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Advances in preference function modelling

We have reconstructed the foundation of decision theory and the theory of measurement based on a classification of model type by the mathematical operations that are applicable to the scales generated by the model. We establish that addition and multiplication are not applicable to scales constructed by the standard models of classical measurement theory, including utility theory. Inter alia, the new theory implies that utility theory cannot serve as a foundation for decision theory; that Suppes and Zinnes's relational model cannot serve as a foundation for proper measurement; and it in validates the analytic hierarchy process as well as Torgerson's theory.