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1、SOCIALWELFAREFUNCTIONFORRESTRICTEDPREFERENCEDOMAINK.OHBO,M.TSURUTANI,M.UMEZAWAANDY.YAMAMOTOAbstract.Weconsiderthesocialpreferenceorderinginasocietywhereeachindividual’spreferencedomainisrestrictedtoasubsetofthewholesetofalter-natives.Weshowthatthesocialwelfarefunctionsatisfyingunrestricteddomai
2、nproperty,independenceofirrelevantalternativesandweakParetooptimalityisalwaysdictatorialwhenatleastoneindividualisentitledtoexpresshis/herpref-erenceonthewholesetofalternatives.1.IntroductionWeoftenencountertheproblemofaggregatingopinionsofindividualsinasociety.Arrow[2]introducedthesocialchoice
3、theoryforthisproblem,andgavethemonu-mentalimpossibilitytheorem:asocialwelfarefunctionwhichsatisfiesunrestricteddomainproperty,independenceofirrelevantalternativesandParetooptimalityisdictatorial.Fromthenonward,thedifficultyoftheproblemhasbeenwellrecog-nized,andavarietyofimpossibilitytheoremsintheA
4、rrow’sframeworkhavebeendeveloped.ThereaderisrecommendedreferringtoSen[14].Thispaperstudiestheexistenceandpropertiesofasocialpreferenceorderingwhenindividual’spreferencedomainisrestricted:oneexpressesone’spreferenceonone’salternativesetthatisasubsetofthewholesetofalternatives.Thismodi-ficationcan
5、beviewedasarelaxationoftheunrestricteddomainpropertyintheArrow’sframework.Forrelaxationoftheunrestricteddomainproperty,therearemanyresearchessuchasBlairandMuller[3],BordesandLeBreton[4],FishburnandKelly[5],Kalai,MullerandSatterthwaite[8]andRedekop[10].Inparticular,KalaiandMuller[7],Ritz[11]andR
6、itz[12]dealwitharestrictiononpermissiblepreferencesforindividualsinsteadofprofilerestrictions.Ando,Ohara,andYamamoto[1]dealswiththeprobleminasocietywhereindivid-ualsevaluatemutually.Thesetofalternativescoincideswiththesetofindividuals,andeachindividualexpressesone’spreferenceorderingonthewholese
7、tofindividu-alsexceptoneself.Theystudiedpropertiesofthesocialwelfarefunction,andprovedthatanoutcomeofsocialwelfarefunctionsatisfyingunrestricteddomainproperty,independenceofirrelevantalternativesandParetooptimalitycanbecyclic,henc
