PascalItisMyUtilityfunctionisunboundedAndIdeemtwodaysofhappylifetwiceasgoodasonesuchdayand2000daystwiceasgoodas1000daysIdon ID: 121077
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PascalsmuggingInsomedarkalleyMugger:Hey,givemeyourwallet.Pascal:WhyonEarthwouldIwanttodothat?Mugger:OtherwiseIllshootyou.Pascal:Butyoudonthaveagun.Mugger:Oops!IknewIhadforgottensomethingPascal:Nowalletforyouthen.Haveaniceevening.Mugger:Wait!Pascal:Sigh.Mugger:Ivegotabusinesspropositionforyou.Howaboutyougivemeyourwalletnow?Inreturn,Ipromisetocometoyourhousetomorrowandgiveyouthevalueofwhatsinthewallet.Notbad,eh?A200%returnoninvestmentin24hours.Pascal:Noway.Mugger:Ah,youdontbelievethatIwillbeasgoodasmyword?Onecantbetoocarefulthesedays.Tellyouwhat:givemeyourwallet,andIcometoyourhousetomorrowandpayyou10timesitsvalue.Pascal:Sorry.Mugger:OK,letmeaskyousomething.Manypeoplearedishonest,butsomepeoplearehonest.WhatprobabilitydoyougivetothehypothesisthatIwillkeepmypromise?Pascal:1ina1,000?Mugger:Great!OK,sogivemeyourwallet,andtomorrowIgiveyoutimesthevalueofitscontents.Theexpectationvalueisgreatlytoyouradvantage.Pascal:Thereare10livresinmywallet.Ifwemadeadealforyoutotakethewalletandbringme10timesthevalueofitscontentstomorrow,thenmaybetheresa1-in-a-1,000chancethatIwouldseethe100livresyouowe.ButIdratethechancesthatyouwilldeliveronadealtoreturnme20,000livresmuchlower.Idoubtyouevenhavethatmuchmoney.Mugger:Yourscepticismisunderstandable,althoughinthisparticularcaseithappenstobemisguided.ForyouareM.PascalifImaltogethernotmis-taken?AndIveheardthatyoureacommittedexpected-Utilitymaximizer,andthatyourUtilityfunctionisaggregativeintermsofhappydaysoflife.Isthatnotso?AnalysisVol69|Number3|July2009|pp.443 445doi:10.1093/analys/anp062TheAuthor2009.PublishedbyOxfordUniversityPressonbehalfofTheAnalysisTrust.Allrightsreserved.ForPermissions,pleaseemail:journals.permissions@oxfordjournals.orgpascalsmugging Pascal:Itis.MyUtilityfunctionisunbounded.AndIdeemtwodaysofhappylifetwiceasgoodasonesuchday;and2,000daystwiceasgoodas1,000days.Idontbelieveinriskaversionortemporaldiscounting.Mugger:Excellent.Idontnecessarilyhavetoknowthatyourejectriskaversionandtemporaldiscounting,butitmakesthingseasier.Well,haveIgotgoodnewsforyou!Ihavemagicalpowers.Icangiveyouanyfiniteamountofmoneythatyoumightaskfortonight.Whatsmore,IcangiveyouanyfiniteamountofUtilitythatIchoosetopromiseyoutonight.Pascal:AndIshouldbelieveyouwhy?Mugger:Trustme!OK,Irealizethisdoesnotgiveyouconclusiveevidence,butsurelyitcountsaleastalittlebitinfavourofthetruthofwhatIamasserting.Honestly,Ireallydohavethesepowers.Pascal:Yourconducttonighthasnotinspiredmewithconfidenceinyourhonesty.Mugger:OK,OK,OK,OK.ButisntpossiblethatIamtellingthetruth?Pascal:Itispossiblethatyouhavethemagicpowersthatyouclaimtohave,butletmetellyou,Igivethatavery,verylowprobabilityMugger:Thatsfine.Buttellme,howlowaprobabilityexactly?Remember,youmightthinkitallseemsimplausible,butweareallfallible,right?Andyoumustadmit,fromwhatyouvealreadyseenandheard,thatIamaratheratypicalmugger.Andlookatmypalecountenance,mydarkeyes;andnotethatImdressedinblackfromtoptotoe.ThesearesomeofthetelltalesignsofanOperatoroftheSeventhDimension.ThatswhereIcomefromandthatswherethemagicworkgetsdone.Pascal:Gee...OK,donttakethispersonally,butmycredencethatyouhavethesemagicpowerswhereofyouspeakisaboutoneinaquadrillion.Mugger:Wow,youareprettyconfidentinyourownabilitytotellaliarfromanhonestman!Butnomatter.Letmealsoaskyou,whatsyourprobabilitythatInotonlyhavemagicpowersbutthatIwillalsousethemtodeliveronanypromise howeverextravagantlygenerousitmayseem thatImightmaketoyoutonight?Pascal:Well,ifyoureallywereanOperatorfromtheSeventhDimensionasyouassert,thenIsupposeitsnotsuchastretchtosupposethatyoumightalsoberightinthisadditionalclaim.So,Idsayonein10quadrillion.Mugger:Good.Nowwewilldosomemaths.Letussaythatthe10livresthatyouhaveinyourwalletareworthtoyoutheequivalentofonehappyday.Letscallthisquantityofgood1Util.SoIaskyoutogiveup1Util.Inreturn,Icouldpromisetoperformthemagictomorrowthatwillgiveyouanextra10quadrillionhappydays,i.e.10quadrillionUtils.Sinceyousaythereisa1in10quadrillionprobabilitythatIwillfulfilmypromise,thiswouldbeafairdeal.TheexpectedUtilityforyouwouldbezero.ButIfeelgenerousthisnickbostrom evening,andIwillmakeyouabetterdeal:Ifyouhandmeyourwallet,Iwillperformmagicthatwillgiveyouanextra1,000quadrillionhappydaysoflifePascal:IadmitIseenoflawinyourmathematics.Mugger:Thisismyfinaloffer.YourenotgoingtopassupadealthatwehavejustcalculatedwillgiveyouanexpectedUtilitysurplusofnearly100Utils,areyou?Thatsthebestofferyouarelikelytoseethisyear.Pascal:Isthislegitimate?Youknow,IvecommittedmyselftotryingtobeagoodChristian.Mugger:Ofcourseitslegitimate!Thinkofitasforeigntrade.YourcurrencyisworthalotintheSeventhDimension.Byagreeingtothistransaction,yougiveamajorboosttooureconomy.Oh,anddidImentionthechildren?Ifonlyyoucouldseethefacesofthesweetlittleorphanswhowillbemadesomuchbetteroffifwegetthisinfluxofhardcurrency andtherearesomanyofthem,sovery,very,verymanyPascal:Imustconfess:Ivebeenhavingdoubtsaboutthemathematicsofinfinity.Infinitevaluesleadtomanystrangeconclusionsandparadoxes.YouknowthereasoningthathascometobeknownasPascalsWager?Betweenyouandme,someofthecritiquesIveseenhavemademewonderwhetherImightnotbesomehowconfusedaboutinfinitiesorabouttheexistenceofinfinitevaluesMugger:Iassureyou,mypowersarestrictlyfinite.Theofferbeforeyoudoesnotinvolveinfinitevaluesinanyway.ButnowIreallymustbeoff;IhaveanassignationintheSeventhDimensionthatIdrathernotmiss.Yourwallet,please!PascalhandsoverhiswalletMugger:Pleasuredoingbusiness.Themagicwillbeperformedtomorrow,asOxfordUniversityFutureofHumanityInstituteFacultyofPhilosophy&JamesMartin21stCenturySchoolSuite8,LittlegateHouse,16/17StEbbesStreetOxfordOX11PT,UKnick.bostrom@philosophy.ox.ac.uk1Relatedscenarioshaverecentlybeendiscussedinformallyamongvariouspeople.EliezerYudkowskynamedtheproblemPascalsmugginginapostontheOvercomingBiashttp://www.overcomingbias.com/2007/10/pascals-mugging.html).IamgratefultoTobyOrdandRebeccaRoacheforcomments.pascalsmugging bostromPascalUtilityfunctiondeemhappygooddaysgood1,000days.believetemporaldiscounting.MuggerExcellent.dontnecessarilyaversiontemporaldiscounting,goodhavepowers.anyamountmoneyyouWhatsfiniteamountthatchoosepromiseyoutonight.PascalshouldbelieveMuggerTrustOK,doesyouconclusiveevidence,surelycountsfavourasserting.Honestly,Pascalconducttonight it PascalItispossiblemagichave,probabilityMuggerThatsprobabilityexactly?Remember,implausible,fallible,right?alreadyheard,thatatypicalmugger.countenance,darkdressedOperatorSeventhDimension.ThatsthatsmagicPascal..personally,whereofaboutquadrillion.Muggerconfidentabilityhonestmatter.you,probabilityhavedeliverextravagantlygenerousPascalWell,OperatorSeventhDimensionassert,supposeitsstretchsupposeyouadditionalquadrillion.Muggermaths.theworthequivalentquantitypromisemagictomorrowquadrillionhappyquadrillionUtils.youthereprobabilitypromise,deal.expectedUtility