Measurement Theory - With Applications to Decisionmaking, Utility, and the Social Sciences (Encyclopedia of Mathematics and its Applications (No. 7))

Cover......Page 1
Frontmatter......Page 2
Contents......Page 8
Editor's Statement......Page 14
Foreword......Page 16
1. Measurement Theory......Page 18
3. Use as a Textbook......Page 19
4. Acknowledgments......Page 20
References......Page 21
Measurement Theory......Page 22
1. Measurement......Page 24
3. Decisionmaking......Page 28
4. Utility......Page 29
5. Mathematics......Page 31
6. Organization of the Book......Page 32
References......Page 34
1.2 Definition of a Relation......Page 36
1.3 Properties of Relations......Page 42
1.4 Equivalence Relations......Page 48
1.5 Weak Orders and Simple Orders......Page 51
1.6 Partial Orders......Page 59
1.7 Functions and Operations......Page 64
1.8 Relational Systems and the Notion of Reduction......Page 67
References......Page 69
2.1 The Theory of Fundamental Measurement......Page 72
2.2 Regular Scales......Page 80
2.3 Scale Type......Page 87
2.4 Examples of Meaningful and Meaningless Statements......Page 94
2.5 Derived Measurement......Page 99
2.6 Some Applications of the Theory of Meaningfulness: Energy Use, Air Pollution, and the Consumer Price Index......Page 104
References......Page 121
3.1 Ordinal Measurement......Page 124
3.2 Extensive Measurement......Page 145
3.3 Difference Measurement......Page 157
References......Page 169
4.1 The Psychophysical Problem......Page 172
4.2 The Possible Psychophysical Laws......Page 181
4.3 The Power Law......Page 202
4.4 A Measurement Axiomatization for Magnitude Estimation and Cross-Modality Matching......Page 209
References......Page 216
5.1 Obtaining a Product Structure......Page 220
5.2 Calculating Ordinal Utility Functions by Reducing the Dimensionality......Page 225
5.3 Ordinal Utility Functions over Commodity Bundles......Page 228
5.4 Conjoint Measurement......Page 232
5.5 Nonadditive Representations......Page 254
5.6 Joint Scales of Individuals and Alternatives......Page 260
References......Page 265
6.1 Semiorders and Interval Orders......Page 269
6.2 The Theory of Probabilistic Consistency......Page 294
References......Page 321
7.1 The Expected Utility Rule and the Expected Utility Hypothesis......Page 327
7.2 Use of the EU Rule and Hypothesis in Decisionmaking......Page 334
7.3 Multidimensional Alternatives......Page 358
7.4 Mixture Spaces......Page 374
7.5 Subjective Probability......Page 386
References......Page 387
8.1 Objective Probability......Page 391
8.2 Subjective Probability......Page 393
8.3 Direct Estimation of Subjective Probability......Page 396
8.4 Subjective Probability from Preferences among Lotteries: The SEU Hypothesis......Page 401
8.5 The Existence of a Measure of Subjective Probability......Page 408
References......Page 422
Author Index......Page 427
Subject Index......Page 433