Group for Research in Decision Analysis

Conditions for Applicability of Addition and Multiplication to Preference Scales

Jonathan Barzilai

Measurement of preference is at the core of decision theory and operations research yet some of the most fundamental issues of preference modelling are not adequately treated in the classical theory of measurement. As a result, many methodologies contain errors. For example, the construction of scales to which the operations of addition and multiplication are applicable is related to measurement units: measurement without units, or without properly specified units results in weak scales to which addition and multiplication are not applicable.

We will present a new classification of measurement scales ("scale type"), the Principle of Reflection, and homogeneity considerations and we will show that commonly used methodologies produce scales that do not enable the operations of addition and multiplication.