DiscussionPaperNo、 ３１６

ＡＮＩＭＰＯＳＲｍｎｌ'ＴＹＴＨＥＯＹｍＭ

ＩＮＰＵＲＥＰＵＵＴＩＩＣＧＯＯＤＳＥＣＯＮＯＭｍＲ

ＷＩＴＨＦＥＡＲｍｌＴＪＴＹＣＯＮＳＴＲＡＩＮＴＳ：

ＶＯＴＩＮＧＢＹＣＯＭＭＩＴＴＩｕ田Ｓ

ＩＮＮＯＮ－ＲＥＣＴＡＮＧＵＬＡＲＦＥＡＳｍｎＥＳＥＴＳ

ｂy

ShigehiroSerizawa＊

凸

Mayl992

RevisedJanuaryl994

ThelnstituteofSocialandEconomicResenTch

OsakaUmversity

6-1Mihogaoka,Ibaraki,Osaka56ZJapan

＊＊Firstofall,IwishtothankProfessorWilliamThomsonfbrhisdetajledcommentshelpfUlsuggestions・IalsowishtothankProfbssorsSalvadorBarbera,MarcusBerliaMatthewJacksonandLionelMckenziefbrtheiruselUlcomments．

mentsand

Berliant，

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

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

P

animportantdomajnofpreferences,whicharecalled oｒ

lAschemeis…2111△hl且iffOrsomeprofileofpreferences,somevotercanobtamanoutcomethatheprefersbymisrepresentinghispreferenceiotherwisetheschemeisnonmanimmable

１

璽旦且＝h旦旦且dpreferences,thereexistaclassofnonmanipulablevotingschemesmuchwider

thanthecla88ofdictatorships・Suchschemesarecalled EeneralizedmedianvoterBch⑨ｍ曙

Furthermore,ｗｉｔｈａｖｅｒｙｗｅａｋａ｡domofef5ciencyｏｒ uHUUI臣ＨｕＩＶ【】ⅡⅡ【】Ｖ

calledvoterBovereignty2,ｔｈｅｙcharactelizedvotmgbycommittees：IfavotingBcheme

satisEesvotersovereigntyandnonmanipulabilityonthedomajnofcro8s-Bhaped

preferenceB,ｔｈｅｎitiBaschemeofvotmgbycommittee8．

However,thereareimportantca8e8whenthefeasiblesetis ､Ｆｏｒａｎ

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/theU0teribbe8teleme7ztmZ、

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)＝LThusifthex-thcoordinateofi'ｓｂｅｓｔｅｌｅｍｅｎｔｉｎＺｉｓ２ｏｒ３,thentheoutcomelevelofxmustbeequal

toitiifitisl,thentheoutcomelevelofxisatleastaslargeasl(butmaybe2or3）

Therefbreundertheassumptionsabove,ｔｈｅｒｅｍｕｓｔｂｅａｖｏｔｅｒｗｈｏｉｓｖｅｒｙｐｏｗｅrfm

althoughheisnotnecessarilyadictator,However,ＣＯnsiderthecaseswhenfOreachgoodx，

●

３Apreferenceisadditively竜epara

ifitisrepresentedbyanionofeachgoodissingle-peaked．

、【

３

minFx(P)＝0,thati8,if8omegoodisproducedatitsmaximalfeasiblelevel,thennoother

goodcanbeproduced・SuchcasestypicallyoccurwhentheresourceshomwhichthegoodB

areproducedarenxed,InthosecaseB,thevotingBcheme8becomedictatoriaL

２ModelandCharacterizationofVotingbycommittees

ThesetofvotersisN＝{1,2,…,､},、三2．￣ ｌ＞２.ＧｉｖｅｎＷＥＮ,wedenotethecardinality

(or幽型)isＸ＝{1,2,…,k},ｋｚ２ＧｉｖｅｎｘＥＸｏｆＷｂｙ＃WThesetof ｕｒｅｐｕＲｏ

ａｎｄＡＥＸ,wedenoteXN{x}by証andXlAby-AThesetof DotentiallevelsofxEX 1s

Lx={0,1,…,mx},mx≧landL=x1Xいi…EX,AEXand`EL,w'ed…thox-thcoordinateofZbWk,andtheprohles((b,)yEA,((i,)y#xand(WAbWA,し，[andLArespectivelyGivenxEXandL'〔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－

1s

EPERx,wedenototh…ｔ

{LAEHEXlRxl(LWEZ}byZ(２A）GiventhePreferencerelationPiE身ｌｅｔＲｉ

ThesetofstrictDreferencerelatioｎｓｏｎＬ ｉｓ臭

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 hensiveifzｅｒＯ－ＣＯｍＤｒｅ

ＶＺＥＬ',VZ'ＥＬ，［Ｏ≦Z'二２－２'ＥＬ'］

５１nthispaper,Ｚ’２ZmeansthatZ′＞ZandZ'＃ＺｉａｎｄＺ′＞ZmeansthatfOreachxEX，

A'〉を

４

ｉｓａｆｉｍｃｔｉｏｎｈｏｍＰｎｔｏＺ．Dp6nition：

ｍｏＰ′〔。｡ⅡDe5mtion：Avoting8chemefsatisnes-

V2EZ,ｮＰＥＰ'suchthatf(P)＝

iｆ

suchthatnP)＝Ｚ

LetP-Pi×…×夕ｈＥＰｎ･Avoting8chemefis

P'，ョｉＥＮ'＆ｮPiEPi8uchthatIPi,Pｺﾞ)Ｐif(P)，

Denmtion：￣

ヨＰＥ

manipulableonP' iｆ

andotherwisefis nonmaniDulableon,′

DpfiTnition：＿

ＶｐＥ

AvotingschemefisdictatorialifthereisavoteriENsuchthat

，n,f(p)＝Ｂ(Pi,Z）

旦旦且ﾕﾕi旦旦:Avotingschemefsatisnes

VxEx,ｖｐＥｐｎ,minB-(p:,Ｉ

iｆ

，､,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

ﾌﾟﾘR(4)of2NsuchthatDefmition： Oisasubset

aThisdeEnitionofasetofwinmngcoalitionsisdifIerentfromthatinSerizawa(1992)iｎ

５

ＷＥ翼(い＆ＷＯＷ－Ｗ'ＥｉＩＲ(い￣

De5nitiom:AUst（灘(い)xEX僻x({0｝ＶｘＥＸ,VUk,4,ELx){0}，Ａ≦Ａ'＝Ｚ(4)ﾕﾌﾟﾘK(い

iｆofBetBofwinningcoalitionBiBmonotonic

MonotomcityoflistofsetBofwinmngcoalitionsimpUesthatifacoalitioniB

winningfOrsomelevelいfgoodx,thenthecoalitionmustalsobewmningfbranylower

consumptionleveLInordertodiscussthevotingschemesdeEnedbyspecifyingalistofsets

ofwinmngcoalitions,wedehnemaquasivotingscheme1i．

ｉｓａｆｉｍｃｔｉｏｎｆｒｏｍｌｎｔｏＬ．Dennition：

De5nition：Aquasivotingschemefsatisnes￣】Ｌｉｆ

ＶｐＥ，n,f(p)ＥＺ

AquasivotingschemeisavotingschemeifitsatisEesfeasibiUty．

7ifthereisamonotomcnstDe5njition：Aquasivotingschemefis

(塩(』k))xEX,LELx1{O}ofsetsofwinnmgcoalitionssuchthａｔＶｘＥＸ,VいLxH0},VpEpn，＆(P)≧(k＝{ｉＥＮｌＢｘ(Pi,Z)≧ｐＥ漣(4)

neednotsatishestheconditionofPropositionlbelow．翼(剣that

磯鯛謡搬聯雛MH:澱lﾋﾞii3lMil澱淫慨織鯛⑭iBnOn-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，ｄＢ(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・ThensatishesfeasibilityonlyiffsatisnesConditions(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

ルーmax{(y'ELylWy')EZ((_(x,y})}LetPbesuchthaty

{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…dictsthefeasibilityoff QED．

Eｴ９２g§1119ﾕｰﾕ：AssumethatX＝{x,y）Letfbeaschemeofvotingbycommitteeswith

thelist(潅凹)xEM【ELxl{0}ofsetsofwmnmgcoalitions・ThenfsatisnesfeasibilityifandonlyiffsatisnesCondition(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×z

DenneWx鎚{ilBx(Pi,z)≧qandwya`{ilBy(Pi,z)≧U1,)ThenZ=f(P)imp1ie8that(3)ＷｘＥ堪(い､dWyEjV(9)NowitfbUowsfromCondition(1),(2)and(3)

that(ii)implythatWxnWy#OThenfbriEWxnWy,Ｂ(Pi,Z)≧fSinceZiszero-comprehensive,(1)impUesB(Pi,Z)EZThiscontradictsthedefinitionofB(Pi,Z)．HenceZEZ．ＱＥ.、

Ｚｙ.

0

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)ForanyWxEXt(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.ThusthislistalsosatisEesCondition(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}）

ApreferencerelationPiEPis聖旦竺旦hlEifDennition：

ＶｘＥｘ,vq-x,AEL-x,v4,4ELx（(k,(_x)Pi(4,`_x)－((k,(▲x)Pi(《i,魁）

ＤｅｎｏｔｅｂｙＰＳＥ，theclassofseparablepreferences．

iｆpeak-SeDarableDefinition： AprelerencerelationPiEPis

ＶＸＥＸ,VLXEL証,ZX((_X)＝Ｂｘ(Pi,L）DenotebylPSEptheclassofpeak-separablepreferences．

ifthereemBtBalistDe5mtion：ApreferencerelationPiE’ｉｓ￣

(UxLX-R)xEXofutiUtyfimctionssuchthatfOrallZandZ′

UPi′￣X:XUX(ｐ>x:XU(いDenotebyPAStheclassofadditively-separablepreferences．

ＥＬ，

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-sepambleandsingle-peaked

DenotePC＝ｐＰＳｎｐＳＰ

NotethatlASnPSP[PQA1sonotethatiffOreachxEX,Lx={0,1},then－

single-peakednessisautomaticanysatisEedThusiffbreachxEX,Lx＝{0,1},sincePPScoincideswiththenotionofseparablepreferenceofB,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

quasivotingschemef:Ｚｎ一LisnonmanipulableonthedomamP

Theoreml：Ifatops-only

(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・VoteriENisadecisivevoterinWE襲(4)

riENisadecisivevoterinZK(4)if{i}Ｅｚ(9Voter

ifheisavetoanddecisivevoterin藍(9iＥＮｉｓ

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、§・

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（］』）閂（旧）Ⅳ』』．

甸臣ユロの］ロロ自鈩

（』）時（届）Ⅱ↓（岳）く」ｍｚ－｛】｝）国Ｘ（田］）函）Ⅱ貯、八鰈》（』）時（屋）Ｉ（旨）炉（句）八鮓）

（埠函）》（】②）時（］『）Ⅱ↓（岳）（鶴田】兵甸）

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

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』・（岳）時（』ｃ）８昌国ａｎ冨皀○口ロ】餌己己昌号】］】ご・

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

餌冒。》 ｓ̄ｐ￣￣グー

ｐ￣￣'

盾。￣

￣

Ｃ□、－ン

ｌ｛」ｍｚｌ国『（勺」】国）ｗ傘、｝Ⅱ雪、一｛】｝

ⅡＵ（］⑫）隼弓）八＄雷す『（②））

￣

←

Lx×Lyisnon-rectangularFurtherassumethat(2)votingbycommitteeBfsatisne8feasibilityandgoodwise-unanimity,andi8nonmanipulableon(PASnPSP)n.Thenthe

竃(…Zx)xEXhaveacommondictat．■．sets

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)＝maxZyTheconditionX

{ix}ＥＸｔ(maxZx)impUesthat《c(P)＝maxZx,while{iy}Ｅ藩(…Zy)impnesthatfi,(P)＝…ZyBy(1),thiscontmdictsthefeasibintyoffSoix＝iy

Notethatalsoby(1),Proposition2impUes：

ＶＷｘＥ薦(maxZx),VWyEXt,WxnWy＃USettingWy＝{ix},wehave

VWxE落(maxZx),ixEWxSoixi8adictatorin裏(maxZx）

Therefbreeach恵(maxZx)hasadictat・rButalsoby(1),Pmpositi・n2impliesthatthesedictatorsareｔｈｅｓａｍｅｖｏｔｅＬ ＱＥＤ．

Ｅ[gEg§jllgﾕｰﾑ：Assumethatfbreachxandy,theprojectionZxyofthefeasiblesetZonLxxLyisnon-rectangular,Furtherassumethatvotingbycommitteesfsatisnes

feasibintyandgoodwise-unanimity,andisnonmanipulableonthedomain(，ASmPPS)nofadditively器eparableandpeak-separablepreferencesThenthereisavoteriENsuch

that

(i)fbranyxEX,fbranyLEZxl(0},iisadecisivevoterofﾌﾟﾘH(4)

１５

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。

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）

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』

】）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）｝

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．

（》】）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）。

￣

。、

。。■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

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．

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□．

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、。。」

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

旧】、（、諺、っ、亀）吊官の画の昌の」ごＰ］堂（己忌田望－当）］ｍｘ目＆吾皀

一○Ｃロロ巨巴。■

■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

￣

へ］

の

□・郡川（ぶ《ざ鮴

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

（［Ｉ（湯日×樅）Ｖ’（＄）浅□－（［＋や）門Ｐ｜《門目粋＄ア《Ｈ升浅シ宮甸

筥》ｖ鞭Ⅶ二鶴》｛（郡‐潔》）「（料鋤一Ｎ（鞭）澱ＰＸ白Ⅶ鞭Ⅶ昌》増

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㎡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）

｛（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

。ｘ》八騨言）剣邸Ⅲ（釘（》）醜（、［）

諸昌目昌麗起・｛｛敏ＭＨ》’

ロ・轍川（。（｝》）醜三一・日苗二《（『）ご目（［）宣言臼

（。←曹宮国（。《｝曽舅・月言冨宣冨日目・ロ《（面）釘

（［－（浅目蹴門）ｖ’（や）門Ｐ－（［＋や）閉Ｐ一・湧日一＄シ冒甸涕莨ア勺目

”州附Ｍ一鯛‐艸肌Ⅲ‐測一‐（二

．（ぷ）潔山、凄」審三：ご目』房の参三。』

匡貰｝Ⅱ二割釧川（＄《…｛［『）出・苫産山『（》）ｍｌｚ芯［《×白山鍜己局〆ｗｘｐｇ己

｛轍川Ｘ》｜ｚ岩｝Ⅱ三（ト）已冒騨川（手…（［『）単（②）

ご的二一二○．函の閂“

・園山（堵Ｉ〉》（×函禺曾目）苗二一二９．ｍ程

三三目、宅石（》）①局①』の三《（ぷ）灘四三台

四三参・畠：ご月影の参三Ｃ二超（＄）灘山彦

川（＄《…《［『）出・當宅『（》）１｜屋山夢｝Ⅱ（ぷ）灘

００円

-J．

』』一、』安し｛》『（Ｈ１》｛》《ｘ国Ｈ⑤ｐＨ）

、１割八「》（箪巳剣）八

℃目⑭｝》《》《＄篇三①日冨里

①四巨漢閏①二一。

や》Ⅱ》

．恩３日）

玲二産出（｝》）ぜ■昌臼己。

－テー、、－》①閂①二生←

餉口①一ｍ｝Ｃ」○○肖由

薗巨の一ｍ｝。］○○出凸

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。［

諜一押碍）ｗ鮓》言且ｍｏｐ－匠のｇ丘円彦顛回。》君彦

輔（拾）…》堵））ｗか．吾

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。

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

己ＰＨ←。ｐ胃留。

（⑫）】目ご］］三、ｍ験（鮨）・ロ

ｚⅡ（亀｛）】ｍごま「の冨己の“（垣）津（虫》…》よ）ｗ鮓・（、）目』

Ⅱザ。、。ご窪の亘．】一二・雪「鷺蔓鈩（串』）…》宅））ｗか．）》ご理のご】》炉（（一一）…）品」））ｗ鮮・円冨Ｈの召局さ吋邑」一

函回国固函回国○因、

得

《｡

謡（渉）》一二の胃。。［善の二盛一

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

ＣｈａｒｌｅｓＹｕｊｉｌｌｏｒｉｏｋａ，、ＴｈｅｌｍｐａｃｔｏｆｔｈｅＡｇｅＳｔｒｕｃｔｕｒｅｏｆｔｈｅ

ＰｏｐｕｌａｔｉｏｎｏｎｔｈｅＨｏｕｓｅｈｏｌｄＳａｖｉｎｇＲａｔｅｉｎｊａｐａｎ：ＡＣｏｉｎｔｅｇｒａｔｉｏｎ

Ａｎａｌｙｓｉｓ．■Ｄｅｃｅｍｂｅｒｌ９９２．

Ｎｏ．２８７

Ｎｏ．２８８ＡｔｓｕｓｈｉＴｓｕｎｅｋｉ．￣ＡＮｅｗｌｎｔｅｒｐｒｅｔａｔｉｏｎｏｆＨａｒｏｌｄＨｏｔｅｌｌｉｎｇ・ｓＰｒｏｏｆｏｆ

ｔｈｅＯｐｔｉＩＩｌａｌｉｔｙｏｆＭａｒｇｉｎａｌＣｏｓｔＰｒｉｃｉｎｇ．￣Ｆｅｂｒｕａｒｙｌ９９３．

￣

Ｎｏ．２８９ＡｔｓｕｓｈｉＴｓｕｎｅｋｉ，ｐＴｈｅＭｅａｓｕｒｅｍｅｎｔｏｆＷａｓｔｅｗｉｔｈＮｏｎｃｏｎｖｅｘＴｅｃｈｎｏｌｏｇｙ，

Ｆｅｂｒｕａｒｙｌ９９３．

ＨａｊｉｎｌｅＯｎｉｋｉ，嵐ＯｎｔｈｅＯｐｔｉｍａｌＳｉｚｅｏｆＥｃｏｎｏｍｉｃＯｒｇａｎｉｚａｔｉｏｎｓ：

ＴｈｅＢｅｎｅｆｉｔｓａｎｄＣｏｓｔｓｏｆＣｅｎｔｒａｌｉｚａｔｉｏｎａｎｄＤｅｃｅｎｔｒａｌｉｚａｔｉｏｎ，薄

Ｆｅｂｒｕａｒｙｌ９９３．

Ｎｏ．２９０

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．

ＷｕＪｉａｐｅｉ・画ＭａｃｒｏｃｏｎｔｒｏｌｉｓｔｈｅＧｕａｒａｎｔｅｅｏｆｔｈｅＤｅｖｅｌｏｐｍｅｎｔｏｆ

ＭａｒｋｅｔＥｃｏｎｏＩｎｙ－ＯｂｓｅｒｖｅＣｈｉｎａ・ｓＭａｒｋｅｔＥｃｏｎｏｍｙｆｒｏｎｔｈｅＡｎｇｌｅｏｆ

Ｊａｐａｎ・ｓＭａｃｒｏｃｏｎｔｒｏｌ，￣Ｍａｙ1９９３．

Ｎｏ．２９８

Ｎｏ．Ｚ９９ＭｏｔｏｔｓｕｇｕＳｈｉｎｔａｎｉ，￣ＥｘｃｅｓｓＳｍｏｏｔｈｎｅｓｓｏｆＣｏｎｓｕｍｐｔｉｏｎｉｎ」ａｐａ、，￣Ｍａｙ

1９９３．

Ｎｑ３００ＡｔｓｕｓｈｉＹｏｓｈｉｄａ，。Ｄｕｒｂｉｎ－Ｗｕ－ＨａｕｓｍａｎＴｅｓｔｆｏｒＮｏｎｌｉｎｅａｒＴｗｏＥｒｒｏｒ

ＣｏｌｎｐｏｎｅｎｔｓＭｏｄｅｌｓＲｏｂｕｓｔｔｏＨｅｔｅｒｏｓｋｅｄａｓｔｉｃｉｔｙ，画ｊｕｎｅｌ９９３．

戸

Ｎｏ．３０１ＤｏｎａｌｄＷ、Ｋａｔｚｎｅｒ．・ＴｈｅＬｏｃａｔｉｏｎｏｆＤｅｃｉｓｉｏｎ－ＭａｋｉｎｇｉｎｔｈｅＦｉｒｍ，

ｊｕｎｅｌ９９３．

Ｎｏ．３０２ ＴａｔｓｕｏＨａｔｔａ

ｔｈｅＪａｐａｎｅｓｅ

Ｊｕｌｙｌ９９３．

andNoriyoshiOguchi，TheNetPublicPensionDebtof

Government.￣（ｉｎJapanese「日本国政府の年金純債務」），

Ｎｏ．３０３ＷｉｌｆｒｅｄＪ・ＥｔｈｉｅｒａｎｄＪａｍｅｓＲＭａｒｋｕｓｅｎ，ＰＭｕｌｔｉｎａｔｉｏｎａｌＦｉｒｍｓ，

ＴｅｃｈｎｏｌｏｇｙＤｉｆｆｕｓｉｏｎａｎｄＴｒａｄｅ，￣Ａｕｇｕｓｔ1９９３．

Ｎｏ．３０４ＷｉｌｆｒｅｄＬＥｔｈｉｅｒａｎｄＨｅｎｒｉｋＨｏｒｎ，鰯Ｒｅｓｕｌｔｓ－０ｒｉｅｎｔｅｄＴｒａｄｅＰｏｌｉｃｙ，鯵Ａｕｇｕｓｔ1９９３．

Ｎｑ３０５ＦｕｍｉｏＯｈｔａｋｅａｎｄＣｈ…LesYujiHorioka．、SavingMotives,厨（ｉｎJapanese「貯蓄動機」）。August1９９３．

ＣｈｉｎＬｉｍ，画ＥｒｏｓｉｏｎｏｆＩｎｔｅｒｎａｔｉｏｎａｌＰｕｂｌｉｃＧｏｏｄｓａｎｄＴｈｒｅａｔｓａｎｄ

ＣｈａｌｌｅｎｇｅｓＦａｃｉｎｇｔｈｅＡｓｉａ－ＰａｃｉｆｉｃＥｃｏｎｏｍｉｅｓ，鴬Ａｕｇｕｓｔ1９９３．

Ｎｏ．３０６

ＫｉｙｏｓｈｉＫｕｇａ，￣ＦａｍｉｌｙＥｘｐｅｎｄｉｔｕｒｅｓａｓＯｕｔｃｏｍｅｓｏｆＲｅｃｉｐｒｏｃａｌＣａｒｉｎｇ，￣Ａｕｇｕｓｔ1９９３．

Ｎｏ．３０７

ＣｈａｒｌｅｓＹｕｊｉＨｏｒｉｏｋａ，”ｌｓＪａｐａｎ，ｓＨｏｕｓｅｈｏｌｄＳａｖｉｎｇＲａｔｅＲｅａｌｌｙＨｉｇｈＴ

Ｓｅｐｔｅｍｂｅｒｌ９９３．

Ｎｏ．３０８

ＣｈｉｋａｓｈｉＭｏｒｉｇｕｃｈｉ，”Ｊａｐａｎ･ｓＭａｃｒｏｅｃｏｎｏｍｉｃＰｏ１ｉｃｙａｎｄＪａｐａｎ－ＵＳ

ＥｃｏｎｏｍｉｃＲｅｌａｔｉｏｎｓＤｕｒｉｎｇｔｈｅＥｉｇｈｔｉｅｓ，“Ｏｃｔｏｂｅｒ1９９３．

Ｎｏ．３０９

ＤｏｎａｌｄＷ・Ｋａｔｚｎｅｒ，ＷｅｓｔｅｒｎＥｃｏｎｏｍｉｃｓａｎｄｔｈｅＥｃｏｎｏｍｙｏｆｊａｐａｎ，”

Ｏｃｔｏｂｅｒ1９９３．

Ｎｏ．３１０

ＭｏｔｏｔｓｕｇｕＳｈｉｎｔａｎｉ･同ＣｏｉｎｔｅｇｒａｔｉｏｎａｎｄＴｅｓｔｓｏｆｔｈｅＰｅｒｍａｎｅｎｔｌｎｃｏｍｅｈ

Ｈｙｐｏｔｈｅｓｉｓ：ｊａｐａｎｅｓｅＥｖｉｄｅｎｃｅｗｉｔｈｌｎｔｅｒｎａｔｉｏｎａｌＣｏｍｐａｒｉｓｏｎｓ，

Ｎｏｖｅｍｂｅｒｌ９９３．

Ｎｏ．３１１

HajimeOniki，Ｔａｅ

ｐＴｈｅＰｒｏｄｕｃｔｉｖｉｔｙ

Ｔｅｌｅｃｏｍｍｕｎｉｃａｔｉｏｎ

ＨｏｏｎＯｕｍＲｏｄｎｅｙＳｔｅｖｅｎｓｏｎａｎｄＶｉｍｉｎＺｈａｎｇ，

ＥｆｆｅｃｔｓｏｆｔｈｅＬｉｂｅｒａｌｉｚａｔｉｏｎｏｆＪａｐａｎｅｓｅ

Ｐｏｌｉｃｙ，原ＤｅｃｅＨｌｂｅｒｌ９９３．

Ｎｏ．３１２

ＨａｊｉｍｅＯｎｉｋｉ，鰯ＯｎａＤｅｓｉｒａｂｌｅＯｒｇａｎｉｚａｔｉｏｎ

ｌｎｄｕｓｔｒｙｉｎｔｈｅＡｇｅｏｆＢｒｏａｄｂａｎｄＮｅｔｗｏｒｋ，鰯

ク産業としての電気通信：広帯域通信（BISDN）

織」），Decemberl993．

Ｎｏ．３１３ ｏｆｔｈｅＴｅｌｅｃｏｍｍｕｎｉｃａｔｉｏｎｓ

(ｉｎJapanese：「ネットヮー

時代における電気通信産業組

』

Ｎｑ３１４ＫｉｙｏｓｈｉＫｕｇａ，ＰＢｕｄｇｅｔＣｏｎｓｔｒａｉｎｔｏｆａＦｉｒｍａｎｄＥｃｏｎｏｍｉｃＴｈｅｏｒｙ，ｗ

Ｊａｎｕａｒｙｌ９９４･

Ｎｑ３１５ＳｈｉｇｅｈｉｒｏＳｅｒｉｚａｗａ，園Ｅｘｔｅｎｓｉｏｎｏｆ・ＶｏｔｉｎｇｂｙＣｏｍｍｉｔｔｅｅｓ,ｔｏａＭｏｄｅｌ

ｗｉｔｈＭｕｌｔｉｐｌｅＣｏｎｓｕｍｐｔｉｏｎＬｅｖｅｌ，衝Ｊａｎｕａｒｙｌ９９４．

ＳｈｉｇｅｈｉｒｏＳｅｒｉｚａｗａ．”ＡｎｌｍｐｏｓｓｉｂｉｌｉｔｙＴｈｅｏｒｅｍｉｎＰｕｒｅＰｕｂｌｉｃＧｏｏｄｓ

ＥｃｏｎｏｍｉｅｓｗｉｔｈＦｅａｓｉｂｉｌｉｔｙＣｏｎｓｔｒａｉｎｔｓ：ＶｏｔｉｎｇｂｙＣｏｍｍｉｔｔｅｅｓｉｎ

Ｎｏｎ－Ｒｅｃｔａｎｇｕ１ａｒＦｅａｓｉｂｌｅＳｅｔｓ，￣Ｍａｙ１９９２，ｒｅｖｉｓｅｄＪａｎｕａｒｙｌ９９４．

Ｎｏ．３１６