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Determinateness of the Utility Function: Revisiting a Controversy of the Thirties

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  • Kaushik Basu

Abstract

It has been alleged that, contrary to the assumptions in Pareto's Manual, the ability to compare first-differences of utility implies cardinality. It is shown here that the validity of this theorem hinges critically on the framework of analysis. In the framework of the thirties it is valid because of the implicit use of an ‘unrestricted domain’ assumption. In the modern choice-theoretic context it is not in general true but it becomes valid if utility functions are continuous and are defined on a connected topological space.

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  • Kaushik Basu, 1982. "Determinateness of the Utility Function: Revisiting a Controversy of the Thirties," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(2), pages 307-311.
    • Handle: RePEc:oup:restud:v:49:y:1982:i:2:p:307-311.
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    File URL: http://hdl.handle.net/10.2307/2297277
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    Cited by:

    1. Jean Baccelli & Philippe Mongin, 2016. "Choice-based cardinal utility: a tribute to Patrick Suppes," Journal of Economic Methodology, Taylor & Francis Journals, vol. 23(3), pages 268-288, July.
    2. Pivato, Marcus, 2013. "Multiutility representations for incomplete difference preorders," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 196-220.
    3. Georgios Gerasimou, 2019. "Simple Preference Intensity Comparisons," Discussion Paper Series, School of Economics and Finance 201905, School of Economics and Finance, University of St Andrews, revised 27 Apr 2020.
    4. Michael Mandler, 2001. "Compromises Between Cardinality and Ordinality in Preference Theory and Social Choice," Cowles Foundation Discussion Papers 1322, Cowles Foundation for Research in Economics, Yale University.

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