  We consider MultiCriteria Decision Analysis models which are defined over
discrete attributes, taking a finite number of values. We do not assume that
the model is monotonically increasing with respect to the attributes values.
Our aim is to define an importance index for such general models, considering
that they are equivalent to $k$-ary games (multichoice games). We show that
classical solutions like the Shapley value are not suitable for such models,
essentially because of the efficiency axiom which does not make sense in this
context. We propose an importance index which is a kind of average variation of
the model along the attributes. We give an axiomatic characterization of it.
