  Shapley value attribution (SVA) is an increasingly popular explainable AI
(XAI) method, which quantifies the contribution of each feature to the model's
output. However, recent work has shown that most existing methods to implement
SVAs have some drawbacks, resulting in biased or unreliable explanations that
fail to correctly capture the true intrinsic relationships between features and
model outputs. Moreover, the mechanism and consequences of these drawbacks have
not been discussed systematically. In this paper, we propose a novel error
theoretical analysis framework, in which the explanation errors of SVAs are
decomposed into two components: observation bias and structural bias. We
further clarify the underlying causes of these two biases and demonstrate that
there is a trade-off between them. Based on this error analysis framework, we
develop two novel concepts: over-informative and underinformative explanations.
We demonstrate how these concepts can be effectively used to understand
potential errors of existing SVA methods. In particular, for the widely
deployed assumption-based SVAs, we find that they can easily be
under-informative due to the distribution drift caused by distributional
assumptions. We propose a measurement tool to quantify such a distribution
drift. Finally, our experiments illustrate how different existing SVA methods
can be over- or under-informative. Our work sheds light on how errors incur in
the estimation of SVAs and encourages new less error-prone methods.
