helpfUlsuggestions・IalsowishtothankProfbssorsSalvadorBarbera

DiscussionPaperNo、
３１６
ＡＮＩＭＰＯＳＲｍｎｌ'ＴＹＴＨＥＯＹｍＭ
ＩＮＰＵＲＥＰＵＵＴＩＩＣＧＯＯＤＳＥＣＯＮＯＭｍＲ
凸
ＷＩＴＨＦＥＡＲｍｌＴＪＴＹＣＯＮＳＴＲＡＩＮＴＳ：
ＶＯＴＩＮＧＢＹＣＯＭＭＩＴＴＩｕ田Ｓ
ＩＮＮＯＮ－ＲＥＣＴＡＮＧＵＬＡＲＦＥＡＳｍｎＥＳＥＴＳ
ｂy
ShigehiroSerizawa＊
Mayl992
RevisedJanuaryl994
ThelnstituteofSocialandEconomicResenTch
OsakaUmversity
6-1Mihogaoka,Ibaraki,Osaka56ZJapan
＊
＊Firstofall,IwishtothankProfessorWilliamThomsonfbrhisdetajledcomments
mentsand
helpfUlsuggestions・IalsowishtothankProfbssorsSalvadorBarbera,MarcusBerlia
Berliant，
MatthewJacksonandLionelMckenziefbrtheiruselUlcomments．
Abstract
Weconsidertheproblemofchoosinganaltemativeinapurepublicgoodseconomy
withfeasibiUtyconBtraintBwhenvoter8haveooadditively-separableandBingle-peakedIo
preferences・Ourpurposeistoidentifyvotingprocedure8satisfying1itop8-only１１，
１１nonmanipulabiUtyooand1IvotersovereigntyⅡ、FYrst,weshowthatsuchproceduresare
△
generalizationBoftheschemesof1Ivotingbycommittee811introducedbyBarbera，
SonnenscheinandZhou(1991）Second,weestablishthatwhennotwogood8canbe
Bimultaneouslyproducedattheirmaximalfeasiblelevels,thoseproceduresare
characterizedbytheexistenceofaverypowerfUlvoter．
Keywords
Feasibintyconstrajnts,Additive-separableandsingle-peakedpreferences,Tops-only，
Nonmanipulability,Votersovereignty,Votingbycommittees
llntroduction
Thispaperconcemstheproblemofchoosinganaltemativeinapurepublicgoods
economywithfeasibintyconstraintswheneachvoterha8preferencesinacertaincla88of
Ioadditively-separableandsingle-peakedoopreference8・ｗｅlookfOrvotingprocedure8which
satisfythepropertiesofiitops-only11,Iinonmanipulability1iandIivoter8overeigntyi1・We
P
establishthatsuchproceduresaregeneralizationsoftheschemesofoovotingbycommitteeslo
introducedbyBarbera,Sonnen8cheinandZhou(1991,hereafterB,Ｓ＆Ｚ）JustUkethe
schemesofvotingbycommittees,thegeneralizedschemeshaveacertainpropertyof
1IdecomposabiUtygoodbygoodoo・Further,weestabUshthatwhennotwogoodscanbe
simultaneouB1yproducedattheirmaximalfeasiblelevel8,fOreachproceduresati8fying
thoseproperties,thereisavoterwhoisverypowerhll,althoughheisnotanecessaIilya
dictator・
ｗｅconBiderthefOUowingpurepubncgoodseconomies・Therei8annitenumberof
voterBanｄａＥｍｔｅｎｕｍｂｅｒｏｆｐｕｂｎｃｇｏｏｄｓ・ThesetofpotentiallevelsofeachgoodisEmte，
andthefeasibleBetZisasubsetoftheproductLoftheBetsofpotentiallevelsofgoods・
EachvoterhasapreferencerelatioｎｄｅｈｎｅｄｏｎｔｈｅｐroductL・Avotingschemeisamethod
fOra66igmngtoeachpossiblepreferenceprohleanelementofthefeasibleset・Whenthere
areatleastthreeelementsinthefeasiblesetandthedomajnofpreferencesislargeenough，
theGibbard-Satterthwajtetheoreｍｃａｎｂｅａｐｐｌｉｅｄ：itsaysthatanynondictatorialscheme
ismaImpulablel・But,extendingtheresultofB,Ｓ＆Ｚ,recently,Barbera,Guland
Stacchetti(1991)andSerizawa(1992)showedthatifthefeasiblesetiBarectangle,thenoｎ
animportantdomajnofpreferences,whicharecalled
lAschemeis…2111△hl且iffOrsomeprofileofpreferences,somevotercanobtaman
outcomethatheprefersbymisrepresentinghispreferenceiotherwisetheschemeis
nonmanimmable
１
oｒ
璽旦且＝h旦旦且dpreferences,thereexistaclassofnonmanipulablevotingschemesmuchwider
thanthecla88ofdictatorships・Suchschemesarecalled EeneralizedmedianvoterBch⑨ｍ曙
ｏｒ
uHUUI臣ＨｕＩＶ【】ⅡⅡ【】Ｖ
Furthermore,ｗｉｔｈａｖｅｒｙｗｅａｋａ｡domofef5ciency
calledvoterBovereignty2,ｔｈｅｙcharactelizedvotmgbycommittees：IfavotingBcheme
satisEesvotersovereigntyandnonmanipulabilityonthedomajnofcro8s-Bhaped
preferenceB,ｔｈｅｎitiBaschemeofvotmgbycommittee8．
However,thereareimportantca8e8whenthefeasiblesetis
ａｎ
､Ｆｏｒ
eg〔ample,Bupposethattherearesomenxedresources(inputs),fromwhichthepublicgood8
areproduce｡､Thefeasiblesetwillcertainlydependonthetechnologyandtheresources，
andtypicallyitwillnotbearectangleWealsoassumefreedisposabilityofresources，
Thenwheneversomeproductionofthepubncgoodsisfeasible,anysmaUerproductionis
alBofeasible・Suchaconditioni8caUedzero-comprehensiveneB81nthispaper,wetreat
8uchcasesofnon-rectangularbutzero-comprehensivefeasiblesets・
ＩｎＳｅｃｔｉｏｎ２,ｗｅｓｅｔｕｐｔｈｅｍｏｄｅｌａｎｄｄｅｈｎｅｖｏｔｉｎｇｂycommittees・Onenotable
featureofaBchemeofvotingbycommitteesisthatitcanbemdecomposedoointoBeparate
rules,onefbreachgoodForexample,thelevelof8omegoodcouldbedeterminedby
majorityrule,andthatoftheothergoodbydictatorship,Thuswhenthefeasiblesetisnot
rectangular,someoutcomesoftheschemeofvotingbycommitteesmaybeinfeasibleSo
next,we8tudytherestrictionsonschemesofvotingbycommitteesimpnedbyfea8ibinty、
Although,ｉｎgeneral,votingschemesdependonalltheinfOrmationcontainedinthe
prohlesofpreference8,someclassesofvotingschemesdependonlyonpartofthat
infOrmation・AndifthereisanycostoftransmittinginfOrmation,votingschemeswhich
dependonlessinfOrmationwillbepreferable､Avotingschemeis辺I…Xiftheoutcome
fOranypreferenceproEledepend8onlyonthebestelementsoftheproE1einthefeasible
set､Wecharacterizevotingbycommitteesintheclassoftops-onlyvotingｓｃｈｅｍｅｓｏｎｔｈｅ
２AvotingBchemesatisEes
ifitisontothefbasiblesetZ
２
domainofadditively-6eparableandsingle-peaked3preferences,whichi8smanerthanthe
domainofCross詔hapedpreference8・Themainre8ultofSection2isthefbUowing：
〃qtop8-o汎lyuot”sdieme3at雛e8uote780Ue7e地冗tya狐｡〃o几､α〃jPUltLbility0冗ﾒﾉbe
domQi几q/Gdditjuel1ﾉｰsepG7qblea〃dsin9le-pCM;edpre/b7e〃CCS,仇elzthe8cﾉbeme…scheme
Q/Uo2i几963ﾉcomm樅ee3tUhichsqt蛾Csノセ“iMitzﾉCO勉ditio〃8．
ＩｎＳｅｃｔｉｏｎ３,wemakethenatmala88umptiononthefeasiblesetthatnotwogoodB
●
canbeproducedattheirmaximalfeasiblelevelsatthesametimeThehontierF(Z)ofthe
feasiblesetZisdenneda8thesetofelement8ofZsuchthattheproductionofnogoodcan
beincreasedwithoutdecreasingtheproductionofsomeothergoodGivenagoodx,Ｆｘ(Z）
istheprojectionofF(Z)onthesetofpotentiallevelsofxWeestabUshthefOUowing：
A83TmOetﾉbatGtOP8-07M1/UOtm93Cheme8Gtiq/iie3UOter80Uerej97LtVmd酌
冗o"､叩jptllq61eo〃tbedOm皿冗0/qddjtjUely-sepGmbleG〃d8町le-pe此edpre/b7e"CCS.、be〃
仇e7e曲Guote7isucMj(Ｗｂ７ｍＺﾉp7e/i27e几cep7砿led几thedomqj几，
りめeOUtcomcleUeMeQch9oodZ…tJeos…lc7ye“theZ-fhcoo7di"CLfeQ/Uotcr
ibbe8tpomt伽Ｚ，
iWbreoCb900dzjVtheZ-tﾉiCoo7dj"CUC〃tﾉjeUoterjbb"teIeme〃t醜Ｚ曲atlecSt
“町…ｍ`伽Fと(Z）,tﾉjc"仇eoutcomclcツビ'0/ziScq"ltotﾉtcz-仇coordj"qteq/theU0ter
ibbe8teleme7ztmZ、
Ｆｏｒｅｇ[ample,ｓｕｐｐｏｓｅｔｈａｔｔｈｅｒｅａｒｅｔｗｏｇｏｏｄｓｘａｎｄｙ,thatthe8etofpotential
levelsofxis{0,1,2,3}andthatofyis{0,1,2},andthatZ＝{0,1,2,3脾{0,1,2｝
({(3,2)）ThenＦ(Z)＝{(3,1),(2,2)},minFx(Z)＝2,andminFy(Z)＝LThusifthe
x-thcoordinateofi'ｓｂｅｓｔｅｌｅｍｅｎｔｉｎＺｉｓ２ｏｒ３,thentheoutcomelevelofxmustbeequal
toitiifitisl,thentheoutcomelevelofxisatleastaslargeasl(butmaybe2or3）
Therefbreundertheassumptionsabove,ｔｈｅｒｅｍｕｓｔｂｅａｖｏｔｅｒｗｈｏｉｓｖｅｒｙｐｏｗｅrfm
althoughheisnotnecessarilyadictator,However,ＣＯnsiderthecaseswhenfOreachgoodx，
３Apreferenceis
additively竜epara
ifitisrepresentedbyan
ionofeachgoodissingle-peaked．
、【
３
minFx(P)＝0,thati8,if8omegoodisproducedatitsmaximalfeasiblelevel,thennoother
goodcanbeproduced・SuchcasestypicallyoccurwhentheresourceshomwhichthegoodB
areproducedarenxed,InthosecaseB,thevotingBcheme8becomedictatoriaL
２ModelandCharacterizationofVotingbycommittees
ThesetofvotersisN＝{1,2,…,､},、三2．
ｌ＞２.ＧｉｖｅｎＷＥＮ,wedenotethecardinality
￣
ｏｆＷｂｙ＃WThesetof
ｕｒｅｐｕＲｏ
(or幽型)isＸ＝{1,2,…,k},ｋｚ２ＧｉｖｅｎｘＥＸ
ａｎｄＡＥＸ,wedenoteXN{x}by証andXlAby-AThesetof
DotentiallevelsofxEX
1s
Lx={0,1,…,mx},mx≧landL=x1Xいi…EX,AEXand`EL,w'ed…tho
x-thcoordinateofZbWk,andtheprohles((b,)yEA,((i,)y#xand(WAbWA,し，[and
LArespectivelyGivenxEXandL'〔Ｌ,wedenotetheprojectionofL'onLxbyLjt,and
themammalelementofnLjtbyM(L'）Azero-comprehensive4setL'ＥＬｉｓ型型gﾕlユエ
Ｘ
ifＭ(LリＥＬ';otherwiseL'iｓ
､ThefeasiblesetZisasubsetofLWe
assumethatZiszero-comprehensivebutnon-rectangular・
dennedas{CEZ’2'2Ｍ－２'２Z｝GivenＡ〔Ｘand`Ａ
－
{LAEHEXlRxl(LWEZ}byZ(２A）
1s
EPERx,wedenototh…ｔ
ThesetofstrictDreferencerelatioｎｓｏｎＬ ｉｓ臭
GiventhePreferencerelationPiE身ｌｅｔＲｉ
GiventhepreferencerelationPiE身letHbetheweakpreferencerelationassociatedwith
Pi（fbr2＆Z'ＥＬ,ＺＲｉＺ'ifandonlyifZ'＝ZorZPiZ'）Givenapreferencerelation
PiEPandasetL'ＥＬ,wedenotethebestelementofPiinL'ｂｙＢ(Pi,L')andthex-th
coordinateofB(Pi,L')byBx(PiL）
４ＡｓｅｔＤＣＬｉｓ
zｅｒＯ－ＣＯｍＤｒｅ hensiveif
ＶＺＥＬ',VZ'ＥＬ，［Ｏ≦Z'二２－２'ＥＬ'］
５１nthispaper,Ｚ’２ZmeansthatZ′＞ZandZ'＃ＺｉａｎｄＺ′＞ZmeansthatfOreachxEX，
A'〉を
４
Dp6nition：
ｉｓａｆｉｍｃｔｉｏｎｈｏｍＰｎｔｏＺ．
ｍｏＰ′〔。｡Ⅱ iｆ
De5mtion：Avoting8chemefsatisnes
-
V2EZ,ｮＰＥＰ'suchthatf(P)＝
suchthatnP)＝Ｚ
Denmtion：
￣
ヨＰＥ
LetP-Pi×…×夕ｈＥＰｎ･Avoting8chemefis manipulableonP'
iｆ
P'，ョｉＥＮ'＆ｮPiEPi8uchthat
IPi,Pｺﾞ)Ｐif(P)，
andotherwisefis nonmaniDulableon,′
DpfiTnition：
＿
AvotingschemefisdictatorialifthereisavoteriENsuchthat
ＶｐＥ ，n,f(p)＝Ｂ(Pi,Z）
旦旦且ﾕﾕi旦旦:Avotingschemefsatisnes
iｆ
VxEx,ｖｐＥｐｎ,minB-(p:,Ｉ
，､,mlnBx(Pi,Z)≦R(P)≦…Bx(Pi,Z）
１
Remark：Goodwise-unanimityimphesunanimityandvotersovereignty．
￣
WewillconsiderthevotingschemesdennedbyspecibringfbreachxEXandeach
levelいOofxaclassXWE2Nof11winnmgcoalitions比suchcoalitionscan1ifbrceⅡ
thelevelofxtobehigherthan,orequalto,ikForexample,inmajorityrule,anycoalition
whosecaｴdinalityisgreaterthann/2iswinningWerequirethatthebiggeracoalitionis，
thegreateritspoweris:ＷＥﾌﾟﾘ;t(い＆Ｗ'。Ｗ－Ｗ'Ｅｘ(紗
Defmition：
Oisasubset
ﾌﾟﾘR(4)of2Nsuchthat
aThisdeEnitionofasetofwinmngcoalitionsisdifIerentfromthatinSerizawa(1992)iｎ
５
ＷＥ翼(い＆ＷＯＷ－Ｗ'ＥｉＩＲ(い
￣
De5nitiom:AUst（灘(い)xEX僻x({0｝ ofBetBofwinningcoalitionBiBmonotonic
iｆ
ＶｘＥＸ,VUk,4,ELx){0}，
Ａ≦Ａ'＝Ｚ(4)ﾕﾌﾟﾘK(い
MonotomcityoflistofsetBofwinmngcoalitionsimpUesthatifacoalitioniB
winningfOrsomelevelいfgoodx,thenthecoalitionmustalsobewmningfbranylower
consumptionleveLInordertodiscussthevotingschemesdeEnedbyspecifyingalistofsets
ofwinmngcoalitions,wedehnemaquasivotingscheme1i．
Dennition：
ｉｓａｆｉｍｃｔｉｏｎｆｒｏｍｌｎｔｏＬ．
De5nition：Aquasivotingschemefsatisnes￣】Ｌｉｆ
ＶｐＥ，n,f(p)ＥＺ
AquasivotingschemeisavotingschemeifitsatisEesfeasibiUty．
7ifthereisamonotomcnst
De5njition：Aquasivotingschemefis
(塩(』k))xEX,LELx1{O}ofsetsofwinnmgcoalitionssuchthａｔ
ＶｘＥＸ,VいLxH0},VpEpn，
＆(P)≧(k＝{ｉＥＮｌＢｘ(Pi,Z)≧ｐＥ漣(4)
that
翼(剣 neednotsatishestheconditionofPropositionlbelow．
磯鯛謡搬聯雛MH:澱lﾋﾞii3lMil澱淫慨織鯛⑭
iBnOn-reCtangular．
６
塗２２§11坐：A66umethatfi6votingbycommitteeswithalj鹸(iiR((k))xEX,いｪ({O｝
ofsetsofwinningcoalitions・ThenfsatisneBvotersovereigntyo、，′〔,nifandonlyif
-
thenstsatishes：
ＶｘＥＸ,VいZx1{0}，襲((k)*０and“刃K(を）
Ｗｅｏｍｉｔｔｈｅｐｒｏｏｆ,whichiBstraightfOrward．
●
Ｒｅｍａｒｋ：PropositionlimpliesthatifvotingbycommitteessatisEesvotersovereignty，
thenitalsosatishesgoodwise-unanimity・ThusfOrvotingbycommittees,voter
sovereigntyandgoodwise-unanimityareequivalent．
Votingbycommitteesmaynotsatisblfeasibinty．
…pl且-1：SupposethatN＝{1,2},Ｘ＝{x,y},Ｚ＝{(0,0),(1,0),(0,1)}，
藁(1)＝渚(1)＝{ＷＥＮｌＷｆ０}LetP1andP2besuchthatB(P,,Z)＝(1,0)３，ｄ
Ｂ(P2)＝(0,1).Thenf(P)＝(1,1)僧Ｚ,thatis,fisnotfeasible
Proposition2belowprovidesthenecessaryconditionsonaUstof8et8ofwinning
､
coalitionsfOrtheassociatedvotingbycommitteestosatisfyfeasibility．
型旦旦旦1119ﾕｰﾕ：Letfbeaschemeofvotingbycommitteesassociatedwiththenst
(ｚ((l[))xEX,tkELxl{0}ofsetsofwmningcoalitionssatisfymggoodwi6e-ummmjty・Then
satishesfeasibilityonlyiffsatisnesConditions(i)and(ii)below．
（i)ForanyxEX,andfbranyAEZx,雍(い＝０
（ii)G…'@x'ＬＭ〔z1選,←，
let(ＷＥ[Zx(し側昨Zy((_{x,y})ﾊZ(４－{x,y})TheⅢ
７
VWxExW,VWyE
琴(9),wxnwy#仏
R燈markCondition(ii)…：GivenL{x,y},eachcoordmateofwhichisintheprojection
ofZontheco…omdmgaDd`,sUcethefe殿ible8etZpamneltothex-yplane・IfUhandUi，
areinthepzojection8oftheslicedsurfaceZ(`_{x,y})omthex-agd…dthey-…
Z．…ively,but(A,U1,,Ｌ{x,y})iSnotfeasible,thenanytwoelementsofXt(い､。
琴(Ui,)mu8th…non宅mptyintersectiom
ProofSinceCondition(i)istrivial,weproveCondition(ii)omy．
Ｌ…`X,L{x,，}｡z1x,ﾘｯ(Ｗ‘[Zx(しＭﾙZy(し{x,,})ﾊZ(し{x,,}）
WxE灘(⑨andWyE巧(;)Suppose,bycontradiction,thatWxnWy＝q
DenoWk'＝max{`ＩＣ''ELxl(いいZ(し{x,y})}and
y
ルーmax{(y'ELylWy')EZ((_(x,y})}LetPbesuchthat
{ilB(Pi,Z)＝((ＩＣ,いし{x,y})}＝N1Wy,and{ilB(Pi,Z)＝(い』i,,(_{x,y}}＝Ｗｙ・
Thengoodwise-umammityimplies:(1)L{x,y}(P)＝し{x,y)ＷｙＥ藩(，implies：
(2)､(P)≧UirSmceWxnWy＝OimpUesthatN1WyﾕＷｘ,ＷｘＥ蕗(い､plie8：
(3)＆(P)≧Uk
Smce(Ｗｌ【Z(し{x,y})andZ(し{x,y))i…ro-compZehensive,itfbllow8企０ｍ
(1),(2)and(3)thatRy(P)ビZ(f_{x,y}(P))ThatMP)EZⅡhiSc…dictsthe
feasibilityoff
QED．
Eｴ９２g§1119ﾕｰﾕ：AssumethatX＝{x,y）Letfbeaschemeofvotingbycommitteeswith
thelist(潅凹)xEM【ELxl{0}ofsetsofwmnmgcoalitions・Thenfsatisnesfeasibilityif
andonlyiffsatisnesCondition(i)and(ii)below．
（i)Forany\Zx,翼(tk)＝OandfbranyZi,EZy,琴((i,)＝Ｏ
（ii)ＬｅｔＺＥ[Zx×ＺｙＭＴｈｅｎ
８
vwXEHWR(4),vwyE堵(9),wxnwy#０
ProofSincetheproofofiIonlyifoIi8simnartoPropoBition2,weproveIoifuIPartonly，
ASSumethatthelistsatishesConditio､(i)and(ii).ＬｅｔＰＥ，nandZ＝f(P）We
wanttoshowthatCＥＺ
Suppose,bycontradiction,that(1)“ZCondition(i)impnesthat(2)ZEZx×zＺｙ.
0
DenneWx鎚{ilBx(Pi,z)≧qandwya`{ilBy(Pi,z)≧U1,)ThenZ=f(P)imp1ie8
that(3)ＷｘＥ堪(い､dWyEjV(9)NowitfbUowsfromCondition(1),(2)and(3)
that(ii)implythatWxnWy#OThenfbriEWxnWy,Ｂ(Pi,Z)≧fSinceZis
zero-comprehensive,(1)impUesB(Pi,Z)EZThiscontradictsthedefinitionofB(Pi,Z)．
HenceZEZ．ＱＥ.、
ThelistinExampleldoesnotsatisfyCondition(ii)ofProposition3,since
(1)Ｅ，i;t(1)and(2)Ｅ藩(2)but(1)､(2)＝0．
…121旦旦:SupposethatN＝{1,2},Ｘ＝{x,y},Lx＝Ly＝{0,1,2}，
Z＝(Lx"Lyﾊ{(2,2)},andthatXt(1)＝渚(1)＝{ＷＥＮｌＷナルnd
Xt(2)＝務(2)＝{ＷＥｌ１ＥＷ)LetZE(Zx×Z，ﾊ((2,2))ThenZ＝(2,2)Forany
WxEXt(2)andWyE渚(2),lEWxnWySotheUstsatishesconditions(i)and(ii)，
andtheassociatedvotingbycommitteesisfeasible．
壁巫２１且-且:SupposethatX,LandZarethesameasofExample2,andthatN＝{1,2,3｝
and蕗(1)＝ｚ(2)＝琴(1)＝iWi(2)＝{ＷＥＮ|＃Ｗ三2)IfWxE薦(2)ＷｙＥ考(2)，
thensince十Ｗx＋＃Ｗｙ≧４and＃Ｎ＝３，ＷｘｎＷｙ#０.ThusthislistalsosatisEes
Condition(i)and(ii),theassociatedvotingbycommitteesisfeasible．
WenowdennethedomamsofpreferencesthatwewiUuseinthecharacterizationof
●
９
votingbycommitteeaIngeneral,ａｎａgent，spreferenceonthepotentiallevelｓｏｆａ
particulargooddepend8ontheconsumptionlevelsoftheothergood8,SeparabUityde5ned
below8ayBthatthepreferenceontheavajlablelevelsofeachgoodisindependentofthe
con8umptionlevelBoftheothergood8.Aweakerver8ionofBeparabiUtyi8
peak宅eparabinty,whichBaysthatthemostpreferredlevelofeachgoodiBindependentof
theconsumptionlevel8oftheothergoods・Astrongversionisadditive-8eparability,which
saysthatapreferencecanberepresentedbyanadditively宅epaｴablefUnction・Givena
preferencerelationPiEPand2-xELざ,letZk(《_x)＝Bx(Pi,{WLx)|UkELx}）
Dennition：
ApreferencerelationPiEPis聖旦竺旦hlEif
ＶｘＥｘ,vq-x,AEL-x,v4,4ELx
（(k,(_x)Pi(4,`_x)－((k,(▲x)Pi(《i,魁）
ＤｅｎｏｔｅｂｙＰＳＥ，theclassofseparablepreferences．
Definition：
AprelerencerelationPiEPis
peak-SeDarable iｆ
ＶＸＥＸ,VLXEL証,ZX((_X)＝Ｂｘ(Pi,L）
DenotebylPSEptheclassofpeak-separablepreferences．
ifthereemBtBalist
De5mtion：ApreferencerelationPiE’ｉｓ
￣
(UxLX-R)xEXofutiUtyfimctionssuchthatfOrallZandZ′
ＥＬ，
UPi′￣X:XUX(ｐ>x:XU(い
DenotebyPAStheclassofadditively-separablepreferences．
NotethatlAS〔PSEPPSButiffbreachxEX,Ｌｘ＝{0,1},thenＰＳ＝，PS，
￣￣
andbothnotionscoincidewiththenotionofseparablepreferencesofB,Ｓ＆Ｚ．
10
DeEnition：ApreferencerelationPiE
-
Pismonotomcif
Ｖｘ〔x,vL,[EyHxLA,いLx，
゛(k'＝((k,Lx)Pi(を',Lx）
ＤｅｎｏｔｅｂｙｌＭｔｈｅｃｌａｓｓｏｆｍｏｎｏｔｏｍｃｐｒeference8．
ｪｌｇ且ﾕｪｪ：ApreferencerelationPiEPi8且118些匹且ょ旦旦ｉｆ
ＶｘＥｘ,VL,[EL-x,VIMfELx，
［(k<《t≦Zh[(しx)｡ｒ４>４≧zk(しx)]￣W-x)PA'しx）
DenotebypSPEPtheclassofsingle-peakedPreferences.
Definition：APreferencerelationPiE,is些旦且旦二旦旦旦旦difPiispeak-sepambleand
single-peaked
DenotePC＝ｐＰＳｎｐＳＰ
NotethatlASnPSP[PQA1sonotethatiffOreachxEX,Lx={0,1},then
single-peakednessisautomaticanysatisEedThusiffbreachxEX,Lx＝{0,1},sincePPS
－
coincideswiththenotionofseparablepreferenceofB,Ｓ＆Ｚ,ｓｏｄｏｅｓＰＣ,Westudythe
schemesofvotingbycommitteeｓｏｎｔｈｅｄｏｍａｍｌＡＳｎＰＳＰｏｆａｄｄｉｔｉｖｅｌｙ竜epalableand
single-peakedpreferences．
Although,ｉｎgeneral,quasivotingschemesdependonalltheinfbrmationcontained
inthepron1esofpreferences,ｓｏｍｅclassesofqUasivotingschemesdependonlyonpartof
thatinfOrmation､Votingbycommitteesdependsomyonthevoters'mostpreferredset・
Thispropertyiscalled11tops-only'１．
些型i旦旦ﾕ:Aquasivotingschemefis辺I…xiｆ
1１
Ｖｐ,ｐ，Ｅｐｎ，
[ＶｉＥＮ,Ｂ(Pi,Z)＝Ｂ(Pi',Z)]－f(P)＝f(P'）
FortheclassoftopB-onlyqua8ivoting8cheme8,weusethefOUowingnotation：
fZn-L
Theoremli8acharacterizationofvotingbycommitteesintheclassoftopB-onlyqua8i
votingBchemea
Theoreml：Ifatops-only
quasivotingschemef:Ｚｎ一Lisnonmanipulableonthedomam
P
(PASnlSP)nofadditively-8eparableandsingle-peakedpreferences,thenitisaquasi
schemeofvotingbycommittees
ProofAssumethatfZn-Lisnonmanipulableon(PASnPSP)n.ThestatementBofStep
l,2,3＆４belowimplythatfisaquasischemeofvotingbycommittees・TheproofSofthese
statementsareinAppendix．
蝕旦E-l蝿,《,ZiandLiaresuchthatR(《,`_i)≧Aand2ix≧いhenfk(（{,Li)≧Uk・
旦堕n-21fUk,<,Ziand(_iaresuchthatH(（,(_i)≧Landいくx,thenを(（{,(_i)≧を
旦堕E-aGivenxEXandAELx,let
藁(Uk)＝{ＷＥＮｌﾖ(↓i)iEN８．tい`1,…,Uh)≧(k＆Ｗ={ｉＥＮ|<x≧Uk)）
ThenWx(い…etofgeneralizedwmmngcoalitiona
且ﾑﾆE-4GivenxEX,((1)iEN,andtkELx,wehave：
Ｒ(4,,…,』h)≧“andonlyif{ｉＥＮｌ４ｘ≧Ａ}ＥﾌﾟﾘK(4)□
Q1gll旦互：Ifatops-onlyvotingschemef:Zn-ZsatisEesvotersovereigntyand
nonmanipulabilityon(ＰＡＳｎＰＰＳ)n,thenfisvotingbycommitteesassociatedwithaust
of8et8ofwinningcoalitionswhichsatisnesConditions(i)and(ii)ofProposition2．
1２
３AnlmpossibilityTheorem
ＩｎＳｅｃｔｉｏｎ２,wecharacterizedvotingbycommittee8inthecla88oftop8-onlyvoting
8cheme8bythemdomBofvoterBovereigntyandnonmanipulabinty､InthiB8ection,we
deriveastrongerreBulthomsuchａｍｏｍ８・UBingthere8ultsofSection2,wee8tablishan
impossibintytheoremwiththeadditionala8BumptiononthefeasiblesetthatnotwogoodB
canbeproducedattheirmammalfeasiblelevel8atthesametime・Thata8Bumptionho1d8
whentherearesomeExedresourcesthatarepubUclyownedandgoodsareproducedby
uBingtheresources．
Dehmtion：Ｌｅｔａｓｅｔ
翼(を)ofwinningcoalitionsbegivenVoteriENi…etovoterin
』ＲｉｆｉＥｎＷ・VoteriENisadecisivevoterin
riENisadecisivevoterinZK(4)if{i}Ｅｚ(9Voter
WE襲(4)
iＥＮｉｓ
ifheisavetoanddecisivevoterin藍(9
旦旦且ﾕﾕﾕｪ:Twoelements2andZ'ＥＦ(Z),２#('areadjace型ｉｆ
Ｖ２,,ＥＬ,[(,,〉(min{』k,い)xEX-Z''EZl
…ﾕｰLAssumethatvotingbycommitteesfsatishesfeasibilityand
goodwi8e-unanimity,andisnonmampulableon(，ASnPSP)n.ＬｅｔＺＥＦ(Z)andxEXIf
therei8Z'ＥＦ(Z)adjacenttoZand4くいhe、翼(phasadecisivevoter．
Remark：NotethatM(Z)EZimpnesF(Z)＝{Ｍ(Z)}・ThustheconditionsZ,Z'ＥＦ(Z）
andｋ'くいogetherimplyM(Z)EZSoLemmalandthesubsequentresult8canbe
appUedonlytothecasesofnon-rectangularfbasiblesets．
ProofofLemmal
ＬｅｔＺＥＦ(Z),ｄＥＦ(Z),andxEXbesuchthat
1３
（】）へｊ⑰畳」胃自二。（Ｐ員（閨）鮮、八貯
留弓。ｍの》ごＢ骨昌三目》一言一（閨）謡（鈩）盲目二の畠言号。一日・
田の一望、〆ワの冒○庁←ず鷺
（吟）小、ｖ李目」（廟）菫、ｍ鎖（＄『）目。（。）ベミ、、輻三、）雪、【愚（中、）・
閉具（『）（、、Ⅱ（旨昌■｛か》紙箪｝）酎、〆・円肩口
（噌）ⅡＵ（⑪）鮴、、Ⅱ鮮、
（とⅡ↓（⑫）小管、Ⅱ牟
田の二ｍ三、）目已甸、（、シ⑫。、富）己ワの⑫巨昌吾鴛
（旨）江」ｍ己で一｛】｝》国］（弓」》函）Ⅱ鯲富・
（臣）邸ｍｚ－君、）国邑（勺」》頃）Ⅱ傘ミⅡ傘（八＄『）
（届）舐ｍｚ－｛】｝》くい辞］）田園（宅」》国）Ⅱ紙、
（』』）国（宅】】国）Ⅱ〈Ｐロロ虹（、、、ｍ国箏ユーロ（、§弾く辱》甸、田】閂、§・
ｐ
￣'
￣
￣
盾。
、－ン
Ｃ□
￣
ｌ｛」ｍｚｌ国『（勺」】国）ｗ傘、｝Ⅱ雪、一｛】｝
ⅡＵ（］⑫）隼弓）八＄雷す『（②））
望。←の菩菖ごＨｇ＆」ｍｚ）国（田」一頃）ｗ亀、、．、。ごｍ○○二重函の－臣曰冒旨已ご》看の房圏⑩
ー
￣
（］』）閂（旧）Ⅳ』』．
￣グ
￣
←
Ｃ・国・ロ。
旧腕陶膳膳陣‐障師鈩鴎巨曰の吾自（■）ず円のＰｇＨ目』望）この己【。」の○一】○自国ｘ望。［吾の詩麗】す］の、曾国Ｃ臣
（岳）時（』ｃ）８昌国ａｎ冨皀○口ロ】餌己己昌号】］】ご・
鮴（団】、）田‐』）Ⅱ傘、．シ三ｍ○○已菖器－皀息己旦ご）（届）目』（】②）】曰己］超号Ｐ←ず門騨皇国寺］》
鮴（石】、》田‐山）Ⅱ紗、・目冨垣（９）門（甸一、）田‐』）Ⅱ』・
国巨←］の一℃】、す⑩函房○け←ずＰ←（］垣）国（田へ】国）Ⅱ｛、．目彦の■ず望（】。）秒ｐＰｐ］）》（画）一日己毎の函一彦皀
（埠函）》（】②）時（］『）Ⅱ↓（岳）（鶴田】兵甸）
（』）時（屋）Ｉ（旨）炉（句）八鮓）
（』）時（届）Ⅱ↓（岳）く」ｍｚ－｛】｝）国Ｘ（田］）函）Ⅱ貯、八鰈》
ｐ
甸臣ユロの］ロロ自鈩
￣
餌冒。》
ｓ
Lx×Lyisnon-rectangularFurtherassumethat(2)votingbycommitteeBfsatisne8
feasibilityandgoodwise-unanimity,andi8nonmanipulableon(PASnPSP)n.Thenthe
sets
竃(…Zx)xEXhaveacommondictat．■．
且ﾆﾕﾕｭｴ上：Assumption(1)saysthatnotwogood8canbeproducedattheirma｡｡mal
feasiblelevelsatthesametime．
2ｴggfBy(1)andLemmal,eachset蕗(maxZx)hasadecisivevoterix・
ＬｅｔｘａｎｄｙＥＸ,Weclaimthatix＝iySuppose,bycontradiction,thatixナiy、
ThenletPbesuchthatBx(Pi,Z)＝maxZxandBy(Piy,Z)＝maxZyThecondition
X
{ix}ＥＸｔ(maxZx)impUesthat《c(P)＝maxZx,while{iy}Ｅ藩(…Zy)impnesthat
fi,(P)＝…ZyBy(1),thiscontmdictsthefeasibintyoffSoix＝iy
Notethatalsoby(1),Proposition2impUes：
ＶＷｘＥ薦(maxZx),VWyEXt,WxnWy＃U
SettingWy＝{ix},wehave
VWxE落(maxZx),ixEWx
Soixi8adictatorin裏(maxZx）
Therefbreeach恵(maxZx)hasadictat・rButalsoby(1),Pmpositi・n2implies
thatthesedictatorsareｔｈｅｓａｍｅｖｏｔｅＬ
ＱＥＤ．
Ｅ[gEg§jllgﾕｰﾑ：Assumethatfbreachxandy,theprojectionZxyofthefeasiblesetZon
LxxLyisnon-rectangular,Furtherassumethatvotingbycommitteesfsatisnes
feasibintyandgoodwise-unanimity,andisnonmanipulableonthedomain(，ASmPPS)n
ofadditively器eparableandpeak-separablepreferencesThenthereisavoteriENsuch
that
(i)fbranyxEX,fbranyLEZxl(0},iisadecisivevoterofﾌﾟﾘH(4)
１５
（》】）言曽］×ｍ〆》言②這鈩ご目弓門（函）八鮮貼目貫国Ｈ》三：曰目鷺自己鋸（炉）。
開陳仁隠、冒吊す］苦の曰。■○一○日。】ご己屋訪○崗駕誌。｛ヨロ日ｐｍ８興巨】Ｃ畠］（】】）旨】已岸〔輯（一）》ニョの
冨冒：已冨：ご「（】】）辱いの目自己》晉露の冨謡（目賀国Ｈ）》Ｈｍｘ臣弓：８月ロ８日・曾◎二
円肩口耳苦①日日。←ＣＢＢご◎安房房一一忽．一の亘】画」の曰巴弓の曽舜の由ＳＨＰ目昏門の闇屋鮴、函縄・画◎
蓋『の冨弓の。已罠一。吾○一コ吾輿晉の弓。←①旦旨Ｐ『⑩一。ご○←⑦Ｈ昏息騨昌禺自」ず：ＰＳ鮨》
昌口再禺（酌）八鈩肪目胃国Ｈ・
晋君○ｍの）ごｇ己ＨＰ已昌Ｃ目）吾菖晉②『の胃のＨｍ※）鮮）巨口匂〆（国）八鈩川目貝国然自Ｐ
二言〆、錦（鮮）圏の三富茸【雪済．、旨の目弓〆（宅）八炉》吾曾の】翼、ｍ国（国）召・三富←鮴、八小・
田巴勺彦の呂呂菩鷺ヨーミＨⅡ｛］｜国（甸」）田）Ⅱ辱｝牌己君ＨⅡ｛」｜国〆（勺」）国）Ⅱ貯｝・盟昌＆】画騨
』のＢ、葛①ざＨのＰ呂望、滉凹且ざＨの凹号中、国『》Ｐ呂巴員の】扇君ｘ】目ご房、一言三ｍ雪乏『Ｋ）鴬
蓉巨◎劃「賀意一壱）ｗ閂、・句巨昌の『）雪Ｈｍ謡（鮨）言旨の、言農鈩（石）Ⅱ酢Ｖ鮮、・二房兵弓）Ⅳ
』・堕冒。①（、ｍ国（国）】要「のザＰ『のＰ３員Ｈ且】○詮Ｃｐｇ弓の諒酔巴亘豈］。【閑・国の曰○の』ｍご『Ｈ》餌■⑨二頭湧
く§ぐ。一円目謡（許）．ｐ・固已。
弓昏の日の目］Ｐロロ田８℃Ｃ昌一】○口』一○ｍの一彦のＨ】曰己］】弓臣のｏｎの目幽．
哨贋値随旧ｒ呼尹留巨目①吾筥昏Ｈの餌ｇＨ目』］》曽の目。」の○二．ロ国〆］○重房諒麗」匡⑩器一頃。■
■Ｈｘい］］ｍｐｇｌ尉○冨信已胃。句日昏のＨ麗冒目の菩呉餌一○冨○巳］己○一百ｍ⑰○房目の閉園ご島の⑫『○一円
、。『円国、具望目」】、ロ○日目己や已号］の○口吾の。Ｃ目巴目（、シ、。、四句）唇。【且＆←ご色］－諾ご胃昌一の
目。⑫旨、］①－℃の異の。胃の葡甸の月のｍ・自営の口昏の息】、餌『○一の旦冒昌一富》ず円冒］
田、（、シ、。尅印宅）田）
】）好、〆］炉（田）ｗ田渕（田一》国）
】】）ベｘｍ〆》一目已包甸滉（国）Ｍ団榴（田】）国）ⅡＵ鮪（田）Ⅱ■〆（弓】》国）｝
Ｐ膳恒に僧隅如巨②。＆ごＣ回３言のＰ麗冒口宮】Ｃ易。円周房○円の目凹）麗冒目の昏鷺昏吋ｇｓＨｍ〆》
。、
ロ曰口吋Ｈ（国）ⅡＰ豈昏菖當》罵切○日の、○○。】、己【。』巨口の曰菖】富目凹凶目こ］の『の】》吾のロロＣＯ言ＲｍＣＣ』
￣
ｐＰｐすの胃。ｑ巨○の』・目冨口苦の『○一百ｍ胃言目①閂目冨←ずの昌○苗８国巳．
。。■圏ロ円固Ｈ閏曰や］の閨・田思閂すの『。一一ロ、ず望ロ○日ロ目諄の①■Ｐ露。。旨←⑩』雪ヨーけ←庁⑪辱黒・匹口。①
肴肩口国（田】》園）Ⅱ（ＰＣ）餌ロ已国（弓噌頃）Ⅱ（』》ロ）】兵団）Ⅱ（揖己）》函Ｃ宙画■。←曰○菌一○塾些・団員『
愚言面⑩函詩麗ご】］】ご目。『○一円、。『の円四ｍ目ご》目已】匝已○日ロＰ巳已已吾］の。■（、尹切二、⑫勺）ロ・日ロ畠
○Ｃロロ巨巴。■
号の昌曰淳○目巳伊圏巨目已》Ｃロ。【ＣＣＢ臣胃］旨百日壱⑩ロ患巨のざ円昌黛鷺Ｃ勗亘□．
一
旨号巨、已餌己曾》二石の切言＆＆已冒①已巨すぼ○ｍｇ烏の８口◎日】の⑰量晉詩麗】亘屋］８口異同圏ロ訂．
。ｐ苫①。。Ｂ匿自○門鯉」曰←ご巴望１土の己胃騨》］の餌ロロ圏信一①－ロ①昌呂官の訂円のロ○畠》毛》の】」の具冨＆苦の
一○息－Ｃ己］『○一旨、函呂の曰（溺君「亘呂麗爵②ごＣ一閏、。『の【の】、ｐご目。■ＣｐＢＰ昌勺已由亘巨】・雪の
（出冨ケ］】号のロ晉鷺目○崖『。←旨ｍｍｓ①目の、房湧くの凹弓の昌已○頭「の］餡巨］ごＣ←のユロニのロＰ冨円巴８ｍの肴ケ①曰
：量『。□臣す厚ｃｍｏａｍＣ圏ず①官呂目の□鴛晉の一目ロ買砕曰臣涛麗】す】の］の『の］由巴日昌一Ｐ目のＣｇ｝豊・
甸冒晉曾ＢＣＨの晉目己。弱『⑩『辱』『○一国ワの８日の、餌島○一呉○ユロニ①ご目○国｝⑤鶴の看戸のロ】［碗。Ｂの、。。」
■ＨＣＣ［。［叩一ｍ己
奮巨目の言壹貯上》（｛騨巨距胃の目・亘宣
シ石田固三己閂〆
旨官。」言の皀鷺】訪日騨邑曰巴】の急］）善のロロ○○二円、。。』＆皀官。』臣、の。。
ＵＢＣ［。【曰苣の。吊曰
（】）鈩（ず庇）ｗ鮮》胃（』）へ｛瀦ｗ鮮
円冨曰ワ電（⑬）】曽曾の】切宅一ｍ（、シ函。、⑫勺）冒呂晉菖
（酉）国（勺】》国）Ⅱ閂一目』（←）く『》ベ》》［》Ｈｗ鮮Ｖ（ｘｌ（旧】（｝
（可・尉関圓已】の》Ｓ８ｍの冒岱＆葺くの］鐘上の己閂昌の目已冒函］中古の異＆官の膏の貝の
へ］
旧】、（、諺、っ、亀）吊官の画の昌の」ごＰ］堂（己忌田望－当）］ｍｘ目＆吾皀
￣
の
・園山（堵Ｉ〉》（×函禺曾目）苗二一二９．ｍ程
①四巨漢閏①二一。
や》
》①閂①二生←
Ⅱ》
餉口①一ｍ｝Ｃ」○○肖由
□・郡川（ぶ《ざ鮴
芯［《×白山鍜己局〆ｗｘｐｇ己
川（＄《…《［『）出・當宅『（》）１｜屋山夢｝Ⅱ（ぷ）灘
匡貰｝Ⅱ二割釧川（＄《…｛［『）出・苫産山『（》）ｍｌｚ
四三参・畠：ご月影の参三Ｃ二超（＄）灘山彦
．（ぷ）潔山、凄」審三：ご目』房の参三。』
｛轍川Ｘ》｜ｚ岩｝Ⅱ三（ト）已冒騨川（手…（［『）単（②）
三三目、宅石（》）①局①』の三《（ぷ）灘四三台
玲二産出（｝》）ぜ■昌臼己。
．恩３日）
』』一、』安し｛》『（Ｈ１》｛》《ｘ国Ｈ⑤ｐＨ）
－テ
円
薗巨の一ｍ｝。］○○出凸
。ｘ》八騨言）剣邸Ⅲ（釘（》）醜（、［）
、１割八「》（箪巳剣）八
℃目⑭｝》《》《＄篇三①日冨里
”州附Ｍ一鯛‐艸肌Ⅲ‐測一‐（二
（［－（浅目蹴門）ｖ’（や）門Ｐ－（［＋や）閉Ｐ一・湧日一＄シ冒甸涕莨ア勺目
（。←曹宮国（。《｝曽舅・月言冨宣冨日目・ロ《（面）釘
ロ・轍川（。（｝》）醜三一・日苗二《（『）ご目（［）宣言臼
ご的二一二○．函の閂“
-J．
｛（虹一害百四（１＄Ｖ溌傍｝《（ン（、》）己月》Ⅱ（国一百曲）囚（為）
篇二９局（四ｍｑ巨切くい）し『凸砦①思量（（【）門ムロの毎日
の。ｐ巴昌①己で①望⑤①曰－①［四目堕已曰飼①［二国飼口の噸１門［①倉碧ロロ両ロ⑤①聟固《。【曰目甸滉。Ｈ○四）
苗二二○扇×罠（唾Ｔ－謁自缶Ｐ）重『⑤勇二己①旨麗の員留（凸、色巨画くｑ）四㎡
Ｘ白Ⅶ鞭Ⅶ昌》増
筥》ｖ鞭Ⅶ二鶴》｛（郡‐潔》）「（料鋤一Ｎ（鞭）澱Ｐ
（［Ｉ（湯日×樅）Ｖ’（＄）浅□－（［＋や）門Ｐ｜《門目粋＄ア《Ｈ升浅シ宮甸
三一③冒三裳（（、》）官鐵（、［）白・由．（釘（誓一虜（虹《彗星白目三富亘冨日ロ・ロ（（、魚）台
諸昌目昌麗起・｛｛敏ＭＨ》’
ー、、－
００
ｚｇのど（『）》肴の冨弓①、｛⑰）言、Ⅱ｛』ｍｚｌ毎｛Ｈｗ鮓｝・
田の←（《」））】ｍｚ》」Ⅱｃ》】》…》ロケの、巨⑤面一彦鷺（《。））】ｍｚⅢ（《）】ｍｚＰｐ』
昏旦Ⅱ】》…一口》《」）Ⅱ一一一一許←洲】（の
ロ
謡（渉）》一二の胃。。［善の二盛一
ｚⅡ（亀｛）】ｍごま「の冨己の“（垣）津（虫》…》よ）ｗ鮓・（、）目』
）》ご理のご】》炉（（一一）…）品」））ｗ鮮・円冨Ｈの召局さ吋邑」一
Ⅱザ。、。ご窪の亘．】一二・雪「鷺蔓鈩（串』）…》宅））ｗか．
壽言Ｂご旨ｓ三目冨一昏昌】」》鮪（酷一）…》お））ｗ鮨・
二言」‐二（・）ふ（《｝一）…》僻。））ｗ鈩薑：鮴（鵬Ｔ一）：》今』））ｗ好・壽。
諜一押碍）ｗ鮓》言且ｍ
ｏｐ－匠のｇ丘円彦顛回。》君彦
輔（拾）…》堵））ｗか．吾
（⑫）】目ご］］三、ｍ験（鮨）・
侮恒ｂ償鳫‐陣原曙トト盟月①吾の一一○昼］盛一口胃一ぽ。】身ケ望曾の』＆昌一］○回。［
己ＰＨ←。ｐ胃留。
田の←（少）…》＄）ｍ頃曰冒』言ｈ国富豊・亘言こぐⅡ｛一ｍ二一〈Ｈｗ鮴｝ｍ鋸（貯）．この
毛自鷺：冒買冒鯲（鳧忌…少）ｗ貯・二言。＆且】。：［謡（無）》←盲の胃の（《）】ｍ雪圏・亘蔓
（旨）鮴（《］…》よ）ｗ鮓Ｐ己（旨）江】ｍｚ）（《汁ｗ鈩介ｌ《ｘｗ鮮）
■の一（《」））】ｍｚ》」ⅡＰ】）』》…］ロケの旨⑤彦一彦鷺←。）Ⅱ（（｛）示国②ロ』
ず、」Ⅱ』》函）…》回）《」）Ⅱ｜》一一ぽ》円汕】》の．
この皀凰日す］亘冒宮言一言巴］］》鈩（亀｛一）…》全））ｗ炉．ご二目」ⅡＰす］（９）》
湫董》慈順鵠一朏竃馴師鷆篝奪璽』課
態）蕊満一Ｍ窯蕊鞠瀦鋪）獺一一篭灘薫鯛厘一一
《｡
函回国固函回国○因、
得
Barbera,Ｓ,,HSonnenschein,andL・Zhou(1991):I1VOTINGBYCOMMITTEES,Ii
Econometnca59,595-609．
Bazbera,Ｓ,Ｆ・Gul,３，ｄＢ・Stacchetti(1991):IIGENERALIZEDMEDIANVOTER
ＳＣＨＥＭＥＳＡＮＤＣＯＭＭＩＴＴＥＥＳ,Iomimeo・
Bazbera,S・andMatthewJack8on(1991):I1ACHARACTEmZATIONOF
STRAＴＥＧＹ－ＰＲＯＯＦＳＯＣＩＡＬＣＨＯＩＣＥＦＵＮＣＴＩＯＮＳＦＯＲＥＣＯＮＯＭＩＥＳＷＩＴＨ
ＰＵＲＥＰＵＢＬＩＣＧＯＯＤＳＩＩ，DiscmBionPaPerNO､964．
Border,MinOandJSJordan(1983):ⅡSTRAIGHTFORWARDELECTIONS，
ＵＮＡＮＩＭＩＴＹＡＮＤＰＨＡＮＴＯＭＶＯＴＥＲＳＩＩ，ReviewofEconomicStudieB,153-170．
Gibbard,Ａ(1973):I1MANIPULATIONOFVOTINGSCHEMES：AGENERAL
RESULTII,EconometIica,40,587-602．
LinZhou(1991):IiIMPOSSIBILITYOFSTRATEGY-PＲＯＯＦＭＥＣＨＡＮＩＳＭＳＩＮ
ＥＣＯＮＯＭＩＥＳＷＩＴＨＰＵＲＥＰＵＢＬＩＣＧＯＯＤＳＩＩ,R2FiewofEconomicStudie8,107-119．
Satterthwaite,ＭＡ.(1975):I1STRATEGY-PROOFNESSANDARROW'Ｓ
ＣＯＮＤＩＴＩＯＮＥＸＩＳＴＥＮＣＥＡＮＤＣＯＲＲＥＳＰＯＮＤＥＮＣＥＴＨＥＯＲＥＭＳＦＯＲＶＯＴＩＮＧ
ＰＲＯＣＥＤＵＲＥＳＡＮＤＳＯＣＩＡＬＷＥＬＦＡＲＥＦＵＮＣＴＩＯＮＳ,'１JoumalofEconomicTheoIy，
10,187翅17．
Serizawa,Ｓ(1992):I1EXTENSIONOF'VOTINGBYCOMMITTEES'ＴＯＡ
ＭＵＬＴＩＰＬＥＣＯＮＳＵＭＰＴＩＯＮＬＥＶＥＬＳｏＩ,mimeo・
Sprumont,Ｙ､(1991):IITHEDIVISIONPROBLEMWITHSINGLE-PEAKED
PRnmaRENCES:ＡＣＨＡＲＡＣＴＥＲＩＺＡＴＩＯＮＯＦＴＨＥＵＮＩＦＯＲＭＡLＬＯＣＡＴＩＯＮ
ＲＵＬＥ,IIEconometrica,59,509-519．
Thomson,ｗ・(1990):I1CONSISTENTSOLUTIONSＴＯＴＨＥＰＲＯＢＬＥＭＯＦ
ＦＡＩＲＤＩＶＩＳＩＯＮＷＨＥＮＰＲＥＦＥＲＥＮＣＥＳＡＲＥＳＩＮＧＬＥ－ＰＥＡＫＥＤ,IIURmimeo，1990,
JournalofEconomicTheoIy,fbrthcoming．
2０
ＯＳＡＫＡＵＮＩＶＥＲＳＩＴＹ
ＴｈｅｌｎｓｔｉｔｕｔｅｏｆＳｏｃｉａｌａｎｄＥｃｏｎｏｍｉｃＲｅｓｅａｒｃｈ
ＤｉｓｃｕｓｓｉｏｎＰａｐｅｒｓ
Ｎｏ．２８７
ＣｈａｒｌｅｓＹｕｊｉｌｌｏｒｉｏｋａ，、ＴｈｅｌｍｐａｃｔｏｆｔｈｅＡｇｅＳｔｒｕｃｔｕｒｅｏｆｔｈｅ
ＰｏｐｕｌａｔｉｏｎｏｎｔｈｅＨｏｕｓｅｈｏｌｄＳａｖｉｎｇＲａｔｅｉｎｊａｐａｎ：ＡＣｏｉｎｔｅｇｒａｔｉｏｎ
Ａｎａｌｙｓｉｓ．■Ｄｅｃｅｍｂｅｒｌ９９２．
Ｎｏ．２８８ＡｔｓｕｓｈｉＴｓｕｎｅｋｉ．￣ＡＮｅｗｌｎｔｅｒｐｒｅｔａｔｉｏｎｏｆＨａｒｏｌｄＨｏｔｅｌｌｉｎｇ・ｓＰｒｏｏｆｏｆ
ｔｈｅＯｐｔｉＩＩｌａｌｉｔｙｏｆＭａｒｇｉｎａｌＣｏｓｔＰｒｉｃｉｎｇ．￣Ｆｅｂｒｕａｒｙｌ９９３．
Ｎｏ．２８９ＡｔｓｕｓｈｉＴｓｕｎｅｋｉ，ｐＴｈｅＭｅａｓｕｒｅｍｅｎｔｏｆＷａｓｔｅｗｉｔｈＮｏｎｃｏｎｖｅｘＴｅｃｈｎｏｌｏｇｙ，
Ｆｅｂｒｕａｒｙｌ９９３．
Ｎｏ．２９０
ＨａｊｉｎｌｅＯｎｉｋｉ，嵐ＯｎｔｈｅＯｐｔｉｍａｌＳｉｚｅｏｆＥｃｏｎｏｍｉｃＯｒｇａｎｉｚａｔｉｏｎｓ：
ＴｈｅＢｅｎｅｆｉｔｓａｎｄＣｏｓｔｓｏｆＣｅｎｔｒａｌｉｚａｔｉｏｎａｎｄＤｅｃｅｎｔｒａｌｉｚａｔｉｏｎ，薄
Ｆｅｂｒｕａｒｙｌ９９３．
Ｎｏ．２９１ＫａｚｕｙａＫａｍｉｙａ．￣ＯｐｔｉｍａｌＣｏｓｔＡ１１ｏｃａｔｉｏｎＲｕｌｅｉｎＧｅｎｅｒａｌＥｑｕｉｌｉｂｒｉｕｌｎ
Ｍｏｄｅｌｓ，衝Ｆｅｂｒｕａｒｙｌ９９３．
No.２９２ＳａｊａｌＬａＭｒｉａｎｄＰａｓｃａｌｉｓＲａｉｎｏｎｄｏｓ，、ＯｎｔｈｅＣｏｒｒｅｃｔｉｏｎｏｆＴｒａｄｅ
ＤｉｓｔｏｒｔｉｏｎｓｉｎａＳｍａｌｌＯｐｅｎＥｃｏｎｏｍｙ，￣Ｆｅｂｒｕａｒｙｌ９９３．
Ｎｏ．２９３ＪｕｎＩｒｉｔａｎｉａｎｄＫｉｙｏｓｈｉＫｕｇａ，吟ＡｌｍｏｓｔＵｎｉｆｏｒｍＣｏｍｍｏｄｉｔｙＴａｘａｔｉｏｎ
Ｄｏｃｔｒｉｎｅ－ＥｑｕｉｌｉｂｒｉｕｍａｎｄＥｆｆｉｃｉｅｎｃｙ－･ｐＭａｒｃｈｌ９９３．
Ｎｏ．２９４ＫａｚｕｙａＫａｍｉｙａ，ロＯｐｔｉｍａｌＰｕｂｌｉｃＵｔｉｌｉｔｙＰｒｉｃｉｎｇ：ＡＧｅｎｅｒａｌＥｑｕｉｌｉｂｒｉｕｍ
Ａｎａｌｙｓｉｓ，園Ａｐｒｉｌｌ９９３．
No.２９５ＨａｊｉｍｅＭｉｙａｚａｋｉ．、Ｅｍｐｌｏｙｅｅｉｓｍ・ＣｏｒｐｏｒａｔｅＧｏｖｅｒｎａｎｃｅａｎｄｔｈｅｊ－Ｆｉｒ、.￣
Ｍａｙ1９９３．
●
Ｎｏ．２９６ＡｔｓｕｓｈｉＹｏｓｈｉｄａｐＡｍｅｍｉｙａ，ｓＰＧＬＳｆｏｒＮｏｎｌｉｎｅａｒＴｗｏＥｒｒｏｒＣｏｍｐｏｎｅｎｔｓ
Ｍｏｄｅｌｓ，ｐＭａｙｌ９９３．
Ｎｏ．２９７ＡｔｓｕｓｈｉＴｓｕｎｅｋｉ，・Ｓｈａｄｏｗ－ｐｒｉｃｉｎｇｌｎｔｅｒｐｒｅｔａｔｉｏｎｏｆｔｈｅＰｉｇｏｖｉａｎＲｕｌｅ
ｆｏｒｔｈｅＯｐｔｉｍａｌＰｒｏｖｉｓｉｏｎｏｆＰｕｂｌｉｃＧｏｏｄｓ，菌Ｍａｙ1９９３．
Ｎｏ．２９８
ＷｕＪｉａｐｅｉ・画ＭａｃｒｏｃｏｎｔｒｏｌｉｓｔｈｅＧｕａｒａｎｔｅｅｏｆｔｈｅＤｅｖｅｌｏｐｍｅｎｔｏｆ
ＭａｒｋｅｔＥｃｏｎｏＩｎｙ－ＯｂｓｅｒｖｅＣｈｉｎａ・ｓＭａｒｋｅｔＥｃｏｎｏｍｙｆｒｏｎｔｈｅＡｎｇｌｅｏｆ
Ｊａｐａｎ・ｓＭａｃｒｏｃｏｎｔｒｏｌ，￣Ｍａｙ1９９３．
Ｎｏ．Ｚ９９ＭｏｔｏｔｓｕｇｕＳｈｉｎｔａｎｉ，￣ＥｘｃｅｓｓＳｍｏｏｔｈｎｅｓｓｏｆＣｏｎｓｕｍｐｔｉｏｎｉｎ」ａｐａ、，￣Ｍａｙ
1９９３．
Ｎｑ３００ＡｔｓｕｓｈｉＹｏｓｈｉｄａ，。Ｄｕｒｂｉｎ－Ｗｕ－ＨａｕｓｍａｎＴｅｓｔｆｏｒＮｏｎｌｉｎｅａｒＴｗｏＥｒｒｏｒ
ＣｏｌｎｐｏｎｅｎｔｓＭｏｄｅｌｓＲｏｂｕｓｔｔｏＨｅｔｅｒｏｓｋｅｄａｓｔｉｃｉｔｙ，画ｊｕｎｅｌ９９３．
Ｎｏ．３０１ＤｏｎａｌｄＷ、Ｋａｔｚｎｅｒ．・ＴｈｅＬｏｃａｔｉｏｎｏｆＤｅｃｉｓｉｏｎ－ＭａｋｉｎｇｉｎｔｈｅＦｉｒｍ，
ｊｕｎｅｌ９９３．
戸
￣
Ｎｏ．３０２
andNoriyoshiOguchi，TheNetPublicPensionDebtof
ｔｈｅＪａｐａｎｅｓｅ Government.￣（ｉｎJapanese「日本国政府の年金純債務」），
Ｊｕｌｙｌ９９３．
ＴａｔｓｕｏＨａｔｔａ
Ｎｏ．３０３ＷｉｌｆｒｅｄＪ・ＥｔｈｉｅｒａｎｄＪａｍｅｓＲＭａｒｋｕｓｅｎ，ＰＭｕｌｔｉｎａｔｉｏｎａｌＦｉｒｍｓ，
ＴｅｃｈｎｏｌｏｇｙＤｉｆｆｕｓｉｏｎａｎｄＴｒａｄｅ，￣Ａｕｇｕｓｔ1９９３．
Ｎｏ．３０４ＷｉｌｆｒｅｄＬＥｔｈｉｅｒａｎｄＨｅｎｒｉｋＨｏｒｎ，鰯Ｒｅｓｕｌｔｓ－０ｒｉｅｎｔｅｄＴｒａｄｅＰｏｌｉｃｙ，鯵
Ａｕｇｕｓｔ1９９３．
Ｎｑ３０５ＦｕｍｉｏＯｈｔａｋｅａｎｄＣｈ…LesYujiHorioka．、SavingMotives,厨（ｉｎJapanese
「貯蓄動機」）。August1９９３．
Ｎｏ．３０６
ＣｈｉｎＬｉｍ，画ＥｒｏｓｉｏｎｏｆＩｎｔｅｒｎａｔｉｏｎａｌＰｕｂｌｉｃＧｏｏｄｓａｎｄＴｈｒｅａｔｓａｎｄ
ＣｈａｌｌｅｎｇｅｓＦａｃｉｎｇｔｈｅＡｓｉａ－ＰａｃｉｆｉｃＥｃｏｎｏｍｉｅｓ，鴬Ａｕｇｕｓｔ1９９３．
Ｎｏ．３０７
ＫｉｙｏｓｈｉＫｕｇａ，￣ＦａｍｉｌｙＥｘｐｅｎｄｉｔｕｒｅｓａｓＯｕｔｃｏｍｅｓｏｆＲｅｃｉｐｒｏｃａｌＣａｒｉｎｇ，￣
Ａｕｇｕｓｔ1９９３．
Ｎｏ．３０８
ＣｈａｒｌｅｓＹｕｊｉＨｏｒｉｏｋａ，”ｌｓＪａｐａｎ，ｓＨｏｕｓｅｈｏｌｄＳａｖｉｎｇＲａｔｅＲｅａｌｌｙＨｉｇｈＴ
Ｓｅｐｔｅｍｂｅｒｌ９９３．
Ｎｏ．３０９
ＣｈｉｋａｓｈｉＭｏｒｉｇｕｃｈｉ，”Ｊａｐａｎ･ｓＭａｃｒｏｅｃｏｎｏｍｉｃＰｏ１ｉｃｙａｎｄＪａｐａｎ－ＵＳ
ＥｃｏｎｏｍｉｃＲｅｌａｔｉｏｎｓＤｕｒｉｎｇｔｈｅＥｉｇｈｔｉｅｓ，“Ｏｃｔｏｂｅｒ1９９３．
Ｎｏ．３１０
ＤｏｎａｌｄＷ・Ｋａｔｚｎｅｒ，ＷｅｓｔｅｒｎＥｃｏｎｏｍｉｃｓａｎｄｔｈｅＥｃｏｎｏｍｙｏｆｊａｐａｎ，
”
Ｏｃｔｏｂｅｒ1９９３．
Ｎｏ．３１１
ＭｏｔｏｔｓｕｇｕＳｈｉｎｔａｎｉ･同ＣｏｉｎｔｅｇｒａｔｉｏｎａｎｄＴｅｓｔｓｏｆｔｈｅＰｅｒｍａｎｅｎｔｌｎｃｏｍｅ
Ｈｙｐｏｔｈｅｓｉｓ：ｊａｐａｎｅｓｅＥｖｉｄｅｎｃｅｗｉｔｈｌｎｔｅｒｎａｔｉｏｎａｌＣｏｍｐａｒｉｓｏｎｓ，
ｈ
Ｎｏｖｅｍｂｅｒｌ９９３．
Ｎｏ．３１２
HajimeOniki，Ｔａｅ ＨｏｏｎＯｕｍＲｏｄｎｅｙＳｔｅｖｅｎｓｏｎａｎｄＶｉｍｉｎＺｈａｎｇ，
ｐＴｈｅＰｒｏｄｕｃｔｉｖｉｔｙ ＥｆｆｅｃｔｓｏｆｔｈｅＬｉｂｅｒａｌｉｚａｔｉｏｎｏｆＪａｐａｎｅｓｅ
Ｔｅｌｅｃｏｍｍｕｎｉｃａｔｉｏｎ Ｐｏｌｉｃｙ，原ＤｅｃｅＨｌｂｅｒｌ９９３．
Ｎｏ．３１３
ＨａｊｉｍｅＯｎｉｋｉ，鰯ＯｎａＤｅｓｉｒａｂｌｅＯｒｇａｎｉｚａｔｉｏｎ
ｏｆｔｈｅＴｅｌｅｃｏｍｍｕｎｉｃａｔｉｏｎｓ
(ｉｎJapanese：「ネットヮー
ク産業としての電気通信：広帯域通信（BISDN） 時代における電気通信産業組
織」），Decemberl993．
ｌｎｄｕｓｔｒｙｉｎｔｈｅＡｇｅｏｆＢｒｏａｄｂａｎｄＮｅｔｗｏｒｋ，鰯
Ｎｑ３１４ＫｉｙｏｓｈｉＫｕｇａ，ＰＢｕｄｇｅｔＣｏｎｓｔｒａｉｎｔｏｆａＦｉｒｍａｎｄＥｃｏｎｏｍｉｃＴｈｅｏｒｙ，
ｗ
Ｊａｎｕａｒｙｌ９９４･
Ｎｑ３１５ＳｈｉｇｅｈｉｒｏＳｅｒｉｚａｗａ，園Ｅｘｔｅｎｓｉｏｎｏｆ・ＶｏｔｉｎｇｂｙＣｏｍｍｉｔｔｅｅｓ,ｔｏａＭｏｄｅｌ
ｗｉｔｈＭｕｌｔｉｐｌｅＣｏｎｓｕｍｐｔｉｏｎＬｅｖｅｌ，衝Ｊａｎｕａｒｙｌ９９４．
Ｎｏ．３１６
ＳｈｉｇｅｈｉｒｏＳｅｒｉｚａｗａ．”ＡｎｌｍｐｏｓｓｉｂｉｌｉｔｙＴｈｅｏｒｅｍｉｎＰｕｒｅＰｕｂｌｉｃＧｏｏｄｓ
ＥｃｏｎｏｍｉｅｓｗｉｔｈＦｅａｓｉｂｉｌｉｔｙＣｏｎｓｔｒａｉｎｔｓ：ＶｏｔｉｎｇｂｙＣｏｍｍｉｔｔｅｅｓｉｎ
Ｎｏｎ－Ｒｅｃｔａｎｇｕ１ａｒＦｅａｓｉｂｌｅＳｅｔｓ，￣Ｍａｙ１９９２，ｒｅｖｉｓｅｄＪａｎｕａｒｙｌ９９４．
』