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SocialChoice:TheoryandResearchSage
UniversityPapersSeries.No.07-123
Johnson,P.E.
SagePublications,Inc.
0761914064
9780761914068
9780585181073
English
Socialchoice--Mathematicalmodels,
Decisionmaking--Mathematicalmodels.
1998
HB846.8.J651998eb
302/.13
Socialchoice--Mathematicalmodels,
Decisionmaking--Mathematicalmodels.
SocialChoiceTheoryandResearch
SAGEUNIVERSITYPAPERS
Series:QuantitativeApplicationsintheSocialSciences
SeriesEditor:MichaelS.Lewis-Beck,UniversityofIowa
EditorialConsultants
RichardA.Berk,Sociology,UniversityofCalifornia,LosAngeles
WilliamD.Berry,PoliticalScience,FloridaStateUniversity
KennethA.Bollen,Sociology,UniversityofNorthCarolina,Chapel
Hill
LindaB.Bourque,PublicHealth,UniversityofCalifornia,Los
Angeles
JacquesA.Hagenaars,SocialSciences,TilburgUniversity
SallyJackson,Communications,UniversityofArizona
RichardM.Jaeger,Education,UniversityofNorthCarolina,
Greensboro
Garyking,DepartmentofGovernment,HarvardUniversity
RogerE.Kirk,Psychology,BaylorUniversity
HelenaChmuraKraemer,PsychiatryandBehavioralSciences,
StanfordUniversity
PeterMarsden,Sociology,HarvardUniversity
HelmutNorpoth,PoliticalScience,SUNY,StonyBrook
FrankL.Schmidt,ManagementandOrganization,UniversityofIowa
HerbertWeisberg,PoliticalScience,TheOhioStateUniversity
Publisher
SaraMillerMcCune,SagePublications,Inc.
INSTRUCTIONSTOPOTENTIALCONTRIBUTORS
Forguidelinesonsubmissionofamonographproposaltothisseries,
pleasewrite
MichaelS.Lewis-Beck,Editor
SageQASSSeries
DepartmentofPoliticalScience
UniversityofIowa
IowaCity,IA52242
Pagei
Series/Number07-123
SocialChoice:TheoryandResearch
PaulE.Johnson
UniversityofKansas
SAGEPUBLICATIONS
InternationalEducationalandProfessionalPublisher
ThousandOaksLondonNewDelhi
Pageii
Copyright©1998bySagePublications,Inc.
Allrightsreserved.Nopartofthisbookmaybereproducedor
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LibraryofCongressCataloging-in-PublicationData
Johnson,P.E.(PaulE.)
Socialchoice:theoryandresearch/PaulE.Johnson.
p.cm.(Quantitativeapplicationsinthesocialsciences;
vol.123)
Includesbibliographicalreferences(p.).
ISBN0-7619-1406-4(pbk.:alk.paper)
1.SocialchoiceMathematicalmodels.2.Decision-making
Mathematicalmodels.I.Title.II.Series:Sageuniversity
papersseries.Quantitativeapplicationsinthesocialsciences;
07-123.
HB846.8.J65199898-20634
302'.13-dc21
Thisbookisprintedonacid-freepaper.
98990001020310987654321
AcquiringEditor:C.DeborahLaughton
EditorialAssistant:EileenCarr
ProductionEditor:AstridVirding
EditorialAssistant:NevairKabakian
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Whencitingauniversitypaper,pleaseusetheproperform.
RemembertocitetheSageUniversityPaperseriestitleandincudethe
papernumber.Oneofthefollowingformatscanbeadapted
(dependingonthestylemanualused):
(1)JOHNSON,PE.(1998).SocialChoice:TheoryandResearch.Sage
UniversityPapersSeriesonQuantitativeApplicationsintheSocial
Sciences,07-123.ThousandOaks,CA:Sage.
OR
(2)Johnson,P.E.(1998).Socialchoice:Theoryandresearch(Sage
UniversityPapersSeriesonQuantitativeApplicationintheSocial
Sciences,seriesno.07-123).ThousandOaks,CA:Sage.
Pageiii
Contents
SeriesEditor'sIntroduction
v
Acknowledgments
vii
Preface
ix
1.WhatisSocialChoiceTheory
1
TheVoter'sParadox
2
TheBigPicture
3
AnOutlineofthisBook
7
2.FundamentalTerminology:DiscreteSocialChoice
3.Arrow'sTheorem
9
12
TheSocialPreferenceFunction
12
Arrow'sPossibilityTheorem
13
TheMeaningofArrow'sTheorem
21
4.FundamentalTerminology:ContinuousSetsof
Alternatives
31
TheEuclideanSpatialModel
31
UtilityFunctions
32
ContinuityandUtilityRepresentationsonthe
Continuum
37
ConvexityandSingle-Peakedness
41
5.TheUnidimensionalSpatialModel
49
TheImportanceofSingle-PeakedPreferences
49
TheMedianVoterTheorem
50
ReversionPointsandTake-It-or-Leave-ItOffers
53
UnravelinginDemocraticallyGovernedGroups
55
6.TheMultidimensionalSpatialModel
TheImportanceofConvexity
60
60
StabilityAnalysis:MajorityRuleinSeveralDimensions 64
TheChaosTheorems
77
Pageiv
AddressingtheDisequilibriumProblem
80
Structure-InducedEquilibrium
81
BehavioralSourcesofStability
93
7.Conclusion:LookingBackwardandForward
97
References
102
AbouttheAuthor
109