An Alternative View of Importance Indices for Multichoice Games

Abstract

We consider MultiCriteria Decision Analysis (MCDA) models where the underlying attributes are discrete. Without any additional feature, such general models are equivalent to multichoice games in cooperative game theory. Our aim is to define an importance index for attributes. In specific models based on capacities, fuzzy measures, the Shapley value is often taken as an importance index. We show that in our general framework, taking the Shapley value extended to multichoice games is not meaningful, due to the efficiency axiom which has no natural interpretation in MCDA. We propose instead an importance index based on variational calculus and give an axiomatization of it.