Consequentialism NonArchimedean Probabilities a

Authors: Peter J Hammond

Publish Date: 1994

Volume: , Issue: , Pages: 219-250

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Abstract

Earlier work Hammond 1988a b on dynamically consistent “consequentialist” behaviour in decision trees was unable to treat zero probability events satisfactorily Here the rational probability functions considered in Hammond 1992 as well as other nonArchimedean probabilities are incorporated into decision trees As before the consequentialist axioms imply the existence of a preference ordering satisfying independence In the case of rational probability functions those axioms together with continuity and a new refinement assumption imply the maximization of a somewhat novel lexicographic expected utility preference relation This is equivalent to maximization of expected utility in the ordering of the relevant nonArchimedean fieldLatest version August 1992 An incomplete earlier version last revised in August 1988 was entitled “Consequentialism Extended Probabilities and Lexicographic Expected Utility” In June 1992 an extensive revision was incorporated in a presentation to the Second Workshop on “Knowledge Belief and Strategic Interaction The Problem of Learning” at Castiglioncello Livorno Italy

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