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1、CompositionRulesin†OriginalandCumulativeProspectTheoryRichardGonzalezGeorgeWuAugust14,2003UniversityofMichiganUniversityofChicagoDept.ofPsychologyGraduateSchoolofBusinessAnnArbor,MI48109Chicago,IL60637gonzo@umich.edugeorge.wu@gsb.uchicago.eduAbstract:Originalandcumulativeprospecttheorydifferinthe
2、compositionruleusedtocombinetheprobabilityweightingfunctionandthevaluefunction.Wetestthesecompositionrulesbyperforminganoveltest.Weapplyestimatesofprospecttheory’sweightingandvaluefunctionobtainedfromtwo-outcomecashequivalents,adomainwhereoriginalandcumulativeprospecttheorycoincide,tothree-outcom
3、ecashequivalents,adomainwherethecompositionrulesofthetwotheoriesdiffer.Wefindsystematicunder-predictionforcumulativeprospecttheoryandsystematicover-predictionfororiginalprospecttheory.Weusethesefindingstomotivatenewareasfortheoreticalandempiricalinvestigation.RunningHeader:CompositionRulesinProsp
4、ectTheoryKeyWords:Rank-dependentexpectedutility;prospecttheory;compositionrules†WethankPeterWakkerforhisusualpreciseandinsightfulcomments.1.INTRODUCTIONTheSt.Petersburg’sParadoxchallengedthenotionthatdecisionmakersshouldchoosetheoptionthatmaximizesexpectedvalue.Bernoulli’s(1738)resolutionoftheSt.
5、Petersburg’sParadoxgeneralizedexpectedvaluemaximizationinoneimportantrespect:thelineartransformationofoutcomesrequiredbyexpectedvaluewasgeneralizedtoallownonlineartransformationsofoutcomes,inparticular,alogarithmicutilityfunction.InthenearlythreecenturiessinceBernoulli,expectedvalueasadescriptive
6、theoryofdecisionmakingunderriskhasadvancedintwoadditionalrespects.First,thelineartreatmentofprobabilitiesunderexpectedvalueandexpectedutilityhasbeengeneralizedundermodelsthatare“nonlinearinprobability”(e.g.,Edwards,1954;Kahneman&Tversky,1979;Preston&Baratta,1948).Second,thecompositionruleusedinex
7、pectedvalue,thesumofoutcomesweightedbytheirrespectiveprobabilities,hasbeengeneralized(e.g.,Kahneman&Tversky,1979;Quiggin,1982).Alargefamilyofmoderndescriptivetheoriesofdecisionunderriskdepartfromexpectedvaluemaximizati
