The conditions for applicability of the operations of addition and multiplication to scale values have not been identified in the literature and are not satisfied by the models of the classical theory of measurement whether the underlying variables are physical or psychological (including the models of "conjoint measurement"). As a result, addition and multiplication, e.g. expressions of the form m(3)=m(1)+m(2) and m(2)=5m(1) for a given mass scale, are not applicable to scale values that are based on these models. The implications of a new theory of measurement which addresses these problems will be reviewed. The main elements of this theory include a new scale classification, the Principle of Reflection, and homogeneity considerations. In particular, it will be demonstrated that utility theory cannot serve as a foundation for decision theory, game theory, or economics. |