Valuation of Vague Prospects with Mixed Outcomes

Previous work on the joint effects of vagueness in probabilities and outcomes in decisions about risky prospects has documented the decision-makers' (DMs) differential sensitivity to these two sources of imprecision. Budescu et al. [6] report two studies in which DMs provided certainty equivalents (CEs) for precise and vague prospects involving gains or losses. They found (a) higher concern for the precision of the outcomes than that of the probabilities, (b) vagueness seeking for positive outcomes, (c) vagueness avoidance for negative outcomes, and (d) stronger attitudes towards vague gains than for vague losses (see also, [13]). They proposed and tested a new generalization of prospect theory (PT) for options with vaguely specified attributes. The present work extends this model to the case of vague mixed prospects.We report results of a new experiment where 40 DMs used two methods (direct judgments of numerical CEs, and inferred CEs from a series of pairwise comparisons) of valuation of positive (gains), negative (losses), and mixed (gains and losses) prospects with vague outcomes. The results confirm the previous findings of vagueness seeking in the domain of gains, vagueness avoidance for losses, and stronger effects of vagueness in the domain of gains. The CEs of mixed prospects are also consistent with this pattern. The DMs overvalue prospects with vaguely specified gains and precise losses, and undervalue prospects with precisely specified gains and imprecise losses, relative to mixed prospects with precise parameters. Parameter estimates of the generalized model indicate that in the mixed cases the attitudes to vagueness in the two domains are slightly less pronounced, and they are treated more similarly to each other than in the strictly positive, or negative, cases.