Information Processing under Imprecise Risk with the Hurwicz criterion

An agent has Hurwicz criterion with pessimismoptimism index α under imprecise risk and adopts the root dictatorship version of McClennen’s Resolute Choice in sequential decision situations, i.e. evaluates strategies at the root of the decision tree by the Hurwicz criterion and enforces the best strategy, thus behaving in a dynamically consistent manner. We address two questions raised by this type of behavior: (i) is information processed correctly? and (ii) to what extent do unrealized outcomes influence decisions (non-consequentialism)? Partial answers are provided by studying: (i) the random sampling of a binary variable, and finding the influence of the pessimism-optimism index to be decreasing with the sample size, and the optimal decision rule to asymptotically only depend on the relative frequencies observed; and (ii) an insurance problem in which the agent chooses his coverage at period two after observing the period one outcome (accident or no accident); when no accident happened, a seemingly irrelevant data the first period deductible levelis found to be able to influence the second period insurance choice. We analyse this result in relation with the existence and value of the pessimism-optimism degree.