Table Of ContentTheory of Value Structure
Theory of Value Structure
From Values to Decisions
Erich H. Rast
LEXINGTON BOOKS
Lanham•Boulder •NewYork•London
PublishedbyLexingtonBooks
AnimprintofTheRowman&LittlefieldPublishingGroup,Inc.
4501ForbesBoulevard,Suite200,Lanham,Maryland20706
www.rowman.com
86-90PaulStreet,LondonEC2A4NE
Copyright©2022byTheRowman&LittlefieldPublishingGroup,Inc.
Allrightsreserved. Nopartofthisbookmaybereproducedinanyformorby
anyelectronicormechanicalmeans,includinginformationstorageandretrieval
systems,withoutwrittenpermissionfromthepublisher,exceptbyareviewer
whomayquotepassagesinareview.
BritishLibraryCataloguinginPublicationInformationAvailable
LibraryofCongressCataloging-in-PublicationData
Names:Rast,ErichH.,author.
Title:Theoryofvaluestructure:fromvaluestodecisions/ErichH.
Rast.
Description:Lanham:LexingtonBooks,[2022]|Includesbibliographical
referencesandindex.
Identifiers:LCCN2021057416(print)|LCCN2021057417(ebook)|ISBN
9781793616944(cloth)|ISBN9781793616951(ebook)
Subjects:LCSH:Values.
Classification:LCCBD232.R2532022 (print)|LCCBD232 (ebook)|DDC
170−dc23/eng/202201191
LCrecordavailableathttps://lccn.loc.gov/2021057416
LCebookrecordavailableathttps://lccn.loc.gov/2021057417
™ The paper used in this publication meets the minimum requirements of
∞
AmericanNationalStandardforInformationSciences—PermanenceofPaperfor
PrintedLibraryMaterials,ANSI/NISOZ39.48-1992.
Contents
Preface xi
I Preliminaries 1
1 BasicMonistValueStructure 3
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 ComparativeForms . . . . . . . . . . . . . . . . . . . . . . 7
1.3 RepresentationbyPreorders . . . . . . . . . . . . . . . . . 8
1.4 IncommensurabilityandPartialOrderings . . . . . . . . . 17
2 RelaxingRequirements 25
2.1 NontransitiveValueEqualityandEquipreference . . . . . 25
2.2 PartialSemiorders . . . . . . . . . . . . . . . . . . . . . . . 32
2.3 WeakEligibility . . . . . . . . . . . . . . . . . . . . . . . . 32
2.4 StrongEligibility . . . . . . . . . . . . . . . . . . . . . . . . 34
2.5 WhatConsistencyRequirementsAreNeeded? . . . . . . . 35
3 UtilityFunctions 43
3.1 AHistoricalRemark . . . . . . . . . . . . . . . . . . . . . . 43
3.2 RepresentationoftheStandardModel . . . . . . . . . . . . 45
3.3 RepresentationsforAllModels . . . . . . . . . . . . . . . . 48
3.4 OrdinalVersusCardinalUtilities . . . . . . . . . . . . . . . 52
4 TheComplexityofValue 59
4.1 Positive,Comparative,Superlative . . . . . . . . . . . . . . 59
4.2 GoodinTermsofBetterThan . . . . . . . . . . . . . . . . 62
vi CONTENTS
4.3 Satisficing . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.4 HowContext-SensitiveAreValues? . . . . . . . . . . . . . 65
5 MultidimensionalValue 69
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.2 AdditiveValueAggregation . . . . . . . . . . . . . . . . . 74
5.3 OtherFormsofUtilityAggregation . . . . . . . . . . . . . 78
5.4 ValueAggregationandSocialChoice . . . . . . . . . . . . 82
5.5 TheMostGeneralAggregationMethod? . . . . . . . . . . 92
II PhilosophyofValueStructure 95
6 ProblemsofValueAnalysis 97
6.1 TheGoodasaPrimitive. . . . . . . . . . . . . . . . . . . . 97
6.2 TheParadoxofAnalysis . . . . . . . . . . . . . . . . . . . 100
6.3 AFregeanSolution . . . . . . . . . . . . . . . . . . . . . . 101
6.4 TheConnectiontoMeaningandValueMetaphysics . . . . 104
7 Parity 109
7.1 MotivationandKeyProperties . . . . . . . . . . . . . . . . 109
7.2 UsingIntervalOrders . . . . . . . . . . . . . . . . . . . . . 113
7.3 ModelingParitybySetsofRelations . . . . . . . . . . . . . 118
7.4 TrichotomicParity . . . . . . . . . . . . . . . . . . . . . . 120
7.5 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . 122
8 SpectrumCases 129
8.1 TypicalScenarios . . . . . . . . . . . . . . . . . . . . . . . 129
8.2 WaystoPreserveTransitivity . . . . . . . . . . . . . . . . 132
8.3 WhyaLexicographicApproach? . . . . . . . . . . . . . . . 136
9 ATheoryofBetterness 141
9.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
9.2 FormalizationforOrdinalValue . . . . . . . . . . . . . . . 142
9.3 TheAggregationProblem . . . . . . . . . . . . . . . . . . . 146
9.4 ExplainingthePuzzles . . . . . . . . . . . . . . . . . . . . 151
9.5 TowardsaGeneralAxiology . . . . . . . . . . . . . . . . . 157
CONTENTS vii
10 Risk 161
10.1 RiskversusUncertainty . . . . . . . . . . . . . . . . . . . . 161
10.2 BasicNotions . . . . . . . . . . . . . . . . . . . . . . . . . 163
10.3 ExpectedValue. . . . . . . . . . . . . . . . . . . . . . . . . 167
10.4 ChoquetExpectedUtility . . . . . . . . . . . . . . . . . . . 171
10.5 OntheRationalityofRiskAttitudes . . . . . . . . . . . . . 176
10.6 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Notes 185
Index 199
Bibliography 205
AbouttheAuthor 219
TomyparentsHerbertandLuiseRast,
whomadethisbookpossible.
