Measurement Theory

There is a large body of research work in a gray area which seems to have no disciplinary home; it can be called measurement theory. This work has been performed by philosophers of science, physicists, psychologists, economists, mathematicians, and others. In the past several decades, much of this work has been stimulated by the need to put measurement in the social sciences on a firm foundation. As well as being closely tied to applications, measurement theory has a very interesting and serious mathematical component, which, surprisingly, has escaped the attention of most of the mathematical community.

This book presents an introduction to measurement theory from a representational point of view. The emphasis is on putting measurement in the social and behavioral sciences on a firm foundation, and the applications will be chosen from a variety of problems in decision theory, economics, psychophysics, policy science, etc. The purpose of this book is to present an introduction to the theory of measurement in a form appropriate for the nonspecialist. I hope that both mathematics students and practicing mathematicians with no prior exposure to the subject will find this material interesting, both as mathematics in its own right and because of its applications. I hope, indeed, that a number of mathematicians will find this subject interesting enough to solve some of the open problems posed in the text. I also hope that nonmathematicians with sufficient mathematical background will find the work thought-provoking and useful.