Measurement and preference function modelling

Jonathan Barzilai

66 citations0/0 files storedInternational Transactions in Operational Research

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Multi-Criteria Decision Making Psychometric Methodologies and Testing Decision-Making and Behavioral Economics

Abstract

The application of the principles of mathematical modelling to measurement theory is reviewed and the implications of a classification of measurement models by the mathematical operations that are applicable to the resultant scales are summarized. The conditions for the applicability of the operations of addition and multiplication imply that the models of classical measurement theory do not enable the application of these operations. For example, measurement without units does not enable the operations of addition and multiplication. Ratios of preference scales are shown to be undefined thus invalidating the analytic hierarchy process. The models of classical measurement theory, including utility theory, are weak and do not enable the operations of addition and multiplication as well.

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References

1977A scaling method for priorities in hierarchical structures 1946On the Theory of Scales of Measurement 1945Theory of Games and Economic Behavior 1963Handbook Of Mathematical Psychology 1990Remarks on the Analytic Hierarchy Process 1983On a short-coming of Saaty's method of analytic hierarchies 1991Foundations of Measurement:1970Mathematical psychology : an elementary introduction

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