Nonstandard numbers for qualitative decision making

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dc.creatorLehmann, Daniel
dc.date2002-02-20
dc.date.accessioned2026-07-07T03:18:09Z
dc.date.available2026-07-07T03:18:09Z
dc.descriptionThe consideration of nonstandard models of the real numbers and the definition of a qualitative ordering on those models provides a generalization of the principle of maximization of expected utility. It enables the decider to assign probabilities of different orders of magnitude to different events or to assign utilities of different orders of magnitude to different outcomes. The properties of this generalized notion of rationality are studied in the frameworks proposed by von Neumann and Morgenstern and later by Anscombe and Aumann. It is characterized by an original weakening of their postulates in two different situations: nonstandard probabilities and standard utilities on one hand and standard probabilities and nonstandard utilities on the other hand. This weakening concerns both Independence and Continuity. It is orthogonal with the weakening proposed by lexicographic orderings.
dc.description14 pages. Presented at TARK'98
dc.identifierhttps://arxiv.org/abs/cs/0202029
dc.identifierhttp://arxiv.org/abs/cs/0202029
dc.identifierProceedings of the 7th Conference on Theoretical Aspects of Reasoning and Knowledge, I. Gilboa ed., Evanston Ill., July 1998, pp. 161-174
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/30999
dc.subjectComputer Science and Game Theory
dc.subjectI.2.3
dc.titleNonstandard numbers for qualitative decision making
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