Explaining Multi-Criteria Decision Aiding Models with an Extended Shapley Value

The capability to explain the result of aggregation models to decision makers is key to reinforcing user trust. In practice, Multi-Criteria Decision Aiding models are often organized in a hierarchical way, based on a tree of criteria. We present an explanation approach usable with any hierarchical multi-criteria model, based on an influence index of each attribute on the decision. A set of desirable axioms are defined. We show that there is a unique index fulfilling these axioms. This new index is an extension of the Shapley value on trees. An efficient rewriting of this index, drastically reducing the computation time, is obtained. Finally, the use of the new index is illustrated on an example.