Additive and Polynomial Representations

Foundations of Measurement

by David H. Krantz, R Duncan Luce, Patrick Suppes

Additive and Polynomial Representations deals with major representation theorems in which the qualitative structure is reflected as some polynomial function of one or more numerical functions defined on the basic entities. Examples are additive expressions of a single measure (such as the probability of disjoint events being the sum of their probabilities), and additive expressions of two measures (such as the logarithm of momentum being the sum of log mass and log velocity terms). The book describes the three basic procedures of fundamental measurement as the mathematical pivot, as the utilization of constructive methods, and as a series of isomorphism theorems leading to consistent numerical solutions. The text also explains the counting of units in relation to an empirical relational structure which contains a concatenation operation. The book notes some special variants which arise in connection with relativity and thermodynamics. The text cites examples from physics and psychology for which additive conjoint measurement provides a possible method of fundamental measurement. The book will greatly benefit mathematicians, econometricians, and academicians in advanced mathematics or physics.

577 pages, Kindle Edition

First published January 1, 1971

Reviews

[Leonardo]

The measurement-theoretic approach was first articulated by Dana Scott and Patrick Suppes (1958) but received its canonical statement in David Krantz, R. Duncan Luce, Patrick Suppes, and Amos Tversky’ Foundations of Measurement (1971). Instead of constructs, this approach emphasizes observable orderings and representation theorems (Krantz 1991, 1).

Capabilities and Happiness Pág.293-294