  Recent work uncovered examples of classifiers for which SHAP scores yield
misleading feature attributions. While such examples might be perceived as
suggesting the inadequacy of Shapley values for explainability, this paper
shows that the source of the identified shortcomings of SHAP scores resides
elsewhere. Concretely, the paper makes the case that the failings of SHAP
scores result from the characteristic functions used in earlier works.
Furthermore, the paper identifies a number of properties that characteristic
functions ought to respect, and proposes several novel characteristic
functions, each exhibiting one or more of the desired properties. More
importantly, some of the characteristic functions proposed in this paper are
guaranteed not to exhibit any of the shortcomings uncovered by earlier work.
The paper also investigates the impact of the new characteristic functions on
the complexity of computing SHAP scores. Finally, the paper proposes
modifications to the tool SHAP to use instead one of our novel characteristic
functions, thereby eliminating some of the limitations reported for SHAP
scores.
