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ISIPTA
2003
IEEE

Extensions of Expected Utility Theory and Some Limitations of Pairwise Comparisons

14 years 4 months ago
Extensions of Expected Utility Theory and Some Limitations of Pairwise Comparisons
We contrast three decision rules that extend Expected Utility to contexts where a convex set of probabilities is used to depict uncertainty: Γ-Maximin, Maximality, and E-admissibility. The rules extend Expected Utility theory as they require that an option is inadmissible if there is another that carries greater expected utility for each probability in a (closed) convex set. If the convex set is a singleton, then each rule agrees with maximizing expected utility. We show that, even when the option set is convex, this pairwise comparison between acts may fail to identify those acts which are Bayes for some probability in a convex set that is not closed. This limitation affects two of the decision rules but not E-admissibility, which is not a pairwise decision rule. E-admissibility can be used to distinguish between two convex sets of probabilities that intersect all the same supporting hyperplanes.
Mark J. Schervish, Teddy Seidenfeld, Joseph B. Kad
Added 04 Jul 2010
Updated 04 Jul 2010
Type Conference
Year 2003
Where ISIPTA
Authors Mark J. Schervish, Teddy Seidenfeld, Joseph B. Kadane, Isaac Levi
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