Von Neumann-Morgenstern Utilities and Cardinal Preferences

Chichilnisky, G. (1983). Von Neumann-Morgenstern Utilities and Cardinal Preferences. IIASA Collaborative Paper. IIASA, Laxenburg, Austria: CP-83-038

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Abstract

We study the aggregation of preferences when intensities are taken into account: the aggregation of cardinal preferences and also of von Neumann- Morgenstern utilities for cases of choice under uncertainty. We show that with a finite number of choices, there exist no continuous anonymous aggregation rules that respect unanimity for such preferences or utilities. With infinitely many (discrete sets of) choices, such rules do exist and they are constructed here. However, their existence is not robust: each is a limit of rules that do not respect unanimity. Both results are for economies with a finite number of individuals.

The results are obtained by studying the global topological structure of spaces of cardinal preferences and of von Neumann-Morgenstern utilities. with a finite number of choices, these spaces are proven to be noncontractable. With infinitely many choices, on the other hand, they are proven to be contractable.

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