprecinctswerereshuedinthelastdecade,someoutcomesarenotavailableforall95precincts.Allofthepredeterminedvariablesarebalancedacrosstreat-mentgroups.Onlythenumberofeligiblevotersdisplaysacoecientsignicantatthe10percentlevel,becauseofthepresenceofafewsmallprecinctsinthecountrysidethatcouldnotbespreadacrossallgroups.Removingtheseprecinctsfromtheanalysis,however,doesnotaltertheresults.Inordertoincreasethee ectivenessofthecampaignmessages,wedrewusefulinsightsfromtheU.S.experimentalevidencesummarizedbyGreenandGerber(2004).First,weactedintheweekbeforeelectionday,soastoensurethemessagesticksinvoters'minds.Second,wehadourmail yersdesignedbyprofessionalsanddirectlysenttoindividualswiththeirnameandaddressontheenvelope.15Third,wedidnotuseautomatedrobocalls.Weinsteadtrainedvolunteerstomakethecampaignphonecalls.Specically,fromthecandidate'sheadquarters,volunteerscalledallselectedhouseholdswiththefollowingprotocol:rst,theywereinstructedtotalkwiththevotersandaskfortheiropinionforabouttwominutes.Then,theywouldaskthevotertolistentoarecordedmessagefromthecandidate.Attheendofthecall,therecordedvoiceofthecandidatereada30-secondscriptwiththeabovevalenceandideologymessages(oracombinationofthetwo).16Ourrandomizedcampaignusedtheabovetools|mailersandphonecalls|onalargescale.Allhouseholdsinthecityreceivedanenvelopefromtheincumbentcampaign.Theenvelopecontainedtheocialplatformofthepoliticalpartiessupportingthecandidateplusoneofour yers(orbothofthem)accordingtotheassignedtreatmentgroup.Votersinthecontrolgroupreceivedjustthe 14Aswewerealreadypushingtheboundariesintermsofsamplesize,wedecidedthattheaccuracylosscouldnotjustifyanadditionalsubgrouptreatedbyphonecallsonly.15Toavoidsendingmultipleenvelopestothesamehousehold,werandomizedthenameofthereceiverwithineachhousehold,becausewedidnotwanttotargetonlyhouseholdheads.16IntheAppendix,wereporttheEnglishtranslationofthetextofthethreerecordedmessages.Originalaudiolesareavailableonthewebsite:www.igier.unibocconi.it/randomized-campaign.16 platform,butnotthe yerwithourinformationaltreatment.Thisprocedureallowedustokeepthecandidateunawareoftherandomizationoutcome.Ofcourse,thecandidateapprovedallmessagesandpaidforthecostsofthecampaign,butwegavehimclosedenvelopessothathecouldnotinferwhichprecinctswerereceivingone yerasopposedtotheother.Insummary,allhouseholdswithatleastonememberenlistedasaneligiblevoterreceivedourmailers.Ontopofthis,about25percentofthehouseholdsinthetreatmentgroupsalsoreceivedacampaignphonecall.173.3DataToelicitbeliefsaboutthevalenceandideologyofthetwomaincandidatesalongthelinesdescribedinSection2,werantwosurveysof2,042eligiblevotersdistributedacrossalltreatmentgroups.Werantherstsurveytendaysbeforetheelectionand,mostimportantly,beforevotersreceivedtheinformationaltreatments,soastomeasurepriorsanddemographiccharacteristics.Thesecondsurveywasconductedthedayaftertheelectionandwasmeanttomeasureposteriorsand(self-declared)votechoices.Toimplementoursurveys,wecontractedacompanyfromanotherItalianregion,soastohaveinterviewerswithdi erentaccentsfromthecampaignvolunteersandtoremoveanylinkbetweenthecampaignandthesurveyphonecalls.About71percentoftherespondentsintherstsurveyalsorepliedtothequestionaboutwhethertheyvotedornotinthesecondsurvey.Therefore,oursampleismadeupof1,455voters,1,306ofwhomactuallyvotedforoneofthecandidates.However,231ofthe1,306votersdidnotspecifyforwhichcandidatetheyvotedandforthisreasonweaccommodateforpotentiallynon-randomnon-responsesinthemodelestimation.Tofurthervalidateourrandomizationdesignexpost,wecheckedforbalancingofthecharac-teristicsofvotersacrosstreatmentgroups.Surveyvariablesincludedemographiccharacteristics,educationalattainment,politicalorientation,homeownership,andhowoftenvotersreadnewspa-persorwatchTV.TheresultsarereportedinAppendixTableA2.Noneofthese(self-declared)individualcharacteristicsisstatisticallydi erentacrosstreatmentgroups.18Table1summarizeselectionresultsattheprecinctlevel.Theincumbentmayorwonhisbidforreelectionwithavoteshare51.3percent,enoughtoavoidaruno .Table2showsthe(self- 17Becauseofbudgetandtimeconstraints,wecouldnotreachallhouseholdsbyphone.18Asanadditionalex-postvalidationoftherandomizationdesign,webuiltproxiesofCensuscharacteristicsattheprecinctlevel.Thisexercisehastwolimitations,however.First,datafromthelastavailableCensusreferto2001.Second,precinctsarenoteasilymatchablewithCensuscells.Toovercomethesecondlimitation,weimplementedthefollowinggeocodingprocedure:1)foreachstreet(i.e.,line)belongingtoaprecinctwecalculatedtheweightedaverageofthecharacteristicsoftheCensuscells(i.e.,polygons)overlappingwiththatstreet(withweightsequaltotheoverlappingsegments);2)foreachprecinct,wecalculatedtheweightedaverageofthecharacteristicsoftheassociatedstreets(withweightsequaltothepopulationlivingineachstreet).AppendixTableA3reportsthebalancingtestsoftheseCensuscharacteristicsacrosstreatmentgroups.Althoughtheestimatesarelikelytosu erfromattenuationbiasduetomeasurementerror,noneofthemisstatisticallydi erentfromzero.17 declared)votechoicesofsurveyedindividuals.Asoftenhappensinpost-electoralpolls,thereisaslightbandwagone ectinvotedeclarationsfavoringthewinningcandidate(57.1percent).Thebandwagonisnotaconcernforestimationunderthe(plausible)assumptionthatthise ectisorthogonaltoourtreatmentgroups.Inanycase,recallthatastrengthofourapproachisthatwecancross-validatetheconsistencyoftreatmente ectsinthesurveydata(attheindividuallevel)withthoseintheaggregateactualvotingdata(attheprecinctlevel).4EvidenceonChoicesInthissection,weevaluatewhetherourinformationaltreatmentshadanye ectonvotingchoicesatboththeprecinctandindividuallevel.Basedontheexperimentaldesigndescribedintheprevioussection,the(reduced-form)causale ectsofcampaigningonvalenceversusideologycanbeestimatedthroughtheOLSmodel:Yi=6Xk=1 kDki+i(3)whereYiistheelectoraloutcomeofinterest,Dkiarebinaryindicatorscapturingtreatmentgroupstatus,andiistheerrorterm.19Thesixtreatmentgroups,Dk;include:valencemessagebyphone(andmail);valencemessagebymailonly;ideologymessagebyphone(andmail);ideologymessagebymailonly;doublemessagebyphone(andmail);anddoublemessagebymailonly.Observationsreceivingnoinformationaltreatmentaretheexcludedreferencegroup.Table3summarizestheresultsintheaggregatesample,whoseunitsofobservationarethe95electoralprecincts.Atthemargin,partisanadshavenoimpactonturnout.Thereisevidence,however,thatcampaigningonvalencebringsmorevotestotheincumbentwhenphonecallsareusedasacampaigntool.Phonecallsdeliveringthevalencemessageincreasetheincumbent'svoteshareby4.1percentagepoints(i.e.,byabout8.4percentwithrespecttotheaverageshareinthecontrolgroup).Thisestimatede ectissizable,becauseitmustbeinterpretedasanintention-to-treate ect:infact,only25percentofthehouseholdsinthetreatedprecinctsreceivedacampaignphonecallandnotallofthemacceptedourinvitationtolistentothemessagerecordedbythecandidate.Becauseofthesmallsamplesize,however,coecientsarenotpreciselyestimatedandwecannotrejectthenullhypothesisthattheyarestatisticallyequaltoeachother. 19Toaccountforpotentialintra-classcorrelationbetweenneighboringprecinctsweclusterstandarderrorsatthepollingplacelevel,whiletoaccountforcorrelatedtimeshocksinsurveydataweincludexede ectsfortheinterviewdate;resultsarenotsensitivetothesemodelingchoices.Empiricalresultsarequalitativelysimilarwhenweincludepredeterminedvariablesasadditionalcovariates,althoughthespecicationbecomesdemandingintermsofdegreesoffreedomintheaggregatedata(resultsavailableuponrequest).18 Whatwecanrejectintheaggregatedataisthenullthatthetwocampaigntools|mailersversusphonebanks|areequallye ective.Ifwemergetogetherallgroupsthatreceivedaninformationaltreatmentwiththesamecampaigntool,wendthat|withrespecttothecontrolgroup|phonecallsincreasetheincumbentvoteshareby2.7percentagepoints(p-value:0.019),while,statistically,thee ectofmailersisbothdi erentfrom2.7andnotdi erentfromzero.ThisresultisinlinewithU.S.experimentalevidenceshowingthatmailersareusuallyine ectiveinpoliticalcampaigns(seeGreenandGerber,2004).Inourcase,however,mailersarealsoadministeredtovoterswhoreceiveaphonecall.Therefore,wecannotruleoutthepossibilitythatmailersaloneareine ective,buttheybecomee ectivewheninteractedwithothercampaigntoolsdeliveringthesamemessage.Basedontheaboveevidenceontheine ectivenessofmailersalone,Table4estimatesequation(3)imposingthisrestriction:includingboth\mail"and\nomessage"inthecontrolgroup.Stan-darderrorsareslightlylower,andthepointestimatesandthestatisticalsignicanceoftheincludedregressorsarealmostidenticalwithrespecttothefullmodel.Inordertovalidatetheaggregateevidenceandtogainstatisticalaccuracy,weestimateequation(3)usingtheindividual-levelsurveydata,wheresamplesizeislessofanissue.Theunitsofobservationarethe1,455eligiblevotersforturnoutorthe1,306actualvotersforthevoteshares.Asalloutcomesarebinary,estimationisbyprobit.Thepricewepayisthathereoutcomesareself-reported,thatis,basedonvotedeclarationsandnotonactualchoices.Theunderlyingassumptionisthatself-reportingbiasisthesameacrosstreatmentgroups.20Table5reportstheestimatesforalltreatmentgroups.Resultsareconsistentwiththeaggregateevidence.Phonecallsdeliveringthevalencemessageincreasetheincumbent'svoteshareby9.5percentagepoints(i.e.,byabout16percentwithrespecttothecontrolgroup).Thise ectislargerthanintheaggregatedata,buttreatmentintensityisalsohigherinthiscontext,becauseallsurveyedhouseholdsreceivedthecampaignphonecall,asopposedtoonly25percentintheaggregatedata.Phonecallsarestillthemoree ectivecampaigntool,withadi erencesignicantatthe1percentlevel.Moreimportantly,conditionaloncampaigntool,thevalencemessageisnowstatisticallymoree ectivethantheideologymessageatthe10percentlevel.21Table6furtheremphasizesthispointby 20Aswedocumentinthenextsection,non-responseinvotedeclarationsislikelytobenon-random,i.e.,tobeassociatedwithindividualcharacteristicssuchasideologyorpriorbeliefs.Thisdoesnotimply,however,that(non-random)non-responseshouldnotbeorthogonalto(random)treatmentassignment.21Althoughourexperimentaldesign|basedonrandomizationattheprecinctlevel|didnotallowforstraticationonindividualcharacteristics,wenonethelessinvestigatedpotentiallyheterogeneousresponsesbyrepeatingthebaselineestimationinsplitsamplesalongmanyobservabledimensions.Thepositiveimpactofvalencephonecallsontheincumbent'svoteshareturnsouttobestatisticallylargerforfemales,individualsolderthan65years,individualswithoutacollegedegree,andless-informedvoters.Instead,thereisnosignicantheterogeneityalongpreviouspoliticalorientation,homeownership,ortypeofoccupation(resultsavailableuponrequest).19 focusingoninformationaltreatmentsadministeredbyphone:campaigningonvalencebringsmorevotestotheincumbentandtothepartyliststhatsupporthim,andthesepointestimatesarestatisticallylargerthanthoseofcampaigningonideologyalone.Finally,inAppendixTableA4,weevaluatethepotentialimpactofspilloversacrossneighboringprecincts.AsacounterparttoTable5,weestimatethee ectsonvotingchoicesoftheaveragetreatmentintensityforindividualsvotinginthesamepollingplace,althoughtheymaybelongtodi erentprecinctsandthereforetreatmentgroups.IfAssumption1(SUTVA)ismet,weexpectthesemeasurestohavenoimpactonchoicesfortreatmentsdetectedasine ectiveinTable5,andtohavealesssignicantimpactfortreatmentsdetectedase ectiveinTable5.Itisthusreassuringthatnoneofthesespilloverestimatesisstatisticallydi erentfromzero.225ModelEstimationWenowreporttheresultsfromthemaximumlikelihood(ML)estimationofourvotingmodel.Theestimationprocedureisstraightforwardandreliesonttingindividualvotedeclarations,which|inSection4|wehaveshowntocloselymatchactualvoteoutcomes.23Thespecicationselectionwarrantssomediscussion,however.Section2discussednon-responseparameters[A;B],preferenceparameters[ ;; ],beliefpa-rameters[ P;2; V;2; P;3; V;3; P; V;A;B],andthechoiceofacopulafamily[Independent;Frank;FGM].Concerningthepreferenceparameters,alargeliteratureinpoliticaleconomicsandpoliticalsciencehasemphasizedpreferenceheterogeneity,forinstanceinthecaseofdistasteforspecicpolicyoutcomes,suchasin ationorunemployment.24Wecaneasilyaccommodatethisfeaturebyallowingadi erent[ ;; ]vectorforleft-wing(L),centrist(C),andright-wing(R)vot-ers.Wecanaswellaccommodateheterogeneityinthedependencestructureofthebeliefs[A;B]byallowingthemtodi erforL,C,andRvoters.Concerningtheskewnessofthemarginalbeliefs,onecanexperimentwithrelaxingthesimple[ P; V]toamore exible[ P;2; V;2; P;3; V;3],thus 22NoticethatpointestimatesarenotdirectlycomparablewiththoseinTable5becausetheregressorsarenolongerdummiesbutshares.Comparedtotheaveragevaluesandstandarddeviationsofthespillovershares,however,pointestimatesaregenerallysmall,and|asexpected|theyarelargerfortheadministrationofthevalencemessagebyphone,becauseinthosecasesthesharesalsoincludetreatedvotersforwhomthereexistsanon-zeroe ect.23TheidenticationofthemodelisassessedthroughseveralroundsofMonteCarlosimulations.Forgivenparametervalueswesimulatedindividualvotesandensuredthattheestimationbasedonthesimulateddataconvergedtotheoriginalstructuralvalues.Ourlikelihoodfunctiondependsonarelativelysmallnumberofparameters.Thisallowsforafairlyextensivesearchforglobaloptimaovertheparametricspace.WeusethepatternsearchalgorithmofMatlabwithdi eringinitialvalues.Repeatingtheoptimizationprocedureconsistentlydeliversidenticalglobaloptima.Wealsoemployedageneticalgorithm(GA)globaloptimizerwithalargeinitialpopulationof10;000valuesfollowedbyasimplexsearchmethodusingtheGAvaluesasinitialvaluesforthelocaloptimizer.Bothmethodsresultedinthesameestimatesbutthepatternsearchalgorithmconvergesfasterinourenvironment.24Amongothers,seeDiTella,MacCulloch,andOswald(2001);GerberandLewis(2004).20 allowingtheextentoftheskewtochangewiththevariance.Allthesearetestableparametricconstraintsthatcanbeassessedbasedonlikelihoodratiotests.Ontheotherhand,thechoiceofthecopulafamilyrequiresageneralizedlikelihoodratiotestapproach,asthecopulafamiliesweconsiderarenon-nested.TheVuong(1989)modelselectiontestisappropriateforthispurpose.InAppendixTablesA5andA6wereportthefullsetofmodelestimatesforalltherelevantcombinationsofparametricandcopulaassumptions,whicharepairwisetestedinAppendixTablesA7,A8,andA9throughlikelihoodratiotestsandVuongtests(forthecopula).Accordingtothetests,thepreferredspecicationallowsforheterogeneityinpreferenceparametersalongthevoter'sself-declaredideologicalstance,forindependencebetweentheideologicalandvalencedimensionsofbothcandidates,andforcommon[ P; V].Thus,thepreferredmodelspecicationestimates=[A;B;f z;z; zgz=L;C;R; P;2; V;2; P;3; V;3; P; V].WereporttheMLestimatesforthismodelinTable7.Werstnotethattheestimatesoftheprobabilityofresponse(i.e.,theprobabilityofdisclosingone'svote)are0:76and0:99forpredictedvotesforA(A)andB(B),respectively,andareverypreciselyestimated.WhilewecannotrejectthenullthattheprobabilityofresponseisoneforvotersthatvotedforB,wecanstronglyrejectthenullforvotersthatvotedforA;whichjustiesourchoiceofmodelingnon-randomnon-response.25Interestingly,voterswhoarepredictedtohavevotedBaremorelikelytodisclosetheirvote,contrarytothepossiblehypothesisthatthosewhovotedforthewinner(A)shouldbemorewillingtodisclosetheirpreferenceforthewinner.ThisresultsquareswiththeintuitionofconservativevotersinTuscanybeingparticularlyassertive.Generally,thepreferenceparametersareestimatedwithprecision.Theparametergoverningtheinteractionbetweenvalenceandideologyvaluesforthevoter, ,isestimatedtobeafairlyprecisezero.Imposing =0clariestheinterpretationof astherelativeweightinpreferencesofvalence(x0)totheweightofideology(1�x0).Hence, =x0 1�x0=1impliesequalweightsalongbothdimensionsandthisiswhatwendforLandCvoters.TheweightonvalenceforRvotersis,however,muchlower,around27percent,versusa73percentweightonideology.Concerningthecurvatureoftheideologicallossfunctionu(:),surprisingly,wend1forallthreetypesofvoters,indicatingincreasinglossesbutatdiminishingratesfrompoliciesfurtherawayfromthevoter'sblisspoint.Thisisincontrastwiththestandardassumptionof=2,quadratic 25Asfurtherevidenceinsupportoftheprobabilityofdisclosingone'svotebeingnon-random,weranaprobitregressionofadummyindicatingwhetherornotavotewasdisclosedontheelicitedposteriorbeliefsandvoter'sideology.AnFteststronglyrejectsthenullhypothesisofnoexplanatorypowerandhencerandomnon-response(p-value=0.000).Interestingly,thestrongervoters'beliefsaboutthevalenceofeithercandidate,themorelikelyvotersaretodisclosetheirvote.21 losses,forexample.Forcentristvoters,isactuallyestimatedtobezero,althoughtheestimateisratherimprecise.With=0,thelossduetodeviationsfromthevoter'sblisspointisconstantandindependentofthecandidate'spolicy.Thebeliefparametersarealsopreciselyestimatedforthemostpart.Interestingly,thespeci-cationfeedsbackinformationwhichallowsustoassesscertainfeaturesofthesurveydesign.Themodelclearlycapturesanintermediatelevelofuncertaintybetween at(s=1)anddegeneratepri-ors(s=4)forbothvalenceandideology.Theon-the-modeprobabilitymass, V;3;isestimatedataround0:40forvalenceandthecorrespondingparameterforideology, P;3;isestimatedataround0:58.Hence,votersanswering2to5toQ2aremorecertainthanhaving atpriors,butdenitelynotsureaboutthecandidatebeingatthemode(i.e.,answer1toQ2).Alongthevalencedimen-sion,votersdonotperceivethedistinctionbetween\veryuncertain"(s=2)and\ratheruncertain"(s=3)giventhat,attheestimatedvalues, V;3= V;2.However,alongtheideologydimension,\ratheruncertain"doesresultinlessdispersioninthemarginaldistribution.Inaddition,thean-swersgiventotheskewnessdimensionseemtobeimportantonlyalongtheideologicaldimension,where P�1=2,butnotonthevalencedimensionwhere Visnotsignicantlydi erentfrom1=2,indicatingasymmetricpartitioningoftheo -modeprobabilitymass.Finally,concerningthechoiceofthecopulaandtheestimatesofthedependenceparameters,wenotethat,althoughboththeFGMandFrankcopulamodelshavetypicallyhigherlikelihoodvaluesthanunderindependence,thelossofparsimonyofthemodeldoesnotjustifytheadditionalparametersaccordingtotheVuongtests(seeAppendixTableA9).Thisresultoccursbecausewecanonlyestimate[A;B]veryimprecisely,whichcanbeeasilyrationalized.Theparameters[A;B]areessentiallyidentiedbyvotersthatare:i)closetoachangeintheirvotechoicebetweenAandB;andii)characterizedbynon-degenerateandnon- atbeliefsalongboththeideologyandvalencedimensions.Thesejointrestrictionssubstantiallyreducethenumberofobservationsprovidingusefulidentifyingvariationforestimating[A;B].Notwithstandingthelackofprecision,lookingatthesignsoftheestimateddependenceparametersinAppendixTablesA5andA6isintriguing.WegenerallyndevidenceofapositiveassociationbetweenleftpositionandvalenceperceptionsforAdrivenbyleft-wingvoters,andapositiveassociationbetweenrightpositionandvalenceperceptionsforBdrivenbyright-wingvoters.Moreextremepositionsappeartobecorrelatedwithhighervalence,inaccordancewiththetheoreticalresultsinBernhardtetal.(2011).TheFrankcopulaispreferredovertheFGMcopula,althoughwecannotrejectthenullofequalt.Thestructuralestimationhasallowedustofullyrecoveralloftheparametersnecessarytocharacterizetheindividualbeliefdistributions.Weproceedtotheanalysisofvoters'beliefsnext.22 6EvidenceonBeliefsThee ectofpartisanadsonbeliefsisinterestingperse,anditcanshedlightontherobustnessoftheimpactofthesameadsonvotingchoices,basedontheirmutualconsistency.Toincreaseaccuracy,werestrictourattentiontoinformationaltreatmentsdeliveredbyphone,thatis,bymeansofthee ectivecampaigntool.InTables8and10,theoutcomesaretheaverageandthestandarddeviationoftheindividualbeliefdistributions|frommodelestimation|ofbothvalenceandideologyoftheincumbentandoftheopponent,respectively.InTables9and11,welookatthesamemomentsoftheindividualbeliefdistributions,butweinsteadusesurveyresponsesasopposedtoestimatesfromthestructuralmodel.Specically,theoutcomesarethe(self-reported)modeandabinarymeasureof\uncertainty"(namely,adummycapturing atpriorsinsurveyresponses).EstimationisbyOLSformultivaluedorcontinuousoutcomesandbyprobitforbinaryoutcomes.26Fortheincumbent,boththevalenceandideologymessageshavetheexpecteddirecte ects.Informationonvalenceincreasesperceivedcompetencebyabout5percentwithrespecttotheaverageperception.Thesameholdsforinformationonideology,asperceivedideologydecreases(i.e.,movestotheleft)byabout5percent.Interestingly,secondmomentsarealsoa ectedbythetwotreatments:uncertaintyabouttheincumbent'svalenceorideologyisreducedbyadditionalcampaigninformationalongthecorrespondingdimension.Decreaseduncertaintyisarelevantchannelofthee ectofcampaigninformationonchoices.Asamatteroffact,thepositivee ectofvalencephonecallsontheincumbent'svoteshareisstrongerinthesubsampleofvoterswhosepriorsare at.Inthetreatedgroup,weobserveasharptighteningofthebeliefdistribution,whichcontributestotheoveralle ect.Thenegativeimpactofideologymessagephonecallsonthecandidate'sideologydoesnottrans-lateintomore(orless)votesforA.Notwithstandingthelargeutilityweightvotersplaceonthisdimension,theshiftinthebeliefdistributionscausedbytheideologyphonecallsisnotstrongenoughtoa ectvotingchoices.27Withrespecttoideology,informationontheincumbent'spositionhasinterestingcross-e ectsontheperceptionoftheopponent'sposition.VoterswhoreceivedtheideologyphonecallfromtheincumbentcampaignmovetheirsubjectiveevaluationoftheopponentBtotherightby3percent.Thetreatmentalsoreducesuncertaintyalongthisdimension.Thismightbeduetotheincreased 26Forthesakeofintuition,weuseOLSalsofortheideologymode,whichcanonlytakeve(ordinal)values.ResultsfromorderedProbitarequalitativelyidentical(availableuponrequest).27Analternativeexplanationmightbethattheideologymessagea ectsright-wingandleft-wingintheoppositeway,butthisisnotwhatwendinoursample.Ideologyphonecallshadnegligiblee ectsonvotingbehaviorforbothtypesofvoters,whiletheirimpactonbeliefswasalmostequivalent.23 salienceoftheleft/rightdistinctionortoitsrelativenature,anditiscausalevidenceofcross-learningbetweenpoliticalcampaigns.Thisndingisconsistentwithasophisticatedsubjectiveupdatingbehavioronthepartofthevoters.Forexample,thistypeofevidencewouldbeconsistent(albeitnotproofof)Bayesianupdatinginatwo-candidatesignalinggame.7ModelFitandCounterfactualElectoralCampaignsToconcludeouranalysiswediscussmodeltresultsandcounterfactualelectoralsimulationsbasedonourstructuralestimates.Overall,thestructuralmodelunderthebaselinespecicationpredictstheactualvotecorrectly88:7percentofthetime.Inparticular,wepredictcorrectly95:9percentofthevotesforcandidateAand70:7percentofthevotesforB.Here,thesampleunderconsiderationisrestrictedtothevoterswhodisclosedtheirvoteonly,sincewedonotknowtheactualvoteofthosewhochosenottodiscloseit.Turningtocounterfactuals,nostandardprotocolexistsintheliteratureforrunningthesetypesofexercises,sowehavedevisedone.SupposeonewishestoassesswhatwouldhavehappenedtotheaggregatevoteshareofAifeverybodyinthecityhadreceivedthevalencemessage(i.e.,hadgottentreatmentH=1).Wesimulatethiscounterfactualcampaignusingavestepprocedure.UnderourstabilityAssumption6,foreachvoteri;itispossibletogeneratepriorbeliefdis-tributionsaboutAandBbasedupontheirpriorsurveyanswersand0,thestructuralparametervectorestimatedfromvotesandposteriorbeliefs.Thisistherststep.Secondly,foreachvoteri2T(h)withh6=1(i.e.,nottreatedwiththevalencemessagetobeginwith),itisalwayspossibletondthenearestneighbortreatedmatchinthegrouph=1,i02T(1),basedontheMahalanobisdistancemetricderivedfromcovariates(suchasage,gender,maritalstatus,education,priors,andideology).Voteri0istheclosestmatchtovoteriforwhichthecausale ectofvalenceonbeliefsisactuallyobserved.Essentially,thisisthesameintuitiononewouldfollowinpropensityscoreestimation.Oncetheclosestmatchi0hasbeenidentied,asthirdstepwecomputethedi erencebetweeni0'smarginalposteriorandpriorbeliefsateverypointofthesupportofeachofthevalenceandideologydimensions.Fourth,weapplyi0'spointwisechangesinbeliefstoi'spriorstocalculatethecounterfactualposteriormarginalbeliefsofi,undertheassumptionthat,hadigottenthesametreatmentasi0,shewouldhaveupdatedherbeliefsinthesamewayasi0.Fifth,wecomputejointposteriorbeliefsusingtheappropriatecopulafamilyandtheestimated's.Giventheposteriorsforeachvoteri,weobtainasimulatedelectoraloutcome,bycalculatingtheexpectedutilityofeachcandidateforiandthenpredictingtheirvoteforthecandidatewiththehighestexpectedutility.24 Importantly,thissimulationproceduredoesnotrequirethesimulatedelectoralcampaigntoonlyfocusonasingletreatment,butitcanbetweakedtotargetingspecicsubgroupswithdi erenttreatments.Forinstance,wecansimulateacampaigninwhichvalencemessagesaresenttoknowncentristandright-wingvoterswhileideologicalmessagesaresenttoleft-wingvoters.Thisisofparticularrelevanceatapointintimewhenpoliticalcampaigns,especiallyintheUS,haveincreasinglyturnedtospecializedcompanies,suchasAristotle,formicrodataacquisitionandselectivecampaignadvertising,atrendwellunderwayalsoincommercialandonlinemarketing.WeexploresomeofthepossibleelectoralcounterfactualsinTable12.Foreachcounterfactual,weincludeallvoters,eventhosewhodidnotdisclosetheiractualvote.Table12reportscounterfactualelectoraloutcomesforvetypesofcampaignsbyA:(1)ablanketvalencecampaign;(2)ablanketideologicalcampaign;(3)ablanketdoublevalence-ideologycampaign;(4)atargetedcampaignofvalencemessagestocenterandright-wingvotersanddoublemessagestoleft-wingvoters;(5)atargetedcampaignofideologicalmessagestocenterandright-wingvotersanddoublemessagestoleft-wingvoters.Allresultsarebenchmarkedtothesimulatedelectoraloutcomethatwouldhaverealizedintheabsenceofanycampaignmessageonourpart.Thecounterfactualsarealsoassessedintheirprecisionbyconstructing95percentasymptoticcondenceintervalsbasedonbootstrappingfromtheasymptoticdistributionoftheparameters.Allourcounterfactualestimatesappearstatisticallyprecise.Themoste ectivepossiblecampaignistheelectoralcampaigninwhichvalencemessagesalonearesenttoallvoters.AblanketvalencecampaignincreasesthevoteshareofAby2:2percentagepointsrelativetonocampaign,whichismorethanenoughtomakethedi erenceinaclosely-contestedelection.Interestingly,ablanketcampaignofideologymessagesactuallyreducesthevoteshareofAsubstantially,infactbythesame2:2percentagepointsthatablanketvalencecampaignwouldinsteadbringtoA.Infact,the95percentcondenceintervalsforthetwosimulatedcampaignsdonotoverlap,sowecanbereasonablycertainthatablanketvalencecampaignwouldhaveoutperformedablanketideologycampaign.Tounderstandwhytheideologycampaignreducesvoteshares,recallthattheideologicalmessageinourexperimenthasaleftistbent,reducingtheexpectedutilityfromAforR,CandpossiblythemostmoderateoftheLvoters.Overall,thelossofsupportfromCandRinoursampleturnsouttomorethansucienttoo setthegaininLvoters.Forthesamereason,adoublecampaignofbothideologyandvalencemessagesincreasesthevoteshareofAby0:5percentagepoints,which,whilee ective,isnotase ectiveastheblanketvalence-onlycampaign.Finally,themixedcampaigninwhichLvotersgetbothtypesofmessageswhileCandRvotersgetvalencemessagesonlyisalmostase ectiveasthevalencecampaign,25 whilethecampaigninwhichLvotersgetbothtypesofmessageswhileCandRvotersgetideologymessagessubstantiallydecreasesA'svoteshare.Insummary,consistentlywithouroverallresults,campaigningonvalenceappearedthemoste ectivetooltopersuadevoters.8ConclusionThispaperpresentsnovelevidenceonthee ectsofcampaigninformationonvoters'decisionsinalarge-scaleeldexperiment.Importantly,oure ectsareobservedbothinvotedeclarationsofsurveyedvotersandinactualvoteoutcomesattheprecinctlevel.Tothebestofourknowledge,thisistherstempiricalrandomizationexerciseintheliteraturethatoperatesatthescaleofanentireelectionandcoverstheentirevotingpopulationinamaturedemocracy.Bothourreduced-formandstructuralestimationresultsuncoverlargeelectoralgainsfromvalence-basedinformationalcampaigning,possiblyduetotherelativelyhigherlackofpriorinformationaboutthecandidatesalongthisdimension.Anadditionalcontributionofourpaperistopresentabeliefelicitationprotocolthatallowsus,whencombinedwithinformationontheelectoralchoicesofvoters,tocompletelycharacterizevoters'beliefsaboutcandidatesalongboththeideologicalandvalencedimensions.Ourmethodologyallowsusto exiblyincorporatemultivariatebeliefdistributionswithinastructuralrandomutilityvotingmodel.Wethenemploythisempiricalmodeltostructurallyestimatebothbeliefdistributionsandvoters'preferenceparameters.Fromamethodologicalviewpoint,weincorporateageneralstructureofbeliefsupdatingthatgoeswellbeyondwhatnormallyachievablewithstandardassumptionsinthepoliticalandcom-mercialadvertisingliterature.Forinstance,letusconsiderconjugatepriorsoftheGaussianfamily.Withnormalbeliefsnewsignalscannotreducetheprecisionofthesubjectivedistributions,theyalwaysreducethevarianceofthesedistributions.Butrelyingonsuchbeliefsisveryrestrictive.Toseethisconsideranotherintuitivebeliefdistribution:abinomial.Whentherearetwo(ormoregenerallynite)states,theprobabilityofthe\good"statecangoupordowndependingonthesignalvalue.Asaresult,thevarianceofthebeliefscanactuallyincreaseordecreaseafterreceivingadditionalinformation.Hence,theimportanceofleavingthebeliefsfamilyunrestrictediscrucialinnotforcingerroneousassumptionsontothedata.Ourestimatesshowthattheutilityweightplacedbyvotersonacandidate'spolicypositionisofapproximatelyequalmagnitudetothatplacedonacandidate'svalenceandthatthecommonassumptionofconvexityofthelossesfromideologicaldistanceisnotsupportedbythedata.We26 alsoshowhowtheinformationaltreatmentswedesignedsystematicallyin uenceboththerstandsecondmomentsofvoters'marginalbeliefsaboutbothcandidatesintheelectoralrace,notonlythebeliefsaboutthecandidateoriginatingthemessage.Webelievethiscausalevidenceofcross-campaignlearningcanproveusefulforunderstandingthelevelofsophisticationinsubjectiveupdatingbyvoters.Potentialapplicationsofourelicitationmethodologyandestimationappeartobequitewide,in-cluding,inadditiontopoliticalcampaigning,commercialadvertisingandmarketing.Ourapproachcouldbeofusefortheassessmentofanytypeofinformationaltreatmentforrandomizedcontrolledtrials,mostofthemcurrentlyperformedindevelopingcountries.Finally,ourincorporationoftheprobabilityofnon-responsemaybeappliedinmanyothercontextsinwhichnon-randomnon-responsetosurveyquestionsseemsplausible(e.g.,reportsofincomeorotherlabor-relatedquestionsforwhichthosesurveyedmaybeuncomfortabledisclosinginformation).27 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Turnout0.7080.7140.0500.3890.78895Incumbentshareovervalidvotes0.5130.5080.0610.3540.66795Incumbentpartiesovervalidvotes0.5410.5420.0650.3580.67995 Notes.Descriptivestatisticsattheprecinctlevelofthevariablesspeciedintherstcolumn.\In-cumbentparties"refertothevotesharesofthepartylistssupportingtheincumbent.Table2{VoteDeclarationsattheIndividualLevel MeanMedianS.d.MinMaxObs. Declaredturnout0.8981.0000.3030.0001.0001,455Declaredvotefortheincumbent0.5711.0000.4950.0001.0001,306Declaredvoteforincumbentparties0.4930.0000.5000.0001.0001,306 Notes.Descriptivestatisticsattheindividuallevelofthevariablesspeciedintherstcolumn.\Incumbentparties"refertothe(self-declared)voteinfavorofthepartylistssupportingtheincumbent.31 Table3{Reduced-FormAggregateEstimates,AllGroups Referencegroup:nomessage ValenceValenceIdeologyIdeologyDoubleDoublebyphonebymailbyphonebymailbyphonebymail Turnout-0.011-0.0000.0130.010-0.006-0.006[0.031][0.015][0.011][0.013][0.009][0.013]Incumbent0.041**0.0040.0130.0210.027*-0.023share[0.019][0.025][0.016][0.025][0.015][0.015]Incumbent0.032*0.0180.0150.0290.021-0.015parties[0.018][0.023][0.016][0.026][0.014][0.015] Notes.Observations:95precincts.OLScoecientsreported;dependentvariablesinrowheadingsandtreatmentgroupsincolumnheadings.Robuststandarderrorsclusteredatthepollingplacelevelinbrackets.Signicanceatthe10%levelisrepresentedby*,atthe5%levelby**,andatthe1%levelby***.Table4{Reduced-FormAggregateEstimates,PhoneCalls Referencegroup:mailornomessage ValenceIdeologyDoublebyphonebyphonebyphone Turnout-0.0120.012-0.006[0.030][0.011][0.010]Incumbent0.040**0.0120.026*share[0.019][0.015][0.013]Incumbent0.0260.0080.014parties[0.020][0.016][0.012] Notes.Observations:95precincts.OLScoecientsreported;dependentvariablesinrowheadingsandtreatmentgroupsincolumnheadings.Robuststandarderrorsclusteredatthepollingplacelevelinbrackets.Signicanceatthe10%levelisrepresentedby*,atthe5%levelby**,andatthe1%levelby***.32 Table5{Reduced-FormIndividualEstimates,AllGroups Referencegroup:nomessage ValenceValenceIdeologyIdeologyDoubleDoublebyphonebymailbyphonebymailbyphonebymail Turnout-0.024-0.0190.0060.033-0.019-0.003[0.027][0.034][0.026][0.022][0.028][0.029]Incumbent0.095**-0.0610.018-0.0280.0350.004share[0.039][0.049][0.049][0.043][0.050][0.050]Incumbent0.109***-0.007-0.008-0.0440.009-0.014parties[0.040][0.060][0.061][0.046][0.051][0.049] Notes.Observations:1,455eligiblevoters(turnout);1,306actualvoters(voteshares).Probitmarginale ectsreported;dependentvariablesinrowheadingsandtreatmentgroupsincolumnheadings.Fixede ectsforsurveydateincluded.Robuststandarderrorsclusteredattheprecinctlevelinbrackets.Signicanceatthe10%levelisrepresentedby*,atthe5%levelby**,andatthe1%levelby***.Table6{Reduced-FormIndividualEstimates,PhoneCalls Referencegroup:mailornomessage ValenceIdeologyDoublebyphonebyphonebyphone Turnout-0.0260.005-0.021[0.023][0.023][0.023]Incumbent0.110***0.0350.051share[0.033][0.043][0.045]Incumbent0.123***0.0050.022parties[0.032][0.053][0.044] Notes.Observations:1,455eligiblevoters(turnout);1,306actualvoters(voteshares).Probitmarginale ectsreported;dependentvariablesinrowheadingsandtreatmentgroupsincolumnheadings.Fixede ectsforsurveydateincluded.Robuststandarderrorsclusteredattheprecinctlevelinbrackets.Signicanceatthe10%levelisrepresentedby*,atthe5%levelby**,andatthe1%levelby***.33 Table7{ModelEstimates,BaselineSpecication Model'sEstimateparameters[s.e.] A=Pr(responsejA)0.76[0.01]B=Pr(responsejB)0.99[0.01] L1.08[0.21] C1.10[0.14] R0.37[0.13]L0.34[0.21]C0.00[0.49]R0.98[0.32] L0.18[0.14] C0.02[0.09] R-0.03[0.05] V;30.40[0.15] V;20.40[0.28] V0.56[0.05] P;30.58[0.16] P;20.38[0.19] P0.71[0.19] Loglikelihood-1,043.60Observations1,306 Notes.Asymptoticstandarderrorsinbrackets.Theselectedspeci-cationassumesindependenceofmarginals,heterogeneouspreferenceparameters,andforcessameskewofmarginaldistributionofbeliefsfordi erentstatedlevelsofuncertainty.34 Table8{BeliefsaboutIncumbentfromModelEstimates Referencegroup:mailornomessage ValenceIdeologyDoublebyphonebyphonebyphone Average0.310**-0.022-0.100valence[0.148][0.142][0.098]Valence0.0050.0630.025std.dev.[0.082][0.095][0.093]Average0.015-0.121**-0.102*ideology[0.063][0.056][0.055]Ideology-0.036-0.090**-0.127***std.dev.[0.060][0.039][0.044] Notes.Observations:1,306actualvoters.OLScoecientsreported;dependentvariablesinrowheadingsandtreatmentgroupsincolumnheadings.Fixede ectsforsurveydateincluded.Robuststandarderrorsclusteredattheprecinctlevelinbrackets.Signicanceatthe10%levelisrepresentedby*,atthe5%levelby**,andatthe1%levelby***.Table9{BeliefsaboutIncumbentfromSurveyResponses Referencegroup:mailornomessage ValenceIdeologyDoublebyphonebyphonebyphone Valence0.326**-0.039-0.092mode[0.157][0.144][0.096]Valence-0.052***0.002-0.003uncertainty[0.013][0.018][0.018]Ideology-0.049-0.104**-0.052mode[0.052][0.052][0.059]Ideology-0.052*-0.046**-0.032uncertainty[0.023][0.019][0.019] Notes.Observations:1,455eligiblevoters.OLScoecients(mode)orProbitmarginale ects(uncertainty)reported;dependentvariablesinrowheadingsandtreatmentgroupsincolumnheadings.Fixede ectsforsurveydateincluded.Robuststandarderrorsclusteredattheprecinctlevelinbrackets.Signicanceatthe10%levelisrepresentedby*,atthe5%levelby**,andatthe1%levelby***.35 Table10{BeliefsaboutOpponentfromModelEstimates Referencegroup:mailornomessage ValenceIdeologyDoublebyphonebyphonebyphone Average-0.127-0.045-0.071valence[0.081][0.133][0.094]Valence-0.077-0.096-0.048std.dev.[0.110][0.107][0.132]Average-0.0750.189**-0.032ideology[0.067][0.075][0.070]Ideology0.041-0.177***-0.091std.dev.[0.075][0.064][0.057] Notes.Observations:1,306actualvoters.OLScoecientsreported;dependentvariablesinrowheadingsandtreatmentgroupsincolumnheadings.Fixede ectsforsurveydateincluded.Robuststandarderrorsclusteredattheprecinctlevelinbrackets.Signicanceatthe10%levelisrepresentedby*,atthe5%levelby**,andatthe1%levelby***.Table11{BeliefsaboutOpponentfromSurveyResponses Referencegroup:mailornomessage ValenceIdeologyDoublebyphonebyphonebyphone Valence-0.094-0.043-0.051mode[0.106][0.133][0.088]Valence-0.028-0.0290.008uncertainty[0.047][0.045][0.054]Ideology0.0230.141**-0.016mode[0.048][0.062][0.063]Ideology-0.044-0.089***0.001uncertainty[0.028][0.030][0.032] Notes.Observations:1,455eligiblevoters.OLScoecients(mode)orProbitmarginale ects(uncertainty)reported;dependentvariablesinrowheadingsandtreatmentgroupsincolumnheadings.Fixede ectsforsurveydateincluded.Robuststandarderrorsclusteredattheprecinctlevelinbrackets.Signicanceatthe10%levelisrepresentedby*,atthe5%levelby**,andatthe1%levelby***.36 Table12{PredictedVoteDi erencesunderCounterfactualElectoralCampaigns CounterfactualtreatmentPredictedvotedi erenceinpercentagepoints Blanketvalence2.2treatment[0.77,3.33]Blanketideology-2.2treatment[-3.37,-0.27]Blanketvalence&ideology0.5treatment[-0.73,1.84]Valencetreatmenttocenter&right1.3valence&ideologytoleftvoters[-0.19,2.37]Ideologytreatmenttocenter&right-2.4valence&ideologytoleftvoters[-3.87,-0.92]Actualelectoral1.8campaigne ect[1.23,3.14] Notes.Counterfactualadditionalvotes(inpercentagepoints)thatcandidateAwouldhaveobtainedwiththesimulatedcampaignsdescribedintherstcolumnrelativetonoelectoraltreatmentbeingadministered.Bootstrapped95percentcondenceintervalsinbrackets.Condenceintervalsarebasedon1,000drawsfromtheasymptoticdistributionoftheMLparametervectors.37 Figure1{PriorValenceMarginalDistributionforVoter#371 Figure2{PriorJointProbabilityDistributionforVoter#369 38 Figure3{PosteriorJointProbabilityDistributionforVoter#369 39 AppendixForallmaterialsrelatedtothedesignofourrandomizedcontrolledtrial(includingsurveyquestion-naires;coloredtreatment yers;audiolesofthetreatmentphonecalls;andmapsofthetreatmentgroups)pleaserefertothewebsite:www.igier.unibocconi.it/randomized-campaign.Inthenexttwosubsections,wereporttheEnglishtranslationsofthetextofthemail yers(whicharethenshowedinFigureA1andFigureA2)andofthetextofthecandidate'srecordedmessagesforthecampaignphonecalls.Inthesubsectiondevotedtotablesandgures,wereport:balancingtestsofprecinctcharacteristicsacrosstreatmentgroups(TableA1);balancingtestsofindividualcharacteristicsacrosstreatmentgroups(TableA2);balancingtestsof2001Censuscharacteristicsacrosstreatmentgroups(TableA3);estimatesofpotentialspillovere ects(TableA4);completesummaryofthestructuralmodelestimations(TablesA5andA6);LRandVoungtestsofmodelselection(TablesA7,A8,andA9); yersforboththevalenceandideologymessage(FiguresA1andA2).A1MailFlyers:EnglishTranslationsValence yer.COMPETENCEANDEFFORT.100millionworthofinvestments:SpentinpartontheFortress,squares,streets,andparkinglots.PIUSS,theintegratedplanforthedevelopmentofthecity:ThecityofArezzowasrankedrstinTuscany;thisisanimportantaccomplishment.Inno-vation:Thedigitalcenter,thehydrogenpipeline,andtheenergyhouse.FANFANIFORMAYOR.Ideology yer.AWARENESSANDSOLIDARITY.Children:Createdanintegratedsystemtocatertheneedsofall,opened3newpublicnurseryschools.Elderly:In-homeassistance,newpublicservicestohelpfamilies.Anetworkofsolidarityfortheneediest:Housing,mealcenters,workintegrationservices.FANFANIFORMAYOR.A2PhoneCallRecordedMessages:EnglishTranslationsValencemessage.DearVoter,the15thand16thofMay,thecitizensofArezzowillvotetoelectthemayorandcitycouncilmen.WeallthereforehavetheopportunitytomakeaninformedchoiceforthefutureofArezzo.Overthelastyears,myadministrationinvested100millionEurostodevelopandimproveourcity.ResultsareundertheeyesofeveryoneandcanbeobservedbysimplylookingattheFortress,thesquares,thestreets,andtheparkinglots.Thankstothequalityofour40 work,thePIUSS|theplanforthedevelopmentofthecityofArezzo|wasrankedrstamongthoseinTuscany.Thiswasanimportantaccomplishmentthatalsoenabledustogainaccesstoimportantnancialresourcestoimprovetheprominenceofourcity.However,wedidmuchmorethanthis,westrivedtoboostinnovationwiththedigitalcenter,thehydrogenpipeline,andtheenergyhouse.Givenalsoallthesereasons,Itakethelibertytoaskforyourvoteintheelectionofthe15thand16thofMay.RewardourCOMPETENCEandourEFFORT.BestregardsfromGiuseppeFanfani.Ideologymessage.DearVoter,the15thand16thofMay,thecitizensofArezzowillvotetoelectthemayorandcitycouncilmen.WeallwillhavetheopportunitytomakeaninformedchoiceforthefutureofArezzo.Forus,futurestandsforSOLIDARITY.Intheseveyearsofcitygovernment,wedealtwithissuesregardingchildhoodcreatinganintegratedsystemofservicesabletoprovideanswerstoallfamiliesandopeningthreenewpublicnurseryschools.Wealsotookcareofourelderlypeople,providingnewservicestohelpfamiliesassistthemandincreasingin-homeassistance.Atthesametime,wedenitelydidnotforgetaboutthosethatfoundthemselveslivingindicultcircumstancesalsobecausetheywerea ectedbytheinternationalcrisisthatseverelystruckourregion.Infact,weincreasedhousing,mealcenters,andprofessionalintegrationservicesforallthoseinneed.Givenalsoallthesereasons,Itakethelibertytoaskforyourvoteintheelectionofthe15thand16thofMay.MakeSOLIDARITYwin!Foran\Arezzo"carefulandopentothehardshipsofthoseinneed.BestregardsfromGiuseppeFanfani.Valenceplusideologymessage.DearVoter,the15thand16thofMay,thecitizensofArezzowillvotetoelectthemayorandcitycouncilmen.WeallthereforehavetheopportunitytomakeaninformedchoiceforthefutureofArezzo.Overthelastyears,myadministrationinvested100millionEurostodevelopandimproveourcity.ResultsareundertheeyesofeveryoneandcanobservedbysimplylookingattheFortress,thesquares,thestreets,andtheparkinglots.Thankstothequalityofourwork,thePIUSS|theplanforthedevelopmentofthecityofArezzo|wasrankedrstamongthoseinTuscany.Atthesametime,wedenitelydidnotforgetaboutthosethatfoundthemselveslivingindicultcircumstancesalsobecausetheywerea ectedbytheinternationalcrisisthatseverelystruckourregion.Infact,weincreasedhousing,mealcenters,andprofessionalintegrationservicesforallthoseinneed.Givenalsoallthesereasons,Itakethelibertytoaskforyourvoteintheelectionofthe15thand16thofMay.RewardourCOMPETENCEandourEFFORT.MakeSOLIDARITYwin!ForanArezzocarefulandopentothehardshipsofthoseinneed.BestregardsfromGiuseppeFanfani.41 AppendixTablesandFiguresTableA1{Ex-AnteBalancingTestsatthePrecinctLevel Referencegroup:nomessage ValenceValenceIdeologyIdeologyDoubleDoublebyphonebymailbyphonebymailbyphonebymail Eligiblevoters-66.083-101.58319.250-63.667*-65.500-6.083[96.591][70.235][57.771][36.922][66.886][56.033]Firstneighborhood0.0360.0360.203-0.0470.203-0.047[0.136][0.112][0.178][0.112][0.123][0.109]Secondneighborhood0.116-0.051-0.051-0.051-0.0510.033[0.188][0.140][0.151][0.154][0.086][0.128]Thirdneighborhood-0.0140.236-0.0980.152-0.014-0.098[0.190][0.172][0.134][0.199][0.169][0.134]Fourthneighborhood-0.138-0.221-0.054-0.054-0.1380.112[0.149][0.141][0.146][0.164][0.139][0.129]Regional'10turnout-0.005-0.0030.0160.0120.000-0.002[0.025][0.016][0.010][0.010][0.010][0.014]Regional'10left0.0110.0130.0130.0120.004-0.021[0.015][0.019][0.013][0.017][0.013][0.013]Regional'10right-0.015-0.0170.0110.007-0.0060.019[0.015][0.014][0.012][0.018][0.011][0.018]European'09turnout-0.0040.0080.0190.0130.0020.007[0.026][0.012][0.012][0.013][0.011][0.012]European'09left-0.0120.015-0.016-0.0140.018-0.028[0.030][0.026][0.016][0.025][0.019][0.021]European'09right0.009-0.0150.0180.009-0.0140.026[0.022][0.021][0.015][0.024][0.020][0.020]National'08turnout-0.0140.0120.0020.0020.0050.000[0.025][0.008][0.006][0.007][0.007][0.009]National'08left0.0160.026-0.015-0.0040.020-0.019[0.019][0.019][0.019][0.028][0.020][0.017]National'08right-0.018-0.0230.0130.004-0.0240.023[0.020][0.017][0.017][0.028][0.021][0.018]City'06turnout-0.0020.0080.0120.0090.011-0.006[0.020][0.011][0.009][0.013][0.011][0.013]City'06left0.0160.035-0.029-0.0170.009-0.029[0.029][0.024][0.023][0.034][0.021][0.022]City'06right-0.014-0.0370.0280.014-0.0080.022[0.029][0.024][0.022][0.033][0.021][0.024] Notes.Observations:95precincts,86(European),84(National),83(City).OLScoecientsreported;dependentvariablesinrowheadingsandtreatmentgroupsincolumnheadings.Eligiblevotersisthenumberofeligiblevotersintheprecinct(average820.168).Theneighborhooddummiescapturethecity-wideneighborhoodtheprecinctbelongsto.Theothervariablesaretheelectoraloutcomesinpastelectionsandareexpressedasvoteshares.Robuststandarderrorsclusteredatthepollingplacelevelinbrackets.Signicanceatthe10%levelisrepresentedby*,atthe5%levelby**,andatthe1%levelby***.42 TableA2{Ex-PostBalancingTestsattheIndividualLevel Referencegroup:nomessage ValenceValenceIdeologyIdeologyDoubleDoublebyphonebymailbyphonebymailbyphonebymail Male0.0080.0140.0340.0040.0060.042[0.039][0.050][0.038][0.038][0.047][0.039]Over65-0.0350.004-0.0120.086-0.0460.056[0.053][0.048][0.048][0.053][0.042][0.048]College-0.004-0.0270.0100.0080.035-0.016graduate[0.035][0.041][0.041][0.047][0.045][0.040]Outof-0.0190.010-0.0370.048-0.0410.050laborforce[0.052][0.054][0.058][0.059][0.050][0.053]White0.029-0.0050.032-0.0130.008-0.013collar[0.045][0.043][0.038][0.041][0.039][0.038]Other-0.010-0.0050.006-0.0350.033-0.037occupation[0.049][0.041][0.040][0.039][0.042][0.051]Center-left0.0450.058-0.009-0.033-0.0590.014[0.044][0.055][0.048][0.040][0.042][0.059]Homeowner-0.017-0.007-0.0450.0270.007-0.037[0.040][0.030][0.039][0.036][0.033][0.028]Read0.037-0.0070.025-0.0240.0320.048thepress[0.036][0.038][0.042][0.052][0.049][0.047]WatchTV0.034-0.0160.0380.068-0.0330.055[0.042][0.055][0.039][0.046][0.042][0.038] Notes.Observations:1,455eligiblevoters.OLScoecientsreported;dependentvariablesinrowheadingsandtreatmentgroupsincolumnheadings.Allvariablesaredummies.ReadthepressandWatchTVcapturewhetherthevoterdeclarestodothis\veryoften"or\often."Fixede ectsforsurveydateincluded.Robuststandarderrorsclusteredattheprecinctlevelinbrackets.Signicanceatthe10%levelisrepresentedby*,atthe5%levelby**,andatthe1%levelby***.43 TableA3{Ex-PostBalancingTestsof2001CensusCharacteristics Referencegroup:nomessage ValenceValenceIdeologyIdeologyDoubleDoublebyphonebymailbyphonebymailbyphonebymail Males-5.112-1.318-8.103-1.957-2.5871.187[7.450][6.922][6.353][7.245][5.220][8.773]Marriedpeople-5.780-1.608-8.986-2.040-2.8631.256[8.041][7.496][6.905][7.955][5.697][9.541]Collegegraduates-0.5070.093-0.7120.473-0.1770.748[0.661][0.568][0.492][0.725][0.499][1.058]Foreigners-0.400-0.178-0.311-0.255-0.395-0.129[0.339][0.339][0.330][0.339][0.310][0.395]Employmentrate0.002-0.003-0.000-0.0020.005-0.001[0.006][0.006][0.005][0.004][0.005][0.004]Unemploymentrate-0.0010.0040.0010.000-0.0010.003[0.005][0.004][0.004][0.004][0.005][0.004]Homeownership0.011-0.028-0.012-0.023-0.012-0.003[0.025][0.038][0.030][0.025][0.027][0.025] Notes.Observations:95precincts.OLScoecientsreported;dependentvariablesinrowheadingsandtreatmentgroupsincolumnheadings.Allvariablesareimputedattheprecinctlevelfrominformationonthe2001Censuscells.Males,Marriedpeople,Collegegraduates,andForeignerscapturetheaveragenumberofindividualswiththatattributeattheprecinctlevel.Employmentrate,Unemploymentrate,andHomeownershipareexpressedasshares.Inparticular,homeownershipistheshareofhousesoccupiedbytheowner.Robuststandarderrorsclusteredatthepollingplacelevelinbrackets.Signicanceatthe10%levelisrepresentedby*,atthe5%levelby**,andatthe1%levelby***.44 TableA4{EvaluatingPotentialSpillovers,AllGroups Referencegroup:nomessage ValenceValenceIdeologyIdeologyDoubleDoublebyphonebymailbyphonebymailbyphonebymailspilloversspilloversspilloversspilloversspilloversspillovers Turnout0.032-0.0340.0100.0470.0030.028[0.048][0.055][0.044][0.060][0.042][0.054]Incumbent0.099-0.1130.064-0.0200.1240.005share[0.077][0.082][0.080][0.100][0.076][0.099]Incumbent0.081-0.147-0.035-0.1180.0380.006parties[0.079][0.098][0.096][0.104][0.089][0.115] Notes.Observations:1,455eligiblevoters(turnout);1,306actualvoters(voteshares).OLScoecientsreported;dependentvariablesinrowheadingsandtreatmentgroupsincolumnheadings.Eachspilloversvariablecapturestheshareofobservationswhoreceivedthecorrespondingtreatmentinthesamepollingplaceofeveryobservation.Averagevaluesare:0.135(valencebyphone);0.099(valencebymail);0.151(ideologybyphone);0.106(ideologybymail);0.135(doublebyphone);0.113(doublebymail).Fixede ectsforsurveydateincluded.Robuststandarderrorsclusteredattheprecinctlevelinbrackets.Signicanceatthe10%levelisrepresentedby*,atthe5%levelby**,andatthe1%levelby***.45 TableA5{ModelEstimateswithHeterogeneousPreferenceParameters ModeldescriptionCopulafamily:FGMFrankIndpFGMFGMFGMFrankFrankFrankIndpSamealpha:NoNoNoYesYesYesYesYesYesYesRhospecication:StandardStandard-StandardHeteroRestrictedStandardHeteroRestricted-Parameter A=Pr(responsejA)0.760.760.760.760.760.760.760.760.760.76(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)B=Pr(responsejB)0.990.990.990.990.990.990.990.990.990.99(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01) = L1.081.081.071.091.091.091.101.101.081.08(0.23)(0.23)(0.21)(0.23)(0.23)(0.22)(0.23)(0.23)(0.22)(0.21) C1.111.111.111.101.111.111.101.121.111.10(0.14)(0.14)(0.14)(0.14)(0.14)(0.14)(0.14)(0.15)(0.15)(0.14) R0.360.370.360.360.350.350.350.330.370.37(0.13)(0.13)(0.13)(0.13)(0.13)(0.13)(0.13)(0.14)(0.13)(0.13)=L0.340.340.340.340.340.340.330.330.340.34(0.22)(0.22)(0.21)(0.22)(0.22)(0.22)(0.21)(0.21)(0.22)(0.21)C0.000.000.000.000.000.000.000.000.000.00(0.49)(0.49)(0.48)(0.48)(0.47)(0.47)(0.49)(0.45)(0.45)(0.49)R1.031.031.001.021.041.021.031.100.980.98(0.33)(0.32)(0.32)(0.32)(0.33)(0.32)(0.32)(0.33)(0.31)(0.32) = L0.180.180.180.190.190.180.190.200.190.18(0.15)(0.15)(0.14)(0.15)(0.15)(0.15)(0.15)(0.15)(0.15)(0.14) C0.020.020.020.030.030.030.020.040.040.02(0.09)(0.09)(0.09)(0.09)(0.09)(0.09)(0.09)(0.10)(0.09)(0.09) R-0.04-0.04-0.04-0.04-0.04-0.04-0.04-0.05-0.03-0.03(0.05)(0.05)(0.05)(0.05)(0.05)(0.05)(0.04)(0.04)(0.05)(0.05) V;30.380.370.400.370.370.360.360.360.400.40(0.15)(0.15)(0.15)(0.15)(0.16)(0.16)(0.15)(0.16)(0.16)(0.15) V;20.380.370.400.370.370.360.360.360.400.40(0.32)(0.32)(0.31)(0.29)(0.30)(0.29)(0.28)(0.28)(0.30)(0.28) V= V;30.590.580.590.560.560.560.560.560.560.56(0.06)(0.06)(0.07)(0.05)(0.05)(0.05)(0.05)(0.05)(0.06)(0.05) V;20.510.510.51-------(0.10)(0.10)(0.10)------- P;30.580.580.590.570.570.570.570.550.560.58(0.17)(0.16)(0.16)(0.16)(0.16)(0.16)(0.16)(0.15)(0.15)(0.16) P;20.380.380.380.370.360.370.370.330.370.38(0.20)(0.20)(0.20)(0.20)(0.20)(0.20)(0.19)(0.19)(0.19)(0.19) P= P;30.710.710.720.700.690.700.690.680.700.71(0.23)(0.23)(0.24)(0.18)(0.18)(0.18)(0.18)(0.17)(0.18)(0.19) P;20.690.690.69-------(0.30)(0.30)(0.30)-------A=LA-1.00-13.67--1.00-1.00-1.00-8.24-30.00-30.00-(10.62)(261.31)-(10.37)(11.69)(11.58)(90.46)(1703.1)(1717.1)-CA----1.001.00-14.1713.22-----(134.16)(136.54)-(4054.00)(4003.60)-RA----1.00--30.00------(15.42)--(786.89)--B=LB-1.00-30.00--1.00-1.00-1.00-30.00-30.00-29.99-(18.42)(2035.20)-(17.90)(18.95)(13.53)(1952.30)(1969.40)(1796.20)-CB----1.001.00-8.438.23-----(190.48)(195.53)-(2618.30)(3160.70)-RB-----1.00---30.00------(42.58)--(5325.70)--Loglikelihood-1043.20-1042.90-1043.30-1043.40-1043.30-1043.40-1043.10-1042.60-1043.10-1043.60Observations1,3061,3061,3061,3061,3061,3061,3061,3061,3061,306 Notes.Asymptoticstandarderrorsinbrackets.Preferenceparametersareallowedtovarywithvoter'sideology(L,C,R);basedonLRtests,ourpreferredspecicationiswithindependentcopulaandsamealpha.Copulafamily:\FGM"standsforFarlie-Gumbel-Morgensen;\Frank"standsforFrankfamily;\Indp"for.Samealpha:\yes"forcesskewofmarginalstobethesameforeachlevelofstateduncertainty;\no"allowstheskewtodi er.Rhospecication:\standard"meansbaselineAandB;\hetero"allowsAandBtovarywithvoter'sideology;\restricted"forcesLA=RBandRA=LB. TableA6{ModelEstimateswithoutHeterogeneousPreferenceParameters ModeldescriptionCopulafamily:FGMFrankIndpFGMFGMFGMFrankFrankFrankIndpSamealpha:NoNoNoYesYesYesYesYesYesYesRhospecication:StandardStandard-StandardHeteroRestrictedStandardHeteroRestricted-Parameter A=Pr(responsejA)0.770.770.770.770.770.770.770.770.770.77(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)B=Pr(responsejB)0.980.980.980.980.980.980.980.980.980.98(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01) = L0.890.910.900.880.880.900.910.910.910.89(0.09)(0.09)(0.09)(0.09)(0.09)(0.09)(0.09)(0.09)(0.09)(0.09) C-------------------- R--------------------=L0.650.680.690.690.680.650.660.660.68(0.14)(0.14)(0.14)(0.14)(0.14)(0.14)(0.14)(0.14)(0.14)(0.14)C--------------------R-------------------- = L0.050.060.050.040.040.050.060.060.060.05(0.05)(0.05)(0.05)(0.05)(0.05)(0.05)(0.05)(0.05)(0.05)(0.05) C-------------------- R-------------------- V;30.400.350.350.340.400.340.340.340.340.34(0.17)(0.16)(0.15)(0.15)(0.17)(0.17)(0.16)(0.16)(0.16)(0.16) V;20.400.350.350.340.400.340.340.340.340.34(0.30)(0.29)(0.29)(0.24)(0.30)(0.25)(0.28)(0.29)(0.29)(0.28) V= V;30.540.540.540.510.520.520.520.520.520.52(0.07)(0.06)(0.06)(0.05)(0.06)(0.05)(0.05)(0.05)(0.05)(0.05) V;20.500.500.50-------(0.11)(0.10)(0.10)------- P;30.600.580.610.650.650.600.610.580.620.65(0.17)(0.15)(0.15)(0.17)(0.17)(0.15)(0.16)(0.15)(0.15)(0.15) P;20.600.550.610.650.650.600.610.580.610.65(0.33)(0.32)(0.32)(0.27)(0.28)(0.26)(0.26)(0.27)(0.26)(0.26) P= P;30.800.770.810.810.820.770.770.740.770.81(0.26)(0.23)(0.27)(0.28)(0.28)(0.22)(0.23)(0.20)(0.23)(0.27) P;20.690.650.70-------(0.42)(0.35)(0.44)-------A=LA-1.00-30.00--1.00-1.001.00-30.00-30.0029.99-(18.09)(1993.00)-(22.79)(38.48)(24.90)(2120.70)(3038.50)(2786.20)-CA----1.001.00-30.0029.60-----(53.29)(41.32)-(1849.70)(7268.40)-RA-----1.00---30.00------(41.50)--(2997.90)--B=LB1.0029.99-1.00-1.00-1.0029.99-30.00-30.00-(29.21)(1633.70)-(37.36)(51.93)(22.23)(3674.60)(4066.60)(2467.70)-CB----1.001.00-22.4227.94-----(86.81)(63.35)-(6915.90)(11627.00)-RB-----1.00---30.00------(81.43)--(7895.00)--Loglikelihood-1057.70-1057.40-1057.70-1057.90-1057.94-1057.70-1057.50-1057.50-1057.40-1057.90Observations1,3061,3061,3061,3061,3061,3061,3061,3061,3061,306 Notes.Asymptoticstandarderrorsinbrackets.UnlikeTableA3,preferenceparametersarenotallowedtovarywithvoter'sideology(L,C,R);basedonLRtests,thesearenotourpreferredspecicationsbutwereportthemforcompleteness.Copulafamily:\FGM"standsforFarlie-Gumbel-Morgensen;\Frank"standsforFrankfamily;\Indp"for.Samealpha:\yes"forcesskewofmarginalstobethesameforeachlevelofstateduncertainty;\no"allowstheskewtodi er.Rhospecication:\standard"meansbaselineAandB;\hetero"allowsAandBtovarywithvoter'sideology;\restricted"forcesLA=RBandRA=LB. TableA7{LRTests:RestrictionofPreferenceParametersToBetheSameacrossVoter'sIdeology CopulaTeststatisticP-value FGM28.940.00Frank28.860.00Independent28.620.00 Notes.Skewrestrictedtobethesameacrosslevelsofstateduncertainty.Standardspecication.TableA8{LRTests:RestrictionofSkewToBetheSameacrossLevelsofUncertainty PreferencesCopulaTeststatisticP-value HomogeneousFGM0.290.86HomogeneousFrank0.370.83HomogeneousIndp0.380.83HeterogeneousFGM0.490.78HeterogeneousFrank0.390.82HeterogeneousIndp0.540.76 Notes.Standardspecication.TableA9{VuongTests:CopulaComparisons PreferencesCopulaRhoTestP-valuePreferredcomparisonspecicationstatisticcopula HomogeneousFrankvs.FGMStandard0.760.45FrankHomogeneousIndependentvs.FGMStandard39.480.00IndependentHomogeneousIndependentvs.FrankStandard17.930.00IndependentHeterogeneousFrankvs.FGMStandard1.050.29FrankHeterogeneousIndependentvs.FGMStandard22.670.00IndependentHeterogeneousIndependentvs.FrankStandard12.610.00IndependentHeterogeneousIndependentvs.FGMHeterogeneous52.080.00IndependentHeterogeneousIndependentvs.FrankHeterogeneous26.590.00IndependentHomogeneousIndependentvs.FGMHeterogeneous12.90.00IndependentHomogeneousIndependentvs.FrankHeterogeneous35.930.00IndependentHeterogeneousIndependentvs.FGMRestricted37.190.00IndependentHeterogeneousIndependentvs.FrankRestricted30.780.00IndependentHomogeneousIndependentvs.FGMRestricted40.570.00IndependentHomogeneousIndependentvs.FrankRestricted34.770.00Independent Notes.Skewrestrictedtobethesameacrosslevelofstateduncertainty.48 FigureA1{CampaignFlyerwiththeValenceMessage FigureA2{CampaignFlyerwiththeIdeologyMessage 49