Rational decision making with imprecise probabilities
Résumé
Decision criteria based on an imprecise probability representation of uncertainty have been criticized, from the normative point of view, on the grounds that they make the decision maker (DM) vulnerable to manipulations and, more generally, likely to take up a dominated strategy. This is indeed the case when the DM is both consequentialist (his choices in a subtree are not in uenced by data concerning the rest of the tree) and sophisticated (his present choice, determined by backward recursion, is best given his future choices). Renouncing consequentialism, which, as shown by Machina, is a way out of the difficulty, may seem to increase excessively the complexity of the model. We revisit the whole question, and first argue that in sequential decision situations it is possible to separate preference from choice, without abandoning the Revealed Preference Creed; then, we propose to assume consequentialist preference and accept non-consequentialist behavior; building on these assumptions, we discuss McClennen's Resolute Choice model and its interpretation involving multiple Selves; finally, taking the decision aiding point of view, we suggest an implementation of Resolute Choice in which the consensus goal among the Selves is to select an non-dominated strategy.