Philosophical and Foundational Issues in Measurement Theory

3	Qualitative Axioms for Random-Variable Representation of Extensive Quantities

Patrick SuppesMario Zanotti

Stanford University

In the standard theory of fundamental extensive measurement, qualitative axioms are formulated that lead to a numerical assignment unique up to a positive similarity transformation. The central idea of the theory of random quantities is to replace the numerical assignment by a random-variable assignment. This means that each object is assigned a random variable. In the case of extensive quantities, the expectation of the random variable replaces the usual numerical assignment, and the distribution of the random variable reflects the variability of the property in question, which could be intrinsic to the object ...