  Shapley values are one of the main tools used to explain predictions of tree
ensemble models. The main alternative to Shapley values are Banzhaf values that
have not been understood equally well. In this paper we make a step towards
filling this gap, providing both experimental and theoretical comparison of
these model explanation methods. Surprisingly, we show that Banzhaf values
offer several advantages over Shapley values while providing essentially the
same explanations. We verify that Banzhaf values: (1) have a more intuitive
interpretation, (2) allow for more efficient algorithms, and (3) are much more
numerically robust. We provide an experimental evaluation of these theses. In
particular, we show that on real world instances.
  Additionally, from a theoretical perspective we provide new and improved
algorithm computing the same Shapley value based explanations as the algorithm
of Lundberg et al. [Nat. Mach. Intell. 2020]. Our algorithm runs in $O(TLD+n)$
time, whereas the previous algorithm had $O(TLD^2+n)$ running time bound. Here,
$T$ is the number of trees, $L$ is the maximum number of leaves in a tree, and
$D$ denotes the maximum depth of a tree in the ensemble. Using the
computational techniques developed for Shapley values we deliver an optimal
$O(TL+n)$ time algorithm for computing Banzhaf values based explanations. In
our experiments these algorithms give running times smaller even by an order of
magnitude.
