nicholson微观经济理论（答案+ppt+习题库）-250-03-033593-0

POLITICALECONOMICSMANYDECISIONSABOUTRESOURCEALLOCATIONAREMADETHROUGHTHEPOLITICALPROCESSVOTERSMAYCASTBALLOTSONFUNDINGFORLOCALSCHOOLSELECTEDREPRESENTATIVESVOTEONBUDGETSFORPUBLICGOODSSUCHASDEFENSEANDFORPUBLICTRANSFERSWELFAREORUNEMPLOYMENTCOMPENSATIONANDGOVERNMENTREGULATORYAGENCIESSETSTANDARDSFORABROADRANGEOFGOODS,SUCHASSTOCKMARKETTRANSACTIONSORALLOWABLELEVELSOFAIRPOLLUTIONTRADITIONALLYECONOMISTSAVOIDEDANYSPECICANALYSISOFSUCHPROCESSES,ARGUINGTHATTHEYWEREOUTSIDETHECONNESOFSTANDARDECONOMICANALYSISINRECENTYEARS,HOWEVER,THATVIEWHASBEENINCREASINGLYCHALLENGEDASECONOMISTSHAVESOUGHTTOEMPLOYTHESAMEKINDSOFMODELBUILDINGTHATAREUSEDTOSTUDYMARKETSTO,INSTEAD,EXAMINEPOLITICALDECISIONSINTHISCHAPTERWETAKEABRIEFLOOKATTHISRAPIDLYGROWINGAREAOFRESEARCH1TOSETTHESTAGEFORTHISMATERIAL,WERSTPROVIDEABRIEFREVIEWOF“STANDARD”WELFAREECONOMICS,ENDINGWITHARROWSFAMOUSNEGATIVECONCLUSIONABOUTTHEHOPEOFNDINGACCEPTABLEGENERALSOCIALWELFAREFUNCTIONSTHECHAPTERTHENTAKESADECIDEDLYMOREPOSITIVISTTONEBYILLUSTRATINGAVARIETYOFMODELSOFHOWTHEPOLITICALPROCESSACTUALLYWORKS25CHAPTER1THERESTRUCTURINGOFTHISCHAPTERFROMEARLIEREDITIONSWASSUGGESTEDBYTHERECENTAPPEARANCEOFSEVERALTEXTSONTHE“NEWPOLITICALECONOMY”SEETHESUGGESTEDREADINGSFORTHISCHAPTERANDBYMANYHELPFULCONVERSATIONSWITHMYCOLLEAGUEJOHNIRONSSOCIALWELFARECRITERIAWEWILLBEGINOURSTUDYOFTHEPOLITICALPROCESSBYEXAMININGSOMEOFTHEPROBLEMSASSOCIATEDWITHDEVISINGWELFARECRITERIAFORCHOOSINGAMONGFEASIBLEALLOCATIONSOFRESOURCESTHISSUBJECTISTHEMOSTNORMATIVEBRANCHOFMICROECONOMICS,BECAUSEITNECESSARILYINVOLVESMAKINGHARDCHOICESABOUTTHEUTILITYLEVELSOFDIFFERENTINDIVIDUALSINCHOOSINGBETWEENTWOALLOCATIONS,AANDB,THEPROBLEMARISESTHATSOMEINDIVIDUALSPREFERAWHEREASOTHERSPREFERBCOMPARISONSAMONGPEOPLEMUSTBEMADEINORDERTOJUDGEWHICHALLOCATIONISPREFERABLEASMIGHTBEEXPECTED,THEREISNOUNIVERSALLYACCEPTEDCRITERIONFORMAKINGSUCHCHOICESSOCIALWELFARECRITERIAINANEXCHANGEMODELTHEMODELOFEFCIENCYINEXCHANGEDEVELOPEDINCHAPTER17ISUSEFULFORDEMONSTRATINGTHEPROBLEMSINVOLVEDINESTABLISHINGSOCIALWELFARECRITERIACONSIDERTHEEDGEWORTHBOXDIAGRAMINFIGURE251ONLYPOINTSONTHECONTRACTCURVEARECONSIDEREDASPOSSIBLECANDIDATESFORASOCIALOPTIMUMPOINTSOFFTHECONTRACTCURVEAREPARETOINEFCIENTBECAUSEBOTHINDIVIDUALSCANBEMADEBETTEROFFINSODOINGPRESUMABLY,SOCIALWELFARECOULDBEIMPROVEDALONGTHECONTRACTCURVETHEUTILITIESOFTHETWOINDIVIDUALSSMITHANDJONESVARY,ANDTHESEUTILITIESAREDIRECTLYCOMPETITIVESMITHSUTILITYCANBEINCREASEDONLYBYDECREASINGJONESSGIVENTHIS686PARTVIIILIMITSOFTHEMARKETEDGEWORTHBOXDIAGRAMOFEXCHANGETHISDIAGRAMISSIMPLYAREDRAWINGOFFIGURE177THECURVEOS,OJISTHELOCUSOFEFCIENTALLOCATIONSOFXANDYBETWEENSMITHANDJONESALLOCATIONSOFTHISLOCUSAREDOMINATEDBYTHOSEONITINTHATBOTHINDIVIDUALSCANBEMADEBETTEROFFBYMOVINGTOTHECONTRACTCURVEUJ1UJ3US3UJAUSAYSAYJAXJAXSAUS1ABOJOSTOTALYTOTALXFIGURE251SETOFEFCIENTALLOCATIONS,WENOWWISHTODISCUSSPOSSIBLECRITERIAFORCHOOSINGAMONGTHEMIFWEAREWILLINGTOASSUMETHATUTILITYCANBECOMPAREDAMONGINDIVIDUALS,WECANUSETHEPOSSIBLEUTILITYCOMBINATIONSALONGTHECONTRACTCURVEINFIGURE251TOCONSTRUCT2THEUTILITYPOSSIBILITYFRONTIERSHOWNINFIGURE252THECURVEOS,OJRECORDSTHOSEUTILITYLEVELSFORSMITHANDJONESTHATAREOBTAINABLEFROMTHEXEDQUANTITIESOFAVAILABLEGOODSANYUTILITYCOMBINATIONSUCHASPOINTCTHATLIESINSIDETHECURVEOS,OJISPARETOINEFCIENTUSINGTHEUTILITYPOSSIBILITYFRONTIER,WECANNOWREPHRASETHE“PROBLEM”OFWELFAREECONOMICSASBEINGTHEDEVELOPMENTOFCRITERIAFORSELECTINGAPOINTONTHISFRONTIEREQUALITYCRITERIONAFEWSIMPLECRITERIAFORCHOOSINGAPOINTONOS,OJAREEASILYSHOWNONEPOSSIBLEPRINCIPLEWOULDREQUIRECOMPLETEEQUALITYSMITHANDJONESSHOULDENJOYTHESAMELEVELOFWELFARETHISSOCIALWELFARECRITERIONWOULDNECESSITATECHOOSINGPOINTAONTHEUTILITYPOSSIBILITYFRONTIERBECAUSEPOINTACORRESPONDSTOAUNIQUEPOINTONTHECONTRACTCURVE,THESOCIALLYOPTIMALALLOCATIONOFGOODSHASBEENDETERMINEDBYTHISCHOICEINFIGURE251THISALLOCATIONISSEENTOREQUIRETHATSMITHGETSXASANDYAS,WHEREASJONESGETSXAJANDYAJNOTICETHATTHEGOODSXANDYARENOTNECESSARILYCHAPTER25POLITICALECONOMICS6872THISCONSTRUCTIONISIDENTICALTOTHATWEUSEDINCHAPTER16TODERIVETHEPRODUCTIONPOSSIBILITYFRONTIERUTILITYPOSSIBILITYFRONTIERASSUMINGMEASURABILITYOFUTILITY,THEUTILITYPOSSIBILITYFRONTIERCANBEDERIVEDFROMFIGURE251THISCURVEOS,OJSHOWSTHOSECOMBINATIONSOFUTILITYTHATSOCIETYCANACHIEVETWOCRITERIAFORCHOOSINGAMONGPOINTSONOS,OJMIGHTBECHOOSE“EQUAL”UTILITIESFORSMITHANDJONESPOINTAORCHOOSETHEUTILITIESSOTHATTHEIRSUMISTHEGREATESTPOINTBUNDERTHERAWLSCRITERION,THEEFCIENTALLOCATIONBWOULDBEREGARDEDASINFERIORTOEQUALALLOCATIONSBETWEENDANDA45ABCCH11032CH11032DJONESSUTILITYSMITHSUTILITYOSOJUJAUSAFIGURE252DISTRIBUTEDEQUALLYITISEQUALITYOFUTILITIESTHATISREQUIREDBYTHECRITERION,NOTEQUALITYOFGOODSUTILITARIANCRITERIONASIMILARTHOUGHNOTNECESSARILYIDENTICALCRITERIONWOULDBETOCHOOSETHATPOINTONTHEUTILITYPOSSIBILITYFRONTIERFORWHICHTHESUMOFSMITHSANDJONESSUTILITIESISTHEGREATESTTHISWOULDREQUIRETHATTHEOPTIMALPOINTBBECHOSENTOMAXIMIZEUJH11001USSUBJECTTOTHECONSTRAINTIMPLIEDBYTHEUTILITYPOSSIBILITYFRONTIERASBEFORE,POINTBWOULDIMPLYACERTAINALLOCATIONOFXANDYBETWEENSMITHANDJONES,ANDTHISALLOCATIONCOULDBEDERIVEDFROMFIGURE251LATERINTHISCHAPTERWEWILLMAKESOMEUSEOFTHISCRITERIONBECAUSEITISCOMMONLYENCOUNTEREDINPOLITICALANALYSISTHERAWLSCRITERIONANALCRITERIONWECANEXAMINEWASRSTPOSEDBYTHEPHILOSOPHERJOHNRAWLS3RAWLSBEGINSBYENVISIONINGSOCIETYASBEINGINAN“INITIALPOSITION”INWHICHNOONEKNOWSWHATHISORHERNALPOSITIONANDULTIMATEUTILITYWILLBEHETHENASKSWHATKINDOFWELFARECRITERIONWOULDBEADOPTEDBYPEOPLEWHONDTHEMSELVESINSUCHAPOSITIONPOSEDINTHISWAY,SELECTIONOFAWELFARECRITERIONISAPROBLEMINBEHAVIORUNDERUNCERTAINTY,BECAUSENOONEKNOWSEXACTLYHOWTHECRITERIONCHOSENWILLAFFECTHISORHERPERSONALWELLBEINGFROMHISINITIALPREMISERAWLSCONCLUDESTHATINDIVIDUALSWOULDBEVERYRISKAVERSEINTHEIRSELECTIONOFACRITERIONSPECICALLY,HEASSERTSTHATMEMBERSOFSOCIETYWOULDCHOOSETODEPARTFROMPERFECTEQUALITYONLYONTHECONDITIONTHATTHEWORSTOFFPERSONUNDERANUNEQUALDISTRIBUTIONOFUTILITIESWOULDACTUALLYBEBETTEROFFTHANUNDEREQUALITYINTERMSOFFIGURE252UNEQUALDISTRIBUTIONSSUCHASBWOULDBEPERMITTEDONLYWHENTHEATTAINABLEEQUALDISTRIBUTIONSWHICHLIEALONGTHE45LINEWEREBELOWPOINTDEQUALDISTRIBUTIONSTHATLIEBETWEENDANDAARE,ACCORDINGTORAWLS,SUPERIORTOBBECAUSETHEWORSEOFFINDIVIDUALSMITHISBETTEROFFTHERETHANUNDERALLOCATIONBTHERAWLSCRITERIONTHEREFORESUGGESTSTHATMANYEFCIENTALLOCATIONSMAYNOTBESOCIALLYDESIRABLEANDTHATSOCIETIESMAYCHOOSEEQUALITYEVENATCONSIDERABLEEFCIENCYCOSTSSUCHACONCLUSIONISNOTUNIVERSALLYSHAREDBYECONOMISTS,MANYOFWHOMARGUETHATTHECRITERIAPROPOSEDAREUNNECESSARILYRISKAVERSEINDIVIDUALSINTHEINITIALPOSITIONMAYINSTEADPREFERTOGAMBLETHATTHEYWILLBETHEWINNERSUNDERANUNEQUALNALDISTRIBUTION,ANDSUCHMOTIVESMAYDOMINATEIFTHELIKELIHOODOFBEINGTHEWORSEOFFINDIVIDUALISSMALL4STILL,RAWLSSCONCEPTIONOFUSINGTHE“INITIALPOSITION”METHODOLOGYTOCONCEPTUALIZEHOWINDIVIDUALSMIGHTMAKESOCIALDECISIONSISANINTRIGUINGONETHATHASBEENWIDELYUSEDINOTHERINVESTIGATIONSSOCIALWELFAREFUNCTIONSAMOREGENERALAPPROACHTOSOCIALWELFAREWHICHASSPECIALCASESINCLUDESTHETHREECRITERIAWEDISCUSSEDABOVECANBEOBTAINEDBYEXAMININGTHECONCEPTOFA688PARTVIIILIMITSOFTHEMARKET3JRAWLS,ATHEORYOFJUSTICECAMBRIDGE,MAHARVARDUNIVERSITYPRESS,19714SEE,FOREXAMPLE,KJARROW,“SOMEORDINALISTUTILITARIANNOTESONRAWLSSTHEORYOFJUSTICE,”JOURNALOFPHILOSOPHYMAY1973245263SOCIALWELFAREFUNCTION5THISFUNCTIONMIGHTDEPENDONLYONSMITHSANDJONESSUTILITYLEVELSSOCIALWELFAREH11005WUS,UJ251THESOCIALCHOICEPROBLEM,THEN,ISTOALLOCATEXANDYBETWEENSMITHANDJONESSOASTOMAXIMIZEWTHISPROCEDUREISPICTUREDINFIGURE253THECURVESLABELEDW1,W2,ANDW3REPRESENTSOCIALINDIFFERENCECURVES,INTHATSOCIETYISINDIFFERENTABOUTWHICHUTILITYCOMBINATIONONAPARTICULARCURVEISCHOSEN6POINTEISTHEOPTIMALPOINTOFSOCIALWELFAREUNDERTHEBERGSONCRITERIONTHISISTHEHIGHESTLEVELOFWACHIEVABLEWITHTHEGIVENUTILITYPOSSIBILITYFRONTIERASBEFORE,ITISNECESSARYTOGOFROMPOINTETOTHEEDGEWORTHBOXDIAGRAMTODETERMINETHESOCIALLYOPTIMALALLOCATIONOFGOODSCONICTSBETWEENEFCIENCYANDEQUITYFIGURE253DEMONSTRATESACONCEPTUALWAYOFCHOOSINGADISTRIBUTIONOFUTILITIESTHATMAXIMIZESSOCIALWELFARETHEGUREAGAINILLUSTRATESTHEIMPORTANTDISTINCTIONTOBEMADEBETWEENTHEGOALSOFEQUITYANDEFCIENCYALLOFTHEPOINTSONOS,OJCHAPTER25POLITICALECONOMICS6895THISCONCEPTWASRSTDEVELOPEDBYABERGSONIN“AREFORMULATIONOFCERTAINASPECTSOFWELFAREECONOMICS,”QUARTERLYJOURNALOFECONOMICS52FEBRUARY19383103346UNDERTHE“EQUALITY”CRITERIONTHESOCIALWELFAREFUNCTIONWOULDHAVELSHAPEDINDIFFERENCECURVES,WHEREASAUTILITARIANSOCIALWELFAREFUNCTIONTHATSOUGHTTOMAXIMIZETHESUMOFUTILITIESWOULDHAVEINDIFFERENCECURVESTHATAREPARALLELSTRAIGHTLINESWITHASLOPEOFH110021USINGASOCIALWELFAREFUNCTIONTOFINDTHESOCIALOPTIMUMIFWECANPOSTULATETHEEXISTENCEOFASOCIALWELFAREFUNCTIONHAVINGTHEINDIFFERENCECURVESW1,W2,ANDW3,ITISPOSSIBLETOCONCEPTUALIZETHEPROBLEMOFSOCIALCHOICEITISCLEARTHATEFCIENCYBEINGANOS,OJISNECESSARYFORAWELFAREOPTIMUM,BUTTHISISNOTSUFCIENT,ASMAYBESEENBYCOMPARINGPOINTSDANDFJONESSUTILITYSMITHSUTILITYOSOJW1W2W3UJEUSEDEFFIGURE253AREEFCIENTBYTHEPARETOCRITERIONHOWEVER,SOMEOFTHEEFCIENTPOINTSREPRESENTFARMORESOCIALLYDESIRABLEDISTRIBUTIONSTHANDOOTHERSASWITHTHERAWLSCRITERION,THEREAREINFACTMANYINEFCIENTPOINTSSUCHASFTHATARESOCIALLYPREFERREDTOEFCIENTPOINTSSUCHASDITSOMETIMESMAYBEINSOCIETYSINTERESTTOCHOOSESEEMINGLYINEFCIENTALLOCATIONSOFRESOURCESIFTHETRULYOPTIMALALLOCATIONPOINTEISUNATTAINABLEEXAMPLE251EQUITABLESHARINGAFATHERARRIVESHOMECARRYINGANEIGHTPIECEPIZZAHOWSHOULDHESHAREITBETWEENHISTWORAVENOUSTEENAGERSSUPPOSETEEN1HASAUTILITYOFPIZZAFUNCTIONOFTHEFORMU1H110052H20857X1H33526,252ANDTEEN2THELARGEROFTHETWOHASAUTILITYFUNCTIONOFTHEFORMU2H11005H20857X2H33526253THELEASTRESISTANCEOPTIONWOULDBETOSHARETHEPIZZAEQUALLYFOURSLICESEACHINTHISCASEU1H110054,U2H110052ALTERNATIVELY,ABENEVOLENTFATHERRECOGNIZESTEEN2SGREATERNEEDSANDOPTSFORANALLOCATIONTHATPROVIDESEQUALUTILITYINTHISCASEX1H1100516,X2H1100564,U1H11005U2H11005253ASATHIRDSIMPLEALTERNATIVE,AUTILITARIANFATHERMIGHTSEEKTOMAXIMIZETHESUMOFHISTEENSUTILITYBYCHOOSINGX1H1100564,X2H1100516,U1H11005506,U2H11005126ANDU1H11001U2H11005632APROBABILISTICFATHERAFATHERFAMILIARWITHPROBABILITYTHEORYMIGHTTURNTHISWHOLEPROBLEMOVERTOTHETEENSTODECIDEBUTBECAUSETHETEENSDESIRESAREDIRECTLYCOMPETITIVE,ITISUNLIKELYTHEYWILLARRIVEATAUNANIMOUSDECISIONWITHFULLINFORMATIONIF,HOWEVER,THEFATHEROFFERSTHETHREEPOSSIBLEALLOCATIONSLISTEDABOVEANDSAYSHEWILLIPACOINTODETERMINEWHOGETSWHICHPORTIONUNDEREACH,EXPECTEDUTILITYMAXIMIZATIONWOULDYIELDUNANIMITYEXPECTEDUTILITIESFROMACOINIPTHATYIELDSTEEN1EITHER16OR64PIECESISEU1H110055253H110015506H11005380SIMILARLY,FORTEEN2,254EU2H110055253H110015126H11005190HENCE,INTHISCASE,EACHTEENWOULDOPTFORTHERST,EQUALALLOCATION,BECAUSEEACHGETSHIGHEREXPECTEDUTILITYFROMITTHANFROMTHEIPARAWLSIANFATHERIFTHEFATHERCOULDSUBJECTEACHOFHISTEENSTOA“VEILOFIGNORANCE”SONEITHERWOULDKNOWHISORHERIDENTITYUNTILTHEPIZZAISSERVED,THEVOTINGMIGHTBESTILLDIFFERENTIFEACHTEENFOCUSESONAWORSTCASESCENARIO,EACHWOULDOPTFORTHEEQUALUTILITYALLOCATIONBECAUSEITENSURESTHATUTILITYWILLNOTFALLBELOW253BUTTHATMAYASSUMETOOMUCHRISKAVERSIONIFEACHTEENBELIEVESHEORSHEHASA5050CHANCEOFBEINGLABELED“1”OR“2,”EXPECTEDUTILITIESAREIX1H11005X2H110054EUH1100554H1100152H110053255IIX1H1100516,X2H1100564EUH110055253H110015253H11005253IIIX1H1100564,X2H1100516EUH110055506H110015126H11005316690PARTVIIILIMITSOFTHEMARKETIFTHETEENSVOTEONLYONTHEBASISOFEXPECTEDUTILITY,EACHMIGHTNOWOPTFORTHEUTILITARIANSOLUTIONTHATIS,IIIQUERYMIGHTTHEDEGREEOFRISKAVERSIONEXHIBITEDBYTHETEENSCHANGETHEIRVOTINGINTHERAWLSIANSITUATION,ORHASITALREADYBEENACCOUNTEDFORINTHECALCULATIONTHEARROWIMPOSSIBILITYTHEOREMTHEBERGSONSOCIALWELFAREFUNCTION,THEN,PROVIDESAUSEFULTOOLFORDEMONSTRATINGPARTICULARASPECTSOFTHEPROBLEMOFSOCIALCHOICEWEMUSTRECOGNIZE,HOWEVER,THATTHISTOOLISONLYACONCEPTUALONEOFFERINGLITTLEGUIDANCEFORTHEDEVELOPMENTOFPRACTICALPOLICYWEHAVESOFARBEGGEDTHEQUESTIONOFHOWSUCHAFUNCTIONISESTABLISHEDORWHATTHEPROPERTIESOFTHEFUNCTIONARELIKELYTOBEHEREWEWILLEXAMINETHEAPPROACHTOSUCHQUESTIONSTAKENBYKJARROWANDOTHERS7THEBASICPROBLEMARROWVIEWSTHEGENERALSOCIALWELFAREPROBLEMASONEOFCHOOSINGAMONGSEVERALFEASIBLE“SOCIALSTATES”ITISASSUMEDTHATEACHINDIVIDUALINSOCIETYCANRANKTHESESTATESACCORDINGTOTHEIRDESIRABILITYTHEQUESTIONARROWRAISESIS,DOESTHEREEXISTARANKINGOFTHESESTATESONASOCIETYWIDESCALETHATFAIRLYRECORDSTHESEINDIVIDUALPREFERENCESSYMBOLICALLY,ASSUMETHEREARETHREESOCIALSTATESA,B,ANDCANDTWOINDIVIDUALSINSOCIETYSMITHANDJONESSUPPOSETHATSMITHPREFERSATOBWEWILLDENOTETHISBYAPSB,WHEREPSREPRESENTSTHEWORDS“ISPREFERREDBYSMITHTO”ANDBTOCTHESEPREFERENCESCANBEWRITTENASAPSBANDBPSCIFSMITHISTOBE“RATIONAL,”ITSHOULDTHENBETHECASETHATAPSCPREFERENCESSHOULDBETRANSITIVESUPPOSEALSOTHATAMONGTHETHREESTATES,JONESHASPREFERENCESCPJA,APJB,ANDCPJBARROWSIMPOSSIBILITYTHEOREMCONSISTSOFSHOWINGTHATAREASONABLESOCIALRANKINGOFTHESETHREESTATESCALLTHISRANKINGPCANNOTEXISTTHEARROWAXIOMSTHECRUXOFTHISTHEOREMISTODENEWHATISMEANTBYA“REASONABLESOCIALRANKING”ARROWASSUMESTHATANYSOCIALRANKINGPSHOULDOBEYTHEFOLLOWINGSIXSEEMINGLYUNOBJECTIONABLEAXIOMSHEREPISTOBEREAD“ISSOCIALLYPREFERREDTO”1ITMUSTRANKALLSOCIALSTATESEITHERAPB,BPA,ORAANDBAREEQUALLYDESIRABLEAIBFORANYTWOSTATESAANDB2THERANKINGMUSTBETRANSITIVEIFAPBANDBPCORBIC,THENAPC3THERANKINGMUSTBEPOSITIVELYRELATEDTOINDIVIDUALPREFERENCESIFAISUNANIMOUSLYPREFERREDTOBBYSMITHANDJONES,THENAPBCHAPTER25POLITICALECONOMICS6917SEEKJARROW,SOCIALCHOICEANDINDIVIDUALVALUES,2NDEDNEWHAVEN,CTYALEUNIVERSITYPRESS,19634IFNEWSOCIALSTATESBECOMEFEASIBLE,THISFACTSHOULDNOTAFFECTTHESOCIALRANKINGOFTHEORIGINALSTATESIF,BETWEENAANDB,APB,THENTHISWILLREMAINTRUEIFSOMENEWSTATEDBECOMESFEASIBLE85THESOCIALPREFERENCERELATIONSHOULDNOTBEIMPOSED,SAY,BYCUSTOMITSHOULDNOTBETHECASETHATAPBREGARDLESSOFTHETASTESOFINDIVIDUALSINSOCIETY6THERELATIONSHIPSHOULDBENONDICTATORIALONEPERSONSPREFERENCESSHOULDNOTDETERMINESOCIETYSPREFERENCESARROWSPROOFARROWWASABLETOSHOWTHATTHESESIXCONDITIONSALLOFWHICHSEEMETHICALLYREASONABLEONTHESURFACEARENOTCOMPATIBLEWITHONEANOTHERNOGENERALSOCIALRELATIONSHIPOBEYINGCONDITIONS1TO6EXISTSUSINGTHEPREFERENCESOFSMITHANDJONESAMONGA,B,ANDC,ITISPOSSIBLETOSEETHEKINDOFINCONSISTENCIESTHATCANARISEINSOCIALCHOICEBECAUSEBPSCANDCPJB,ITMUSTBETHECASETHATSOCIETYISINDIFFERENTBETWEENBANDCBICOTHERWISE,SOCIETYSPREFERENCESWOULDBEINACCORDWITHONLYONEINDIVIDUALANDAGAINSTTHEOTHER,ANDTHISWOULDVIOLATEAXIOM6REQUIRINGNONDICTATORSHIPBECAUSEBOTHSMITHANDJONESPREFERATOB,CONDITIONS3AND5REQUIRETHATAPBHENCE,BYTRANSIVITYAXIOM2,APCBUT,AGAIN,THISISAVIOLATIONOFTHENONDICTATORSHIPASSUMPTION,BECAUSEAPSCBUTCPJATHUS,INTHISSIMPLECASE,ANINCONSISTENCYARISESINTHEATTEMPTTOCONSTRUCTASOCIALPREFERENCERELATIONSHIPADMITTEDLY,THISEXAMPLEISABITCONTRIVED,BUTITDOESILLUSTRATECLEARLYTHEPROBLEMSOFTRYINGTOAGGREGATEDIVERGENTPATTERNSOFINDIVIDUALPREFERENCESINTOSOMEREASONABLESOCIALPATTERNTHEIMPORTANCEOFARROWSWORKISTOSHOWTHATANYSOCIALDECISIONRULECHOSENMUSTVIOLATEATLEASTONEOFTHEPOSTULATESEMBODIEDINAXIOMS1THROUGH6SIGNICANCEOFTHEARROWTHEOREMMUCHRESEARCHINSOCIALCHOICETHEORYHASBEENFOCUSEDONARROWSFUNDAMENTALRESULTANDONWHETHERITCONTINUESTOHOLDUNDERPOTENTIALREVISIONSINTHESETOFBASICPOSTULATESINGENERAL,THEIMPOSSIBILITYRESULTAPPEARSTOBERATHERROBUSTTOMODESTCHANGESINTHESEPOSTULATESSYSTEMSWITHFEWERBASICAXIOMSANDSYSTEMSUNDERWHICHSOMEOFARROWSAXIOMSARERELAXEDCONTINUETODEMONSTRATEAVARIETYOFINCONSISTENCIESITAPPEARSTHATTOEXPECTMETHODSOFSOCIALCHOICETOBEATTHESAMETIMERATIONAL,DENITIVE,ANDEGALITARIANMAYBETOEXPECTTOOMUCHINSTEAD,692PARTVIIILIMITSOFTHEMARKET8CONDITION4ISSOMETIMESCALLEDTHEAXIOMOFTHEINDEPENDENCEOFIRRELEVANTALTERNATIVESMORECONTROVERSYHASARISENOVERTHISAXIOMANDSIMILARONESINTHEVONNEUMANNMORGENSTERNLISTTHANANYOTHERTOSEETHESORTOFFUNCTIONSTHATARERULEDOUTBYTHEAXIOM,CONSIDERINDIVIDUALSVOTINGFORCANDIDATESINANELECTIONSUPPOSEEACHINDIVIDUALCANRANKTHESECANDIDATESINORDEROFTHEIRDESIRABILITYANELECTIONSOMEHOWCOMBINESTHESEINDIVIDUALLISTSINTOASOCIETYWIDELISTACCORDINGTOAXIOM4,THESOCIALLISTMUSTHAVETHEPROPERTYTHATIFCANDIDATEXISPREFERREDTOCANDIDATEY,THISSHOULDREMAINTRUEEVENIFOTHERCANDIDATESENTERORLEAVETHERACETHEMOSTCOMMONELECTIONPROCEDUREINWHICHEACHPERSONVOTESONLYFORHISORHERMOSTPREFERREDCANDIDATEMAYNOTOBEYTHEAXIOMBECAUSEOFTHEPRESENCEOF“SPOILERS”INTHERACEFOREXAMPLE,ITISCONCEIVABLETHATTHEPRESENCEOFRALPHNADERINTHE2000PRESIDENTIALELECTIONCAUSEDALGORETOLOSEWITHTHE“IRRELEVANTALTERNATIVE”NADEROUTOFTHERACE,GOREMIGHTHAVEWONTHEPRESIDENTIALELECTIONSYSTEMTHEREFOREWOULDNOTOBEYARROWSAXIOM4MANYAUTHORSHAVEEXAMINEDTHECONSEQUENCESOFRELAXINGTHEAXIOMCOMPROMISESAREINEVITABLEOFCOURSE,WHERETOMAKESUCHCOMPROMISESISAVERYDIFCULTNORMATIVEQUESTIONDESPITETHENEGATIVENATUREOFARROWSCONCLUSION,ITSHOULDBEREMEMBEREDTHATALLSOCIETIESDOINFACTMAKESOCIALCHOICESTHEUSCONGRESSMANAGESTOPASSABUDGETOFTENATTHELASTMINUTECOLLEGEFACULTIESESTABLISHCURRICULAANDALASKANESKIMOSDECIDEHOWTOIMPROVEUPONTHEIRCOMMUNALSHINGMETHODSFORTHENEXTYEARRATHERTHANEXAMININGTHENORMATIVEQUESTIONOFHOWSUCHCHOICESMIGHTBEMADEINASOCIALLYOPTIMALWAY,THEREFORE,ECONOMISTSHAVEINCREASINGLYTAKENAPOSITIVEAPPROACH,ASKINGHOWDECISIONSAREACTUALLYMADETHATISTHEAPPROACHWEWILLTAKENOWDIRECTVOTINGANDRESOURCEALLOCATIONVOTINGISUSEDASASOCIALDECISIONPROCESSINMANYINSTITUTIONSINSOMEINSTANCESINDIVIDUALSVOTEDIRECTLYONPOLICYQUESTIONSTHATISTHECASEINSOMENEWENGLANDTOWNMEETINGS,MANYSTATEWIDEREFERENDAFOREXAMPLE,CALIFORNIASPROPOSITION13IN1977,ANDFORMANYOFTHENATIONALPOLICIESADOPTEDINSWITZERLANDDIRECTVOTINGALSOCHARACTERIZESTHESOCIALDECISIONPROCEDUREUSEDFORMANYSMALLERGROUPSANDCLUBSSUCHASFARMERSCOOPERATIVES,UNIVERSITYFACULTIES,ORTHELOCALROTARYCLUBINOTHERCASES,HOWEVER,SOCIETIESHAVEFOUNDITMORECONVENIENTTOUSEAREPRESENTATIVEFORMOFGOVERNMENTINWHICHINDIVIDUALSVOTEDIRECTLYONLYFORPOLITICALREPRESENTATIVES,WHOARETHENCHARGEDWITHMAKINGDECISIONSONPOLICYQUESTIONSFOROURSTUDYOFPUBLICCHOICETHEORY,WEWILLBEGINWITHANANALYSISOFDIRECTVOTINGTHISISANIMPORTANTSUBJECTNOTONLYBECAUSESUCHAPROCEDUREAPPLIESTOMANYCASES,BUTALSOBECAUSEELECTEDREPRESENTATIVESOFTENENGAGEINDIRECTVOTINGINCONGRESS,FOREXAMPLE,ANDTHETHEORYWEWILLILLUSTRATEAPPLIESTOTHOSEINSTANCESASWELLLATERINTHECHAPTERWEWILLTAKEUPSPECIALPROBLEMSRAISEDINSTUDYINGREPRESENTATIVEGOVERNMENTMAJORITYRULEBECAUSESOMANYELECTIONSARECONDUCTEDONAMAJORITYRULEBASIS,WEOFTENTENDTOREGARDTHATPROCEDUREASANATURALAND,PERHAPS,OPTIMALONEFORMAKINGSOCIALCHOICESBUTONLYACURSORYEXAMINATIONSHOULDSUGGESTTHATTHEREISNOTHINGPARTICULARLYSACREDABOUTARULEREQUIRINGTHATAPOLICYOBTAIN50PERCENTOFTHEVOTETOBEADOPTEDINTHEUSCONSTITUTION,FOREXAMPLE,TWOTHIRDSOFTHESTATESMUSTADOPTANAMENDMENTBEFOREITBECOMESLAWAND60PERCENTOFCONGRESSMUSTVOTETOLIMITDEBATEONCONTRO