Theory of Social Choice on Networks: Preference, Aggregation, and Coordination

226 Pages·2020·1.562 MB·English

by  Wynn C. Stirling

Theory of Social Choice
on Networks
Classicalsocialchoicetheoryreliesheavilyontheassumptionthatallindi-
vidualshavefixedpreferenceorderings.Thishighlyoriginalbookpresents
a new theory of social preferences that explicitly accounts for important
social phenomena such as coordination, compromise, negotiation, and
altruism. Drawing on network theory, it extends classical social choice
theorybyconstructinga frameworkthat allows for dynamicpreferences
that are modulated by the situation-dependent social influence that they
exertoneachother.Inthiswaythebookshowshowmembersofasocial
network may modulate their preferences to account for social context.
This important expansion of social choice theory will be of interest to
readersinawidevarietyofdisciplines,includingeconomistsandpolitical
scientists concerned with choice theory as well computer scientists and
engineersworkingonnetworktheory.
wynn c. stirling isProfessorofElectricalandComputerEngineer-
ing, as well as Dean of Graduate Studies at Brigham Young University.
He is the author of Satisficing Games and Decision Making (Cambridge
University Press, 2003) and Theory of Conditional Games (Cambridge
University Press, 2012). He is also the co-author of Mathematical Meth-
odsandAlgorithmsforSignalProcessing(2000)withToddMoon.

Theory of Social Choice
on Networks
Preference, Aggregation, and Coordination
wynn c. stirling
BrighamYoungUniversity,Utah
UniversityPrintingHouse,CambridgeCB28BS,UnitedKingdom
CambridgeUniversityPressispartoftheUniversityofCambridge.
ItfurtherstheUniversity’smissionbydisseminatingknowledgeinthepursuitof
education,learning,andresearchatthehighestinternationallevelsofexcellence.
www.cambridge.org
Informationonthistitle:www.cambridge.org/9781107165168
©CambridgeUniversityPress2016
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Firstpublished2016
AcataloguerecordforthispublicationisavailablefromtheBritishLibrary.
LibraryofCongressCataloging-in-PublicationData
Names:Stirling,WynnC.,author.
Title:Theoryofsocialchoiceonnetworks:preference,aggregation,and
coordination/WynnC.Stirling.
Description:Cambridge,UnitedKingdom:CambridgeUniversityPress,2016.|
Includesbibliographicalreferencesandindex.
Identifiers:LCCN2016012075|ISBN9781107165168(Hardback)
Subjects:LCSH:Socialchoice–Mathematicalmodels.|Systemtheory–Social
aspects–Mathematicalmodels.|Systemanalysis–Mathematicalmodels.|
BISAC:BUSINESS&ECONOMICS/Economics/Microeconomics.
Classification:LCCHB846.8.S752016|DDC003/.72–dc23
LCrecordavailableathttps://lccn.loc.gov/2016012075
ISBN978-1-107-16516-8Hardback
CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracy
ofURLsforexternalorthird-partyInternetWebsitesreferredtointhispublication
anddoesnotguaranteethatanycontentonsuchWebsitesis,orwillremain,
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Contents
ListofFigures pagex
ListofTables xii
PrefaceandAcknowledgments xv
Introduction xix
1 Preference 1
1.1 CategoricalPreferences 5
1.2 Reactivevis-à-visResponsiveModels 10
1.3 InfluenceNetworks 17
1.3.1 ConditionalPreferences 17
1.3.2 SocialModels 24
1.4 RelatedResearch 29
1.5 Summary 31
2 Aggregation 32
2.1 ClassicalAggregation 33
2.2 CoordinatedAggregation 37
2.3 SocialCoherence 39
2.3.1 DemocraticSocialChoice 40
2.3.2 AnOrderIsomorphism 44
2.3.3 OperationalDemocracy 45
2.4 Epistemologyvis-à-visPraxeology 51
2.5 CoherentAggregation 57
2.5.1 BayesianNetworks 58
2.5.2 TheAggregationTheorem 59
2.6 SolutionConcepts 62
2.7 Reframing 69
2.8 Summary 71
vii
viii TableofContents
3 Deliberation 74
3.1 DynamicInfluenceModels 75
3.2 Closed-LoopCollaboration 82
3.3 Non-SimpleCycles 89
3.3.1 GraphswithSub-Cycles 89
3.3.2 EmbeddedCycles 91
3.4 Summary 95
4 Coordination 96
4.1 CoordinationConcepts 96
4.2 AMathematicalCharacterizationofCoordination 98
4.2.1 Entropy 102
4.2.2 MutualInformation 106
4.3 CoordinatabilityforNetworks 108
4.4 Summary 113
5 Randomization 115
5.1 SocialChoicewithStochasticAgents 116
5.2 SocialChoicewithRandomizedPreferences 122
5.2.1 ExpectedUtility 123
5.2.2 ExpectedUtilityonNetworks 124
5.3 Summary 131
6 Satisficing 133
6.1 SolutionConcepts 133
6.2 AChangeinPerspective 137
6.2.1 ErrorAvoidance 138
6.2.2 FailureAvoidance 142
6.3 TheNeo-SatisficingModel 145
6.3.1 Single-AgentSatisficing 145
6.3.2 MultipleSelves 148
6.3.3 SatisficingSocialChoice 151
6.4 SatisficingCoordinatability 156
6.5 Summary 157
AppendixA DutchBookTheorem 158
AppendixB BayesianNetworks 163
AppendixC ProbabilityConcepts 169
TableofContents ix
AppendixD MarkovConvergenceTheorem 174
AppendixE EntropyandMutualInformation 178
Bibliography 186
ListofAuthors 196
Index 199
Figures
1.1 TheThreeStoogesNetworkwithOrdinalLinkages. page22
1.2 TheThreeStoogesTreeDiagram. 25
2.1 TheThree-StoogesNetworkwithUtilityLinkages. 63
2.2 AnAlternateFramingoftheThree-Stooges
NetworkwithMoTakingtheLead. 70
2.3 AnAlternateFramingoftheThree-Stooges
NetworkwithCurlyTakingtheLead. 71
3.1 TheThreeStoogesDinnerPartywithCyclicPreferences. 75
3.2 TheThreeStoogesdinnerpartyviewedasa
dynamicnetwork. 76
3.3 ASimplek-Cycle. 77
3.4 AnEquivalentDynamicNetwork. 77
3.5 Ak-CycleExpressedinTermsofTransitionLinkages. 79
3.6 AConvergedk-Cycle. 82
3.7 InfluenceCyclesforMeetingSchedulingExample. 85
3.8 AFour-AgentDirectedCyclicGraphwithaSub-Cycle. 90
3.9 ADirectedGraphwithanEmbeddedRootCycle. 92
3.10 TheSteady-StateEquivalentGraph. 92
3.11 ANon-RootCyclicGraph. 93
3.12 TheEquivalentSteady-StateGraphwithParent. 94
3.13 AGraphwithanEmbedded4-Cycle. 94
3.14 ASteady-StateEmbedded4-CycleGraph. 95
4.1 ACommunicationsChannel. 100
4.2 TheConditionalProbabilityModelforaBinary
TransmissionChannel. 100
4.3 ATwo-AgentNetwork. 102
4.4 TheConditionalUtilityModelforaTwoAgent,
TwoAlternativeCoordinationScenario. 102
4.5 TheRangeoftheSubordinationFunction. 103
4.6 TheEntropyFunctionforN=2. 104
x