Deciding under Ignorance: In Search of Meaningful Extensions of the Hurwicz Criterion to Decision Trees

The major paradigm for sequential decision under uncertainty is expected utility. This approach has many good features that qualify it for posing and solving decision problems, especially dynamic consistency and computational efficiency via dynamic programming. However, when uncertainty is due to sheer lack of information, and expected utility is no longer a realistic criterion, the approach collapses because dynamic consistency becomes counterintuitive and the global non-expected utility criteria are no longer amenable to dynamic programming. In this paper we argue against Resolute Choice strategies, following the path opened by Jaffray, and suggest that the dynamic programming methodology may lead to more intuitive solutions respecting the Consequentialism axiom, while a global evaluation of strategies relying on lottery reduction is questionable.