We establish that none of the classical theories of choice can serve as a proper foundation for decision theory (and hence for decision-based design) and we construct a new theory of measurement that provides such a foundation. A proper theory of selection in engineering design cannot be founded on scales and variables to which the mathematical operations of addition and multiplication are not applicable. Yet it has not been proven that addition and multiplication are applicable to von Neumann and Morgenstern's utility scales or to any scales based on classical decision theory (which, in turn, is based on the classical...