Measurement theory with applications to decisionmaking, utility, and the social sciences:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge University Press
1985
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Encyclopedia of mathematics and its applications
7 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XXII, 420 S. graph. Darst. |
| ISBN: | 9780521302272 9780521102438 |
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| 100 | 1 | |a Roberts, Fred S. |d 1943- |e Verfasser |0 (DE-588)13624419X |4 aut | |
| 245 | 1 | 0 | |a Measurement theory with applications to decisionmaking, utility, and the social sciences |c Fred S. Roberts |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge University Press |c 1985 | |
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| 650 | 7 | |a Wiskundige modellen |2 gtt | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Sozialwissenschaften | |
| 650 | 4 | |a Decision making |x Mathematical models | |
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Datensatz im Suchindex
| _version_ | 1804174748587917312 |
|---|---|
| adam_text | Contents
Introduction
1.
Measurement
2.
The Measurement Literature
3.
Dccisionm aking
4.
Utility
5.
Ma thematics
6.
Organization of the Book
References
Editor s
Statement xy
Section Editor s Foreword XVH
Preface
Χ1Λ
1.
Measurement Theory xjx
2.
Other Books on the Subject
xx
3.
Use as a Textbook
xx
4.
Acknowledgments
xxi
References
xxii
1
I
5
5
6
8
9
Π
Chapter
1.
Relations
13
1.1
Notation and Terminology 1
3
1.2
Definition of a Relation
13
1.3
Properties of Relations
19
1.4
Equivalence Relations
25
1.5
Weak Orders and Simple Orders
28
1.6
Partial Orders
36
1.7
Functions and Operations
41
1.8
Relational Systems and the Notion of Reduction
44
References
46
ix
Contents
Chapter
2.
2.1
2.2
2.3
2.4
2.5
2.6
Fundamental Measurement, I>erived
and the Uniqueness Problem
Measurement,
The Theory of Fundamental Measurement
2.1.1
Formalisation
oí
Measurement
2.1.2
Homornorphisms of Relational Systems
2.1.3
The Representation and Uniqueness Problems
Regular Scales
2.2.1
Definition of Regularity
2.2.2
Reduction and Regularity
Scale Type
Examples of Meaningful and Meaningless Statements
Derived Measurement
Some Applications of the Theory of
Energy Use, Air Pollution, and the Consumer Price Index
2.6.1
Energy Use; Arithmetic and Geometric Means
2.6.2
Consumer Price Index
2.6.3
Measurement of Air Pollution
References
49
49
49
51
54
57
57
60
64
71
76
81
81
84
87
98
Chapter
3.
3.1
3.2
3.3
Three Representation Problems: Ordinal, Extensive,
and Difference Measurement
101
Ordinal Measurement
101
3.1.1
Representation Theorem in the Finite Case
101
3.1.2
The Uniqueness Theorem
108
3.1.3
The Countable Case
109
3.1.4
The Birkhoff-Milgram Theorem
111
Extensive Measurement
122
3.2.1
Holder s Theorem
122
3.2.2
Necessary and Sufficient Conditions for
Extensive Measurement
126
3.2.3
Uniqueness
129
3.2.4
Additivity
131
Difference Measurement
134
3.3.1
Algebraic Difference Structures
134
3.3.2
Necessary and Sufficient Conditions
139
3.3.3
Uniqueness
141
References
146
Chapter
4.
Applications to
PsycbopłiysicaJ
Scaling
4.1
The Psychophysical Problem
4.1.1
Loudness
4.1.2
The Psychophysical Function
149
149
Ì49
150
Contents
xi
4.2
The Possible Psychophysical Laws
158
4.2.1
Excursis: Solution of the Cauchy Equations
159
4.2.2
Derivation of the Possible Psychophysical Laws
164
4.3
The Power Law
179
4.3.1
Magnitude Estimation
179
4.3.2
Consequences of the Power Law
181
4.3.3
Cross-Mo-dality Matching
182
4.3.4
Attitude Scaling
184
4.4
A Measurement
Axioma
tiza,
tion
for Magnitude
Estimation and Cross-Modality Matching
186
4.4.1
Consistency Conditions
186
4.4.2
Cross-Modality Ordering
188
4.4.3
Magnitude Estimation as a Ratio Scale
189
References
193
Chapter
5.
Product Structures
197
5.1
Obtaining a Product Structure
197
5.2
Calculating Ordinal Utility Functions by Reducing
the Dimensionality
203
5.3
Ordinal Utility Functions over Commodity Bundles
206
5.4
Conjoint Measurement
210
5.4.1
Additivity
210
5.4.2
Conjoint Measurement and the Balance of Trade
214
5.4.3
The Luce-Tukey Theorem
215
5.4.4
Conjomt Measurement under Equal Spacing
222
5.4.5
Scott s Theorem
224
5.5 Nonadditive
Representations
232
5.5.1
Decomposability and Polynomial Conjoint
Measurement
232
5.5.2
Noudecompo&able Representations
235
5.6
Joint Scales of Individuals and Alternatives
238
5.6.1
Gu
Uman
Scales
238
5.6.2
Unfolding
239
References
243
Chapter
6.
Nontransitive Indifference, Probabilistic Consistency,
and Measurement without Numbers
247
6.1
Semiorders and Interval Orders
247
6.1.1
Non
transitivity of Indifference
247
6.1.2
The Scott-Suppes Theorem
250
6.1.3
Uniqueness
252
6.1.4
Interval Orders and Measurement without
Numbers
253
XĽ
Cem
tentó
6.2
Compatibility between a Weak Order and a
Semi order
Uniqueness Revisited
Proof of the Soott-Suppes Theorem
Semiordered Vermons of Other Measurement
6.1.5
6.1.6
6.1.7
6.1.8
The Theory of
6.2.1
Pair Comparison
Systoa»
6.2.2
ШЕіу
Medek-
■
Ї
Tire WeaJfc
ЛзШ$
Modei
6.2.2.2
The
Stooag Utility Mode}
6.2.2.3
The
FacimetiÄÄ
Utility
Model
6.2.2.4
Tfae Strict
Utiüty
МскШ
6.2.3
Transitivity
Condiţiona
6.2.4
Homogeneous Families of Scmiorders
6.2.5
Beyond Binary Choices
References
255
258
260
264
272
272
273
273
215
277
280
283
287
290
299
Chapter
7.
Decisionmaking under Risk or Uncertainty
305
7.1
The Expected Utility Rule and the Expected Utility
Hypothesis
305
7.2
Use of the
EU RuJe
and Hypothesis in Decisionmakmg
312
7.2.1
Lotteries
312
7.2.2
Utility from Expected Utility
317
7.2.3
A Basic Reference Lottery Ticket
322
7.2.4
The Utility of Money
325
7.2.5
The
Allais
Paradox
327
7.2.6
The Public Health
Problem:
The Value of a Life
329
7.3
Multidimensional Alternatives
336
7.3.1
Reducing Number of Dimensions
336
7.3.2
Additive Utility Functions
337
7.3.3
Quasi-additive Utility Functions
340
7.4
Mixture Spaces
352
7.5
Subjective Probability
364
References
365
Chapter
8.
Subjective Probability
369
8.1
8.2
8.3
8.4
Objective Probability
369
Subj ective Probability
3 71
Direct Estimation of
Subjective
Probability
374
Subjective Probability from Preferences among Lotteries:
The
SEU
Hypothesis
379
Contents xiü
8.4.1
If Utility Is Known
379
8.4.2
If Utility Is Not Known
380
8.4.3
The Savage Axioms for Expected Utility
382
8.5
The Existence of a Measure of Subjective Probability
386
8.5.1
The
de Finetti
Axioms
386
8.5.2
Insufficiency of the
de
Finetti Axioms
388
8.5.3
Conditions Sufficient for a Subjective Probability
Measure
390
8.5.4
Necessary and Sufficient Conditions for a
Subjective Probability Measure in the Finite Case
392
8.5.5
Necessary and Sufficient Conditions for a
Subjective Probability Measure in the General
Case
394
References 4O0
Author Index
405
Subject Index
411
Paperback
Re-issue
An
introduction to measurement theory for
nonspecial
ists, this book
puts measurement in
lhe
social and behavioral sciences on a firm
foundation using a mathematical formulation. Results arc applied to
such topics as measurement of utility, psychophysical scaling, and
decisionmaking about pollution, energy, transportation, and health.
The book ties together a large body of mathematical research work
from philosophy of science, mathematical psychology, economics,
and elsewhere. The mathematical results and questions presented
here should be of interest to both practicing mathematicians and
students of mathematics, since the author sets forth an area of
mathematics which is not well known to most mathematicians, but
which has many potentially significant applications. The tools and
insights of measurement theory introduced here should be of
interest to both theoretical and practical social scientists and to
policy advisers, managers, and others concerned with making
complex decisions.
|
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| id | DE-604.BV042588225 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:05:19Z |
| institution | BVB |
| isbn | 9780521302272 9780521102438 |
| language | English |
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| physical | XXII, 420 S. graph. Darst. |
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| publisher | Cambridge University Press |
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| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Roberts, Fred S. 1943- Verfasser (DE-588)13624419X aut Measurement theory with applications to decisionmaking, utility, and the social sciences Fred S. Roberts 1. publ. Cambridge [u.a.] Cambridge University Press 1985 XXII, 420 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 7 Hier auch später erschienene, unveränderte Nachdrucke Besluitvorming gtt Maattheorie gtt Prise de décision - Modèles mathématiques Sciences sociales - Modèles mathématiques Sciences sociales - Méthodologie Sociale wetenschappen gtt Wiskundige methoden gtt Wiskundige modellen gtt Mathematisches Modell Sozialwissenschaften Decision making Mathematical models Social sciences Mathematical models Social sciences Methodology Maßtheorie (DE-588)4074626-4 gnd rswk-swf Maßtheorie (DE-588)4074626-4 s DE-604 Encyclopedia of mathematics and its applications 7 (DE-604)BV000903719 7 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028021497&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028021497&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Roberts, Fred S. 1943- Measurement theory with applications to decisionmaking, utility, and the social sciences Encyclopedia of mathematics and its applications Besluitvorming gtt Maattheorie gtt Prise de décision - Modèles mathématiques Sciences sociales - Modèles mathématiques Sciences sociales - Méthodologie Sociale wetenschappen gtt Wiskundige methoden gtt Wiskundige modellen gtt Mathematisches Modell Sozialwissenschaften Decision making Mathematical models Social sciences Mathematical models Social sciences Methodology Maßtheorie (DE-588)4074626-4 gnd |
| subject_GND | (DE-588)4074626-4 |
| title | Measurement theory with applications to decisionmaking, utility, and the social sciences |
| title_auth | Measurement theory with applications to decisionmaking, utility, and the social sciences |
| title_exact_search | Measurement theory with applications to decisionmaking, utility, and the social sciences |
| title_full | Measurement theory with applications to decisionmaking, utility, and the social sciences Fred S. Roberts |
| title_fullStr | Measurement theory with applications to decisionmaking, utility, and the social sciences Fred S. Roberts |
| title_full_unstemmed | Measurement theory with applications to decisionmaking, utility, and the social sciences Fred S. Roberts |
| title_short | Measurement theory with applications to decisionmaking, utility, and the social sciences |
| title_sort | measurement theory with applications to decisionmaking utility and the social sciences |
| topic | Besluitvorming gtt Maattheorie gtt Prise de décision - Modèles mathématiques Sciences sociales - Modèles mathématiques Sciences sociales - Méthodologie Sociale wetenschappen gtt Wiskundige methoden gtt Wiskundige modellen gtt Mathematisches Modell Sozialwissenschaften Decision making Mathematical models Social sciences Mathematical models Social sciences Methodology Maßtheorie (DE-588)4074626-4 gnd |
| topic_facet | Besluitvorming Maattheorie Prise de décision - Modèles mathématiques Sciences sociales - Modèles mathématiques Sciences sociales - Méthodologie Sociale wetenschappen Wiskundige methoden Wiskundige modellen Mathematisches Modell Sozialwissenschaften Decision making Mathematical models Social sciences Mathematical models Social sciences Methodology Maßtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028021497&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028021497&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000903719 |
| work_keys_str_mv | AT robertsfreds measurementtheorywithapplicationstodecisionmakingutilityandthesocialsciences |