Where Luce and Krantz do really generalize Savage's decision model

Abstract

In this paper I shall somewhat investigate several formulations of decision theory from a purely quantitative point of view, thus leaving aside the whole question of measurement. Since almost any foundational work on decision theory strives at proving nicer and nicer measurement results and representation theorems, I feel obliged to give a short explanation of my self-imposed limitation. The first and best reason for it is that I have not got anything new to say about measurement, and the second is that one need not say anything: It was hard work to convince economists that cardinalization is possible and meaningful. This was accomplished by proving existence and uniqueness theorems establishing the existence of cardinal functions (e.g. subjective utilities and probabilities) unique up to certain transformations that mirror ordinal concepts (e.g. subjective preferences) in a certain way. And surely, such theorems provide an excellent justification for the use of cardinal concepts. The eagerness in the search for representation theorems, however, is not really understandable but on the supposition that they are the only justification of cardinal concepts, and this assumption is merely a rather dubious conjecture. After all, philosophers of science have been debating about theoretical concepts for at least 40 years, and, though the last word has not yet been spoken, they generally agree that it is possible to have meaningful, yet observationally undefinable theoretical notions.1 And the concepts of subjective probability and utility are theoretical notions of decision theory. Thus if philosophers of science are right, they need not necessarily be proved observationally definable by representation theorems for being meaningful. 2 For that reason I consider quantitative decision models fundamental for decision theory and measurement as part of the confirmation or testing theory of the quantitative models. Of course, the latter is important for evaluating the former, but there may be different (e.g. conceptual) grounds for finding one quantitative decision model more satisfac