Abstract
In the literature of economics (e.g. Allais, 1952; Frisch, 1937; Lange-1934) the notion of utility differences has been much discussed in con, nection with the theory of measurement of utility.1 However, to the best of our knowledge, no adequate axiomatization for this difference notion has yet been given at a level of generality and precision comparable to the von Neumann and Morgenstern construction of a probabilistic scheme for measuring utility. (The early study of Wiener, 1919–1920, is not axiomatically oriented.) The purpose of this paper is to present an axiomatization of this notion and to establish the expected representation theorem guaranteeing measurement unique up-to a linear transformation.
Reprinted from Management Science 1 (1955), 259–270. Written jointly with Muriel Winet.
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Notes
The formally similar notion of sensation differences is important in the literature of psychology (e.g., Coombs, 1950; Guilford, 1936; Hanes, 1949; Stevens, 1936; Stevens and Volkmann, 1940 ).
The intuitive idea of this approach was primarily due to Donald Davidson. It was suggested in Davidson. (1954) and has been the basis for the experiments reported in Davidson et al. (1955).
By considering just six items, we cannot get a realization of the axioms given in Section III. However, by increasing the number of items, we would presumably be able to get a successively closer approximation.
Some experiments are planned in collaboration with Professor Davidson.
We are indebted to Herman Rubin for the proof of this theorem.
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© 1969 Springer Science+Business Media Dordrecht
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Suppes, P. (1969). An Axiomatization of Utility Based on the Notion of Utility Differences. In: Studies in the Methodology and Foundations of Science. Synthese Library, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3173-7_8
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DOI: https://doi.org/10.1007/978-94-017-3173-7_8
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