Publication Date
10-1-2023
Abstract
In many application areas, we rely on experts to estimate the numerical values of some quantities. Experts can provide not only the estimates themselves, they can also estimate the accuracies of their estimates -- i.e., in effect, they provide an interval of possible values of the quantity of interest. To get a more accurate estimate, it is reasonable to ask several experts -- and to take the intersection of the resulting intervals. In some cases, however, experts overestimate the accuracy of their estimates, their intervals are too narrow -- so narrow that they are inconsistent: their intersection is empty. In such situations, it is necessary to extend the experts' intervals so that they will become consistent. Which extension should we choose? Since we are dealing with uncertainty, it seems reasonable to apply probability-based approach -- well suited for dealing with uncertainty. From the purely mathematical viewpoint, this application is possible -- however, as we show, even in simplest situations, it leads to counter-intuitive results. We show that we can make more reasonable recommendations if, instead of only taking into account probabilities, we also take into account our preferences -- which, according to decision theory, can be described by utilities.
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Technical Report: UTEP-CS-23-54