美国大学生数学建模大赛MCM特等奖论文.docx
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美国大学生数学建模大赛MCM特等奖论文.docx
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美国大学生数学建模大赛MCM特等奖论文
PoliticalAdvertisingBudgetingforObama2012Re-election
Summary
Tospecifytheproblem,weconsiderthesituationtheObamacampaignmeetstoprepareforthe2012re-election.Thetotal91millionUSdollarscampaignfundsisdistributedtotwoaspects:
thenewmediaInternetandpoliticalactivities.WeusetheAnalyticalHierarchyProcessmethodtoobtaintheinvestmenttheObamacampaignshouldpourintothemajorInternetcompanies.Theweighteachcompanyownsisinproportionaltotheexpenditurethecampaignspentonthemin2008.Weconcludethatatotal7millionUSdollarsshouldbepreparedfortheInternet,ofwhich5millionisdirectlyspentandtheremaining2millionincrementalbudgetingisforspecialsituations.
Asforthepoliticalactivities,thenumberofelectoralvotesawardedtoeachstateisthemainfactorinourmodel.Consideringthepreviouselections,therearestatestendtosupporttheDemocraticPartyortheRepublicanParty.ThisisrelativelyconvenientforustomodeltheexpendituredistributedtoeachstatebecausesomestatesareofsmallprobabilityfortheDemocraticPartytofightfor.Wedonottakeintoaccountthe8stateswhichstronglysupporttheRepublicanPartyinpreviouselections.Intheremaining42statesandtheDist.ofColumbia,wedesignarank-orientedmethodtodistributetheremaining84milliondollars;thearrangementforeachstateispresentedinthispaper.
1Introduction
IntheUShistory,eachcandidatehasaelectoralteamaimedatwinningthebattleforthepresidentialelection.Beforetheprimaryelection,teammemberswillcollectalargeamountofinformationtoanalyzetheelectoralsituationofeverystatesoastoknowthemeasurestheyshouldtakeineachstaterespectively.Consideringaspecificstate,whetheritappliestheproportionalorthe“winner-takes-all”systemaffectstheelectiongreatly.Howtospendthecampaignfundsdependtoalargeextentonthenumberofelectoralvotesawardedbythestate.
Tobespecific,weassumethecandidatetobetheincumbentUSpresidentBarackHusseinObamaandbudgetthecampaignfundsforhis2012re-election.SinceObamarepresentstheDemocraticParty,ourmodelaimsathelpingtheObamacampaignwinthebattleagainsttheRepublicanParty.Inthelasttenelections,4statesof56electoralvotessupporttheDemocraticPartystrongly;8statesof36electoralvotessupporttheRepublicanParty,includingNebraskawhichtakestheproportionalsystem.Wehave19statesof214electoralvotestendtosupporttheDemocraticPartyand14statesof145electoralvotestendtosupporttheRepublicanParty.Theother6statesof87electoralvotesarenotsurewhichpartytosupport.Fromthisperspective,theDemocraticPartyhasadvantageovertheRepublicanParty.However,thecompetitorwillimplementhisstrategytofightforthepresidentialposition.Asuccessfularrangementshouldtakedynamicfactorsintoconsideration.
2Assumptions
·Weassumethattheincreasedvotersafterthepoliticalpoliciesimplementsisdirectlyproportionaltotheexpenditurespentinacertainstate.
·Thehighertheclickofthepoliticaladvertisementsis,thegreatertheinfluenceofthepoliticaladvertisementis.
·TheimpactofInternetonthepresidentialelectionhaslimitations,sounlimitedexpenditureontheInternetwillnotworkefficiently.
·WhethertheDemocraticPartyortheRepublicanPartyreachesaspecificstateearlierdoesnotinfluencetheeffectivenessofonlinepoliticaladvertisements.
3ModelEstablishment
Torefinetheproblem,weconsiderbudgetingthecampaignfundstohelptheincumbentUSpresidentBarackHusseinObamawinthe2012’sre-election.Takingalookathispreparationforthe2008presidentialelection,wefindthatmediaandpoliticalactivitiesplayaconsiderablyimportantrole.Exceptfortraditionalmediaadvertisements,webudgetthecampaignfundsfromtwoaspects:
·ThenationwideInternet.Accordingtosurveys,thekeypointthatbringsObamatoatotalsuccessinthe2008USpresidentialelectionisthatthecampaignmakesfulluseoftheInternet.SoalargeamountofthecampaignfundsshouldbepouredintopoliticaladvertisementsontheInternet.
·Thetravelingexpenditurespentineachstate.Togetthesupportofaspecificstate,thecandidatemustgoforpoliticalspeechesandaseriesofotherpoliticalactivitiesinthatstate.Thetraveltothestatecostsaproportionofthetotalcampaignfunds.
Topresentasuccessfulbudgeting,weshouldtakeintoaccountthefactorsconcerningtheInternetandthetravelstoeachstate.
3.1TheInfluenceoftheInternet
Accordingtostatistics,anapproximate85%oftheelectoralfundscollectedbytheObamacampaignarefromtheInternet;andthemajorpartsincludesearchengine,onlineadvertising,networkcommunityandmediaandnewspapernetwork.WeusetheAnalyticalHierarchyProcesstodeterminetheinfluenceofsearchengine,onlineadvertising,networkcommunityandmediaandnewspapernetworkontheeffectivenessofonlinepoliticaladvertisements.ThegradeclassificationisshowninFigure1.
Figure1TheGradeClassificationofOnlinePoliticalAdvertisements
AccordingtoourassumptionsandtheactualcaseoftheInternet,theObamacampaignshouldpayeachnetcompanybasedontheclickontheInternet.Basically,theexpenditureofthe2008electionspentoneachpartcanbeusedtoestimatetheratioofcampaignfundsthatshouldbepouredintotheseInternetcompanies.However,astheInternetindustrydevelops,theweightofeachInternetcompanywillchange.
Wetreat
assearchengine,
asonlineadvertising,
asnetworkcommunityand
asmediaandnewspapernetwork.Nowweinvestigatetheinfluenceofthemontheobject
theeffectivenessofonlinepoliticaladvertisements.Let
betheratiosoftheimportanceof
totheimportanceof
.SincetheexpendituretheObamacampaignspentonsearchengine,onlineadvertising,networkcommunityandmediaandnewspapernetworkare﹩
,﹩
﹩
and﹩
respectively.WecombineitwiththeSaaty’Rule,andtake
,
,
,
,
,
.TheComparisonMatrixisthenobtainedasfallows:
ThemaximalcharacteristicvalueoftheComparisonMatrixis
;therebytheconsistencyindexofMatrix
isobtainedas
.Sincetherandomconsistencyindexofafour-ordermatrixis
therandomconsistencyindexratioofMatrix
is
.Theresultisacceptable.Thecorrespondingnormalizedcharacteristicvectoris
whichistakenastheweightvectorofthefourfactors.
3.1.1TheInfluenceofSearchEngineontheObject
Table1presentsthereportonshareofsearchengineintheUSmarketreleasedbytheMarketStatisticCompanyofAmerica:
Table1ShareofSearchEngineintheUSMarket
WeknowfromTable1thatGoogle,YahooandMicrosoftalmostdominateinthemarketshare.Sothenormalizedmarketshareratiosofthethreesearchengines,
and
canbeusedastheweightofthem;thereforetheweightvectorofthethreesearchenginestotheobject
canbeobtainedas
.
3.1.2TheInfluenceofOnlineAdvertisingontheObject
TheUnitedStateshastwomainonlineadvertisingcompanies:
CentroandBroadband.Intheyear2008theObamacampaignspent﹩
and﹩
onthemrespectively.Theweightsofthetwocompaniesontheobjectarecorrespondingly
and
.Sotheweightvectorofthetwocompaniestotheobjectis
.
3.1.3TheInfluenceofNetworkCommunityontheObject
The2008Obamacampaigntotallyspent﹩
and﹩
onthetwomajornetworkcommunitiesFacebookandCommunityConnect.Inthesamemanner,theweightsofthetwonetworkcommunitiesontheobjectare
and
.Weobtaintheweightvectorofthetwonetworkcommunitiestotheobjectas
.
3.1.4TheInfluenceofMediaandNewspaperNetworkontheObject
TheexpendituretheObamacampaignspentonthetwomainmediaandnewspapernetworkPoliticoandTurnerare﹩
and﹩
.Weassumethattheweightsofthetwonetworksontheobjectare
and
;soweobtaintheweightvectorofthetwonetworkstotheobjectas
.
AccordingtotherelatedUSregulations,acandidatecannotacceptthedonationfromindividualsanymoreoncehereceivesthegovernmentfunding.Thatis,allthecampaignfundsexceptforthegovernmentfundingshouldbecollectedbeforethegovernmentfundingreacheshim.Oncehedeclarestoacceptthegovernmentfunding,thecampaignshouldtrytheirbesttoaccomplishthemaintaskofattractingvoters.TheyneedtoincreasetheinputintheInternetintheprocessoftracingmorevoters.
TheObamacampaignspentapproximately﹩8,000,000ontheInternetin2008,ofwhich﹩3,000,000isspentfromJanuarytoJuly.TheexpenditurespentafterJulyisapproximately﹩3,000,000,whichaccountsfor3/8ofthetotalamountspentontheInternet.WefindthattheObamacampaigncollectedatotalamountof﹩650,000,000fundsinthe2008election,ofwhich
isfromtheInternet;thatisanamountof﹩514,250,000.SincetheObamacampaignplanstocollect﹩1billionfundsforthe2012’selection,anincreaseof
comparedtotheyear2008,weassumeasameratio
ofthatwillbefromtheInternet;thatis﹩850,000,000.
AroughcalculationoftheexpenditurethatshouldbeinvestedintheInternetis
millionUSdollars.Afteracceptingthegovernmentfunding,theinputintheInternetisapproximately
milliondollars.ThisisthebasicinvestmentintheInternetduringthelatermonths;itdoesn’tallowforaccidentalsituationthatmayoccur.TheexpenditurethecompetitorJohnMcCainspentinthe2008’selectionisfarlessthanObama.SotheRepublicPartymusthaverealizedtheimportanceoftheInternetintheelection,thusincreasingtheinvestmentintheInternetinthesamemanner
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