Roberts F.S. Measurement Theory: With Applications to Decisionmaking, Utility, and the Social Sciences

Cambridge: Cambridge University Press, 2009. — 442 p.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.Editor's Statement
ForewordMeasurement Theory
Use as a TextbookMeasurement Theory
Measurement
Decisionmaking
Utility
Mathematics
Organization of the BookDefinition of a Relation
Properties of Relations
Equivalence Relations
Weak Orders and Simple Orders
Partial Orders
Functions and Operations
Relational Systems and the Notion of ReductionThe Theory of Fundamental Measurement
Regular Scales
Scale Type
Examples of Meaningful and Meaningless Statements
Derived Measurement
Some Applications of the Theory of Meaningfulness: Energy Use, Air Pollution, and the Consumer Price IndexOrdinal Measurement
Extensive Measurement
Difference MeasurementThe Psychophysical Problem
The Possible Psychophysical Laws
The Power Law
A Measurement Axiomatization for Magnitude Estimation and Cross-Modality MatchingObtaining a Product Structure
Calculating Ordinal Utility Functions by Reducing the Dimensionality
Ordinal Utility Functions over Commodity Bundles
Conjoint Measurement
Nonadditive Representations
Joint Scales of Individuals and AlternativesSemiorders and Interval Orders
The Theory of Probabilistic ConsistencyThe Expected Utility Rule and the Expected Utility Hypothesis
Use of the EU Rule and Hypothesis in Decisionmaking
Multidimensional Alternatives
Mixture Spaces
Subjective ProbabilityObjective Probability
Subjective Probability
Direct Estimation of Subjective Probability
Subjective Probability from Preferences among Lotteries: The SEU Hypothesis
The Existence of a Measure of Subjective ProbabilityAuthor Index
Subject Index