Generalizing the conjunction rule for aggregating conflicting expert opinions

In multi-agent expert systems, the conjunction rule is commonly used to combine expert information represented by imprecise probabilities. However, it is well-known that this rule cannot be applied in case of expert conflict. In this paper, we propose to resolve expert conflict by means of a second-order imprecise probability model. The essential idea underlying the model is a notion of behavioural trust. We construct a simple linear programming algorithm for calculating the aggregate. This algorithm explains the proposed aggregation method as a generalised conjunction rule. It also provides an elegant operational interpretation of the imprecise second-order assessments, and thus overcomes the problems of interpretation that are so common in hierarchical uncertainty models.