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1、AnalysisoftheReliabilityandBehaviorofMajorityandPluralityVotingSystemsSherifYacoub,XiaofanLin,JohnBurnsInformationInfrastructureLaboratoryHPLaboratoriesPaloAltoHPL-2002-118thApril25,2002*E-mail:{sherif_yacoub,xiaofan_lin,john_burns}@hp.commajorityVotingisawell-knowntechniqueusedt
2、ocombinedecisionsofpeerexperts.Itvoting,haswideapplicationinmanydomains.VotingisusedinfaulttolerantapplicationstomaskerrorsfromoneormoreexpertsusingN-ModularpluralityRedundancy(NMR)andN-versionProgramming.Itisalsousedinpatternvoting,expertrecognitionapplicationswheredecisionsfrom
3、severalclassifierscanleadtocombination,betterrecognitionresults.fault-toleranceThereareseveralstrategiesforvotingincluding:majority,weightedvoting,plurality,instancerunoffvoting,thresholdvoting,andthemoregeneralweightedk-out-of-nsystems.Touseavotingschemainanyapplicationdomain,we
4、havetounderstandthevarioustradeoffsandparametersandhowtheyimpactthecorrectness,reliability,andconfidenceinthefinaldecisionmadebythevotingsystem.Inthispaper,weanalyzethebehavioroftwovotingschemas:majorityvotingandpluralityvoting.Weconductsyntheticstudiesusingasimulatorthatwedevelo
5、pedtoanalyzeresultsfromeachexpert,applyavotingmechanism,andanalyzethevotingresults.Thesimulatorbuildsadecisiontreeandusesadepth-firsttraversalalgorithmtoobtainreliabilityofthesystemandotherfactorsthatdescribethevotingbehavior.Forthisanalysis,wedefineandstudythefollowingbehaviorso
6、favotingsystem:1)theprobabilityofreachingaconsensus,“Pc”;2)reliabilityofthevotingsystem,“R”;3)certainlyindex,“T”;and4)theconfidenceindex,“C”.Theparameterscontrollingtheanalysisarethenumberofparticipatingexperts(orunits),thenumberofpossibleoutputsymbolsthatcanbeproducedbyanexpert,
7、theprobabilitydistributionofeachexpert’soutput,andthevotingschema.Thisstudyunleashesseveralbehaviorsofavotingsystemandintroducesasyntheticapproachtocomputeitsreliability.*InternalAccessionDateOnlyApprovedforExternalPublicationãCopyrightHewlett-PackardCompany20021INTRODUCTIONVotin
8、gisageneraltechniquethatfindsapplication
