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L. S. Shapley, “Cardinal Utility Comparisons from Intensity Comparisons,” Report R-1683-PR, The Rand Corporation, Santa Monica, 1975.

has been cited by the following article:

• TITLE: An Axiomatic Derivation of the Logarithmic Function as a Cardinal Utility Function on Money Income Levels

  AUTHORS: Mitsunobu Miyake

  KEYWORDS: Logarithmic Utility Function; Suppes’ Hypothesis; Bernoulli’s Hypothesis; Weber-Fechner Law; Level Comparison; Difference Comparison; Monotonicity Axiom; Consistency Axiom; Homogeneity Axiom

  JOURNAL NAME: Theoretical Economics Letters, Vol.4 No.1, February 12, 2014

  ABSTRACT: This note elaborates Suppes’ (1977, Erkenntnis Vol. 11, No. 1, pp 233-250) derivation of the logarithmic function as a consumer’s cardinal utility function on money income levels, in which the consumer’s preferences are specified by a level comparison relation and a difference comparison relation. Without assuming Suppes’ hypothesis (Bernoulli’s hypothesis or Weber-Fechner law), which asserts that the utility values are proportional to the logarithmic values of income levels, it is shown that the representability of the two relations by logarithmic utility function can be characterized only by the three (mutually independent) axioms on the relations.