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Measurement theory with applications to decisionmaking, utility, and the social sciences /
This book provides an introduction to measurement theory for non-specialists and puts measurement in the social and behavioural sciences on a firm mathematical foundation. Results are applied to such topics as measurement of utility, psychophysical scaling and decision-making about pollution, energy...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge [Cambridgeshire] ; New York, NY, USA :
Cambridge University Press,
[1984]
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| Colección: | Encyclopedia of mathematics and its applications ;
v. 7. Encyclopedia of mathematics and its applications. Section, Mathematics and the social sciences. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Half-title; Title; Copyright; Dedication; Contents; Editor's Statement; Section Editor's Foreword; Preface; 1. Measurement Theory; 2. Other Books on the Subject; 3. Use as a Textbook; 4. Acknowledgments; References; Measurement Theory; Introduction; 1. Measurement; 2. The Measurement Literature; 3. Decisionmaking; 4. Utility; 5. Mathematics; 6.Organization of the Book; References; Chapter 1. Relations; 1.1 Notation and Terminology; 1.2 Definition of a Relation; 1.3 Properties of Relations; 1.4 Equivalence Relations; 1.5 Weak Orders and Simple Orders; 1.6 Partial Orders
- 1.7 Functions and Operations1.8 Relational Systems and the Notion of Reduction; References; Chapter 2. Fundamental Measurement, Derived Measurement, and the Uniqueness Problem; 2.1 The Theory of Fundamental Measurement; 2.1.1 Formalization of Measurement; 2.1.2 Homomorphisms of Relational Systems; 2.1.3 The Representation and Uniqueness Problems; 2.2 Regular Scales; 2.2.1 Definition of Regularity; 2.2.2 Reduction and Regularity; 2.3 Scale Type; 2.4 Examples of Meaningful and Meaningless Statements; 2.5 Derived Measurement
- 2.6 Some Applications of the Theory of Meaningfulness:Energy Use, Air Pollution, and the Consumer Price Index2.6.1 Energy Use; Arithmetic and Geometric Means; 2.6.2 Consumer Price Index; 2.6.3 Measurement of Air Pollution; References; Chapter 3. Three Representation Problems: Ordinal, Extensive, and Difference Measurement; 3.1 Ordinal Measurement; 3.1.1 Representation Theorem in the Finite Case; 3.1.2 The Uniqueness Theorem; 3.1.3 The Countable Case; 3.1.4 The Birkhoff-Milgram Theorem; 3.2 Extensive Measurement; 3.2.1 Holder's Theorem
- 3.2.2 Necessary and Sufficient Conditions for Extensive Measurement3.2.3 Uniqueness; 3.2.4 Additivity; 3.3 Difference Measurement; 3.3.1 Algebraic Difference Structures; 3.3.2 Necessary and Sufficient Conditions; 3.3.3 Uniqueness; References; Chapter 4. Applications to Psychophysical Scaling; 4.1 The Psychophysical Problem; 4.1.1 Loudness; 4.1.2 The Psychophysical Function; 4.2 The Possible Psychophysical Laws; 4.2.1 Excursis: Solution of the Cauchy Equations; 4.2.2 Derivation of the Possible Psychophysical Laws; 4.3 The Power Law; 4.3.1 Magnitude Estimation
- 4.3.2 Consequences of the Power Law4.3.3 Cross-Modality Matching; 4.3.4 Attitude Scaling; 4.4 A Measurement Axiomatization for Magnitude Estimation and Cross-Modality Matching; 4.4.1 Consistency Conditions; 4.4.2 Cross-Modality Ordering; 4.4.3 Magnitude Estimation as a Ratio Scale; References; Chapter 5. Product Structures; 5.1 Obtaining a Product Structure; 5.2 Calculating Ordinal Utility Functions by Reducing the Dimensionality; 5.3 Ordinal Utility Functions over Commodity Bundles; 5.4 Conjoint Measurement; 5.4.1 Additivity; 5.4.2 Conjoint Measurement and the Balance of Trade