New results on scale and size arguments justifying invariance properties of empirical indices and laws
János Aczél; Zenon Moszner
Mathematical Social Sciences 28(1): 3-33
1994
ISSN/ISBN: 0165-4896 DOI: 10.1016/0165-4896(93)00743-eDocument Number: 256731
After giving examples of 'scale' and/or 'size' interpretations of certain assumptions in the natural and social sciences and in architecture, we point out why naive invariance arguments do not work. In their place we offer a rather natural weak assumption and a slightly stronger one, which can result in the function values having a well-defined generalized ratio scale type behavior under certain further conditions. The mathematical results concern exactly variants of these further conditions of different apparent strength and difficulty. In most of the proofs, application of the translation equation is replaced by more direct arguments.