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1、UtilityRepresentationofanIncompletePreferenceRelation∗EfeA.Ok†November2000AbstractWeconsidertheproblemofrepresentinga(possibly)incompletepreferencerelationbymeansofavector-valuedutilityfunction.Continuousandsemicontinuousrepresentationresultsarereportedinthecaseofpref
2、erencerelationsthatare,inasense,not“tooincomplete.”Theseresultsgeneralizesomeoftheclassicalutilityrepresentationtheoremsofthetheoryofindivid-ualchoice,andpavesthewaytowardsdevelopingaconsumertheorythatrealisticallyallowsindividualstoexhibitsome“indecisiveness”onoccasi
3、on.Keywords:Incompletepreferencerelations,utilityrepresentation,partialordersJournalofEconomicLiteratureClassificationnumber:D11.∗WhileIrealizethatthisishighlynonstandardintheprofession,IwouldneverthelessliketodedicatethispapertotheglowingmemoryofmyfatherAyhanTürker;th
4、ebulkofthispaperwaswrittenbyhishospitalbedduringhislastandpainful,yetexceptionallycourageousdays.Inaddition,IthankJamesFosterandMukulMajumdarforbringingtomyattentiontheproblemofrepresentingpartialorderingsbyrealfunctions,JeanPierreBenoit,JuanDubra,BezalelPeleg,BenPola
5、k,andDebrajRayfortheirhelpfulcomments,andJoelSpencerforpointingouttheconnectionbetweenthisproblemandthedimensiontheoryforposets.ThecommentsoftheseminarparticipantsatAlicante,Columbia,NYU,Princeton,Rochester,SMUandYale,andespeciallythoseofthetwoanonymousreferees,haveim
6、provedtheexpositionsubstantially.SupportfromtheC.V.StarrCenterforAppliedEconomicsatNewYorkUniversityisalsogratefullyacknowledged.†DepartmentofEconomics,NewYorkUniversity,269Mercer.St.,NewYork,NY10003,andDepartmentofEconomics,PrincetonUniversity,Princeton,NJ08544.(Emai
7、l:efe.ok@nyu.edu)11TheProblemandMotivationTraditionally,a(weak)preferencerelationonanonemptychoicesetXisdefinedasacomplete,reflexiveandtransitivebinaryrelation(acompletepreorder)onX.Alloftheseassumptionsarecommonlyviewedasrationalitypostulates,thelattertwobeingconsisten
8、cyrequirementsandtheformerbeingadecisivenessprerequisite.Asitisofinteresttomodelthebehaviorofboundedlyrationalindividualsine
