On the foundations of qualitative decision theory
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 2
Generalized qualitative probability: savage revisited
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
Autonomous Agents and Multi-Agent Systems
A unified framework for order-of-magnitude confidence relations
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Qualitative decision under uncertainty: back to expected utility
Artificial Intelligence
The Non-archimedean Polynomials and Merging of Stratified Knowledge Bases
ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Qualitative decision under uncertainty: back to expected utility
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Qualitative decision under uncertainty: back to expected utility
Artificial Intelligence
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The 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.