Imprecise Swing Weighting for Multi-Attribute Utility Elicitation Based on Partial Preferences

We describe a novel approach to multi-attribute utility elicitation which is both general enough to cover a wide range of problems, whilst at the same time simple enough to admit reasonably straightforward calculations. We allow both utilities and probabilities to be only partially specified, through bounding. We still assume marginal utilities to be precise. We derive necessary and sufficient conditions under which our elicitation procedure is consistent. As a special case, we obtain an imprecise generalization of the well known swing weighting method for eliciting multi-attribute utility functions. An example from ecological risk assessment demonstrates our method.