| Description |
1 online resource (xxii, 420 pages) : illustrations |
| Series |
Encyclopedia of mathematics and its applications ; volume 7. Section, Mathematics and the social sciences |
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Encyclopedia of mathematics and its applications ; v. 7.
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Encyclopedia of mathematics and its applications. Section, Mathematics and the social sciences.
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| Contents |
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 |
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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 |
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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 |
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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 |
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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 |
| Summary |
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, transportation and health. The results and questions presented should be of interest to both students and practising mathematicians since the author sets forth an area of mathematics unfamiliar to most mathematicians, but which has many potentially significant applications |
| Notes |
Imprint and ISBN from label on title page verso. Imprint on title page: Reading, Mass. : Addison-Wesley, Advanced Book Program, 1979 |
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Publication taken over by Cambridge University Press in 1984 with a new copyright date |
| Bibliography |
Includes bibliographical references and indexes |
| Notes |
English |
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Print version record |
| Subject |
Social sciences -- Methodology.
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Social sciences -- Mathematical models
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Decision making -- Mathematical models.
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SOCIAL SCIENCE -- Essays.
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SOCIAL SCIENCE -- Reference.
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Decision making -- Mathematical models
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Social sciences -- Mathematical models
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Social sciences -- Methodology
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Sciences sociales -- Modèles mathématiques.
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Calcul économique -- Modèles mathématiques.
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| Form |
Electronic book
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| ISBN |
9781107087477 |
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1107087473 |
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1107102308 |
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9781107102309 |
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1107093708 |
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9781107093706 |
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0511759878 |
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9780511759871 |
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9781139886079 |
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113988607X |
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