Modeling certainty equivalents for imprecise gambles

We present results from two experiments on the relative importance of, and subjects' differential sensitivity to, vagueness on both probabilities and outcomes. Subjects in these studies made certainty equivalent (CE) judgments for precise and vague gambles. In the first study subjects responded to gain gambles only; in the second they judged both gain and loss gambles. Model-free analyses of the results indicate (a) a higher concern for the precision of the outcomes than that of the probabilities, (b) vagueness seeking for positive outcomes and (c) vagueness avoidance for negative outcomes and (d) no strong modal attitude toward vagueness on the probability dimension. The greater salience of the outcomes can be explained by the nature of the response mode (CEs). The reflection of attitudes towards outcome vagueness in the two domains can be explained by the distinct goals of the DMs in the two cases, which cause them to focus on the highest (most desirable) possible gain or the largest (most dreaded) conceivable loss. We propose and fit a new model of decision making with vaguely specified attributes that generalize the Prospect Theory model for the precise case. The new generalized model combines the two submodels (preference among precise lotteries and effects of vagueness) and allows estimation of the vagueness parameters. These estimated parameters are consistent with, and confirm, the patterns uncovered by the qualitative analysis.