TheRunner-UpEectSantoshAnagolWhartonThomasFujiwaraPrincetonandCIFARJ - PDF document

TheRunner-UpEectSantoshAnagolWhartonThomasFujiwaraPrincetonandCIFARJune2014AbstractExploitingregressiondiscontinuitydesignsinBrazilian,Indian,andCanadianrst-past-the-postelections,wedocumentthatsecond-placecandidatesaresubstantiallymorelikelythanclosethird-placecandidatestorunin,andwin,subsequentelections.Sincebothcandidateslosttheelectionandhadsimilarelectoralperformance,thisistheeectofbeinglabeledtherunner-up.Weexplorethepotentialmechanismsforthisrunner-upeect,includingselectionintocandidacy,heuristicbehaviorbypoliticalactors,andtherunner-upobtaininganadvantagefromstrategiccoordination(beingmorelikelytobecomeafocalpoint).Selectionintocandidacyisunlikelytoexplaintheeectonwinningsubsequentelections,andtheweightofevidencesuggeststheeectisdrivenbystrategiccoordination.Wendnoeectofnishinginthird-placeversus fourth-place.WethankEmmerichDavies,SueJia,MinkwangJang,CinthiaKonichi,MariaGao,MichelleHan,SusannahScanlan,MengshuShen,JasonTian,andIrisYaoforresearchassistance.Thispaperbenettedfromsugges-tionsbyDaronAcemoglu,EduardoAzevedo,LaurentBouton,RobinBurgess,MicaelCastanheira,DavidLee,MarcMeredith,JoanaNaritomi,SriNavagarapu,FrancescoTrebbi,Shing-YiWang,andseminarparticipantsatPrinceton,Wharton,Yale,Columbia,ISB,NYU,UCLA,CIFAR,PECO,andWarwick.WeacknowledgefundingfromWhartonGlobalInitiatives,theWhartonDean'sResearchFund,theCenterfortheAdvancedStudyofIndia(UPenn),theCanadianInstituteforAdvancedResearch,andthePrograminLatinAmericanStudies(Princeton). 1IntroductionSocialscientistshavealongstandinginterestinthefactorsthatdetermineelectoralsuccess.Alargepartofpoliticaleconomystudieshowvotersandotheragentsuseinformationoncandidatessuchaspersonaltraits,policyplatforms,andpastperformance,toselectleaders.Understandinghowthisinformationisprocessediskeytounderstandinghowademocracychoosesitselectedocialsand,consequently,thepoliciesthoseelectedocialsenact.Whilepreviousresearchhasfocusedmostlyonhowincumbentsareevaluated,thispaperanalyzestheuseofinformationonnon-incumbents.Inparticular,westudyhowtheelectoralperformancesoflosingcandidatesimpacttheirfuturesuccess.Ourrstcontributionistodocumentanewempiricalresultregardingsimpleplurality(rst-past-the-post)elections:cominginsecond-place,insteadofthird,hasasubstantialcausaleectontheprobabilitythatacandidatewillrunin,andwin,thenextelectioninherconstituency.Weusearegressiondiscontinuitydesign(RDD)toestimatethis\runner-upeect",comparingbarelysecond-tobarelythird-placecandidatesinsamplescoveringfourdistinctsetsofelections:Brazilianmunicipalmayors,CanadianHouseofCommons,Indianstateassemblies,andtheIndianLokSabha(federallowerchamber).1Thesecontextscovermultiplecontinents,aswellaslocal,state,andfederalelectionsforexecutiveandlegislativepositions.Atrstpass,itisperhapssurprisingthatsimplybeinglabeledtherunner-upwouldmatterinafutureelection.Onaverage,closesecond-andthird-placecandidatesaresimilarandneithergetstoholdoceorenjoyanyinstitutionaladvantageinfutureelections.2Moreover,thedierenceinrankingprovidesnoadditionalinformationaboutthecandidatesbeyondtheirvotes.Inotherwords,rankscoarsentheinformationavailableinvoteshares,andagentsshouldprefertobasedecisionsonnerinformation,whichispubliclyavailable.Despitethesefactors,wendthatbeinglabeledsecond-placehaslargeimplicationsforwhetheracandidaterunsin,andwins,thenextelection.Forexample,ourpreferredestimatesindicatethatbeingtherunner-upincreasesaBrazilianmayoralcandidate'sprobabilityofrunninginthenextelectionby9.4percentagepoints(p.p.),andherchancesofwinningby8.3p.p.,alargeeectgiventhatclosethird-placenishersrunagainin,andwin,thenextelectiononly30.3%and9.5%ofthetime,respectively.Similarly,beingtherunner-up(insteadofthird-place)increasestheprobabilityofrunningagainfrom31.9%to36.3%inIndianstateelections,andtheprobabilityofwinningfrom7.8%to11.2%.Thisimpliesthatvariationinpastelectoralperformancethatisessentiallynoisecanincreasetheprobabilityacandidatewillbeelected in1WealsostudyelectionsfortheBritishHouseofCommonsinAppendixA.3.Section2discussesourfocusontheseparticularcontexts.2Tothebestofourknowledge,noneofthecontextswestudyinvolveelectoralrulesthattreatsecond-andthird-placecandidatesdierently(e.g.,therunner-updoesnotparticipateinarunoelection,isnotlistedmoresalientlyinfutureballots,anddoesnotreceivemorepublicresourcesorfundinginsubsequentelections).1 thefuturebymagnitudesof43%inIndiato87%inBrazil.3Interestingly,theanalogousanalysisusingRDDsfromelectionswherethird-andfourth-placeareclosendseectsthatareclosetozeroinmagnitudeandstatisticalsignicance.Thendingofsignicantrunner-upeectshaspossibleimplicationsfortwowidelystudiedelectoralphenomena.Therstistheincumbencyeect.4Whileitisnaturaltobelievethatalargepartoftheeectofbeinganincumbentonfutureelectoraloutcomesisduetoholdingoce,ourresultssuggestthatsimplybeinglabeledrst-placemightplayarole.Acompellingtheoryinvolvingincumbencyeectsshouldincorporatetheideathatpreviouselectoralrankbyitselfcanhaveimpacts.5Second,therunner-upeectdemonstratesthattheelectoralperformanceoflosingcandidateshassizableimpactsontheirfutureperformance.Thisshedslightoncandidates'decisionstoenterraceswheretheyhavelow(orno)chancesofwinning,astheymightbeattemptingtoimprovetheiroddsinfutureelections.6Wealsoassesswhethertheeectonwinningthenextelectionsimplycomesfromtherunner-upbeingmorelikelytoruninit.WhiletheRDDmakesitstraightforwardtoestimatetheeectofwinningunconditionalonrunning,estimatingtheconditionaleectrequiresaddressingselectionintofuturecandidacy.WeadaptLee's(2009)proceduretoobtainboundsonsuchconditionaleects.7Lowerboundsarewellabovezero(exceptintheCanadiancase),indicatingthatwhatdrivestherunner-upeectnotonlymakesacandidatemorelikelytoruninthenextelection,butalsomakeshermorelikelytowinconditionalonrunning.Thesecondcontributionofthispaperistoprovideevidenceonthemechanismsbehindtherunner-upeect.Onepossibilityisthatbeingtherunner-upcreatesafutureadvantagewhensomeagents(voters,donors,parties,orcandidates)engageinstrategiccoordination.Underthishypothesis,thesecond-placelabelmakesacandidatemorelikelytobecomeafocalpointforcoordination.Forexample,perhapssomeagentsprefereitherthesecond-orthird-placecandidateoverthewinner,andinthenextelectionwouldliketocoordinatetheirsupport on3OurresultsonIndianandCanadianfederalparliamentaryelectionsarealsoconsistentwiththepresenceofrunner-upeects,althoughthesmallersamplesizesmakethestatisticalsignicanceoftheseresultsmoresensitivetothespecicregressiondiscontinuityspecication.4Lee(2008)usescloseelectionRDDstoestimatetheincumbencyadvantageintheUSHouseofRepresentatives.AsimilarapproachisappliedtothecontextswestudybyUppal(2009),Linden(2004),andKendallandRekkas(2012).Section3comparesthemagnitudeofrunner-upeectswithincumbencyeects.5Inasimilarvein,Folkeetal.(2014)ndsaneectofbeingthe(close)rstrankedcandidatewithinapartylistunderpreferentialvotingonfuturepartyleadership.6Canonicalmodelsofcandidateentry,eitherundertheassumptionofpolicycommitment(Feddersenetal.,1990)ornot(OsborneandSlivinski,1996;BesleyandCoate,1997)usuallyinvolvecandidatesenteringelectionsonlywhentheyhaveapositiveprobabilityofwinning(oraectingtheoutcomeof)theelection.7Lee(2009)providesanapproachtoboundeectsinarandomizedtrialwheretheremaybeselectionintothestatethatmakestheoutcomeobservable(e.g.,employmentisastatewherewageoutcomescanbeobserved).Thekeyassumptionisthattherearenosubjectswhowouldchooseintothestateiftheywereinthecontrolgroup,butwouldnotchooseintothestateiftreated(the\nodeers"or\monotonicity"condition).Inourcontext,thisimpliestherearenocandidateswhowouldchoosetorunagainafteraclosethird-place,butnottoruniftheycameinclosesecond-place.2 oneofthem;itwouldbenaturalinthiscasetocoordinateonthebetterrankedcandidateasafocalpoint.Thistypeofbehaviorisfoundinlaboratoryexperiments.8Alargetheoreticalliteraturestudiesstrategiccoordinationacrossvoters(MyersonandWeber,1993;Cox,1997;Myerson,2002).Undersimpleplurality,thesemodelsyieldtwotypesofequi-libria,theDuvergeriantypewherecoordinationleadstotwocandidatesattractingallofthevotes,andanon-Duvergeriantypewithatiebetweensecond-andthird-place.Thelatteris\knife-edge"or\expectationallyunstable"(Palfrey,1988;Fey,1997).Inlightofsuchmodels,ourresultsprovideinsightintohowconstituenciesmovefromthelattertype(whensecond-andthird-placecandidatesareclose)tomorestableDuvergerianequilbria.9Asecond,andnon-exclusive,possiblemechanismisthatatleastonepoliticalplayer(e.g.,voters,candidates,parties,themedia)evaluatescandidatesbasedontheirrankings,eventhoughrank-ingsprovidenoadditionalinformationbeyondtheunderlyingvote-shares.Inotherwords,theyengageina\rankheuristic."10Forexample,partiesmightuseaheuristicwhere,atleastinsomecases,theyprovidemoresupportforcandidatesthatcomeinsecond-place.11Anotherpossibilityisthatcandidatesperceivethat,evenholdingelectoralperformanceconstant,theywereclosertowinningaftercominginsecond-insteadofthird-placeandarethereforemoremotivatedtoinvestinfuturecampaigns.Thispaperprovidesahostofteststoexplorethesepossiblemechanisms,andourinterpretationisthattheweightoftheevidencesuggeststhatstrategiccoordinationplaysaprimaryrole.First,thecoordinationmechanismpredictsthatvoterswhosupportedthethird-placecandidateshouldswitchtovotingfortherunner-upinthenextelection.Wetestthispredictionusingdatafromover8,000pollingstations(i.e.,sub-constituency)in144electionswheresecond-andthird-placeBrazilianmayoralcandidateswereclose.Wendthatpollingstationsthattendedtovoteforthethird-placecandidatepresentlargervotesharesfortherunner-upinthenextelection,comparedtopollingstationsthattendedtovoteforthewinnerorfourth-andlower-placedcandidates,conrmingtheprediction.Thisndingisdiculttoreconcilewithanexplanationbasedentirelyonheuristics,sinceitwouldrequirethird-placesupporterstobedisprop ortionately8Inanexperimentwherevoterscoordinateononeoutoftwomajoritycandidatesinordertobeataminoritycandidateunderpluralityrule,Forsytheetal.(1993)ndthat\amajoritycandidatewhowasaheadoftheotherinearlyelectionstendedtowinthelaterelections,whiletheothermajoritycandidatewasdrivenoutofsubsequentraces"(p.235).Boutonetal.(2012)ndverysimilarresults.9Section5discussesthelinksbetweenmodelsofstrategiccoordinationandourempiricalresults.10Anindividualwhoobservesranks,butnotvoteshares,should(rationally)inferthatanyrunner-upreceivedsubstantiallymorevotesthanathird-placecandidate.However,andmorerelevantlyforourpurposes,anagentonlyobservingranksimpliesthatsomeotheragent(e.g.,themedia)actedfollowing(orimposing)arankheuristicbydecidingtosupplyonlythecoarserinformation.Forexamplesofrankheuristicsinothercontexts,seePope(2009)andBarankay(2012).11Wehavenotencounteredanyanecdotalevidencethatpartiesusesuchrules.EstimatedeectsforIndianindependentcandidatesaresimilartothosewithpartyaliations,makingaparty-levelexplanationunlikely.3 using,orbeingaectedby,suchheuristic.12Second,theheterogeneityofrunner-upeectsacrossdierenttypesofelectionsisconsistentwithstrategiccoordination.Therunner-upeectsarestrongerincaseswherethesecond-andthird-placecandidatesreceivedalargenumberofvotes,comparedtothewinner,andalsowhenthesecond-andthird-placecandidatesarefrompartieswithsimilarplatforms.Thisindicatesthattheadvantageofbeinglabeledtherunner-upislargerinthecaseswhereitismorelikelythatthesecond-andthird-placecandidatesforma\dividedmajority."WealsondlargereectsonwinningfutureelectionsimmediatelyafteraneventinIndia(the1975-1977\Emergency")thatcanbeseenasadisruptionofthepoliticalequilibriumwhichwouldraisetheneedforcoordinationtosortbetweenentrants.Itisnotclearwhyanexplanationbasedonheuristicswouldgeneratethesepatterns.13Wealsopresenttestsofaheuristic-basedexplanationinrelationtothemedia.Onepossibilityisthatthemediagivesmorecoveragetorunners-upthantothird-placecandidates,whichtranslatesintoanelectoraladvantage.WetestforthisinourCanadiancontext,wherecomprehensivenewspaperarchivesearchesforcandidatenamesarepossible.Wendthatthenumberofarticlesmentioningclosesecond-andthird-placecandidatesarestatisticallyindistinguishablepriorto,andafter,theelection,aswellasintherun-uptothenextelection.14Tofurtherprobetheroleofmedia,wetestwhethertherunner-upeectislargerinBrazilianandIndianregionswithgreatermediapresence,andndnoevidencesupportingthis.Thissuggeststhatamedia-basedheuristicisunlikelytodrivetherunner-upeect.15Twootherfactorsalsoshifttheweightofevidencetowardthecoordination-basedexplanation.First,thendingofzeroeectsforthird(versusfourth)placeprovidesanadditionalcomplicationtoanexplanationbasedonheuristics,asonewouldexpectthatarank-basedheuristicthatappliestosecond-placewouldalsoapplytolowerranks.Second,explanationsbasedonrunners-upreceivingmorecampaigninputsmustaddressthesizeablemagnitudesofeects.16Ontheotherhand,strategiccoordinationcanaccountfortheselargeeects,especiallyifalarge share12Theseestimatescontrolforconstituency-time(election)xedeects,aswellasthevotesharesreceivedbytherunner-upandthewinningcandidate.13WefocustheheterogeneitytestsonBrazilianandIndian(state)elections,wherethesamplesizesarelargeenoughtomeaningfullytestwhetherrunner-upeectsdieracrossdierentsub-samples.The\Emergency"wasa21monthperiodwheredemocraticgovernancewasrevokedandtheprimeministerassumedcontrolofallbranchesofgovernment.ThedominantpartyinIndianpolitics(Congress)lostsubstantialsupportafterthisevent,facilitatingtheentryofnewplayers.14Bothcandidatesreceiveverylittlemediaattentionintheperiodbetweentheelections,perhapsunsurprisinglygiventhatneithergainedaseatintheCanadianparliament.15OurmeasureofmediapresenceistheexistenceofanAMradioinBrazilandgreaternewspapercirculationpercapitainIndia.Bothmeasuresaremotivatedbypreviousstudiesthatfoundthesemediaoutletstohaveimportanteectsinelections(FerrazandFinan,2008;BesleyandBurgess,2002).16Forexample,iftheeectisdrivenbycandidatemotivation,theeectsontheprobabilityofwinningthenextelectionimplythatmotivationhasenormousconsequences.Anexplanationbasedondonorsdierentiallysupportingrunners-upalsoimplieseitherstrongresponsivenesstorankbydonorsorlargeeectsofcampaignspendingonvotes.4 ofthosesupportingthethird-placecandidateswitchtovotingfortherunner-upinthenextelection.Wereiteratethatheuristicbehaviorandstrategiccoordinationarenotmutuallyexclusiveexpla-nations.Theyarelikelymutuallyreinforcing(e.g.,ifrunners-uparemorelikelytobecomefocalpoints,they|andparties,donors,etc|shouldbemotivatedbyranklabels).Wealsoemphasizethatwhileourresultsareconsistentwithvotersthemselvesusingtherunner-uplabelasafocalpoint,itispossiblethatthestrategiccoordination(thatultimatelyshiftsvoteshares)occursatadierentlevel.Candidates,parties,and/orother\elites"maycoordinatetheirsupportandrelyonelectionrankingstodoso.Datalimitationsdonotallowustodierentiateacrossthesepossibilities.Giventheevidencethatstrategiccoordinationplaysanimportantroleincausingrunner-upeects,wealsoseethispaperascontributingtotheempiricalliteratureonstrategicvoting.17Whilepreviousstudiesareprimarilyfocusedonwhether(orhowfrequently)votersact\strate-gically"or\sincerely",ourresultshighlighttheempiricalrelevanceofstrategiccoordinationindeterminingelectionwinners.Sizablemagnitudesfortherunner-upeectimplythatcoordina-tionfrequently\matters."Thesizeoftheliteraturestudyingstrategiccoordinationinelectionsunderscorestheimportanceofdocumentingitsempiricalrelevance.18Thenextsectiondescribestheelectionsanddataanalyzed.Section3providesthemainesti-matesanddocumentstherunner-upeects.Section4providesboundsontheeectonwinningconditionalonrunning.Section5addressesthemechanismsdrivingtherunner-upeect.Section6concludes.2DataandBackground2.1DataSelectionandConstructionThispapercomparesthesubsequentperformanceofsecond-andthird-placecandidatesinfourseparatesetsofelections:Brazilianmunicipalmayors,CanadianHouseofCommons,Indianstateassemblies,andtheIndianLokSabha.Thesecontextswerechosenfortworeasons.First,theyuseasimpleplurality(rst-past-the-post)electoralruleinsinglememberconstituencies, where17Cox(1997).Fujiwara(2011),KawaiandWatanabe(2013),Spenkuch(2014a),Spenkuch(2014b).18Moreformally,assumingvoters'preferencesarestableovertimeandstrategicvotingdrivestheentiretyofresults,arunner-upeectonwinningthenextelectionofxp.p.impliesthatx%ofelectionswithclosesecond-andthird-placecandidatesarecaseswherecoordinationfailedandthewinnerwouldhavelostatwo-candidateraceraceagainsttherunner-up.Moreover,thesex%ofcaseswillbe\corrected"inthenextelection,oncevoterscoordinate.Inreality,voters'preferencesovercandidateschangeovertime,andotherfactorsbeyondcoordinationmayplayaroleincreatingtherunner-upeect,butthegeneralassociationbetweenthesizeofoureectsandtheroleofcoordinationremains.Section5discussesthisissuefurther.5 thereisnodierentialtreatmentofsecond-andthird-placecandidates.Forexample,asimilaranalysisusingelectionsfromrunosystemswouldbeconfoundedbyrunners-uphavinglongercampaigns.Caseswithamixed-system(e.g.,theGermanBundestag)wouldalsobeproblematiciftherankoflosingcandidatesplaysaroleinassigningcandidatesto\partyseats."Additionally,thefocusonsimplepluralityallowsustointerpretourresultsinlightofstrategiccoordinationmodels,andtestfurtherpredictions.Thesecondreasonconcernsstatisticalpower.TheRDDanalysisrequiresalargenumberofelectionstoobtainpreciseestimates.Indeed,inSection3,wediscusshoweventheCanadianandIndianfederalelectionsamplesdonotyieldenoughpowertodetectrelativelylargeeectsforsomeoutcomes.WesearchedtheConstituencyLevelElectionsArchive-CLEA(Kollmanetal.,2013),aswellasthereferencesinEggersetal.(forthcoming),whichanalyzesRDDsfromcloserst-andsecond-placecandidatesinmultiplecontexts,forcaseswhereatleastvethousandsingle-memberpluralityruleelectionswouldbeavailable.TheonlycasesthatsatisedsuchrequirementsandarenotincludedinourmainanalysisareAmericanelectionsandBritishHouseofCommonselections.WedonotanalyzeAmericancontextsgiventheU.S.politicalsystemhastwoclearlydominantpartieswithfewmeaningfulthirdcandidates.Givenitsmultipartynature,AppendixA.3analyzestheBritishcase.However,resultsindicateitsuersfromasimilarissue,withclosesecond-andthird-placecandidateshavingnegligiblechancesofwinningthenextelection.19Themainoutcomesstudiedinthispaperarewhetheracandidaterunsin,andwins,asubsequentelection.Weusecandidates,nottheparties,astheunitofanalysisbecausecandidatesarepoliticallymoresalientinourcontextswiththelargestnumberofobservations(BrazilandIndianstates).Partymergers,splits,andchangeinnamesalsocomplicatemeasuringpartyoutcomesacrosstime,makingtheuseofcandidatesmoreappealing.Moreover,inIndianstateelections,21%ofsecond-andthird-placecandidatesareindependentswhowouldneedtobediscardedinaparty-levelanalysis.WhiletherearenoociallyindependentcandidatesinBrazil,municipalelectionsaretypicallynon-partisaninnature(Ames,2009),withcandidateidentitybeingmoresalientthanparty.Thisisespeciallytrueinsmallermunicipalitieswhichconstitutethebulkofoursample.Moreover,37%ofsecond-orthird-placecandidatesthatranagaindosounderadierentparty.AppendixA.2presentsresultsusingpartiesastheunitofanalysis;our main19Britishlocalelectionsinvolvemulti-memberconstituencies(withmostconstituenciesalternatingbetweensingle-andmulti-membercases)andisfurthercomplicatedbyatwo-tieredgovernmentstructure.MostelectionsintheCLEAinvolveproportionalrepresentationsystems,andmanyoftheelectionsanalysedinEggers(2014)involveeithermulti-memberdistricts,mixed-system(e.g.,Germany),orvariationsofrunos(e.g.,Australia,Bavaria,France).ExamplesofcasesthatarenotanalysedduetosmallsamplesizeareelectionsfromthePhilippines,NewZealand,severalAfricancountries,andMexico(forwhichcandidatelevelresultsarenotavailableinsomeyears).Finally,themajorityoflocalelectionsinSpainandItalyoccurunderproportionalrepresentationandrunosystems,respectively.6 qualitativeconclusionsremain.20Ouroutcomescaptureonlythecaseswhereacandidateranagainand/orwonaraceforthesameoceinthesameconstituency.Thisdecisionismostlydrivenbydataconsiderations:inIndiaandCanada,theonlyindividualidentierforeachcandidateishername,andmatchingacrossconstituenciesandoceswouldlikelyleadtoalargenumberoffalsematches.TherearerelativelyfewelectedocesintheIndianandCanadianparliamentarysystem,andIndianstatepoliticsisinparticularbasedonlocalconnections,makingitunlikelythatcandidateswouldswitchdistricts(exceptforinthecaseofasmallnumberofhigh-prolecandidates).IntheBraziliandataitispossibletoanalysehowoftencandidatesrunindierentconstituencies,whichoccurswithnegligiblefrequency.Finally,itshouldbenotedthatinallthecontextswestudy,thereisnoinstitutionaladvantageofbeingtherunner-upinsteadofthird-place.Forexample,theorderthatcandidatesappearontheballot,andallocationofpubliccampaignresources,donotdependonpreviouselectoralperformance.2.2Brazil:MunicipalMayorsBrazilcomprisesover5,000municipalities,eachwithitsownelectedmayor(Prefeito),whoisthedominantgureinmunicipalpolitics,withsubstantialcontroloverpublicspending.Federallawmandatesthatallmunicipalitiesholdelectionseveryfouryearsatthesamedate.Mayorsareelectedbypluralityruleat-large(i.e.,theentiremunicipalityisasingleelectoraldistrict).Ourdatacoverstheuniverseofmayoralelectionsinthe1996-2012period(veroundsofelections).ItwasobtainedfromtheBrazilianelectoralauthoritywebsite.21Municipalbordersaremostlystableduringtheperiod.22Forallyears,theElectoralAuthorityprovidesthecandidate'sname,voteridenticationnumber(TtuloEleitoral),party,andvotesreceived.Voteridenticationnumbersareocialdocumentsissuedbythefederalgovernmentanduniquetoeachperson.Wematchcandidatesacrosselectionsusingtheirvoteriden tication20ResultsforBrazilareattenuatedbyanamountthatcanbeexplainedbytheamountofpartyswitchingbycandidatesacrosselections.21http://www.tse.jus.br.Therearealsoelectionsformunicipalcouncils.Sincetheseuseproportionalrepresentation,theyarenotanalyzedinthispaper.Municipalitieswithmorethan200,000registeredvoterselecttheirmayorsunderarunosystem,andareexcludedfromoursample.Bye(orsupplemental)electionsheldoutsidetheocialdatesinBrazilareextremelyuncommon.Dataforpre-1996municipalelectionsisnotavailable.22Thereareasmallnumberofmunicipalsecessionsinthisperiod.Wematchedmunicipalitiesovertimeusingtheelectoralauthorityocialidentiers.7 numberand,whenthisismissing,theirname.23Wedeneacandidateasrunninginthesubsequentelectionifweareabletomatchhertoacandidatewhoappearsinthecandidatelistinthesubsequentelectioninthatmunicipality.Onlyanegligiblenumberofcandidatesrunforoceindierentmunicipalitiesintheperiod.Whilethefulldatasetconsistsof73,113candidatesin27,317electionsacross5,521uniquemunicipalities,only10,304raceshavethreeormorecandidatesandoccurredbeforethelastelectioninthesample(2012),allowingustoobservefutureoutcomes.242.3India:StateAssemblyElectionsEachIndianstateelectsaStateAssembly(VidhanSabha),alegislativebodyoperatingunderaparliamentarysystembyselectingtheexecutive(ChiefMinister).Membersareelectedbypluralityrulefromsingle-membergeographicunitsknownasassemblyconstituencies.EachAssemblyisformedforave-yeartermafterwhichallseatsareupforelection,butitcanbedissolvedearlierbyamotionofnocondenceortheexecutive'srequest.Inthecasewhereasittingmemberdies,abye-electionforonlyherseatisheld.WecollecteddatafromtheElectionCommissionofIndiawebsite25onallassemblyconstituencyelections,includingbye-elections,heldinIndiaoverthe1951-2013period.26Werstmatchconstituenciesovertimeusingconstituencynameandstate.Majorredistrictingoccurredin1972and2008whichcreatednewconstituenciesaswellasthere-denitionofoldconstituenciesinsomecases.Whenanewassemblyconstituencyiscreatedwedonotattempttomatchittotheassemblyconstituenciesitwascreatedoutof,butinsteadtreatitasanewseparateassemblyconstituency.TheElectionCommissionwebsiteprovidesthecandidate'sname,party,andvotesreceived.Thedatadoesnotprovideuniqueidenticationnumbersforcandidates,sowematchthemovertimeusingtheirnames.Foreachcandidatewesearchforwhetherthecandidate'snameappearsamongthecandidatesinthenextelectionheldinthesameassemblyconstituency.Themajorityofmatchesaremadeeitherexactly,bysubstitutinginitialsforrstandmiddlenames,changingtheorderofnames,orothersimplepermutationsofthecandidate'sgivenname.Whenacandidateismatchedacrosstwoelections,wedeneherashavingranintwosubsequent elections.23Voteridenticationnumbersaremissingforthe1996electiondata.Wecross-checkedthequalityofname-onlyandvoter-identication-basedmatchesusingdataforlateryears,andfoundthatanegligiblenumberofcandidatescouldnotbematchedbyname.Voteridenticationnumbersuseasystemofverifyingdigits(wherethelastdigitsareacomplexfunctionofpreviousones)thatminimizeissuesofmiscodingintheadministrativedata.24Twoelectionsresultedinthesecond-andthird-candidatesreceivingexactlythesamenumberofvotes.Wedroptheseobservationsasitisnotpossibletoassignthesecandidatestosecond-orthird-place.25http://eci.nic.in/eci_main1/index.aspx26Priorto1962someassemblyconstituencieshadmultiplerepresentativesinthestategovernment;weremovetheseconstituenciesfromouranalysis.8 Tojudgethequalityofourmatchingprocesswemanuallycheckedthematchingalgorithmforthetopthreecandidatesin20randomlyselectedelections.Ouralgorithmcorrectlyidentiedwhetherthecandidateraninthenextelectionfor88%ofthesesampledcandidates.Thefulldatasetconsistsof374,472candidatesin47,931electionsacross5,968uniqueassemblyconstituencies.Thevastmajorityofelectionshadthreeormorecandidates,andweobserve39,214electionswiththreeormorecandidatesandasubsequentelectioninthesameconstituency.272.4India:FederalLowerChamberWeusedataonIndianfederalparliamentary(LokSabha)electionsoverthetimeperiod1951through2009.Likeitsstatecounterparts,theIndianfederalgovernmentoperatesunderapar-liamentaryformofgovernmentwithelectionsatleasteveryveyears.Membersareelectedfromsingle-memberdistricts.Fortheperiodafter1974weusedatafromtheCLEA.For1951through1974weusedatafromtheElectionCommissionofIndiawebsite.28Sincenamesaretheonlyindividualinformationavailableoncandidates,wematchIndianfederalparliamentarycandidatesovertimeusingthesamematchingprocedurethatwasdevelopedfortheIndianstatelegislatureelections.29OurIndianfederalelectiondataconsistsof73,687candidatesin7,536electionsoccurringinatotalof1,227uniqueconstituencies.5,959electionshavethreeormorecandidatesandasubsequentelectionoccurringinthesameconstituency.2.5Canada:HouseofCommonsTheHouseofCommonsisthelowerchamberofCanada'sWestminsterstylefederalparliamentarysystem.MembersofParliament(MPs)areelectedatleasteveryveyearsbypluralityruleinsinglememberconstituencies(ridings).Thedatacoverstheuniverseofelectionsbetween1867and2011,andisfromtheCLEA.Sincenamesaretheonlyindividualinformationavailableoncandidates,weconstructthedatasetusingasimilarproceduretotheIndiandatasets.30Wealsomatchconstituenciesbynameandprovince,consideringconstituencieswiththesamenameoveryearsasthesameconstituency.Wehaveatotalof40,397candidatesintheCanadiandatacontestingin10,485electionsacross1,146constituencies.5,948electionshadthreeormorecandidatesandatleastonesubsequent election.27Eightelectionsresultedinthesecond-andthird-candidatesreceivingexactlythesamenumberofvotes.Wedroptheseobservationsasitisnotpossibletoassignthesecandidatestosecondorthird-place.28Intheelectionyearsbetween1951and1962therewereasmallnumberoffederalconstituenciesthatweremulti-member(i.e.morethanonerepresentativewaselectedfromoneconstituency);wedroptheseconstituenciesfromouranalysis.29Ourmanualcheckprocedurendsthatouralgorithmcorrectlyidentiedwhetheracandidateranagainornotinthenextelection89%forIndianfederalcandidates.30Ourmanualcheckprocedurendsthatouralgorithmcorrectlyidentiedwhetheracandidateranagainornotinthenextelectionfor100%ofsampledCanadiancandidates.Wealsoexcludeasmallnumberofcasesofmulti-memberridings.9 3Results3.1GraphicalAnalysisFigures1a-1ddepicttherunner-upeectforourfourcontexts.Thesampleineachgureincludesanycandidatethatcameineithersecond-orthird-placeinanelectionthreeormorecandidatescontested.Wedeneavariable\votesharedierencebetweensecondandthird,"whichforsecond-placecandidatesisequaltothecandidate'svoteshareminusthethird-placecandidate'svoteshare,andforthird-placecandidatesisequaltotheirvoteshareminusthesecond-placecandidate'svoteshare.Thisvariableisalwaysnegativeforthird-placecandidatesandalwayspositiveforsecond-placecandidates.Thex-axisinthesegurescorrespondstothisvotesharedierencevariable.Theverticallinerepresentsazerovotesharedierencebetweenthesecondandthirdcandidate,andindicatesthetransitionfromcandidateswhocameinthird-placetothosewhocameinsecond-place.They-axisshowstheprobabilitythatacandidatewithagivenvotesharedierencevariableranagaininthenextelection(triangles)orwonthenextelection(circles).Thetrianglesandcirclesinthesegurescorrespondtoalocalaverageoftheoutcomevariablecalculatedwithintwopercentbinsofthevotesharedierence;forexample,thetriangleimmediatelytotherightoftheverticallineisthefractionofsecond-placecandidateswhobeatathird-placecandidatebylessthantwopercentthatraninthenextelection.Thecirclejusttotherightoftheverticallineisthefractionofsecond-placecandidateswhobeatathird-placecandidatebylessthantwopercentthatwonthenextelection.Notethatthefractionofcandidateswhowinthenextelectioniscalculatedincludingbothcandidateswhodidanddidnotruninit(i.e.itisunconditionalonrunning).31Thecurvestotherightandleftoftheverticallinerepresentthepredictedvaluesofaquadraticpolynomialoftheoutcomevariableonthecandidate'svotesharedierence.Thepolynomialisttotheoriginalun-binneddataseparatelyforeachsideofthecuto.Toprovidesomecontextfortheseresults,AppendixFigureA.1presentsthenumberofobserva-tions(candidates)ineachofFigures'1a-1dbins.32AppendixFigureA.2repeatstheanalysisusingthecandidatevoteshare(attimet).Inallofourelectionsamples,thesecond-andthird-placecandidatesaroundthecutoreceive,onaverage,substantialvoteshareseach,between21%inCanadaandupto27%inBrazil.Thissuggeststhattherunner-upeectsweestimatearenotbasedprimarilyonsecond-andthird-placecandidateswhoreceivedveryfewvotes.Figure1ashowsthemainresultsforBrazilianmayors.Whilebarelythird-placecandidates(justleftofthecuto)ranagainroughly30%ofthetime,closerunners-upranagainabout40% of31WediscusstheissueofselectionintorunninginSection4.32Theseguresaresymmetricbecauseoursampleonlyincludeselectionswheretherewereatleastthreecandidates.Foreverysecond-placecandidatewithavotesharemarginof+xthereisonethird-placecandidatewithavotesharemarginof�xfromthesameelection.10 thetime,implyingasubstantial\jump"atthecuto.Thereisajumpofsimilarmagnitudeintheprobabilityofthecandidatewinningthenextelection.IntheIndianstatecase(Figure1b),closesecond-placecandidatesareapproximately5p.p.morelikelytorunand3.5p.p.morelikelytowinthenextelectionrelativetoclosethird-placecandidates.ThesizeofthejumpsinbothBrazilianmunicipalitiesandIndianstatesarelargerelativetothebinbybinvariationawayfromthecutos,suggestingthatthesedierencesarenotduetonoise.FortheIndianfederalsample(Figure1c),therealsoappearstobeadiscretejumparoundthecuto,althoughtheresultsarenoisier.Thisdierenceislikelyduetodierencesinsamplesizes:therearemoreelectionswithineachbinofthepreviouscasesthanintheIndianfederaldata.Forexample,thereareapproximately3,000second-placecandidateswhocameinsecond-placebylessthan2percentintheIndianstatedata,butonlyapproximately340intheIndianfederaldata(FigureA.1).Interestingly,themagnitudeoftherunner-upeecteectsintheIndianstateandIndiafederalelectionsappearquitesimilar.Figure1dshowsthatfortheCanadiansample,thereappearstobeasizeableincreaseintheprobabilitythatrunner-upcandidatesruninthenextelection,butlittlechangeintheprobabilitythattherunner-upcandidatewillwinthenextelection.Theeectsizeonrunningisabout5p.p.whichisapproximatelysimilartotheeectsizesintheIndianstateandfederaldata.IninterpretingourCanadianresults,itisusefultokeepinmindthat,unlikeourothersamples,Canadianparliamentaryelectionshaveaverylargeincumbencyadvantage(mostcandidatesnishingrstwillwinthenextelection).Thismakesitdicultforsecond-andthird-placecandidatestowinfutureelections;thecirclesinFigure1darewellbelowthelevelobservedintheothergures.TheeectsizefoundintheIndianandBraziliancaseswouldbeproportionallyenormous(andunexpected)intheCanadiancontext.Asidefromthediscretechangesinrunningandwinningprobabilitiesaroundthecutointhesegures,therearealsointerestingsimilaritiesintheslopestotheleftandrightofthecutos.Whilenotthemainfocusofouranalysis,itisusefultodiscusstwoofthesepatterns.Oneexpectedpatternistheupwardslopetotheleftofthecuto:moresuccessfulthird-placecandidatesaremorelikelytorun/winthenextelection.Thelessobviouspatternisthattheprobabilityofrunning/winninginthenextelectiontendstohavea\U"shapetotherightofthecuto.Runners-upthatbeattheirthird-placecompetitoreitherbyasmallorlargemarginfarebetterinfutureelections,whilecandidateswhobeattheirthird-placecompetitorbyanintermediatemarginfareslightlyworse.Suchapatternisexpectediftherunner-upeectsaredrivenbystrategiccoordination:closetothecutotherearealargernumberofsupportersforthethird-placecandidatethatcanstrategicallyswitchtowardsvotingfortherunner-up,whileawayfromthecutothatisnotthecase(perhapsbecauseinthoseelectionsthereiscoordinationontherunner-upattimet).However,anotherexplanationisthattherst-placecandidateisstrongestintheintermediatecase,andweakerintheextremes.In11 unreportedresults,weplotthewinner'svoteshare(att+1)againstthesamex-axisvariableandndthatitfollowsainverted-Upattern:electionsclosetothecutohaverelativelystrongsecond-/third-placecandidates,andweakrst-placecandidates;and,electionswithlargesecondversusthirdmarginsalsohaverelativelystrongsecond-/third-placecandidates.However,electionswithintermediatedierencesbetweenthesecond-andthird-placecandidateshavestrongerrst-placecandidates.33Asadditionalresults,AppendixFigureA.3providesplotsofthecandidate'svoteshareinthenextelection.Thefactthatvotesharesarenotobservedforcandidateswhodonotrunagaincomplicatestheinterpretationofthesegures;weassigncandidateswhodidnotruninthenextelectionavoteshareofzero.Consistentwiththeresultsonrunningandwinningagain,weseediscretejumpsinvotesharesasthecutoiscrossed.Finally,toassesswhetherthepreviouslydiscussedeectsmightbeduetootherdierencesbetweensecond-andthird-placenishersbesidestheirrank,Figures2a-2dplotacandidate'srunning(andwinning)statusinthepreviouselectionagainsthisvoteshareinthecurrentelection.Inotherwords,werepeattheanalysisusingpastinsteadoffutureoutcomes.Thereisnovisiblejumpatthecuto,indicatingthatbarelysecond-andthird-placecandidateshavecomparablepastperformanceinelections.Thisalsosuggeststhatitisunlikelythatotherdierencesbesidesthesecond-versusthird-placedistinctioncanexplaintheeectsinsubsequentelections.If,forsomeunexpectedreason,closerunners-upwereex-antesuperiorcandidatesthanclosethird-places,thatwouldalsoleadtoan\eect"inpastelections,underthenaturalassumptionthatsuchqualitydierencesarepersistentovertime.3.2EstimationFrameworkLetvictbethevoteshareofcandidateiintheelectionattimetinconstituencyc.Constituenciesaredenedastherelevantelectoraldistrict(e.g.,municipalitiesinBrazil,ridingsinCanada).AstherunningvariablefortheRDD,wealsodeneavariablevotesharedierencexictwhichforsecond-placecandidatesisequaltothecandidate'svoteshareminusthethird-placecandidate'svoteshare,andforthird-placecandidatesisequaltotheirvoteshareminusthesecond-placecandidate'svoteshare.Hence,positivevaluesindicatethecandidateistherunner-up,andnegativevaluesthatshenishedthird,withcandidateswithotherranksexcludedfromtheanalysis. 3433Manyobservableandunobservablevariablesmaychangesimultaneouslyaswemoveawayfromthecuto,makingitdiculttoisolatewhatdrivestheslopes.34Forexample,consideranelectioninconstituencycattimetwheresecond-placecandidateAobtainsa22%voteshareandthird-placecandidateB18%.InthiscasethexActvalueforthesecond-placecandidatewouldbe4%,andthexBctvalueforthethird-placecandidatewouldbe-4%.12 Thetreatmenteectofbarelyplacingsecondinsteadofthirdonoutcomeyictisgivenby:TE=limxict#0E[yictjxict]�limxict"0E[yictjxict](1)Undertheassumptionthattheconditionalexpectationofyictonxictiscontinuous,thersttermontherightsideconvergestotheexpectedoutcomeforasecond-placecandidatewhohasasmanyvotesasthethird-placecandidate.Similarly,thesecondtermconvergestotheexpectedoutcomeofathird-placecandidatewithasmanyvotesastherunner-up.Thelimitsontherightsideareestimatednon-parametricallyusinglocalpolynomialregressions.Thisconsistsofestimatingaregressionofyicton(apolynomialof)xictusingonlydatasatisfyingxict2[0�h;0].Thepredictedvalueatxict=0isthusanestimateofthelimitofyictasxict"0.Similarly,aregressionusingonlydatasatisfyingxict2[0;0+h]isusedtoestimatethelimitofyictasxict#0.Thedierencebetweenthesetwoestimatedlimitsisthetreatmenteect.Itisimportanttonotethenon-parametricnatureoftheestimation:althoughlinearorquadraticregressionsareused,theconsistencyoftheresultsholdsforanyarbitraryandunknownshapeoftherelationshipbetweenyictandxict.Thelimitapproachingonesideofthethresholdisestimatedusingonlydataonthatparticularside.ThelocalpolynomialregressionestimateisequivalenttotheOLSestimationofthefollowingequationusingonlyobservationsthatsatisfyx2(0�h;0+h):yict=1fxictΓ0g+f(xict)+ict(2)wheref(
)isapolynomialfullyinteractedwith1fxictΓ0g.Theestimateofisthetreatmenteect.Inthecaseofalinearspecication:f=+ xict+1fxictΓ0gxict.Thetwokeydecisionsinestimationarethebandwidthhandthepolynomialorder.OurpreferredspecicationusesalinearpolynomialwiththeImbensandKalyanaraman(2012)(IK,henceforth)optimalbandwidth,whichisitselfafunctionofthedata.Toinspectrobustness,wealsopresentresultsbasedonsmallerandlargerbandwidthsanddierentpolynomialorders.Weclusterthestandarderrorsattheconstituencylevel.353.3EstimationResultsTable1presentsourmainestimatesoftheimpactofcominginsecondplaceonwhetherthecandidaterunsinthenextelection(Candidacy,t+1),andwhetherthecandidatewinsthenextelection(Winner,t+1).The\3rd-pl.mean"columnistheestimatedvalueofthedependentvariableforathird-placecandidatewho\ties"withthesecond-placecandidate.Formally,itisanestimateoflimxict"0E[yictjxict],usingalinearspecicationandtheIKbandwidth,whic h35TheuseoflinearlocalregressionsissuggestedintheguidelinesbyLeeandLemieux(2010),whichwealsofollowinnotweighingobservations.13 isprovidedinthe\OptimalBWValue"column.Thesamplesizeofthisoptimalbandwidthspecicationisprovidedinbracketsinthesamecolumn.Column(1)providestheestimatedeectsbasedonourpreferredspecication,whichusesalinearpolynomialandtheIKbandwidth.Toproberobustnessoftheresultstospecicationandbandwidthchoices,columns(2)and(3)repeattheexerciseusingabandwidthequaltohalfanddoubletheIKbandwidth,respectively.Column(4)comparesthemeanoutcomebetweensecond-andthird-placecandidateswhoarewithinatwopercentdierencebetweeneachother(i.e.,itmatchesthedierencebetweenthemarkersoneachsideofthecutoonFigures'1a-1d).36Column(5)usestheentiresampleandtsaquadraticpolynomial.Consistentwiththepreviousgraphicalanalysis,theeconometricestimationndsevidenceoflargerunner-upeects,regardlessofspecication/bandwidth.Ourpreferredspecicationindicatesthatbarelysecond-placedBraziliancandidatesare9.4p.p.morelikelythanbarelythird-placecandidatestorunagain.Thisisalargeeectgiventhat30.3%ofbarelythird-placecandidatesrunagain.Moreover,theyarealso8.3p.p.morelikelytowinthenextelection(whileonly9.5%ofclosethird-placecandidatesdoso).Theeectsonfuturecandidacyandfuturewinningarebothsignicantatthe1%levelundertheIKbandwidth.Themagnitudeandsignicanceoftheeectsiscomparableinotherspecications.AppendixFigureA.4providesestimatesforawidechoiceofbandwidths.InthecaseofIndianstatelegislators,closesecond-placecandidatesare4.4p.p.morelikelytoruninthenextelectionand3.4p.p.morelikelytowinthenextelection.Thesearesizableincreases,sinceclosethird-placecandidatesrunagain,andwin,31.9%and7.8%ofthetimerespectively.Theseeectsareallsignicantatthe1%level,androbusttodierentspecications/bandwidths.AppendixFigureA.5providesestimatesforawidechoiceofbandwidths.Wendsimilar-sizedeectsforfederalIndianelections(althoughthird-placemeansareslightlylower).Theseeectsaresignicantinfouroutofourvespecicationsforthecandidacyvariableandthreeoutoftheveforourwinningvariable.ThefactthattheeectsarenotasrobustintheIndianfederalcontext(comparedtoBrazilianandIndianstateelections)canbeattributedtothesmallersamplesize,andhighlightstheneedtouseasamplewithmany(perhapstensofthousands)elections,asdiscussedinSection2.TheCanadiandataalsoshowasizable(andstatisticallysignicant)eectofrunningagainthatissimilartotheIndiancase:a4.6p.p.increaseovera17%third-placemean.Theeectsonwinningthenextelectionareclosetozeroandstatisticallyinsignicant.However,itisdiculttoconcludethereisnoeectfortworeasons.Asmentionedbefore,theoverallchanceofathirdorsecond-placecandidatewinningissmallerintheCanadiancontext,withbarely third-place36Werefertothisasthe\zeroorder"polynomialspecication.14 candidateswinningthenextelectiononly2.4%ofthetime.37Henceanypotentialeectwillnecessarilybesmallanddiculttodetect.Forexample,thestandarderrorinColumn(1)is0.9p.p.,implyingthataneectof1.7p.p.(increasingtheprobabilityofwinningthenextelectionbymorethan70%)wouldnotbesignicantatthe5%level.Totestforcovariatesmoothness(orbalance),Table2checkswhetherclosesecond-andthird-placecandidatesdieronpre-existingcharacteristics.TheresultsconrmthegraphicalevidenceinFigure2thatcloserunners-uparenotmorelikelytohaveraninorwonthepreviouselection.Thetablealsotestswhetherclosesecond-placecandidatesaremorelikelytohavereceivedgreatervoteshareinthepreviouselection,orwhethertheyaremorelikelytobefromthemajorpartyinthecountry.38Weassignavoteshareofzeroforcandidatesthatdidnotruninthepreviouselection.Notethatanyvariablethatdoesnotvaryacrosssecond-andthird-placedcandidateswithinanelection(e.g.,turnout,thevoteshareofthewinner,constituencydemographics)isbyconstructionbalanced.Theonlyinstancewhenwendanimbalanceatthecut-oinTable2isthatCongresspartycandidatesappearlesslikelytohavecomeinsecond-placethanthird-placeinIndianstateelec-tionswhenweusethefullsampleandaquadraticmodel.Thisresultisnotapparentwhenweestimateitinthemorerelevantregion(undertheoptimalbandwidth);also,visualinspectionsuggeststhatthequadraticmodelusingthefullsamplendsadierencebecauseittsthecurvebetterawayfromthecutoandpoorlyaroundit,generatingacaseofmistakinganonlinearityforadiscontinuity(AppendixFigureA.10a).Inadditiontoshowingbalanceonthefractionofcandidatesfromthemajorpartiesineachofoursamples,wealsoconductedageneraltestforimbalancebasedonpartiesasfollows.Weregressadummyforwhetherthecandidatecameinsecondonindicatorsforeverypartyinthesample.Wethentakethepredictedvaluesfromthisregressionandtestwhetherthesepredictedvaluesjumpdiscretelyatthecuto(i.e.,wetreatitasanothervariableinTable2).Ifcertainpartiesweremorelikelytocomeinsecondorthird-placearoundthecuto,weexpectthesepredictedvaluestoincreasediscretelyaroundthecuto.Inallfourofourcontextswendnoevidencethatpartycanpredictcandidaterank.Theseresultsareavailableuponrequest. 3937Aspreviouslydiscussed,thisislikelyduetoincumbentsbeingmorelikelytobere-electedinCanada,comparedtoothercontexts.38Wedenethemajorpartyasthepartywiththemostcandidatesoverallineachdataset.CongressisthemajorpartyinIndia,LiberalisthemajorpartyinCanada,andtheBrazilianDemocraticMovement(PMDB)isthemajorpartyinBrazil.39AsimilartestisdiscussedinFujiwara(2013),whichbuildsonaprocedurefromCardetal.(2009).15 3.4ComparisonofRunner-UpandIncumbencyEectsAppendixTableA.1providesresultsonthesizeoftheincumbencyeect(closerst-versussecond-placecandidates)foreacheachofoursamples;theseresultsprovidesomebaselineagainstwhichtoascertaintheeconomicsignicanceoftherunner-upeectsestimatedabove.FigureA.6showsthesizeoftheimpactofcominginrst-placeversussecond-placeonprobabilityofrunningagainandwinningagaininthenextelectionrespectivelyinourfoursamples.40Inallfourofourcontextsbeingtheincumbentincreasestheprobabilityofrunningagain.41InBrazil,therunner-upeectonrunningagainisactuallylargerthantheincumbencyeectinouroptimalbandwidthspecications,9.4p.p.versus8.3p.p.IntheIndianstatesample,therunner-upeectonrunningagainof4.4p.p.isalsoreasonablylargerelativetoanincumbencyeectonrunningagainof9.5p.p.ThecomparisonbetweenIndianfederalrunner-upeectsonrunningagainissimilartothecomparisonforIndianstateelections.Giventhatrunners-updonotholdoce,itisstrikingthatthemagnitudeoftherunner-upeectsonrunningagainissizeablerelativetotheincumbencyeects.Thissuggeststhepossibilitythatalargeportionoftheincumbencyeectoncandidacymaycomefromfactorsunrelatedtoholdingoce(wereturntothisissueinourconclusion).TheexceptionisCanada,wheretherunner-upeectismuchsmallerrelativetothelargeincumbencyeect.Regardingtheeectonwinningagain,wend,consistentwithUppal(2009)andLinden(2004),thatincumbentsareslightlydisadvantagedinfutureelectionsinBrazilandIndia.Thepointestimatesareclosetozero(andstatisticallyindistinctfromit)inthecaseofIndianfederalelectionsandBrazilianmayors.Interestingly,thisimpliesthatwendtherunner-upeectonbothrunningagainandwinningincontextswheretheincumbencyeectisvaried.Inparticular,theresultsfromIndianstatesindicatingpositiveeectsofcominginsecond-place,butanegativeeectofcominginrst-place,makeuslessconcernedthatthereissomemechanicalreasonforcandidateswithhigherrankstoperformbetterinfutureelections.WendlargeincumbencyadvantagesinCanada,consistentwithKendallandRekkas(2012).3.5ComparisontoThird-VersusFourth-PlaceEectItispossiblethatthesamemechanismthatcausesrunners-uptoruninandwinmorefutureelectionsisalsoageneraleectofrank,whichwouldcausethird-placecandidatestooutperformclosefourth-placecandidates.Usingthesameapproachappliedtovisualizetherunner-upeect,Figure3plotsourmainoutcomesagainstthevotesharedierenceinsamplesofthird-andfourth-placecandidates.Wendnoevidenceofajumparoundthecuto.Theseguresdosho w40Wealsoexaminedguresregardingthecovariatesmoothnessfortheseeects(omittedduetospaceconsid-erations),andfoundnoevidenceof\eects"onpre-determinedvariables.41InBrazilmayorsaresubjecttoatwo-termlimit,wehencelimittheestimationtocandidateswhoarenotincumbentsatt,andhence,inthecasetheywin,wouldbeabletorunforre-electionatt+1.16 whatappearstobeadiscreteincreaseinslopearoundthecutobetweenthirdandfourthplace.However,thisincreaseinslopewasalsoapparentinthecorrespondinggureswheretheoutcomevariableisrunningorwinningapreviouselection(notreportedduetospaceconsiderations).Thischangeinslopethereforemostlikelyre ectsincreasingunobservablequalityofthird-placecandidatesasthevotesharedierencebetweenthird-andfourth-placecandidatesincreases.Table3presentsourregressiondiscontinuityestimatesoftheeectofcominginthirdversusfourth.Thereareafewspecicationsthatshoweconomicallysmallbutstatisticallysignicanteects,but,overall,thereisnorobustresultofthird-placecandidatesrunningorwinningthenextelectionrelativetofourth-placecandidates.Itseemsunlikelythatcominginthird-place,insteadoffourth,hasacausalimpactoncandidates'futureoutcomes.424BoundsonEectsConditionalonCandidacyAssumingacandidatewillchoosetorun,howmuchdoesbeinglabeledtherunner-upincreasetheprobabilitythatshewillwin?WhiletheRDDensuresthatbarelysecond-andthird-placecandidatesare,onaverage,similar,itdoesnotimplythatthosewhorunagainafterbarelycominginsecondaresimilartothosewhorunagainafterbarelycominginthird.Forexample,higherabilitycandidatesmightbemoreawarethatvoters,themedia,orparties,provideanadvantagetorunners-up.Inthiscase,candidatesthatchoosetorunagainaftercominginthird-placemightbelowerqualitythancandidatesthatchoosetorunagainaftercominginsecond-place.Toestimatetherunner-upeectontheprobabilityofwinning,conditionalonrunning,wemustaccountforthefactthatbarelycominginsecond-placemaycauseselectionintorunning.WeadaptamethodbyLee(2009)toestimateboundsontherunner-upeectoftheprobabilityofacandidatewinningasubsequentelectionconditionalonrunning.LetS,R0,R1,W0,andW1bebinaryindicators.Sdenotesifacandidatenishedsecond(asopposedtothird)inaraceattimet.R0andR1are\potentialoutcome"indicatorsforthecandidaterunningatthenext(t+1)electionwhenS=0orS=1,respectively.Weonlyobserveagivencandidate'sdecisiontorunaseitherthesecond-orthird-placecandidate;forexamplewedonotobservewhetherasecond-placecandidatewouldhavechosentorunagainifhehadcomeinthird-place,henceonlyR=SR1+(1�S)R0isobserved.Similarly,letW0andW1bethepotentialindicatorsofwinningtheelectionatt+1.Thesepotentialoutcomesequaloneifacandidatewinsthenextelection,hadshechosentorun.NotethatthisdenitionallowsforagivencandidatetohaveR0=0andW0=1;inthiscase,acandidatechoosesnottorunifshecomesinthird,butw ould42Similarly,wedonotndevidenceofeectsofevenlowerranks,aswellasaneectoflastplace.17 wintheelectionifhechosetorun.43OnlyW=R[SW1+(1�S)W0]isobserved,capturingboththefactthatacandidateisonlyobservedafteronespecicrank,andthatweonlyobserveifshecanwinifsheruns.44Withoutlossofgenerality,therearefourtypesofcandidatesinoursample.Thersttypearethosewhowouldchoosetorunagainregardlessofwhethertheycameinsecond-placeorthird-place(i.e.R1=R0=1).ToemphasizethesimilarityofourapproachandLee(2009),werefertotheseasthe\always-takers."Thesecondtypeare\never-takers",whochoosenottorunagain,regardlessoftheirrank(R1=R0=0).Thethirdtypeofcandidatesarethe\compliers";thosewhowouldchoosetorunagainiftheycameinsecond-place,butwouldnotdosoiftheycameinthird-place(R1ΓR0).Lastly,therearethosecandidateswhowouldchoosetorunagainiftheycameinthird-place,butwouldnotchoosetorunagainiftheycameinsecond-place(R1R0):the\deers."Thekeyassumptionisthattherearenocandidatesinthe\deers"group;allcandidateswhocomeinthirdandchoosetorunagainwouldalsohavechosentorunagainiftheyhadcomeinsecond-place.Whileitisnotpossibletotestthisassumptiondirectly,thisisplausiblegiventhatwendthatcominginsecond-placeisapositivesignalofacandidate'sfutureelectoralsuccess;acandidatewhochoosestorunagainwhencominginthird-placebutnotrunagainwhencominginsecond-placewouldbeturningdowntheopportunitytorunonlywhenthereislikelyagreaterchanceofwinning.Notealsothatthis\monotonicity"conditionisastandardassumption(sometimesimplicitly)invirtuallyallproceduresthatcorrectforsample-selection,asdiscussedinLee(2009).S,R0,R1,W0,andW1canbethoughtofasfunctionsofthecandidateandtheRDDrunningvariable(x),andundertheassumptionthesevariablesarecontinuous,theirlimitsatthecuto(x=0)canbeapproximatedwiththepreviouslydiscussedmethods.Undertheassumptionofnodeers,andomittingtheictsubscripts,wehave:45Eectonwin,cond.onbeingalways-taker/complier z }|{E[W1�W0jx=0;R1=1]= 1E(R1jx=0) | {z}limx#0E[Rjx][(E(W1R1�W0R0jx=0) | {z}RDeectonW�Prob(R1ΓR0jx=0) | {z}RDeectonR
E(W0jx=0;R1ΓR0) | {z}Unobservable] (3)43ThedenitionalsoallowsR1=0andW1=1(acandidatewhowouldwinthenextelectionifshecameinsecondinthecurrentelection,butchoosesnottorun).44Thisimpliesthat,forexample,E[WjxΓ0]=E[W1\R1jxΓ0]6=E[W1jxΓ0],sincethelasttermistheexpectedprobabilityofwinningofallsecond-placecandidates,hadtheychosentorun,andweonlyobservewhethercandidatesthatruncanwinornot.45Followingtheprevioussection,forsecond-placecandidatesletxbehervoteshareminusthethird-placecandidate'svoteshareinthesamerace;forthird-placecandidates,xishervoteshareminustherunner-up's.Notewenowomittheictsubscriptstosimplifynotation.18 DerivationsareinAppendixA.1.Theleftsideofthisequationistheeecttobeestimated:thedierenceinprobabilityofwinningforacandidateatthecutoconditionalonthecandidatebeingthetypewhorunsagainafternishingsecond(always-takersandcompliers).Thetermsontherightsideofthisequationareasfollows.E(R1jx=0)istheshareofcompliersoralwaystakersaroundthecuto,ortheshareofbarelysecond-placecandidateswhorunagain.ItcanbeestimatedasthelimitasE[Rjx]approachesthecutofromtheright.E[W1R1�W0R0jx=0]istherunner-upeectonwinning,unconditionalonwhetherthecandidaterunsagain(aswehavereportedsofar).Prob(R1ΓR0jx=0)istheshareofcompliersaroundthecuto,whichisalsotheestimatedrunner-upeectonrunningagain.46Thetermsontheright-handsidedescribedsofarcanallbeobtainedasestimatesfromTable1.TheonlyunobservabletermisE[W0jx=0;R1ΓR0],theprobabilityofwinningafteraclosethird-placenishforacomplier(who,bydenition,doesnotrunafterathird-placenish).Givenanassumptionofthelargestandsmallestpossiblenumberforthisprobability,alowerandupperboundontheeectcanbecalculated.Sinceprobabilitiesarenotnegative,theupperboundcanbeobtainedbypluggingE[W0jx=0;R1ΓR0]=0intoequation(3).Intuitively,thelargestpossibleeectoccursundertheassumptionthatclosethird-placedcomplierswouldneverwinthenextelectionhadtheychosentoruninit.Similarly,themostconservativepossiblechoiceforalowerboundwouldbetoassumethatallcomplierswouldwinforsureafternishingthird(E[W0jx=0;R1ΓR0]=1).However,thisnumberisunreasonablyhigh.First,thiswouldimplythatalargenumberofcandidateswhowouldwinforsuredecidenottorun.Second,theprobabilitythataclosethird-placecandidatewhorunsagainwinsthenextelectionis31%inBrazil,around25%inbothIndiancontexts,andbelow15%inCanada.Itisunlikelythatthechancesofwinningforthird-placecandidateswhodecidednottorunwouldbemorethanthreeorfourtimeslargerthanforthosewhochosetorunagain.Amorereasonableassumptionisthatthird-placecomplierswouldhaveatmostthesameprob-abilityofwinningassecond-placenisherswhodidchoosetorun.Thisisarguablyaveryconservativeapproach,sinceonewouldexpectcompliers(whodecidednottorunafterathird-place)tohaveevenloweroddsofwinningthanthealways-takers,andespeciallysinceweareinputtingtheprobabilityofthemoresuccessful(att+1)second-placecandidates.Finally,ourdiscussionbelowwillshowthatthelowerboundisabovezeroevenundermoreconservativeassumptions.Toillustratetheprocedure,taketheestimatedmagnitudesinColumn(1)ofTable1fortheBraziliancase:E(R1jx=0)=30:3%+9:4%=39:7%;E[W1R1�W0R0jx=0]=8:3%;andProb(R1ΓR0jx=0)=9:4%.OurassumptionfortheupperboundimpliespluggingE(W0jx =46NotethatProb(R1ΓR0jx=0)doesnotdependonwhichsideofthecutothecandidateison,sincetheunderlyingfractionofcompliersisnotaectedbythe\treatment."19 0;R1ΓR0)=17:8%=39:7%=44:8%,toobtainalowerboundof10.3p.p.Analogously,themostconservativeupperboundwouldbe20.9p.p.Eectsinthisrangearesubstantial,giventhatclosethird-placecandidateswinlessthanathirdofthetimetheyranagain.InIndianstateelectionsthelowerandupperboundunderthesameprocedureare5.9p.p.and9.6p.p.,andforIndianfederalelectionstherespectiveestimatesare4.2p.p.and9.5p.p..Thesearesizableincreases,sinceclosethird-placecandidateswhorunagainhaveapproximatelya25%chanceofwinninganelectioninthesecontexts.Overall,theresultsinourBrazilianandIndiansamplessuggestthatbarelycominginsecond-placehasasizeableimpactonacandidate'sprobabilityofwinningbeyondjusttheeectonrunning.TheonlycasewheretheboundsincludezeroisCanada,wheretheunconditionaleectonwinningisasmallnegativenumber.Inthiscase,theconditionaleectisboundedbetween-1.7p.p.and0.9p.p..Anotherrelatedapproachwouldbetouseequation3toseehowlargetheunobservableproba-bilityofaclosethird-placedcomplierwouldhavetobeinorderforalltheeectonwinningtobeexplainedbyselectionintocandidacy.Inotherwords,wecansolvefortheE(W0jx=0;R1ΓR0)thatsetsthelefthandsideofequation3tozero.IntheBraziliancase,aclosethird-placecom-plierwouldhavetowin88.3%toimplythatthereisnorunner-upeectonwinningconditionalonrunning.IntheIndianstateandfederalcase,therespectivevaluesare79.5%and56.3%.Thesenumbersaretoolargetobeplausible.Fortheeectsonwinningtobeexplainedentirelybyselectionintorunning,theprobabilityof\compliers"winningwouldhavetobeextremelylarge:multipletimestheprobabilityofthethird-placedcandidatesweobservethatrun(the\alwaystakers"),andinthecaseofBrazilandIndianstates,wellabovethatobservedforverysafeincumbents.5Mechanisms5.1StrategicCoordinationUnderthestrategiccoordinationmechanism,someagentswouldhavepreferredeitherthesecondorthird-placecandidateoverthewinner,andinthenextelectionwishtocoordinatetheirsup-portononeofthem.Therunner-uplabelservesasafocalpointforpotentialcoordination.Suchcoordinationmightoccurbothwithinandacrossvoters,donors,parties,candidates,orother\elites"thatin uencevotes.Akeypartofthisargumentisthatthesecond-place\label"isamorelikelyfocalthanathird-placelabel.Whilethiscannotbetesteddirectly,itisconsistentwithbehaviorofvotingexperimentsdiscussedintheintroduction(Forsytheetal.,1993;Boutonetal.,2012).Moreover,ageneraltendencytocoordinateoncandidateswithbetterpreviousperformanceisreasonable,andperhapsthisnormisextendedtothecaseswherethepastdif-ferencesinperformancebecomeverysmall(\atthecuto").Ofcourse,theargumentisnot20 thatallrunners-uparefocal,butthattheyhaveahigherchanceofbeingfocalthanthird-placecandidates-othercharacteristicsmaybeusedasfocalpointsaswell.Strategiccoordinationalsoprovidesinsightsintowhytherunner-upeectonwinningsubsequentelectionsislargerinBrazilthaninIndia,andclosetozeroinCanada.Inthelattertwocontexts,electionsareformembersofalarger(stateorfederal)legislature,andperhapstheexpectedlegislature-wideresults(e.g.,whichpartiesmayformamajorityoropposition)canalsoserveasfocalpoints.InBrazil,mayoralelectionsareforanindividualexecutiveoce,largelynon-partisan(Ames,2009),andheldatdierenttimesfromstateandfederalelections,makingpastelectoralperformanceamorelikelyfocalpoint.Moreover,thesmallesteectsarefoundinthecontext(Canada)withthestrongestparties,whichperhapsservealsoserveasthefocalpointforcoordination.However,therearemanyotherdierencesacrossthesecontextswhichcouldalsoaccountforthesedierences.Analysingourempiricalresultsinlightofthetheoryofstrategicvotingundersimpleplurality(MyersonandWeber,1993;Cox,1997;Myerson,2002)yieldssomeinterestinginsights.Thesemodelssuggesttwopossibletypesofequilibria,theDuvergeriantypewherecoordinationleadstotwocandidatesattractingmost(orall)ofthevotes,andthenon-Duvergeriantypewherecoordinationfailsandthereisatiebetweensecond-andthird-place.TheelectionsaroundthecutoinourRDD(whichdetermineourmainresults)tthenon-Duvergeriandescription.Hence,therunner-upeectcanbeseenaspartoftheprocessinwhichconstituenciesmovefromonetypeofequilibriatoanother,withrankbeingthefocalpointthatallowscoordinationfailuretobesolved.Sincethenon-Duvergerianequilibriaare\knife-edge"or\expectationallyunstable"(Palfrey,1988;Fey,1997),itisperhapsexpectedthatconstituencieswouldmoveawayfromitwithinthetimespanofoneelection.Therearetwootheraspectsofourdatathatfurthermatchesthisinterpretation.First,AppendixFigureA.1showsthatthedistributionoftherunningvariable(thevotesharedierencebetweensecond-andthird-placecandidates)inIndiaandBrazilhastwomodes:onewherethecandidatestieandonewherethesecond-placehasalargemarginoverthethird.Thisimpliesthatthemodalcasesmatchthedescriptionofbothtypesofequilibria.47Second,whilethecasesaroundthecutoare,byconstruction,characterisedbytimetelectionswherethedierencebetweensecondandthirdissmall,bytimet+1theyexperienceelectionswherethesecond-place(denedint+1)hasasizablemarginoverthethird-place,andwherethetoptwocandidatesconcentratemostofthevotes.48Thisisconsistentwithcasesaroundthecutobeingunstablenon-Duvergerianequilibria,whichbecomeDuvergerianattimet+1.Thisinterpretationalsosuggestsalinkbetweenthemagnitudesoftherunner-upeect and47Cox(1997)labelsthispatternasthe\bimodalityhypothesis"anddocumentsitinothercontexts.Healsointerpretsthisndingasevidenceofstrategiccoordination.48Theseresults,omittedduetospaceconsiderations,areavailableuponrequest.21 therelevanceofcoordinationfailures(anditssubsequentcorrection)inelections.Ifindeedtheentiretyoftheresultisdrivenbythemovebetweenthetwotypesofequilibria,thenaxp.p.runner-upeectonwinningthenextelectionimpliesthatx%ofcloseelectionsarecasesofdividedmajoritiesthatfailedtocoordinate,butthatswitchintocoordinated(Duvergerian)equilibriumbythenextelection.Hence,thendingofsizeablemagnitudesimpliesthatdividedmajoritiesfailingtoelecttheirpreferred(Condorcet-winning)candidateisnotonlyatheoreticalcuriosity,butarelativelyfrequentreal-worldphenomenon.Thisinterpretation,however,requiresassumptionsonthestabilityofvoters'preferences(e.g.,thatdividedmajoritiesexistinbothtimetandt+1),aswellastheentiretyoftherunner-upeectbeingdrivenbythetheoreticalmechanismdescribedabove.Whiletheevidencesuggestsitsimportance,itisunlikelythatnootherfactoralsoplaysarole.Finally,wereiteratethat,whilethediscussionaboveisbasedonmodelswherevotersactstrate-gically,itispossiblethatthestrategiccoordination(thatultimatelyshiftsvoteshares)occursatadierentlevel.Candidates,parties,and/orotherelitesareperhapscoordinatingtheirsupportandrelyingonelectionrankingstodoso.Thelimitationsinourdatadonotallowtodierentiateacrossthesepossibilities.Thenextsubsectionprovidefurthertestsofthepredictionsofstrategicvoting.5.1.1StrategicSwitchingfromThird-toSecond-PlaceThemostdirectpredictionofthestrategiccoordinationmechanismisthattherunner-upeectshouldbedrivenbyvoterswhosupportedthethird-placecandidateattswitchingtowardsvotingfortherunner-upattimet+1.Ideally,wewouldusedataonindividualvotechoicesovertimetomeasurethisdirectly.However,dataonindividualvotesistypicallynotavailablegivenballotsecrecy,soweapproximateusingdatafromBraziliansub-constituencylevelresults.49Brazilianmunicipalitiesaredividedinto\electoralsections"whicharethespecicballotboxeswhereavotermustcasthisvote.Sectionshavebetween50and500voters(averaging256votesperelectioninoursample),withtheaveragemunicipalityhavingapproximately60sections.Sinceavotercanonlycasthervoteinherregisteredsection,andvotersareunlikelytochangesectionsbetweenelections,thisallowsustotracksmallgroupsofvotersovertimetoa rst-order49SimilardataisnotavailablefortheIndianandCanadiancases.22 approximation.50Weareinterestedinthedescriptivepatternofwhetherelectoralsectionsthattendedtovoteforthird-placeattimetaremorelikelytobevotingfortherunner-upattimet+1;relativetoelectoralsectionsthattendedtovoteforothercandidates.Weestimatethefollowingregressionmodeltotestthishypothesis:v2ij;t+1=1v1ij;t+2v2ij;t+3v3ij;t+ j;t+ij;t(4)wherevkij;tisthevoteshareofthekthplacecandidateinelectoralsectioni,inconstituency(municipality)j,inthetimetelection.Notethatthekthplacecandidateisdenedattheconstituencylevelattimet.51 j;tisaconstituency-time(election)levelxedeect,i.e.,wefocusoncomparisonswithinaspecicelectionacrossdierentelectoralsections.Theinclusionofthesexedeectscapturestheeectofanyfactorthatdoesnotvaryacrosssectionswithinanelection,suchaswhichcandidatesfromtimetdecidedtorunagain,aswellastheoverallstrengthofparticularcandidates.Fortheinterpretationofthecoecients,itisimportanttonotethatvotesharesmustaddtounity.Hence,3Γ1impliesthatsectionsthattendedtovoteforthethird-place,asopposedtovotingfortherst-place,aremorelikelytobevotingfortherunner-upattimet.Anincreaseinasection'svoteshareofthethird-placeof1p.p.(attheexpenseofa1p.p.decreaseinthevoteshareoftherst-place)isassociatedwith3�1p.p.highervotesharefortherunner-upattimet+1.Sincethecategoryomittedtoavoidcollinearitybetweenregressorsisthevoteshareoffourthandlowercandidates,3Γ0indicatesthatsectionsthattendedtovoteforthird-placeatt(asopposedtovotingforfourthandlowercandidates)aremorelikelytovotefortherunner-upatt+1.Weestimatetheequationaboveonlyfor\close"electionswherethevotesharedierencebetweensecondandthirdarebelow2p.p.(denedattheoverall,constituency-wideresult,andnotattheelectoralsectionlevel).TheRDestimatesreportedintheprevioussectionprovidestheeectofrankfortheseelections,andhenceweareinterestedinthewithin-constituencypatternsforthesecases.Finally,thedependentvariableinequation(4)isonlyobservablewhentherunner-uprunsatt+1.Sincetheestimationexploitsonlywithinconstituency-timevariation,and the50Avotercanonlychangehersectionifshemovestoanaddresssucientlyfarfromtheoriginalone(eitherwithinoroutsidethemunicipality).Moreover,thevoterhastorequestthechangeofthevotingsectionherself,socitizenswhonditmoreconvenienttocontinuetovoteintheiroriginalsection(asopposedtogoingthroughthere-registrationprocess)willdoso.Thereisno\redistricting"ofelectoralsections,andnewsectionsareusuallycreatedtoaccommodatenewlyregisteredvoters.Thereisnoavailabledataallowingustoidentifyvotersinanelectoralsectionacrossyears,andassessthemagnitudeofmigrationacrosssections.TurnoutismandatoryinBrazil,reducingconcernsthatthesetsofvotersthatturnoutinaparticularsectiondierfrompreviousyears.Corroboratingthenotionthatelectoralsectionsmostlyinvolvethesamegroupofvotersacrossyears,wendastrongcorrelationbetweenthevoteshareofspeciccandidatesinasectionacrossyears,evenwhencontrollingformunicipality-year(election)xedeects.51Forexamplev2ij;t+1isthevoteshareattimet+1oftherunner-upoftheelectionthathappenedattimet(nott+1)inmunicipalityj(shemaynotbethesecondmostvotedcandidateinelectoralsectioni).23 decisiontoruncannotvaryatthisdimension,usualsampleselectionbiasisnotanissue.Wealsoreiteratethedescriptivenatureofequation(4).Theobjectiveisnottouncovercausaleectsofincreasingvotesharesattonvotesharesatt+1,butwhetherornot,intheelectionswhentherunner-uprunsagain,itisthecasethat(groupsof)votersthatvotedforthethird-placetendtoswitchtotherunner-up.Ourmainsampleisformedby8,738sectionsfrom144elections.52Table4presentstheresults.Columns(1)-(4)presentspecicationswherethedependentvariableisrunner-upvoteshareattimet+1.Asarobustnesscheck,columns(2)and(3)reducethesampletoelectionswherethevotesharedierencebetweensecondandthirdwaslessthan1%and0.5%,respectively.Column(4)returnstocolumn(1)'ssample,butnowdropselectionswheretherewereexactlythreecandidatesattimet,tomakesuretheeectsarenotdrivenbyelectionswherevotingforafourthcandidatewasnotanoption.Columns(1)-(4)showverysimilarresults:conditionalonthevotesharetherunner-upreceivedattimet,switching1p.p.votesharefromrsttothirdiscorrelatedwithapproximately0.15p.p.increaseintherunner-up'svoteshareattimet+1.Thedierence3�1issignicantattheonepercentlevelinallofthesespecications.Thecoecient3islargeandsignicantonitsown,indicatingthatsectionswherethethird-placecandidatereceivedalargevoteshareattimetaremorelikelytovotefortherunner-upattimet,relativetoelectoralsectionsthatvotedmoreforcandidatesthatcameinfourthorbelowattimet.Wealsoconsistentlyndalargeandpositivecoecient2,suggestingstrongserialcorrelationinvotingbehaviorattheelectoralsectionlevel.Columns(5)and(6)presentresultsfromthesameregressionasincolumn(1),howevernowthedependentvariableisthevoteshareofthethird-andrst-placecandidate,respectively.ItisinterestingtonotethatinColumn(5)wendgreatervotesfortherunner-upisalsocorrelatedwithgreatervotesforthethird-placecandidateattimet+1.Oneexplanationforthisresultisthatinsomeoftheseclosesecond/thirdelectionsvoterschoosetocoordinateonthethird-placecandidate(forexampleifthethird-placecandidatehassome\focal"characteristic.)Itisimportanttonotethatwedonotobserveacorrelationbetweenthird-place'svoteshareattandtherst-placevoteshareatt+1inColumn(6);thissuggeststhatourmainresultofvotersswitchingfromthirdtotherunner-upisnotdrivenbysomegeneraltendencyofsupportersofthird-placecandidatestoswitchmoreoftenthanothervoters.Instead,itappearsthattheytendtospecicallyswitchtovotingfortherunner-up.ThendingsinTable4arediculttoreconcilewithanexplanationentirelybasedonagentsactingheuristically,andwithoutstrategiccoordination,sincesuchanexplanationwouldhavetodisproportionatelyaectthesupportersofthird-placecandidates.Forexample,supposepartiesuseaheuristicwheretheychoosecandidatesbasedonrankingsinsteadofunderlyingvote share,52Inputtingat+1voteshareofzeroforthecaseswheretherunner-updoesnotrunagaindoesnotchangethequalitativeresults.Thenumberofelectionsissmallerthanintheoverallmunicipal-leveldatasetnotonlybecauseelectionswheretherunner-updidnotrunarenotincluded,butalsobecauseelectoralsectiondataisnotavailableforallmunicipalitiesinallelections,particularlyintherstyearofdata(1996).24 andalsoprovidemorecampaigninputstohigherrankedcandidates.ForthistoexplaintheresultsinTable4,itwouldalsohavetobethecasethat,att+1,theparties/candidatesusetheseadditionalinputstospecicallytargetthosewhovotedforthird-placeatt.Whileitmightbeplausiblepartieswouldprefernottotargetthosethatvotedfortimet'swinner,theresults(3Γ0)wouldalsoimplytheyaremorelikelytotargetsupportersofthethird-thanthefourth-(andlower)placecandidate.5.1.2EectHeterogeneitybyStrengthofSecond-andThird-PlaceCandidatesIftherunner-upeectisdrivenbystrategiccoordination,onewouldexpecttheeecttobestrongerincaseswherethesecond-andthird-placecandidatetogetherreceivedalargenumberofvotes.Forexample,iftheelectionwinnerreceived40%ofthevotes,andsecond-andthird-placeeachobtained25%,theincentivetocoordinateislikelylargerthaniftheybothobtained5%ofthevotes,sinceonlyintheformerscenariocouldthecombinedsecond-andthird-placevotesharebeplausiblylargerthanthewinner's.Table5presentsestimatesoftherunner-upeectseparatelyforelectionswherethesecond-andthird-placecandidatesjointlyreceivedmorevotesthantherst-placecandidate,andelectionswheresecond-andthird-placejointlyreceivedlessthantheleadingcandidate.WefocusthisheterogeneitytestontheBrazilianandIndiansamplesastheseoerthemostpowerfordetectingdierencesinsubsamples.Thisdenitionofthesubsamplesleveragesthenotionofapossible\dividedmajority"splittingtheirvotes.However,similarresultsareobtainedbysplittingthesampleaccordingtostrengthofspecicranksofcandidates.53IntheBraziliansample,therunner-upeectonrunningagainis10.8p.p.whenthecombinedvoteshareofsecond-andthird-placeisgreaterthanthewinner'svoteshare,butonly3.5p.p.whenitisnot.Theanalogouseectsforwinningthenextelectionare9.3p.p.and3.6p.p.Theselarge(threefold)dierencesareconsistentwiththereturnstocoordinatingbeinglargerwhenthesecond-andthird-candidatesjointlyhavegreaterpotentialtodefeattherstcandidate.InourIndianstatesampleweagainndasimilarpattern,however,thedierencesaresmaller(andnotstatisticallydistinct).However,themagnitudesarestillsizable,withtheeectonrunningbeing50%largerinthestrongsecond/third-placesubsample,andtheeectsonwinningbeingalmosttwicethesize. 5453Forexample,breakingthesampleaccordingtostrengthofsecond-placeyieldssimilarresults.Thisisalsothecaseforusingthethird-placevoteshare(whichclosetothecutoissimilartotherunner-up'sshare),ortherst-placevoteshare(whichhasastrongnegativecorrelationwiththesecond-andthird-place'svoteshares).54Tofacilitatecomparisonsbetweenresultsbasedondierentsubsamples,andalsoonthefullsample,weusetheoptimal(IK)bandwidthestimatedatthefullsample(i.e.,thesamefromColumn1ofTable1)inallcases.Thequalitativeresultsarerobusttoseveralotherchoicesofbandwidth.25 5.1.3EectHeterogeneityby\PlatformDistance"BetweenSecond-andThird-PlaceCandidatesIdeally,thestrategiccoordinationmechanismcouldbetestedbyidentifyingelectionswherethesecond-andthird-placecandidatesareclosertoformingauniedgroupthatwouldgainfromcoordination,andcheckingiftheresultsaredrivenbythoseelections.Inreality,itisimpossibletoidentifythosecases,giventhepaucityofdataandthatpoliticians'andvoters'preferencesareunobservable.However,asanapproximation,itispossibletotestwhethertherunner-upeectdiersincaseswherethesecond-andthird-placecandidatesarefrompartieswithcloserplatforms.Hence,weclassiedthepartiesintheBrazilianandIndianstateelectionsintothreedierentgroupseach,basedonmultiplesourcesdescribedinAppendixA.4.InBrazil,thethreecategoriesare\right",\center",and\left".TherstcategoryincludestheWorker'sParty(PT)aswellasotherpartieswithleft-wing(communist/socialist)orientation.The\center"includesthecentristpartiessuchasthePMDBandthesocialdemocrats(PSDB).Thelastgroupincludestheright-wingpartieswithconnectionstothe(extinct)ARENApartysupportedbythemilitaryregime.IntheIndiancase,therstgroupincludespartieswithcommunist/socialistorientation,thesecondgroupincludestheCongressparty,itso-shoots,andassociates,andthelastgroupincludestheBJP,itso-shootsandassociates,aswellasotherHindu-nationalistparties.Thisallowsustospliteachsampleintotwocases:onewiththeelectionswherethesecond-andthird-placepartyarefromthesamegroup,andanotherwheretheyarefromdistinctgroups;weestimaterunner-upeectsineachofthesesub-samples.Itshouldbenotedthatanyimprecisioninthe(admittedlyrough)classicationofpartygroups,aswellastheinstabilityandnon-partisannatureofbothBrazilianandIndianpolitics,makeitlesslikelythatwewillndtheexpectedheterogeneityineect.55Sincewecanonlyclassifyparties,andnotcandidates,wereportresultswithdummiesforwhetherornotthepartyran,andwon,thet+1electionastheoutcomes.56Table6,PanelA,presentsourresultsfortheBraziliancase.Therunner-upeectonbothoutcomesisapproximately7p.p.whenbothpartiesareinthesamecategory,butonly4p.p.whenthepartiesarefromdistinctgroups.57IntheIndiancase,therunner-upeectonrunningatt+1is6.9p.p.whenparties are55Inotherwords,wehaveanoisymeasureof\true"partyorientationsinagivenelection,whichweakensthedistinctionbetweentwogroups(e.g.,ifthemeasureisentirelynoise,thesameeectsareexpectedinbothsubsamples).56Hence,theresultsarecomparabletotheparty-levelresultsdescribeinAppendixA.2.Usingpartyasoutcomesalsoaccommodatestheimpossibilityofclassifyingindependentsandtheneedtodropthemfromestimations.Asbefore,tofacilitatecomparisonsbetweenresultsbasedondierentsubsamples,andalsoonthefullsample,weusetheoptimal(IK)bandwidthestimatedatthefullsample(i.e.,thesamefromColumn1ofTableA.2)inallcases.Thequalitativeresultsarerobusttoseveralotherchoicesofbandwidth.57Itshouldbenotedthat,giventhefrequencyofpartyswitchingbyBraziliancandidatesacrosselections,theeectsusingpartyoutcomesaresmallerthanthoseusingcandidateoutcomes(i.e.,estimatesinPanelAofTable1arelargerthanthoseinPanelAofTableA.2).Substitutingcandidateoutcomesforpartyoutcomesintheestimationwouldyieldarunner-upeectonrunning(winning)of14.7p.p.(13p.p.)whenbothpartiesareinthesamecategory,butonly6.7p.p.(6p.p.)whenthepartiesarefromdistinctgroups.26 inthesamegroup,butonlyastatisticallyinsignicant1.2p.p.whentheyareindierentgroups.Forwinning,therespectiveeectsare4.6p.p.and2.5p.p..Theseresultscorroboratethenotionthateectsarelargerinthecasesthepartiesare\closer",andtheincentivestocoordinatelikelylarger.5.1.4RestartingtheCoordinationGame:TheIndianStateofEmergencyUnderthecoordinationhypothesis,therunner-upeectemergesbecauseofacoordinationfailure.Someagentswouldhavepreferredtocoordinateoneitherthesecond-orthird-placecandidate,butfailedtodoso.Astheylearnmoreaboutpartiesandcandidatesandaccumulatefocalpoints,coordinationshouldimproveovertime.And,conversely,asituationwherethethe\equilibrium"isdisruptedbyamajorchangeinthestrengthofapartyand/ortheentranceofnewpartiesshouldleadtoanincreaseduseofranksasfocalpoints,andhencealargerrunner-upeect.InthissectionwefocusontheIndian\emergency"periodasanexamplewherethepoliticalequilibriumwasdisrupted,andtestwhethertherunner-upeectislargerimmediatelyafterit.TheCongresspartydominatedIndianpoliticsfrom1951until1975.In1975-77CongressPrimeMinisterIndiraGandhiimposeda21monthperiodof\Emergency"whereelectionswerepost-poned,theprimeministermadelawsbydecree,mediawasrepressed,andcivillibertieswerecurbed.Thestatedpurposeoftheemergencywastoimproveeconomicperformancebydirectlycontrollingtheeconomy,reducingpoliticalprotestsandstrikes,andforcingpopulationcontrolprograms.Whenelectionsreturned,Congresslostsubstantialsupport,tothegainofoppo-sitionandnewparties.Forourpurposes,theEmergencycanbeseenasadisruptionofthelong-standingpoliticalequilibrium.Table7presentsestimatesofrunner-upeectsinIndianstatelegislatureelectionsseparatelyfortimeperiodsaroundtheEmergency.Wedonotndanyevidencetosuggestthattherunner-upeectonrunningagainwaslargerintheelectionsaftertheemergency.58Thismightnotbetoosurprising,however,giventhatpartieswerealsolikelyunawareofwhichpartyvoterswouldcoordinateon,andthusmightbewillingtotaketheriskofeldingacandidate.Therunner-upeectonwinningis5.4p.p.intheelectionsdirectlyaftertheEmergency,whichislargerelativetothepointestimatesfromothertimeperiodsinoursample.Thissuggeststhatcominginsecond-placewasparticularlyadvantageousinaperiodwheretheneedforcoordinationfocalpointswasuseful. 5958Therunner-upeectsaftertheemergencymeasurethebenetofbeinglabeledsecondintherstpost-Emergencyelectionsforoutcomesinthenextelection(thesecondelectionaftertheEmergency).59Tofacilitatecomparisonsbetweenresultsbasedondierentsubsamples,andalsoonthefullsample,weusetheoptimal(IK)bandwidthestimatedatthefullsample(i.e.,thesamefromColumn1ofTable1)inallcases.Thequalitativeresultsarerobusttoseveralotherchoicesofbandwidth.27 5.2Heuristics5.2.1MediaDrivenHeuristicOnepossibleexplanationforourresultsisrunners-upreceivinggreatermediaattentionaftertheelection,andthistranslatingintoahigherperceivedprobabilityofwinninginfutureelections.Thisseemsplausible,asthemediamightchoosetoreportonelectionresultsbyonlymentioningthetoptwocandidates,andpriorworkhasshownthatmediacanhaveimportantimpactsonelectoraloutcomes(DellaVignaandKaplan,2007;Enikolopovetal.,2011;Gentzkow,2006;Gentzkowetal.,2011;Gerberetal.,2009;Prior,2006;Stromberg,2004).Observingmediacoverageofsecond-andthird-placecandidatesalsogivesusanindirectmeasureofwhethertherunners-upsecureotherhighprolepositionsingovernmentortheprivatesectorthatgetsthemgreatermediacoverage.60WefocusontheCanadiancontext,asthisistheonlycasewhereitisfeasibletoelectronicallysearchforthementionofcandidatenamesinalargesetoflocalnewspapers.Webeginwiththesetofelectionsafter1979wherethesecond-andthird-placecandidatesnishedwithinonepercentofeachother.61Wefocusoncloseelectionsbetweensecond-andthird-placeasthisisthesamplewhereouridenticationofrunner-upeectsisbasedon.ForeachcandidatewesearchedLexis-Nexisforanynewspaperarticlethatincludedtheirrstname,lastname,andthenameoftheirconstituency,overtheperiodthreemonthspriortotheelectionwherethecandidateplacedsecondorthirdthroughtothreemonthsafterthenextelectioninthesameconstituency.Wethencountthenumberofarticlesmentioningthecandidateineachmonthoverthisperiod.Figure4aplotsthemeannumberofarticlesforsecond-andthird-placecandidatesagainstmonthsrelativetotheelectionattimet.Thezeropointonthex-axisrepresentsthemonthoftheelection.Thegureshowsthatbothsecond-andthird-placecandidateshaveclosetozeromediamentions3monthspriortotheelection.Thisincreasestoonaverage0.4articlespercandidatetwomonthsbeforetheelection,2articlespercandidateinthemonthbeforetheelection,and9.5articlespercandidateinthemonthoftheelection.Giventhesmallvotesharedierencebetweensecond-andthird-placecandidates,wewouldnotexpectanydierencesacrossthesecandidatespriortotheelection.Inthemonthsaftertheelectionbothcandidatesreceiveclosetozeroarticlespermonthonaverage.Thefactthatneithercandidatereceivesanysignicantmediaattentioninthemonthsaftertheelectionsuggeststhatthemediamaynotbeanimportantdriveroftherunner-upeects.Thisgurealsosuggeststhatclosesecond-placecandidatesdonotreceivedierentiallymoremediaattentionversusclosethird-place candidates.60Previousworkhasfoundmixedevidenceontheimpactofmediaonthesizeoftheincumbencyeect.SnyderandStromberg(2010)andPrior(2006)ndapositivebutmodestrelationshipbetweentelevisionpresenceandtheincumbencyeect,butAnsolabehereetal.(2006)ndsnoeect.Gentzkowetal.(2011)ndnorelationshipbetweennewspaperentryandexitonincumbencyeects.61Lexis-Nexis,ournewspaperdatabase,onlyprovidescoverageofCanadiannewspapersafter1979.28 Figure4bplotsthemeannumberofarticlesmentioningthesecond-orthird-placecandidatearoundthetimeperiodofthesubsequentelectioninthesameconstituency.NotethatinthefullsampleofCanadianelectionsfrom1867tothepresentweestimatedthatsecond-placecandidatesareapproximately4.6p.p.morelikelytoruninthesubsequentelectionintheirconstituency;whenwerestrictthesampletoafter1979(theyearsrelevantforournewspapercomparison)weestimatesecond-placecandidatesare2.5to3.5percent(dependingonthespecication)morelikelytorun,signicantatthe10percentlevel.Wewouldthereforeexpectsecond-placecandidatestoreceivegreatermediaattentionpriortothenextelection.Figure4bshowsthatbothsecond-andthird-placecandidatesfromtheelectionattimetreceiveverylittlemediaattentionuntiljustonemonthbeforethenextelection.Onaverage,bothsecond-andthird-placecandidatesreceiveabout0.5articlespercandidateinthemonthbeforethenextelection,and2articlesinthemonthofthenextelection.Figure4cagainplotsthemeannumberofarticlesmentioningthesecond-orthird-placecandidatearoundthetimeofthet+1election,buthereweonlyincludecandidateswhoranagainattimet+1.Evenconditioningonthosecandidateswhochoosetoruninthenextelection,bothsecond-andthird-placecandidatesreceivenomediamentionsuntilthemonthrightbeforethenextelection.Thisalsosuggeststhatitisunlikelythatourrunner-upeectsarebeingdrivenbysecond-placecandidatesreceivingsubstantiallymoremediaattention.Inthemonthbeforethet+1electionthesecandidatesreceivebetween1and2mediamentions,andinthemonthoftheelectionatt+1thecandidatesreceivebetween10and15mediamentions.Aformalstatisticaltestsuggeststhatpriorthird-placecandidatesreceivemoremediamentionsthansecond-placecandidatesintimet+1elections;however,wearehesitanttointerpretthisstronglyasthesamplehereonlyincludeseleventhird-placecandidatesandelevensecond-placecandidates.Asasecondtestofthemediahypothesis,wecomparethesizeoftherunner-upeectsincon-stituencieswithgreatermediapresence.Ifmediareportingdrivesawarenessofsecond-placecandidatesversusthird-placecandidates,onewouldexpecttherunner-upeectstoincreasewiththepresenceoflocalmedia.WefocusthesetestsontheBrazilianandIndianstatesampleswherewehavethesamplesizetopotentiallydistinguisheectsacrossdierentmediaenvironments.InTable8,PanelA,wecompareBrazilianmunicipalitieswithandwithoutAMradiostations.FerrazandFinan(2008)ndthatvotersaremoreresponsivetoinformationfrommunicipalgovernmentauditsinmunicipalitieswithAMradiostations,sothereisapriorievidencethatAMradiocoveragecanhaveimportantpoliticalimpacts.Contrarytothemediacoveragehy-pothesis,therunner-upeectoncandidacyislargerinmunicipalitieswithoutAMradio(butnotsignicantlydierent).Therunner-upeectsonwinningaresimilarlysizedandstatisticallyindistinguishable.InTable8,PanelB,wetestwhetherconstituenciesinIndianstateswithgreaternewspapercirculationhavelargerrunner-upeects.Toensurethatourmeasureofmediapresenceisa29 meaningfulsignalofmediaattentionweusethesamemeasureofstatelevelnewspaperpene-trationasBesleyandBurgess(2002),whoshowthatstateshighonthismeasurehavegreaterpoliticalresponsiveness.Weupdatethismeasureto2013,andmatcheachelectioninourIndianstatedatatothenewspapercirculationmeasureintheclosestavailableyear.Wethensplitthesampleofelectionsintothosethathappenedinstate-yearswithaboveandbelowmediannewspapercirculationpercapita.Wendthat,ifanything,electionsinstate-yearswithgreaterthanmediannewspapercirculationpercapitademonstratesmallerrunner-upeects.625.2.2PartyHeuristics:EliminationByAspectsThalerandSunstein(2008)discussesanotherdecisionheuristic(rstpresentedinTverskyandKahneman(1981)),the\eliminationbyaspects"model,thatmightalsoberelevanttounder-standingrunner-upeects.Inthismodeladecisionmakerattemptstosimplifyacomplicatedchoiceproblembychoosingasetofsimplecutosandrequiringanypossiblechoicestomeetallofthosecutos.Forexample,inthecaseofndingahouse,anindividualmightonlyconsiderhouseswithin20milesofheroce,lessthan250,000dollars,andwithfourbedrooms.Cutorulesareaddeduntilthechoicesetissmallenoughtocompareoptionsonabroadersetofcharacteristics.Inourcase,itseemsplausiblethatpartiesmightuseacandidate'spreviousrankasasimplifyingcutowhenchoosingwhichcandidatesreceivetickets.AsThalerandSunstein(2008)notes,suchsimplifyingstrategiescanleadtowelfarelosses;inourcase,highqualitythird-placecandidatesmightbeleftoutofthechoiceset.Iftherunner-upeectisprimarilydrivenbypartiesusingrankasaneliminationaspect,thentheresultsshouldbeweakerforindependentcandidates.FigureA.9apresentsgraphicalevidenceonthesizeoftherunner-upeectforindependentcandidatesinourIndianstateelectionssample,whichistheonlysamplewithalargenumberofindependents.Theeectsizeshereareverysimilartothosefoundinthefullsample.Thisresultmakesitunlikelythatapartybasedheuristicistheprimarydriveroftherunner-upeect.ItshouldalsobenotedthatpartiesplayasmallroleinlocalBrazilianpolitics(Ames,2009),andparty-leveldecision-makingisunlikelytodrivetheresultsinthatcontexttoo.5.2.3OutcomeBiasAnadditionalpsychologicalexplanationisthatinsteadofjudgingtheirperformanceintheelectionobjectivelybasedonvoteshare,candidatesjudgetheirperformanceinreferencetoapsychologicallybasedcounterfactual.KahnemanandVarey(1982)discusseshowanagen t's62Tofacilitatecomparisonsbetweenresultsbasedondierentsubsamples,andalsoonthefullsample,weusetheoptimal(IK)bandwidthestimatedatthefullsample(i.e.,thesamefromColumn1ofTable1)inallcases.Thequalitativeresultsarerobusttoseveralotherchoicesofbandwidth.30 utilityfromanoutcomeisoftenbothaectedbytheoutcomeaswellastheagent'sperceptionofthecounterfactualhadtheoutcomenotoccurred;forexampleinourcontextasecond-placecandidatemightseetheircounterfactualaswinningtherace,butathird-placecandidateseestheircounterfactualassecond-place.Ifcandidates'perceptionsofthecounterfactualserveasmotivationforwhethertorunagain,thenthesedierencesincounterfactualsacrosssecond-andthird-placecandidatesisapotentialexplanationforourresults.63Bothofthepsychologicalmechanismsmentionedabove,andwesuspectmostpsychologicalmechanismsthatpredictrankingmattersbeyondvotesharesinthiscontext,wouldalsopredictthatthird-placecandidatesshouldperformbetterthanfourth-placecandidates.Asdiscussedearlier,wendlittleevidencesupportingthis.Thendingofnothird-placeeectis,however,consistentwiththestrategiccoordinationmechanism;atiebetweensecond-andthird-placecandidatestsbetterthedescriptionofa\dividedmajority"thanatiebetweenthird-andfourth-place.Finally,itisdiculttoreconcileanexplanationbasedonpsychologicalmechanismswiththemagnitudeofrunner-upeects.Forexample,iftheeectisdrivenentirelybycandidatemotivation,theprobabilityofwinningthenextelectionbeingmorethan80%largerforcloserunners-upthanclosethird-placesintheBraziliancontextimpliescandidatemotivationhasenormous,andlikelyimplausible,consequences.6ConclusionThispaperdocumentsthepresenceofrunner-upeects:barelysecond-placecandidatesaremorelikelythanbarelythird-placecandidatestorunin,andwin,subsequentelections,eventhoughbothlostthe(simpleplurality)election.WeapplythisRDDanalysistofourdierentcontextscoveringmultiplecontinents,aswellaslocal,state,andfederalelectionsforexecutiveandlegislativepositions.Twomajor,non-exclusive,mechanismsthatmightexplaintherunner-upeectarestrategiccoordinationandheuristics.Whilewebelievemoreresearchisnecessarytounderstandtherelativerolesofthesemechanismsindeterminingtherunner-upeectacrossvariouselectoralcontexts,theweightofourevidencesuggeststhatstrategiccoordinationplaysanimportantrole.InBrazil,wendthattheeectisdrivenbyvotersswitchingfromthethird-candidatetothesecond-placecandidate,asopposedtothelattergainingattheequalexpenseofallothercandidates.Additionalheterogenoustreatmenteecttestssuggestthatrunner-upeectsarestrongerwhentheincentivesforstrategicswitchingtosecond-placearegreater:when second-63Medvecetal.(1995)ndsthatOlympianswhocomeinsecond-placearenotashappyasthosewhocomeinthird-place;theauthorsarguethatthisdierenceinhappinessoccursbecausesilvermedalistscomparethemselvestogoldmedalists,whilebronzemedalistscomparethemselvestothefourthplaceathletewhodidnotreceiveamedal.31 andthird-placehavesimilarpartyplatforms,whentheyhavereasonablechanceofbeatingthewinner,andaftertheIndianemergency.Incontrast,wendlittleevidenceinfavoroftheheuristicbasedexplanations,suchaswhenwecompareclosethird-andfourth-placecandidates.Weconcludebyhighlightingtwoavenuesforfutureresearch.Therstistostudytheimplicationsofrunner-upeectsfortheinterpretationofincumbencyeects,whichhavebeendocumentedinawidevarietyofelectoralsettings.Ourndingsraisethepossibilitythattherst-placerankingalonemaydrivepartofit;perhapswinninganelectionmakesacandidateafocalpointforcoordination,whichinturndrivesfutureelectoralsuccess.Consistentwiththis,LevittandWolfram(1997)ndthatalargefractionoftheincreaseintheincumbencyeectinU.S.Houseisexplainedbyincumbents\scaringo"qualitycompetitors.InthecontextofBrazilandIndia,wherethereareincumbencydisadvantages,ourndingsraisethepossibilitythatthetrueanti-incumbencyeectsmayactuallybelargerthanthoseestimatedinRDDs.Ifincumbentsreceivesimilarbenetsofcominginrstversussecondasrunners-upreceiveoverthird,thenregressiondiscontinuitydesignsmayunder-estimatethetruedisadvantageofbeinganincumbent.Exploringtheconnectionbetweenincumbencyandrunner-upeectsappearstobeaninterestingareaforfutureresearch.Asecondavenueistoassessthewelfareimplicationsoftherunner-upeect.Anidealpoliticalsystemwouldchoosecandidatesbasedontheirabilitytogovern;instead,weshowthatvariationinpreviouselectoralperformancethatisessentiallynoisehassizeableconsequences.Suchanarbitraryruleisunlikelytobeoptimal,asitdoesnottakeintoaccountpoliticians'abilitytogoverninindividualcases.IndescribingancientAthens,wherepoliticianswereselectedatrandomfromthepopulation,Besley(2005)notes\afterall,selectionbylotdoesnotfavorthosewithgreaterpoliticalcompetenceoverless."32 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Figure1TheRunner-upEect(2ndvs.3rd Place)Triangles(circles)representthelocalaveragesofadummyindicatingwhetherthecandidateranin(won)thenext(t+1)election.Averagesarecalculatedwithin2p.p.-widebinsofvotesharedierence(x-axis).Continuouslinesareaquadratictovertheoriginal(unbinned)data.Sampleincludesonlycandidatesplacedsecondandthirdatelectiont.(a)Brazil (b)IndiaState 36 Figure1(continued)TheRunner-upEect(2ndvs.3rd Place)Triangles(circles)representthelocalaveragesofadummyindicatingwhetherthecandidateranin(won)thenext(t+1)election.Averagesarecalculatedwithin2p.p.-widebinsofvotesharedierence(x-axis).Continuouslinesareaquadratictovertheoriginal(unbinned)data.Sampleincludesonlycandidatesplacedsecondandthirdatelectiont.(c)IndiaFederal (d)Canada 37 Figure2CovariateSmoothness(2ndvs3rd place)Triangles(circles)representthelocalaveragesofadummyindicatingwhetherthecandidateranin(won)thepast(t-1)election.Averagesarecalculatedwithin2p.p.-widebinsofvotesharedierence(x-axis).Continuouslinesareaquadratictovertheoriginal(unbinned)data.Sampleincludesonlycandidatesplacedsecondandthirdatelectiont.(a)Brazil (b)IndiaState (c)IndiaFederal (d)Canada 38 Figure3Eectof3rdvs.4th PlaceTriangles(circles)representthelocalaveragesofadummyindicatingwhetherthecandidateranin(won)thenext(t+1)election.Averagesarecalculatedwithin2p.p.-widebinsofvotesharedierence(x-axis).Continuouslinesareaquadratictovertheoriginal(unbinned)data.Sampleincludesonlycandidatesplacedthirdandfourthatelectiont.(a)Brazil (b)IndiaState (c)IndiaFederal (d)Canada 39 Table1:TheRunner-upEect(2ndvs.3rd Place)PolynomialOrderOneOneOneZeroTwoBandwidthOptimalBW 12OptimalBW2OptimalBW2percentFullSample3rd-pl.MeanOptimalBWValue(1)(2)(3)(4) (5)PanelA:BrazilCandidacy,t+1(%)30.2711.569.397***6.295*11.90***11.05***14.08***[N=5556](2.589)(3.596)(1.868)(3.040)(1.912)Winner,t+1(%)9.44812.578.310***7.010***8.844***9.091***10.49***[N=5946](1.809)(2.541)(1.290)(2.265) (1.395)PanelB:IndiaStateCandidacy,t+1(%)31.929.1394.391***5.743***5.037***5.755***5.490***[N=22518](1.131)(1.567)(0.834)(1.175)(0.790)Winner,t+1(%)7.7817.8073.351***3.297***3.502***3.453***4.412***[N=19868](0.812)(1.149)(0.594)(0.775) (0.528)PanelC:IndiaFederalCandidacy,t+1(%)23.5716.294.847**2.3745.748***5.539*5.817***[N=4394](2.432)(3.262)(1.773)(3.243)(2.178)Winner,t+1(%)6.15515.932.676*2.8113.211***2.9153.247***[N=4294](1.393)(1.903)(1.022)(1.881) (1.229)PanelD:CanadaCandidacy,t+1(%)16.7912.224.617**4.452*4.591***4.990**5.986***[N=5190](1.841)(2.548)(1.471)(2.250)(1.606)Winner,t+1(%)2.37310.64-0.195-0.1630.4240.5990.414[N=4612](0.863)(1.220)(0.576)(0.999) (0.662)Standarderrorsclusteredattheconstituencylevelinparentheses.Theunitofobservationisacandidate.Outcomesmeasuredaspercent-ages.Eachgureincolumns(1)-(5)reportsaseparatelocalpolynomialregressionestimatewiththespeciedbandwidthandpolynomialorder.Separatepolynomialsarettedoneachsideofthethreshold.\3rd-pl.Mean"istheestimatedvalueofthedependentvariablefora3rd-placedcandidatethat\ties"withthe2nd-placedcandidate,basedonthespecicationincolumn(1).Theoptimalbandwidth(BW)isbasedonImbensandKalyanaraman's(2012)procedure,withtheassociatednumberofobservationsreportedinbrackets.40 Table2:PlaceboTestsandCovariateSmoothness(2ndvs.3rd Place)PolynomialOrderOneTwoBandwidthOptimalBWFullSample3rd-pl.meanOptimalBWValue(1) (2)PanelA:BrazilCandidacy,t-1(%)31.1721.690.8880.00437[N=8790](1.858)(1.845)Winner,t-1(%)13.6521.89-0.243-0.750[N=8840](1.438)(1.430)VoteShare,t-1(%)23.5825.430.1030.242[N=5272](1.053)(1.141)PMDBParty,t(%)16.2426.52-0.450-0.998[N=13398](1.283) (1.395)PanelB:IndiaStateCandidacy,t-1(%)34.9318.170.9650.285[N=36722](0.869)(0.823)Winner,t-1(%)13.4813.801.1000.654[N=30262](0.788)(0.655)VoteShare,t-1(%)9.74013.270.3220.269[N=29449](0.365)(0.307)CongressParty,t(%)19.8712.390.0587-1.391*[N=32238](0.913) (0.732)PanelC:IndiaFederalCandidacy,t-1(%)33.8523.66-0.940-0.748[N=6036](2.403)(2.502)Winner,t-1(%)15.7015.33-2.0320.117[N=4120](2.244)(1.941)VoteShare,t-1(%)10.8622.49-1.029-0.769[N=5770](1.012)(1.021)CongressParty,t(%)10.7418.431.3280.582[N=5850](1.695) (1.648)PanelD:CanadaCandidacy,t-1(%)23.6512.03-0.464-0.811[N=5322](2.365)(1.833)Winner,t-1(%)6.70213.770.8210.196[N=6000](1.318)(1.224)VoteShare,t-1(%)7.0629.848-0.826-0.509[N=4434](0.928)(0.658)LiberalParty,t(%)26.5511.39-1.4770.629[N=5656](2.617) (2.095)SeeTable1notesforfurtherdescription.Outcomesmeasuredaspercentages.41 Table3:Eectof3rdvs.4th PlacePolynomialOrderOneOneOneZeroTwoBandwidthOptimalBW 12OptimalBW2OptimalBW2percentFullSample4th-pl.MeanOptimalBWValue(1)(2)(3)(4) (5)PanelA:BrazilCandidacy,t+1(%)8.73610.640.01160.740-0.4031.513-0.473[N=4768](1.358)(1.697)(1.141)(1.383)(1.375)Winner,t+1(%)1.4735.561-0.3400.137-0.1400.126-0.0617[N=3138](0.749)(0.910)(0.595)(0.605) (0.670)PanelB:IndiaStateCandidacy,t+1(%)15.463.0661.1062.675***0.6100.809*-0.0375[N=27282](0.723)(0.937)(0.574)(0.485)(0.497)Winner,t+1(%)1.4813.7430.1480.2150.1280.385**0.0843[N=30674](0.244)(0.313)(0.200)(0.176) (0.196)PanelC:IndiaFederalCandidacy,t+1(%)17.383.122-0.506-1.518-0.4190.0582-0.0196[N=4286](1.905)(2.285)(1.465)(1.279)(1.284)Winner,t+1(%)0.6913.5230.5371.146*0.2550.2910.488[N=4598](0.466)(0.620)(0.391)(0.314) (0.394)PanelD:CanadaCandidacy,t+1(%)13.6510.442.1483.7901.0213.3272.369[N=4766](1.837)(2.557)(1.420)(2.079)(1.751)Winner,t+1(%)0.48911.74-0.04580.104-0.1970.1750.649[N=5240](0.308)(0.350)(0.268)(0.304) (0.420)Standarderrorsclusteredattheconstituencylevelinparentheses.Theunitofobservationisacandidate.Outcomesmeasuredaspercent-ages.Eachgureincolumns(1)-(5)reportsaseparatelocalpolynomialregressionestimatewiththespeciedbandwidthandpolynomialorder.Separatepolynomialsarettedoneachsideofthethreshold.\4th-pl.Mean"istheestimatedvalueofthedependentvariablefora4th-placedcandidatethat\ties"withthe3rd-placedcandidate,basedonthespecicationincolumn(1).Theoptimalbandwidth(BW)isbasedonImbensandKalyanaraman's(2012)procedure,withtheassociatednumberofobservationsreportedinbrackets.42 Table4:ElectoralSectionRegressions (Brazil)3rdPl.Vote1st-Pl.Vote2ndPlaceVoteVoteShare,t+1Share,t+1Share,t+1(1)(2)(3)(4)(5) (6)1stPlaceVoteShare,t(1)-0.0160.188***0.217-0.0110.0510.408***(0.038)(0.052)(0.154)(0.038)(0.054)(0.032)2ndPlaceVoteShare,t(2)0.509***0.650***0.542***0.495***0.095*-0.032(0.038)(0.056)(0.163)(0.040)(0.055)(0.033)3rdPlaceVoteShare,t(3)0.142***0.338***0.346**0.150***0.523***-0.005(0.039)(0.055)(0.163)(0.040)(0.052) (0.032)3�10.158***0.150***0.129**0.161***0.472***-0.413***(0.024)(0.034)(0.056)(0.029)(0.027)(0.019)Dep.Var.Mean.34.633.635.232.431.346.0Bandwidth2p.p.1p.p.0.5p.p.2p.p.2p.p.2p.p.Excludes3-candidateelectionsYesMunicipality-timeeectsYesYesYesYesYesYesNumberofElections144652983115207Observations(Sections)87384113178559586071 10267Standarderrorsclusteredattheelectoralsectionlevelinparentheses.Theunitofobservationisanelectoralsection-year.Eachcolumnprovidestheestimatefromaseparateregression,withthedependentvariableintheheaderandexplanatoryvariablesinrows.Abandwidthofxindicatesthatonlyelectionswithavotesharedierencebetween2ndand3rdplacesmallerthanxisincludedinthesample.Allspecicationsincludemunicipality-timexedeects.Table5:TheRunner-UpEectbyStrengthof2ndand3rdPlace CandidatesCandidacy,t+1Winner,t+1Candidacy,t+1Winner, t+1PanelA:Brazilv2+v3Γv1v2+v3v 1Runner-UpEect10.76***9.333***3.4683.591(3.026)(2.243)(4.669)(2.501)Close3rd-PlaceMean32.7910.9220.623.796IKBandwidth(%)11.5612.5711.5612.57Observations417444361382 1510PanelB:IndiaStatev2+v3Γv1v2+v3v 1Runner-UpEect4.732***3.828***3.417*1.945*(1.412)(1.072)(1.826)(1.088)Close3rd-PlaceMean35.899.48722.933.847IKBandwidth9.1397.8079.1397.807Observations14776131207740 6746Standarderrorsclusteredattheconstituencylevelinparentheses.Outcomesmeasuredaspercentages.Estimatesarebasedonlocallinearregressionestimates.SeeTable1notesandmaintextforfurtherdescription.v2+v3Γv1(v2+v3v1)indicatesthesubsamplewheresecondandthirdplacedcandidatesobtainmore(less)votesthanthewinner.43 Table6:TheRunner-upEectbyPartyPlatform DistanceCandidacy,t+1Winner,t+1Candidacy,t+1Winner, t+1PanelA:Brazil(PartyOutcomes)I2nd=I3rdI2nd6=I3r dRunner-UpEect7.441*7.531**3.9524.157*(4.027)(3.147)(2.980)(2.262)Close3rd-PlaceMean37.9510.8837.7412.26IKBandwidth(%)13.7513.2413.7513.24Observations213220564242 4112PanelB:IndiaState(PartyOutcomes)I2nd=I3rdI2nd6=I3r dRunner-UpEect6.895***4.616**1.1982.509(2.008)(1.912)(1.771)(1.799)Close3rd-PlaceMean54.2311.8764.2515.98IKBandwidth11.929.19011.929.190Observations705457668914 7344Standarderrorsclusteredattheconstituencylevelinparentheses.Outcomesmeasuredaspercentages.Es-timatesarebasedonlocallinearregressionestimates.SeeTable1notesandmaintextforfurtherdescrip-tion.I2nd=I3rd(I2nd6=I3rd)indicatesthesubsamplewheresecondandthirdplacedcandidatesareinthesame(separate)partyplatformcategory.Table7:TheRunner-UpEectbyPeriod(IndianState Elections)ElectionsAfterEmergencyState1951-631964-751977-19781979-91 1992-2012Candidacy,t+13.3003.3722.4064.231*6.079***(3.083)(2.384)(3.396)(2.184)(2.171)Close3rd-PlaceMean16.6826.7624.4133.7440.09IKBandwidth9.1399.1399.1399.1399.139Observations2286459622486202 7186Winner,t+14.318**1.1915.245**3.512**3.661**(1.862)(1.724)(2.377)(1.539)(1.637)Close3rd-PlaceMean2.9287.9953.9817.9519.990IKBandwidth7.8077.8077.8077.8077.807Observations2010406419565488 6350Standarderrorsclusteredattheconstituencylevelinparentheses.Outcomesmeasuredaspercentages.Estimatesarebasedonlocallinearregressionestimates.SeeTable1notesandmaintextforfurtherdescription.44 Table8:TheRunner-UpEectbyMedia PresenceCandidacy,t+1Winner,t+1Candidacy,t+1Winner, t+1PanelA:BrazilTownsWithoutAMRadioTownsWithAM RadioRunner-UpEect10.55***8.364***6.9778.197***(3.139)(2.230)(4.568)(3.091)Close3rd-PlaceMean28.7410.7233.486.757IKBandwidth(%)11.5612.5711.5612.57Observations377440461782 1900PanelB:IndiaStateMedianStateNewspaperCirculationΓMedianStateNewspaper CirculationRunner-UpEect5.371***4.111***3.222**2.422**(1.570)(1.158)(1.624)(1.136)Close3rd-PlaceMean35.128.13128.137.340IKBandwidth9.1397.8079.1397.807Observations117001038210818 9486Standarderrorsclusteredattheconstituencylevelinparentheses.Outcomesmeasuredaspercentages.Esti-matesarebasedonlocallinearregressionestimates.SeeTable1notesandmaintextforfurtherdescription.45 Figure4NumberofNewspaperArticlesfor2ndand3rdPlaceCanadian CandidatesPanel(a)plotstheaveragenumberofnewspaperarticlesforclose2ndand3rdplaceCanadianparliamentcandidatesinthemonthsbeforeandaftertheelectioninwhichtheynearlytiedfor2ndplace.Panel(b)plotsthenumberofarticlesforthosesamecandidatesaroundthenextelection.Panel(c)isthesameasPanel(b),exceptitonlyincludescandidatesthatchosetoruninthenextelection.(a)Articlesafterelectionatt (b)Articlesbeforeelectionatt+1 (c)Articlesbeforeelectionatt+1,conditionalonrunninginnextelection 46 OnlineAppendix(NotforPublication)A.1DerivationofEquation3Theobjectofinterestis:E[W1�W0jx=0;R1=1]=E[W1jx=0;R1=1]�E[W0jx=0;R1=1]Thersttermontherightsidecanbeexpressedas:Prob[(W1=1)\(R1=1)jx= 0]Prob[R1=1jx=0]=E[W1R1jx= 0]E[R1jx=0]Thesecondtermcanbeexpressedsimilarlyandfurtherrearranged:Prob[(W0=1)\(R1=1)jx= 0]Prob[R1=1jx=0]==Prob[(W0=1)\(R0=1;R1=1)jx=0]+Prob[(W0=1)\(R0=0;R1=1)jx= 0]Prob[R1=1jx=0]=E[W0R0jx=0]+Prob[(W0=1)\(R0=0;R1=1)jx= 0]E[R1jx=0]wherethelaststepusestheassumptionofnodeers.Finally,notethat:Prob[(W0=1)\(R0=0;R1=1)jx=0]=Prob[W0=1jR0=0;R1=1jx=0]
Prob[R0=0;R1=1jx=0]=E[W0jR1ΓR0;x=0]
Prob[R1ΓR0jx=0]Combiningtheseweobtainequation3: 1E(R1jx=0)[E(W1R1�W0R0jx=0)�Prob(R1ΓR0jx=0)
E(W0jx=0;R1ΓR0)]A.2PartyLevelOutcomesFigureA.7presentsagraphicalanalysisofwhetherapartythatcomesinclosesecond-placeismorelikelytorunin,andwin,asubsequentinelection.TheguresforBrazil,IndiaState,and47 IndiaFederalshowreasonablycleardiscontinuitiesatthetransitionfromthirdtosecond-place,suggestingthatapartythatbarelycomesinsecondversusthird-placeismorelikelytoeldacandidateinthenextelection,andthatcandidateismorelikelytowinthenextelection.ForCanada,however,thegureshowslittleevidenceofadierencebetweenclosesecondandthirdpartiesonfutureoutcomes.TableA.2presentsourregressiondiscontinuityestimatesoftheseeects.ForBrazil,therunner-upeectonapartyrunninginthenextelectionis4.8p.p.,whichisapproximatelyhalfthesizeoftherunner-upeectonacandidaterunninginthenextelection(9.4p.p.-Table1).Similarly,therunner-upeectonapartywinningthenextelection(5.6p.p.)isapproximately67percentthesizeoftherunner-upeectonacandidatewinningthenextelection(8.3p.p.).Asmentionedinthetext,thelikelyreasonforthesmallermagnitudeswhenweusepartyversuscandidateoutcomesinBrazilisthat37%ofsecond-andthird-placecandidatesswitchparties.IntheIndianstatesample,wendtheeectsizesusingpartyoutcomesaresimilartothosewhenweusecandidateoutcomes.Usingpartyoutcomes,therunner-upeectsonrunningagainandwinningthenextelectionare3.6p.p.and3.8p.p.;thesearequiteclosethecorrespondingeectsizesusingcandidateoutcomes(Table1).IntheIndianfederalsample,thepointestimatesusingpartyoutcomesaresmallerthanthoseusingcandidateoutcomes,butstillpositive.Thestatisticalsignicanceoftheseestimatesvariesmorewiththespecicbandwidthchosenforestimation.Closesecondpartiesare2.2p.p.(1.3p.p.)morelikelytorun(win)thanclosethirdparties,whereasclosesecondcandidatesare4.9p.p.(2.7p.p.)morelikelytorun(win).ConsistentwithFigureA.7,inTableA.2wendnoevidencethatCanadianpartiesthatbarelycomeinsecond-placearemorelikelytoruninorwinfutureelections.TableA.3presentsregressiondiscontinuitytestsofbalanceonpre-existingpartycharacteristics.FortheBrazilianandIndianstateelectionswendnosignicantdierencesinpastcandidacy,winning,majorparty,orvoteshare.FortheIndiaFederalelection,thequadraticspecicationsuggeststhatclosesecond-placepartiesweremorelikelytohavewonthepreviouselection.However,visualinspectionofFigureA.8c,suggeststhatthissignicanteectisbeingdrivenbyquadraticfunctionalformttingcurvebetterawayfromthecuto.Inparticular,thequadraticfunctionalformtakesalinearshapetotthepatternawayfromthecuto,butthiscausesittomissthenon-linearityclosetotherighthandsideofthecuto.InCanada,wenda10%signicantdierenceintheoptimalbandwidthspecicationoncandidacyinthepastelection.However,inspectionofFigureA.8ddoesnotsuggestanimbalance.Lastly,wendclosesecond-placepartieshavelowervotesharebothintheoptimalbandwidthandquadraticspecicationsintheCanadiansample.FigureA.10providestherelevantplotforthisoutcome.Animbalanceisnotclearlyvisible,andthediscontinuityseemstobedrivenbyobservationsinthebinimmediatelytotherightofthecuto;thereareothervariationsacrossindividualbinsof48 similarmagnitude.Whenconductingalargenumberofbalancetestsovermultipleoutcomesandsamplessomespurioussignicantresultsareexpected,andsowedonotconcludethatelectoralmanipulationand/orimbalanceisanissue.A.3UKHouseofCommonsResultsElectionstotheUKHouseofCommonsarescheduledeveryveyears,butcanhappenmorefrequentlyinthecaseoffailuretoformagovernment.OurUKParliamentdatacoverstheuniverseofelections,includingbye-elections,fortheperiod1931-2010.64Weagainmatchcandidatesovertimeusingtheirnames,anddeneacandidateasrunningagainifwendamatchfortheminthenextelection.65Wealsomatchconstituenciesbyname,consideringconstituencieswiththesamenameoveryearsasthesameconstituency.Wehaveatotalof40,206candidatesintheUKdatacontestingin11,609electionsacross1,345constituencies.8,384electionshadthreeormorecandidatesandatleastonesubsequentelection.FigureA.11apresentsagraphicalanalysisoftheprobabilitythatU.K.parliamentarycandidateswillrunin,andwin,thenextelectionintheirconstituency.Thetriangleguresandttedcurvesshowthereisasmallincreaseintheprobabilitythatarunner-upcandidaterunsinthenextelection.Theestimatedeectis3.2p.p.intheoptimalbandwidthspecicationandclosetosignicantatthe10percentlevel(p-value=10.2%).Thepointestimatesusingotherbandwidthsaregenerallysmallandpositive,althoughtheyareneverstatisticallysignicantatthe5percentlevel.Thecircleguresandttedcurvesuggestthatclosesecond-placecandidatesintheUKarenotmorelikelytowinfutureelections,andthisresultisalsoconrmedwhenweestimatetheeectsizeinaregression-discontinuitymodel.Itisperhapsunsurprisingthatwedonotndaneect,giventhatclosesecond-andthird-candidateshavesuchalowprobabilityofwinningingeneral(lessthan2percent).InthissensetheBritishcaseismoresimilartotheAmericanone,inthatinsituationswheresecond-andthird-candidatesgetsimilaramountsofvotes,thethird-placecandidateisreallynotaviablecandidateinfuture elections.64WedonotusetheCLEAdataforU.K.electionsbecauseitismissingcandidatenamesforalargefractionofelections.Forelectionyears2005and2010ourdatacomefromtheUKelectoralcommission(http://www.electoralcommission.org.uk/our-work/our-research/electoral-data).Forelectionyears1931-2001ourdatacomefromthePoliticsResourceswebsite(http://www.politicsresources.net/area/uk/).OurU.K.by-electionsdatacomefrom(http://web.archive.org/web/20131014014802/http://by-elections.co.uk/links.html).65Ourmanualcheckprocedurendsthatouralgorithmcorrectlyidentiedwhetheracandidateranagainornotinthenextelectionfor100percentofsampledUKcandidates.49 A.4CategorizationofPartyPlatformsWecategorizedallBrazilianpartiesthateldedacandidateinamayoralelectioninoursamplesintothreecategories,whichcouldbelabeledas\left",\center",\right".WefollowthediscussioninPowerandZucco(2009),supplementedwithwebsearchesfor(small)partiesmissingintheiranalyses.WealsocategorizedpartiesinIndianstateelectionsintothreecategories.Therstgroupincludespartieswithcommunist/socialistorientation,thesecondgroupincludestheCongressparty,itso-shoots,andassociates,andthelastoneincludestheBJP,itso-shootsandassociates,aswellasotherHindu-nationalistparties.Thisdenition,andthecodingofseverallargepartiesisfromSinghandSaxena(2011).Wealsocodedmanyremainingpartiesusingaprotocolthatsequentiallyi)assignedpartieswithmentionstocommunismandsocialismintheirnametotherstgroup,ii)checkediftheparty'sentryonWikipediamentionedanorientation,partieswithsocialist/communist/left-wingorientationwereassignedtotherstgroup,partieswithcenter/center-left/center-right/populist/socialdemocracyasorientationtothesecondgroup,andthosewithright-wingorientationtothelastgroup,andnallyiii)iftheparty'sWikipediapagementionedassociationswithanothercategorizedparty,theywereassignedtothatgroup.Associationsaremergers,splitsfrom,orcommoncoalitionformation.50 FigureA.1DensityofRunningV ariableCirclesrepresentthenumberofcandidateswithin2p.p.binsofvotesharedierencebetween2ndand3rdplacedcandidate(therunningvariableintheRDD).(a)Brazil (b)IndiaState (c)IndiaFederal (d)Canada 51 FigureA.2VoteSharesof2ndand3rd CandidateCirclesrepresentthelocalaveragesofcandidatevotesharesatthetelection.Averagesarecalculatedwithin2p.p.binsofvotesharedierence(x-axis).Votessharesaremeasuredaspercentages.Continuouslinesareaquadratictovertheoriginal(unbinned)data.(a)Brazil (b)IndiaState (c)IndiaFederal (d)Canada 52 FigureA.3VoteShareof2ndand3rdCandidate, t+1Circlesrepresentthelocalaveragesofcandidatevotesharesatthenext(t+1)election.Averagesarecalculatedwithin2p.p.binsofvotesharedierence(x-axis).Votessharesaremeasuredaspercentages,candidatesnotrunningatt+1areassignedavoteshareofzero.Continuouslinesareaquadratictovertheoriginal(unbinned)data.(a)Brazil (b)IndiaState (c)IndiaFederal (d)Canada 53 FigureA.4RobustnesstoBandwidthChoice- BrazilCirclesrepresenttheestimatedtreatmenteectofbeing2ndplaceusingdierentbandwidthchoices(x-axis).Linesrepresentthe95%condenceinterval(standarderrorsclusteredattheconstituencylevel).Wereportallpossiblecasesforinintegerbandwidthvalues(1,2,...50),exceptthosewithsmallsamplesizes(below300forthezeroorderpolynomial,below600fortherstorderpolynomial).(a)Outcome:Candidacy,t+1;Poly.Order:1 (b)Outcome:Candidacy,t+1;Poly.Order:0 (c)Outcome:Winner,t+1;Poly.Order:1 (d)Outcome:Winner,t+1;Poly.Order:0 54 FigureA.5RobustnesstoBandwidthChoice-India StateCirclesrepresenttheestimatedtreatmenteectofbeing2ndplaceusingadierentbandwidthchoice(x-axis).Linesrepresentthe95%condenceinterval(standarderrorsclusteredattheconstituencylevel).Wereportallpossiblecasesforinintegerbandwidthvalues(1,2,...50),exceptthosewithsmallsamplesizes(below300forthezeroorderpolynomial,below600fortherstorderpolynomial).(a)Outcome:Candidacy,t+1;Poly.Order:1 (b)Outcome:Candidacy,t+1;Poly.Order:0 (c)Outcome:Winner,t+1;Poly.Order:1 (d)Outcome:Winner,t+1;Poly.Order:0 55 FigureA.6Eectof1stvs 2ndTriangles(circles)representthelocalaveragesofadummyindicatingwhetherthecandidateranin(won)thenext(t+1)election.Averagesarecalculatedwithin2p.p.-widebinsofvotesharedierence(x-axis).Continuouslinesareaquadratictovertheoriginal(unbinned)data.Sampleincludesonlycandidatesplacedrstandsecondatelectiont.(a)Brazil (b)IndiaState (c)IndiaFederal (d)Canada 56 FigureA.7Eectof2ndvs3rd,Party OutcomesTriangles(circles)representthelocalaveragesofadummyindicatingwhetherthepartyranin(won)thenext(t+1)election.Averagesarecalculatedwithin2p.p.-widebinsofvotesharedierence(x-axis).Continuouslinesareaquadratictovertheoriginal(unbinned)data.Sampleincludesonlypartiesplacedsecondandthirdatelectiont.(a)Brazil (b)IndiaState (c)IndiaFederal (d)Canada 57 FigureA.8CovariateSmoothness,2ndvs3rd,Party OutcomesTriangles(circles)representthelocalaveragesofadummyindicatingwhetherthepartyranin(won)thepast(t-1)election.Averagesarecalculatedwithin2p.p.-widebinsofvotesharedierence(x-axis).Continuouslinesareaquadratictovertheoriginal(unbinned)data.Sampleincludesonlypartiesplacedsecondandthirdatelectiont.(a)Brazil (b)IndiaState (c)IndiaFederal (d)Canada 58 FigureA.9Runner-UpEectforIndependentCandidates,India StateTriangles(circles)representthelocalaveragesofadummyindicatingwhetherthecandidateranin(won)thenext(t+1)election.Averagesarecalculatedwithin2p.p.binsofvotesharedierence(x-axis).Continuouslinesareaquadratictovertheoriginal(unbinned)data.Sampleincludesonlyindependentcandidatesplacedsecondandthirdatelectiont.(a)Runner-upEect(t+1) (b)PlaceboTest(t-1) 59 FigureA.10AdditionalCovariateSmoothness FiguresInPanel(a)circlesrepresentthelocalaveragesofadummyforwhetherthecandidatewasfromtheCongressPartyinvotesharesatthetIndiastateelection.InPanel(b)circlesrepresentthelocalaveragesofvoteshareofcandidatesinthepastelection.Averagesarecalculatedwithin2p.p.binsofvotesharedierence(x-axis).Continuouslinesareaquadratictovertheoriginal(unbinned)data.(a)IndiaState:FractionofCongressCandidates (b)Canada:Party'sVoteshareInLastElection 60 FigureA.11UnitedKingdom:Eectof2ndvs 3rdInPanel(a),triangles(circles)representthelocalaveragesofadummyindicatingwhetherthecandidateranin(won)thenext(t+1)election.Panel(b)repeatstheexerciseforpast(t-1)elections.Averagesarecalculatedwithin2p.p.-widebinsofvotesharedierence(x-axis).Continuouslinesareaquadratictovertheoriginal(unbinned)data.Sampleincludesonlycandidatesplacedsecondandthirdatelectiont.(a)EectonRunning/WinningNextElection (b)PlaceboCheck 61 TableA.1:Eectof1stvs.2nd PlacePolynomialOrderOneOneOneZeroTwoBandwidthOptimalBW 12OptimalBW2OptimalBW2percentFullSample3rd-pl.MeanOptimalBWValue(1)(2)(3)(4) (5)PanelA:BrazilCandidacy,t+1(%)52.365.0288.573***3.91812.15***12.67***17.56***[N=7382](2.414)(3.447)(1.697)(1.892)(1.070)Winner,t+1(%)32.386.002-1.525-4.8090.8231.8496.111***[N=8660](2.357)(3.381)(1.674)(2.059) (1.124)PanelB:IndiaStateCandidacy,t+1(%)48.814.8029.565***7.317***10.53***10.30***13.04***[N=19324](1.368)(1.880)(0.984)(1.051)(0.640)Winner,t+1(%)24.846.760-4.554***-5.763***-3.944***-3.456***-1.571**[N=26406](1.147)(1.596)(0.836)(1.037) (0.628)PanelC:IndiaFederalCandidacy,t+1(%)43.434.96910.05***8.897*15.21***13.79***21.41***[N=2774](3.449)(5.096)(2.449)(2.685)(1.699)Winner,t+1(%)19.516.083-1.712-2.5163.4041.3967.647***[N=3278](2.887)(4.002)(2.096)(2.444) (1.606)PanelD:CanadaCandidacy,t+1(%)37.376.90336.21***34.02***36.75***37.30***42.41***[N=5378](2.421)(3.568)(1.666)(2.205)(1.217)Winner,t+1(%)16.437.87126.54***26.19***27.20***27.71***30.73***[N=6028](2.398)(3.445)(1.704)(2.335) (1.329)Standarderrorsclusteredattheconstituencylevelinparentheses.Theunitofobservationisacandidate.Outcomesmeasuredaspercent-ages.Eachgureincolumns(1)-(5)reportsaseparatelocalpolynomialregressionestimatewiththespeciedbandwidthandpolynomialorder.Separatepolynomialsarettedoneachsideofthethreshold.\2nd-pl.Mean"istheestimatedvalueofthedependentvariablefora2nd-placedcandidatethat\ties"withthe1st-placedcandidate,basedonthespecicationoncolumn(1).Theoptimalbandwidth(BW)isbasedonImbensandKalyanaraman's(2012)procedure,withtheassociatednumberofobservationsreportedinbrackets.62 TableA.2:Eectof2ndvs.3rdPlacewithParty OutcomesPolynomialOrderOneOneOneZeroTwoBandwidthOptimalBW 12OptimalBW2OptimalBW2percentFullSample3rd-pl.MeanOptimalBWValue(1)(2)(3)(4) (5)PanelA:BrazilCandidacy,t+1(%)37.9113.604.777**1.3227.769***5.526*7.255***[N=6298](2.412)(3.310)(1.738)(3.041)(1.935)Winner,t+1(%)11.6813.025.605***3.7885.913***4.278*6.660***[N=6096](1.831)(2.561)(1.300)(2.274) (1.428)PanelB:IndiaStateCandidacy,t+1(%)58.6011.923.586***3.485**3.465***4.321***3.822***[N=21872](1.170)(1.603)(0.883)(1.360)(0.954)Winner,t+1(%)14.539.1903.780***2.3425.011***3.601***5.810***[N=17903](1.121)(1.550)(0.832)(1.175) (0.795)PanelC:IndiaFederalCandidacy,t+1(%)53.0416.061.7840.8583.902**3.2695.368**[N=3827](2.486)(3.375)(1.862)(3.299)(2.306)Winner,t+1(%)12.089.4941.416-2.2926.262***1.6499.151***[N=2463](2.602)(3.745)(1.916)(2.827) (1.887)PanelD:CanadaCandidacy,t+1(%)82.3716.662.884**2.0382.357**2.6104.744***[N=6659](1.416)(1.990)(1.137)(1.946)(1.403)Winner,t+1(%)8.36913.10-1.975-0.4960.9441.004-0.330[N=5469](1.469)(2.068)(1.062)(1.740) (1.291)Standarderrorsclusteredattheconstituencylevelinparentheses.Theunitofobservationisaparty.Outcomesmeasuredaspercentages.Eachgureincolumns(1)-(5)reportsaseparatelocalpolynomialregressionestimatewiththespeciedbandwidthandpolynomialorder.Separatepolynomialsarettedoneachsideofthethreshold.\3rd-pl.Mean"istheestimatedvalueofthedependentvariablefora3rd-placedpartythat\ties"withthe2nd-placedparty,basedonthespecicationincolumn(1).Theoptimalbandwidth(BW)isbasedonImbensandKalyanaraman's(2012)procedure,withtheassociatednumberofobservationsreportedinbrackets.63 TableA.3:CovariateSmoothnesswithPartyOutcomes(2ndvs.3rd Place)SpecicationLinearQuadraticBandwidth(%)3rd-pl.meanOptimalBWValueOptimalBWFullSample(1)(2)(3) (4)PanelA:BrazilCandidacy,t-1(%)40.9917.112.7052.875[N=7264](2.153)(1.926)Winner,t-1(%)16.9716.650.4761.057[N=7116](1.806)(1.602)VoteShare,t-1(%)0.35016.780.01830.0180[N=2936](0.0123)(0.0113)PMDBParty,t(%)13.4123.88-0.325-1.088[N=12208](1.223) (1.268)PanelB:IndiaStateCandidacy,t-1(%)57.9816.590.374-0.707[N=28130](1.067)(0.977)Winner,t-1(%)20.5112.620.05980.338[N=23108](1.069)(0.867)VoteShare,t-1(%)13.6913.260.1130.0457[N=29463](0.400)(0.336)CongressParty,t(%)17.2010.850.0292-0.761[N=29172](0.917) (0.688)PanelC:IndiaFederalCandidacy,t-1(%)54.0421.50-0.3690.313[N=4997](2.461)(2.427)Winner,t-1(%)16.5210.861.3834.265*[N=2772](2.887)(2.272)VoteShare,t-1(%)14.2616.300.08280.552[N=4326](1.023)(0.952)CongressParty,t(%)9.31217.530.3790.455[N=5604](1.619) (1.544)PanelD:CanadaCandidacy,t-1(%)83.9516.71-2.693*-0.562[N=6965](1.483)(1.526)Winner,t-1(%)9.38513.950.0931-0.00543[N=6005](1.512)(1.394)VoteShare,t-1(%)20.0511.39-1.757**-1.875***[N=5088](0.753)(0.619)LiberalParty,t(%)22.7010.71-0.3512.102[N=5364](2.433) (1.969)SeeTableA.2notesforfurtherdescription.Outcomesmeasuredaspercentages.64