## Abstract

This paper shows how symmetric means can be useful in providing an axiomatic basis for making choices under uncertainty. In section 2 of the paper, symmetric means are defined by means of four axioms which are shown to be independent and they imply an interesting fifth axiom. In section 3, a consistency in aggregation axiom is added and is shown to imply that the symmetric mean must be quasilinear or additively separable. In the final section, the various axioms for a symmetric mean are used to establish a version of the Expected Utility Theorem.

### Keywords

- Preference Function
- Axiomatic Characterization
- Separability Axiom
- Separability Assumption
- Continuous Utility Function

*These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.*

This research was supported by a Strategic Grant from the Social Science and Humanities Research Council of Canada. Thanks are due Shelley Hey and Louise Hebert for typing a difficult manuscript, and to J. Aczél, W. Bossert, D. Donaldson, L.G. Epstein and F. Stehling for valuable comments and to C. Blackorby for valuable discussions. The material in this paper has been adapted from Diewert (1992).

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Diewert, W.E. (1993). Symmetric Means and the Expected Utility Theorem. In: Diewert, W.E., Spremann, K., Stehling, F. (eds) Mathematical Modelling in Economics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-78508-5_48

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DOI: https://doi.org/10.1007/978-3-642-78508-5_48

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