Book contents
- Frontmatter
- Contents
- Editor's Statement
- Foreword
- Preface
- Measurement Theory
- Introduction
- Chapter 1 Relations
- Chapter 2 Fundamental Measurement, Derived Measurement, and the Uniqueness Problem
- Chapter 3 Three Representation Problems: Ordinal, Extensive, and Difference Measurement
- Chapter 4 Applications to Psychophysical Scaling
- Chapter 5 Product Structures
- Chapter 6 Nontransitive Indifference, Probabilistic Consistency, and Measurement without Numbers
- Chapter 7 Decisionmaking under Risk or Uncertainty
- Chapter 8 Subjective Probability
- Author Index
- Subject Index
Chapter 5 - Product Structures
Published online by Cambridge University Press: 04 August 2010
- Frontmatter
- Contents
- Editor's Statement
- Foreword
- Preface
- Measurement Theory
- Introduction
- Chapter 1 Relations
- Chapter 2 Fundamental Measurement, Derived Measurement, and the Uniqueness Problem
- Chapter 3 Three Representation Problems: Ordinal, Extensive, and Difference Measurement
- Chapter 4 Applications to Psychophysical Scaling
- Chapter 5 Product Structures
- Chapter 6 Nontransitive Indifference, Probabilistic Consistency, and Measurement without Numbers
- Chapter 7 Decisionmaking under Risk or Uncertainty
- Chapter 8 Subjective Probability
- Author Index
- Subject Index
Summary
Obtaining a Product Structure
In this chapter we study a variant on the measurement problems we have considered so far. Specifically, we consider measurement when the underlying set can be expressed as a Cartesian product. In making choices, we often consider alternatives with a variety of attributes or dimensions or from several points of view. We talk about multidimensional or multiattributed alternatives. For example, in choosing a job, we might consider salary, job security, possibility for advancement, geographical location, and so on. In buying a house, we might consider price, location, school system, availability of transportation, and the like. In designing a rapid transit system, we might consider power source, vehicle design, right of way design, and so on. In such a situation, each alternative a in the set of alternatives can be thought of as an n-tuple (a1, a2, …, an), where ai is some rating of alternative a on the ith attribute or dimension. For example, in the case of a job, a1 might be salary, a2 might be fringe benefits, a3 might be some measure of job security (for example, amount of notice required), and so on.
Multidimensional alternatives arise in a different way in economics. If there are n commodities in consideration, at might be a quantity of the ith commodity, and (a1a2, …, an) then is a commodity bundle or market basket. Preferences are expressed among alternative market baskets.
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- Chapter
- Information
- Measurement TheoryWith Applications to Decisionmaking, Utility, and the Social Sciences, pp. 197 - 246Publisher: Cambridge University PressPrint publication year: 1984