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- W4327672904 abstract "This paper proves a constructive version of the expected utility theorem. The word constructive is construed here in two senses - first, as in constructive mathematics, whereby the logic underlying proofs is intuitionistic. In a second sense of the word, constructive is taken to mean built up from simpler components. Preferences are defined over lotteries that vary continuously over some topological space and are themselves assumed to vary depending upon some underlying process of measurement, deliberation, or observation. The open sets of the topology serve as the possible truth values of assertions about preference and constrain what can be measured, deduced, or observed. Replacing an open set by an open covering of smaller sets serves as a notion of refinement of information, and deductions made for these smaller sets can be combined or collated to yield corresponding deductions over the larger set. The two notions of constructive turn out to be related because the underlying logic of the objects within the system is generally intuitionistic. The classical expected utility theorem is shown to be non-constructive, and a constructive version is proved for the present setting by narrowing the domain of preferences. The representation of preferences is via comparisons of continuous real-valued functions. A version of the classical theorem is obtained by imposing a restriction on the collection of open sets of the topology, which has the effect of making the logic classical. The proof here illustrates a robustness property of constructive results. They can be carried over virtually unchanged to a variety of mathematical settings. Here the set of variable lotteries replaces the sets of lotteries from the classical setting, but there are other possibilities." @default.
- W4327672904 created "2023-03-18" @default.
- W4327672904 creator A5067326482 @default.
- W4327672904 date "2023-03-13" @default.
- W4327672904 modified "2023-09-24" @default.
- W4327672904 title "Expected Utility from a Constructive Viewpoint" @default.
- W4327672904 doi "https://doi.org/10.48550/arxiv.2303.08633" @default.
- W4327672904 hasPublicationYear "2023" @default.
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